multipleregression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "package 'xlsx' successfully unpacked and MD5 sums checked\n",
      "\n",
      "The downloaded binary packages are in\n",
      "\tC:\\Users\\User\\AppData\\Local\\Temp\\RtmpqkXPjR\\downloaded_packages\n"
     ]
    }
   ],
   "source": [
    "install.packages(\"xlsx\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "TRUE"
      ],
      "text/latex": [
       "TRUE"
      ],
      "text/markdown": [
       "TRUE"
      ],
      "text/plain": [
       "[1] TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: rJava\n",
      "Loading required package: xlsxjars\n"
     ]
    }
   ],
   "source": [
    "# Verify the package is installed.\n",
    "any(grepl(\"xlsx\",installed.packages()))\n",
    "# Load the library into R workspace.\n",
    "library(\"xlsx\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the library into R workspace.\n",
    "library(\"xlsx\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Material vc..m.min. f..mm. ap.mm. Bahn   Fc..N. Stdabw..Fc..N.  Ff..N.\n",
      "1       UHCS         30    0.2      1    1  644.644       19.08340 261.333\n",
      "2       UHCS         30    0.2     NA    2  648.688       19.28020 268.445\n",
      "3       UHCS         30    0.2     NA    3  642.442       21.78050 267.951\n",
      "4       UHCS         30    0.2     NA    4  666.564       22.80450 292.121\n",
      "5       UHCS         30    0.2     NA    5  662.158       19.96830 289.165\n",
      "6       UHCS         30    0.4      1    1 1124.390       44.94990 381.584\n",
      "7       UHCS         30    0.4     NA    2 1138.270       49.25980 397.643\n",
      "8       UHCS         30    0.4     NA    3 1141.370       60.55190 400.039\n",
      "9       UHCS         30    0.4     NA    4 1134.340       54.81470 393.737\n",
      "10      UHCS         30    0.4     NA    5 1133.880       54.91730 392.501\n",
      "11      UHCS         60    0.2      1    1  535.472       12.74600 205.072\n",
      "12      UHCS         60    0.2     NA    2  555.112        6.93385 213.701\n",
      "13      UHCS         60    0.2     NA    3  568.385        8.72320 218.266\n",
      "14      UHCS         60    0.2     NA    4  562.595        8.53484 237.322\n",
      "15      UHCS         60    0.2     NA    5  574.445       11.26600 235.575\n",
      "16      UHCS         60    0.4      1    1  875.987       37.98260 236.199\n",
      "17      UHCS         60    0.4     NA    2  895.183       44.39890 239.778\n",
      "18      UHCS         60    0.4     NA    3  898.506       38.04330 238.532\n",
      "19      UHCS         60    0.4     NA    4  896.405       35.73230 239.669\n",
      "20      UHCS         60    0.4     NA    5  912.448       34.04550 247.868\n",
      "21      UHCS        100    0.2      1    1  510.710       60.81510 199.408\n",
      "22      UHCS        100    0.2     NA    2  528.531       68.84450 219.805\n",
      "23      UHCS        100    0.2     NA    3  536.871       86.45160 234.856\n",
      "24      UHCS        100    0.2     NA    4  551.004       99.78740 250.074\n",
      "25      UHCS        100    0.2     NA    5  553.807       88.32720 255.219\n",
      "26      UHCS        100    0.4      1    1  821.076      121.83800 217.352\n",
      "27      UHCS        100    0.4     NA    3  836.620      234.20900 234.180\n",
      "28      UHCS        100    0.4     NA    4  835.420      119.45000 232.494\n",
      "29      UHCS        100    0.4     NA    5  829.432      211.14500 239.337\n",
      "30      UHCS        200    0.2      1    1  477.262       54.30040 189.408\n",
      "31      UHCS        200    0.2     NA    2  498.171       95.82120 217.334\n",
      "32      UHCS        200    0.2     NA    3  509.668       76.81730 231.355\n",
      "33      UHCS        200    0.2     NA    4  518.934       65.68920 251.998\n",
      "34      UHCS        200    0.2     NA    5  524.923       77.58710 274.295\n",
      "35      UHCS        200    0.4     NA    2  770.849       22.36060 258.529\n",
      "36      UHCS        200    0.4     NA    3  769.884       99.37380 250.438\n",
      "37      UHCS        200    0.4     NA    4  784.871       93.42730 263.343\n",
      "38      UHCS        200    0.4     NA    5  793.928       88.13800 281.869\n",
      "39      UHCS         30    0.2      1    1  636.322       24.46130 259.675\n",
      "40      UHCS         30    0.2     NA    2  658.810       18.75170 274.003\n",
      "41      UHCS         30    0.2     NA    3  633.029       17.03050 275.999\n",
      "42      UHCS         30    0.2     NA    4  673.452       18.58110 294.589\n",
      "43      UHCS         30    0.2     NA    5  655.942       14.73690 296.244\n",
      "44      UHCS         30    0.4      1    1 1079.300       39.40470 359.629\n",
      "45      UHCS         30    0.4     NA    2 1046.950       53.38450 326.989\n",
      "46      UHCS         30    0.4     NA    3 1065.440       57.74530 351.834\n",
      "47      UHCS         30    0.4     NA    4 1136.520       35.97080 384.823\n",
      "48      UHCS         30    0.4     NA    5 1155.440       36.36800 404.098\n",
      "49      UHCS         60    0.2      1    1  542.871        9.41273 213.109\n",
      "50      UHCS         60    0.2     NA    2  558.476        7.22444 217.809\n",
      "51      UHCS         60    0.2     NA    3  571.936        7.61710 243.719\n",
      "52      UHCS         60    0.2     NA    4  581.268        8.82521 248.382\n",
      "53      UHCS         60    0.2     NA    5  585.096       15.96500 250.241\n",
      "54      UHCS         60    0.4      1    1  864.004       31.73150 230.367\n",
      "55      UHCS         60    0.4     NA    2  896.915       29.34660 241.028\n",
      "56      UHCS         60    0.4     NA    3  899.897       29.35850 240.265\n",
      "57      UHCS         60    0.4     NA    4  907.737       27.70140 243.002\n",
      "58      UHCS         60    0.4     NA    5  916.632       25.56370 246.114\n",
      "59      UHCS        100    0.2      1    1  513.044       63.43020 211.550\n",
      "60      UHCS        100    0.2     NA    2  523.007       79.57550 217.995\n",
      "61      UHCS        100    0.2     NA    3  534.014       46.98910 227.828\n",
      "62      UHCS        100    0.2     NA    4  536.684       57.74940 237.343\n",
      "63      UHCS        100    0.2     NA    5  546.141       77.92360 254.338\n",
      "64      UHCS        100    0.4      1    1  842.080       78.17760 254.230\n",
      "65      UHCS        100    0.4     NA    2  838.666       97.24450 243.617\n",
      "66      UHCS        100    0.4     NA    3  848.829      112.91700 255.988\n",
      "67      UHCS        100    0.4     NA    4  854.311      116.90100 260.174\n",
      "68      UHCS        100    0.4     NA    5  864.948      145.91600 270.929\n",
      "69      UHCS        200    0.2      1    1  469.571       69.14780 191.135\n",
      "70      UHCS        200    0.2     NA    2  493.351       87.56180 227.334\n",
      "71      UHCS        200    0.2     NA    3  509.215       84.33250 251.945\n",
      "72      UHCS        200    0.2     NA    4  520.683       78.09700 275.885\n",
      "73      UHCS        200    0.2     NA    5  531.422       65.42940 310.660\n",
      "74      UHCS        200    0.4      1    1  769.730       29.45160 222.892\n",
      "75      UHCS        200    0.4     NA    2  777.751       28.13620 253.785\n",
      "76      UHCS        200    0.4     NA    3  779.225       81.34190 263.080\n",
      "77      UHCS        200    0.4     NA    4  791.117       82.57120 277.646\n",
      "78      UHCS        200    0.4     NA    5  801.681       75.06920 298.288\n",
      "79  C70MnVS4         30    0.2     NA    2  543.170       45.94790 180.840\n",
      "80  C70MnVS4         30    0.2     NA    3  542.234       45.47340 180.377\n",
      "81  C70MnVS4         30    0.2     NA    4  529.900       43.97690 177.372\n",
      "82  C70MnVS4         30    0.2     NA    5  531.342       42.72320 178.083\n",
      "83  C70MnVS4         60    0.2      1    1  616.268       17.32000 233.487\n",
      "84  C70MnVS4         60    0.2     NA    2  551.214       13.01300 205.999\n",
      "85  C70MnVS4         60    0.2     NA    3  545.195       13.05450 202.388\n",
      "86  C70MnVS4         60    0.2     NA    4  541.541       12.51140 200.787\n",
      "87  C70MnVS4         60    0.2     NA    5  537.318       12.74720 200.042\n",
      "88  C70MnVS4        100    0.2      1    1  493.593       53.29820 181.336\n",
      "89  C70MnVS4        100    0.2     NA    2  508.374       35.51780 189.179\n",
      "90  C70MnVS4        100    0.2     NA    3  506.601       38.95220 189.854\n",
      "91  C70MnVS4        100    0.2     NA    4  503.593       40.95650 189.293\n",
      "92  C70MnVS4        100    0.2     NA    5  504.041       41.27790 190.122\n",
      "93  C70MnVS4        200    0.2      1    1  522.246       15.41450 206.122\n",
      "94  C70MnVS4        200    0.2     NA    2  512.043       14.17720 203.200\n",
      "95  C70MnVS4        200    0.2     NA    3  513.748       15.43300 204.312\n",
      "96  C70MnVS4        200    0.2     NA    4  528.453       27.35150 211.346\n",
      "97  C70MnVS4        200    0.2     NA    5  525.503       26.24030 210.834\n",
      "98  C70MnVS4         30    0.4      1    1 1223.170       39.45990 473.260\n",
      "99  C70MnVS4         30    0.4     NA    2 1218.320       44.61880 473.594\n",
      "100 C70MnVS4         30    0.4     NA    3 1124.760       37.60120 435.112\n",
      "101 C70MnVS4         30    0.4     NA    4 1113.650       42.79960 411.935\n",
      "102 C70MnVS4         30    0.4     NA    5 1081.890       37.64410 383.754\n",
      "103 C70MnVS4         60    0.4      1    1  930.457       33.21090 267.760\n",
      "104 C70MnVS4         60    0.4     NA    2  938.697       33.89030 279.616\n",
      "105 C70MnVS4         60    0.4     NA    3  956.165       35.64340 288.679\n",
      "106 C70MnVS4         60    0.4     NA    4  931.320       22.21230 283.832\n",
      "107 C70MnVS4         60    0.4     NA    5  940.579       21.00210 289.141\n",
      "108 C70MnVS4        100    0.4      1    1  869.788       94.39540 223.866\n",
      "109 C70MnVS4        100    0.4     NA    2  864.333       81.57990 228.931\n",
      "110 C70MnVS4        100    0.4     NA    3  873.156      101.87200 238.497\n",
      "111 C70MnVS4        100    0.4     NA    4  872.886       96.67130 238.010\n",
      "112 C70MnVS4        100    0.4     NA    5  867.417      100.01100 238.434\n",
      "113 C70MnVS4        200    0.4      1    1  851.872       35.51820 223.321\n",
      "114 C70MnVS4        200    0.4     NA    2  850.982       41.25710 227.215\n",
      "115 C70MnVS4        200    0.4     NA    3  853.857       43.58920 226.653\n",
      "116 C70MnVS4        200    0.4     NA    4  858.680       56.17760 235.084\n",
      "117 C70MnVS4        200    0.4     NA    5  858.196       74.83590 235.769\n",
      "118     UHCS         30    0.2      1    1  653.615       29.98040 287.678\n",
      "119     UHCS         30    0.2     NA    2  679.369       23.62620 299.828\n",
      "120     UHCS         30    0.2     NA    3  668.991       21.38120 301.618\n",
      "121     UHCS         30    0.2     NA    4  691.259       21.52690 310.069\n",
      "122     UHCS         30    0.2     NA    5  689.712       22.76270 311.117\n",
      "123     UHCS        100    0.2      1    1  529.296       39.23780 231.927\n",
      "124     UHCS        100    0.2     NA    2  540.176       14.30830 238.343\n",
      "125     UHCS        100    0.2     NA    3  541.909       12.68250 238.399\n",
      "126     UHCS        100    0.2     NA    4  553.232       13.42240 242.076\n",
      "127     UHCS        200    0.2      1    1  496.234       28.06620 212.522\n",
      "128     UHCS        200    0.2     NA    2  507.428       10.63534 220.940\n",
      "129     UHCS        200    0.2     NA    3  513.458       11.30462 221.932\n",
      "130     UHCS        200    0.2     NA    4  517.280       11.19304 224.018\n",
      "131     UHCS        200    0.2     NA    5  525.478       11.39632 227.820\n",
      "132     UHCS         30    0.4      1    1 1174.732       67.64900 416.652\n",
      "133     UHCS         30    0.4     NA    2 1183.850       22.59120 462.433\n",
      "134     UHCS         30    0.4     NA    3 1190.250       26.47400 467.126\n",
      "135     UHCS         30    0.4     NA    4 1172.590       27.30950 449.290\n",
      "136     UHCS         30    0.4     NA    5 1184.420       27.55380 456.312\n",
      "137     UHCS         60    0.4      1    1  947.859       46.90740 273.429\n",
      "138     UHCS         60    0.4     NA    2  910.432       64.89890 260.335\n",
      "139     UHCS         60    0.4     NA    3  915.096       43.40640 263.658\n",
      "140     UHCS         60    0.4     NA    4  918.780       60.59000 268.354\n",
      "141     UHCS         60    0.4     NA    5  894.557       48.68490 264.003\n",
      "142     UHCS        200    0.4      1    1  842.589       78.45650 225.132\n",
      "143     UHCS        200    0.4     NA    2  839.011       88.57750 233.717\n",
      "144     UHCS        200    0.4     NA    3  856.521       67.67080 258.799\n",
      "145     UHCS        200    0.4     NA    4  843.355       40.84550 233.000\n",
      "146     UHCS        200    0.4     NA    5  867.236       40.78800 240.809\n",
      "147 C70MnVS4         30    0.2      1    1  550.061       46.41570 176.192\n",
      "148 C70MnVS4         30    0.2     NA    2  541.249       46.31870 175.492\n",
      "149 C70MnVS4         30    0.2     NA    3  540.202       46.32300 174.005\n",
      "150 C70MnVS4         30    0.2     NA    4  535.458       44.42130 174.007\n",
      "151 C70MnVS4         30    0.2     NA    5  530.029       43.13150 172.891\n",
      "152 C70MnVS4         60    0.2      1    1  544.036       12.53770 203.705\n",
      "153 C70MnVS4         60    0.2     NA    2  554.482       12.66500 202.211\n",
      "154 C70MnVS4         60    0.2     NA    3  537.302       12.49450 195.337\n",
      "155 C70MnVS4         60    0.2     NA    4  527.186       12.66970 192.968\n",
      "156 C70MnVS4         60    0.2     NA    5  537.432       12.29510 197.463\n",
      "157 C70MnVS4        200    0.2      1    1  472.295       12.64120 174.346\n",
      "158 C70MnVS4        200    0.2     NA    2  491.988       14.30710 181.509\n",
      "159 C70MnVS4        200    0.2     NA    3  497.453       15.67110 185.270\n",
      "160 C70MnVS4        200    0.2     NA    4  502.198       20.00940 188.696\n",
      "161 C70MnVS4        200    0.2     NA    5  509.982       21.55210 191.570\n",
      "162 C70MnVS4         30    0.4      1    1 1211.680       31.65340 476.336\n",
      "163 C70MnVS4         30    0.4     NA    2 1197.200       35.90610 482.017\n",
      "164 C70MnVS4         30    0.4     NA    3 1191.580       37.02010 480.394\n",
      "165 C70MnVS4         30    0.4     NA    4 1200.090       32.16540 485.972\n",
      "166 C70MnVS4         30    0.4     NA    5 1100.930       40.75850 393.167\n",
      "167 C70MnVS4         60    0.4      1    1  917.548       27.02600 273.809\n",
      "168 C70MnVS4         60    0.4     NA    2  944.439       32.91600 282.283\n",
      "169 C70MnVS4         60    0.4     NA    3  933.838       24.40740 286.665\n",
      "170 C70MnVS4         60    0.4     NA    4  939.153       23.63280 287.937\n",
      "171 C70MnVS4         60    0.4     NA    5  946.296       22.86840 290.963\n",
      "172 C70MnVS4        100    0.4      1    1  845.245       79.72560 229.506\n",
      "173 C70MnVS4        100    0.4     NA    2  856.951       93.97670 234.253\n",
      "174 C70MnVS4        100    0.4     NA    3  859.038      104.21000 240.589\n",
      "175 C70MnVS4        100    0.4     NA    4  872.704      116.50100 246.238\n",
      "176 C70MnVS4        100    0.4     NA    5  860.504      111.09600 244.862\n",
      "177 C70MnVS4        200    0.4      1    1  835.359       14.30770 225.534\n",
      "178 C70MnVS4        200    0.4     NA    2  848.968       17.62990 231.681\n",
      "179 C70MnVS4        200    0.4     NA    3  853.013       18.24480 235.090\n",
      "180 C70MnVS4        200    0.4     NA    4  852.297       17.71860 234.790\n",
      "181 C70MnVS4        200    0.4     NA    5  846.656       16.99360 235.911\n",
      "182     UHCS         60    0.2      1    1  558.997       27.77000 231.256\n",
      "183     UHCS         60    0.2     NA    3  598.498        9.85702 273.117\n",
      "184     UHCS         60    0.2     NA    4  629.616       10.96840 301.288\n",
      "185     UHCS        100    0.2      1    1  522.056       36.61840 213.870\n",
      "186     UHCS        100    0.2     NA    2  532.984       13.35690 215.998\n",
      "187     UHCS        200    0.2      1    1  505.187       15.46140 221.977\n",
      "188     UHCS        200    0.2     NA    2  518.821        9.21436 234.578\n",
      "189     UHCS        200    0.2     NA    3  524.701       10.33050 237.635\n",
      "190     UHCS        200    0.2     NA    4  526.804       13.84700 235.491\n",
      "191     UHCS        200    0.2     NA    5  530.535        9.70343 237.227\n",
      "192     UHCS         30    0.4      1    1 1170.540       70.03860 439.836\n",
      "193     UHCS         30    0.4     NA    2 1181.490       55.81370 447.131\n",
      "194     UHCS         30    0.4     NA    3 1205.750       47.40280 473.929\n",
      "195     UHCS         30    0.4     NA    4 1192.680       37.65190 460.458\n",
      "196     UHCS         30    0.4     NA    5 1114.210       53.05330 402.159\n",
      "197     UHCS         60    0.4      1    1  944.705       35.17750 274.918\n",
      "198     UHCS         60    0.4     NA    2  908.944       27.51810 262.012\n",
      "199     UHCS         60    0.4     NA    3  915.096       43.40640 263.658\n",
      "200     UHCS         60    0.4     NA    4  932.598       25.64620 275.220\n",
      "201     UHCS         60    0.4     NA    5  929.620       24.86850 302.754\n",
      "202     UHCS        100    0.4      1    1  865.355       66.36240 246.432\n",
      "203     UHCS        100    0.4     NA    2  867.897       68.73530 248.465\n",
      "204     UHCS        100    0.4     NA    3  851.027       75.54180 246.201\n",
      "205     UHCS        100    0.4     NA    4  867.456       73.20940 255.289\n",
      "206     UHCS        100    0.4     NA    5  857.039       80.56030 253.050\n",
      "207     UHCS        200    0.4      1    1  844.361       68.09530 228.649\n",
      "208     UHCS        200    0.4     NA    2  837.087       62.06580 239.501\n",
      "209     UHCS        200    0.4     NA    3  856.261       67.74300 258.889\n",
      "210     UHCS        200    0.4     NA    4  815.746       63.54570 246.196\n",
      "211     UHCS        200    0.4     NA    5  810.991       59.18170 256.687\n",
      "212     UHCS         30    0.2      1    1  677.386       26.10900 299.109\n",
      "213     UHCS         30    0.2     NA    2  675.218       21.31740 299.286\n",
      "214     UHCS         30    0.2     NA    3  690.413       21.11240 308.371\n",
      "215     UHCS         30    0.2     NA    4  680.824       19.69620 301.820\n",
      "216     UHCS         60    0.2      1    1  564.240        8.63726 231.097\n",
      "217     UHCS         60    0.2     NA    2  562.102       15.01650 232.120\n",
      "218     UHCS         60    0.2     NA    3  564.093        9.34239 232.566\n",
      "219     UHCS         60    0.2     NA    4  568.136        8.92255 234.487\n",
      "220     UHCS         60    0.2     NA    5  590.656        9.90186 241.264\n",
      "221     UHCS        100    0.2      1    1  504.013       34.88920 213.220\n",
      "222     UHCS        100    0.2     NA    2  517.995       33.33890 225.123\n",
      "223     UHCS        100    0.2     NA    3  524.316       30.25190 229.627\n",
      "224     UHCS        100    0.2     NA    4  518.409       28.97380 230.602\n",
      "225     UHCS        100    0.2     NA    5  526.027       27.90620 235.952\n",
      "226 C70MnVS4        100    0.2      1    1  511.624       12.04830 188.926\n",
      "227 C70MnVS4        100    0.2     NA    2  515.164       11.87290 188.925\n",
      "228 C70MnVS4        100    0.2     NA    3  512.124       12.51500 188.252\n",
      "229 C70MnVS4        100    0.2     NA    4  515.842       15.08020 190.805\n",
      "230 C70MnVS4        100    0.2     NA    5  515.566       16.20670 192.338\n",
      "231 C70MnVS4        100    0.4      1    1  878.807       23.15270 247.046\n",
      "232 C70MnVS4        100    0.4     NA    2  887.407       27.01200 251.963\n",
      "233 C70MnVS4        100    0.4     NA    3  885.353       25.60340 251.013\n",
      "234 C70MnVS4        100    0.4     NA    4  881.076       19.82910 254.986\n",
      "235     UHCS        100    0.4      1    1  887.979       68.94650 244.514\n",
      "236     UHCS        100    0.4     NA    2  868.594       58.21270 241.495\n",
      "237     UHCS        100    0.4     NA    3  870.048       59.46560 255.038\n",
      "238     UHCS        100    0.4     NA    4  871.280       57.92250 252.901\n",
      "239     UHCS        100    0.4     NA    5  859.618       60.89930 254.574\n",
      "    Stdabw..Ff..N.  Fp..N. Stdabw..Fp..N. Zerspankraft.Fz  VB..Âµm. NA. NA..1\n",
      "1        18.837800 417.763       24.26760        811.4103  80.10000  NA    NA\n",
      "2        21.910600 414.582       28.11460        815.3141  82.90000  NA    NA\n",
      "3        25.983500 451.497       32.82510        829.6861  91.70000  NA    NA\n",
      "4        28.455100 439.530       35.60580        850.1934  92.26000  NA    NA\n",
      "5        24.136300 437.376       30.86780        844.6108  96.10000  NA    NA\n",
      "6        41.787700 714.766       74.75840       1385.9111  48.50000  NA    NA\n",
      "7        45.644800 734.600       85.75950       1411.8837  58.10000  NA    NA\n",
      "8        54.374600 722.906      109.54400       1409.0244  61.90000  NA    NA\n",
      "9        50.994100 732.543      104.29400       1406.5473  67.40000  NA    NA\n",
      "10       50.547300 730.718      103.92800       1404.8807  77.20000  NA    NA\n",
      "11        2.258830 341.228        9.69756        667.2491  58.41000  NA    NA\n",
      "12        1.471280 345.275        6.52413        687.7734  83.80000  NA    NA\n",
      "13        2.677710 352.622        7.82896        703.5935 111.97000  NA    NA\n",
      "14        2.040830 363.200        7.71181        710.4570 137.48000  NA    NA\n",
      "15        3.231810 370.415        8.98399        722.9730 159.57000  NA    NA\n",
      "16        5.920130 471.399       42.60360       1022.4286  43.50000  NA    NA\n",
      "17        2.420050 452.194       28.10880       1031.1768  51.10000  NA    NA\n",
      "18        1.841270 448.698       27.10740       1032.2502  60.60000  NA    NA\n",
      "19        1.971890 445.675       26.21580       1029.3733  77.06000  NA    NA\n",
      "20        2.121430 454.786       27.43550       1049.2046  92.30000  NA    NA\n",
      "21       43.930600 327.617       46.02710        638.6871  53.00000  NA    NA\n",
      "22       40.235300 358.399       42.24130        675.3585  85.01000  NA    NA\n",
      "23       30.558700 376.895       31.57110        696.7336  90.54000  NA    NA\n",
      "24       26.441300 401.441       28.26600        726.1524 101.14000  NA    NA\n",
      "25       25.369600 414.335       29.69120        737.2330 126.29000  NA    NA\n",
      "26       61.194400 442.084       69.26210        957.5207  58.03000  NA    NA\n",
      "27       84.638500 452.230       83.74130        979.4311  71.70000  NA    NA\n",
      "28       73.111000 460.919       73.92820        982.0521  76.28000  NA    NA\n",
      "29       93.990700 468.918      104.11900        982.4071  78.56000  NA    NA\n",
      "30        3.336690 320.821       20.93190        605.4589  64.90000  NA    NA\n",
      "31        4.225910 355.650       30.23560        649.5347  80.02000  NA    NA\n",
      "32        5.343590 372.297       23.44690        672.2289  97.21000  NA    NA\n",
      "33        6.601510 399.836       21.43230        701.9005 116.96000  NA    NA\n",
      "34        6.852460 427.079       28.13360        730.1906 121.90000  NA    NA\n",
      "35        2.594730 457.166       31.89790        932.7627  77.46000  NA    NA\n",
      "36        3.892670 471.856       32.90350        937.0638  87.30000  NA    NA\n",
      "37        3.673350 485.825       29.97210        959.8948  90.00000  NA    NA\n",
      "38        4.605220 509.641       28.96920        984.6348  92.50000  NA    NA\n",
      "39        7.750680 417.803       22.37770        804.2985  82.20000  NA    NA\n",
      "40        9.119610 409.531       24.16170        822.6931  88.40000  NA    NA\n",
      "41        9.350190 419.649       24.66650        808.0881  92.30000  NA    NA\n",
      "42       10.403700 437.795       28.09820        855.5611  99.20000  NA    NA\n",
      "43        8.407430 442.065       23.47610        844.6549 111.50000  NA    NA\n",
      "44       19.901000 700.740       66.46550       1336.1355  46.10000  NA    NA\n",
      "45       33.080900 609.432       87.11350       1254.7643  54.50000  NA    NA\n",
      "46       39.237100 668.538      101.61600       1306.0982  65.90000  NA    NA\n",
      "47       22.031100 750.813       68.08400       1415.4457  71.60000  NA    NA\n",
      "48       24.823100 788.465       72.05900       1456.0267  73.30000  NA    NA\n",
      "49        1.700680 347.563        8.95082        678.9141  54.30000  NA    NA\n",
      "50        1.373840 349.328        6.90551        693.8056 102.60000  NA    NA\n",
      "51        2.173960 381.238        8.63131        729.2819 126.00000  NA    NA\n",
      "52        2.856980 381.649        9.11499        738.3915 155.01000  NA    NA\n",
      "53        2.718540 386.740        9.46913        744.6648 162.70000  NA    NA\n",
      "54        4.023430 447.496       32.93410        999.9123  49.30000  NA    NA\n",
      "55        2.580450 454.729       28.33770       1034.0839  58.70000  NA    NA\n",
      "56        2.203510 450.372       27.03160       1034.5902  64.50000  NA    NA\n",
      "57        2.142810 452.505       26.62460       1042.9752  75.00000  NA    NA\n",
      "58        2.023600 456.463       25.81610       1053.1594  86.96000  NA    NA\n",
      "59        2.884920 344.105       35.93390        652.9746  54.25000  NA    NA\n",
      "60        1.694910 352.790       40.05850        667.4720  75.39000  NA    NA\n",
      "61        1.857100 369.807       30.06980        688.3558  85.32000  NA    NA\n",
      "62        2.404360 384.680       35.82400        701.6695  98.70000  NA    NA\n",
      "63        3.111730 412.390       42.28360        730.0845 113.50000  NA    NA\n",
      "64        6.010090 423.390       61.48460        976.2124  51.35000  NA    NA\n",
      "65        1.046240 457.854       83.66410        986.0731  66.23000  NA    NA\n",
      "66        1.782720 478.099       89.61340       1007.2831  67.88000  NA    NA\n",
      "67        0.976930 487.000       93.20300       1017.2054  74.14000  NA    NA\n",
      "68        0.944056 491.870       49.20100       1031.2486  76.40000  NA    NA\n",
      "69        5.837300 317.573       20.91080        598.2325  51.75000  NA    NA\n",
      "70        5.437100 359.917       26.99130        651.6258  79.60000  NA    NA\n",
      "71        5.988550 393.670       31.92750        691.1963 111.18000  NA    NA\n",
      "72        5.996540 429.313       27.75090        729.0631 119.92000  NA    NA\n",
      "73        9.517470 477.974       25.41400        779.3447 131.36000  NA    NA\n",
      "74        6.546510 435.856       24.26790        912.2147  72.64000  NA    NA\n",
      "75        3.896700 472.952       18.21280        944.9799  73.73000  NA    NA\n",
      "76        2.821150 493.939       32.77590        959.3636  74.68000  NA    NA\n",
      "77        3.358500 521.285       27.47980        987.2646  88.61000  NA    NA\n",
      "78        4.042500 547.870       25.65260       1015.7902  93.81000  NA    NA\n",
      "79       22.400000 272.512       29.24000        634.0343  80.66667  NA    NA\n",
      "80       21.720000 273.341       28.66000        633.4579  89.66667  NA    NA\n",
      "81       21.063400 265.351       27.93850        618.6000  93.33333  NA    NA\n",
      "82       20.366500 265.602       27.21270        620.1470  96.33333  NA    NA\n",
      "83       11.503500 346.626       15.48930        744.6153  40.00000  NA    NA\n",
      "84        9.075270 318.490       13.06120        669.1101  50.66667  NA    NA\n",
      "85        9.177670 315.707       13.00200        661.7170  53.33333  NA    NA\n",
      "86        8.530970 315.093       12.59570        657.9253  54.00000  NA    NA\n",
      "87        8.419080 314.345       12.48050        653.8656  58.66667  NA    NA\n",
      "88       31.245400 285.366       61.67700        598.2897  46.00000  NA    NA\n",
      "89       19.819700 297.195       39.81650        618.5125  49.33333  NA    NA\n",
      "90       21.322900 299.874       38.95220        618.5576  50.00000  NA    NA\n",
      "91       22.273200 299.602       45.68850        615.7914  51.33333  NA    NA\n",
      "92       22.272500 301.808       45.90850        617.4883  58.66667  NA    NA\n",
      "93        7.929270 324.721       15.65400        648.5915  55.66667  NA    NA\n",
      "94        7.769610 323.037       15.63560        638.6166  58.66667  NA    NA\n",
      "95        8.571130 330.602       18.17210        644.1879  66.66667  NA    NA\n",
      "96       14.068000 336.298       32.16520        661.0795  69.33333  NA    NA\n",
      "97       14.284700 341.100       31.43890        661.0247  71.33333  NA    NA\n",
      "98       29.454200 774.386       48.55080       1523.0869  53.66667  NA    NA\n",
      "99       35.433900 796.823       58.01540       1530.8566  56.33333  NA    NA\n",
      "100      30.301800 750.522       51.05100       1420.4544  58.66667  NA    NA\n",
      "101      34.394000 703.595       58.36900       1380.2002  60.66667  NA    NA\n",
      "102      29.599000 660.054       51.83400       1324.1693  68.00000  NA    NA\n",
      "103      23.070700 482.587       40.11450       1081.8206  45.00000  NA    NA\n",
      "104      24.666900 496.967       41.60770       1098.3230  49.33333  NA    NA\n",
      "105      26.298900 511.882       42.70170       1122.3236  55.33333  NA    NA\n",
      "106      16.069300 516.314       28.70450       1102.0425  59.33333  NA    NA\n",
      "107      15.558600 522.599       27.18960       1114.1818  60.66667  NA    NA\n",
      "108      42.008000 411.402       67.64270        987.8759  42.66667  NA    NA\n",
      "109      37.005100 422.756       57.35940        989.0417  48.00000  NA    NA\n",
      "110      48.069700 444.708       75.57950       1008.4877  54.33333  NA    NA\n",
      "111      45.148600 444.708       72.05290       1008.1388  57.66667  NA    NA\n",
      "112      48.481600 446.410       74.47420       1004.2634  64.33333  NA    NA\n",
      "113      19.405800 423.099       31.75860        977.0215  50.33333  NA    NA\n",
      "114      20.487100 429.606       36.30890        979.9787  52.33333  NA    NA\n",
      "115      20.108900 430.089       37.87210        982.5578  54.00000  NA    NA\n",
      "116      24.973900 441.312       47.00110        993.6559  55.33333  NA    NA\n",
      "117      33.411900 448.100       60.59390        996.4341  57.00000  NA    NA\n",
      "118      19.959600 445.240       26.77010        841.5521  90.66667  NA    NA\n",
      "119      22.107700 470.409       29.67510        879.0470  93.33333  NA    NA\n",
      "120      22.659800 469.908       29.80400        871.3988  97.66667  NA    NA\n",
      "121      21.705800 483.462       29.21330        898.7309 108.66667  NA    NA\n",
      "122      23.541100 490.741       31.74880        901.8443 118.00000  NA    NA\n",
      "123      24.693600 369.578       40.97780        685.9536  52.66667  NA    NA\n",
      "124       7.438500 381.304       11.04070        702.8444  68.00000  NA    NA\n",
      "125       6.600100 394.642        9.92862        711.5067  82.33333  NA    NA\n",
      "126       6.086370 410.669        9.46356        730.2845  85.66667  NA    NA\n",
      "127      16.888000 340.514       23.29860        638.2504  39.00000  NA    NA\n",
      "128       5.505800 354.830        8.45998        657.4207  59.33333  NA    NA\n",
      "129       5.816600 362.938        9.15920        666.7960  64.66667  NA    NA\n",
      "130       6.133040 367.104        9.37160        672.7020  69.33333  NA    NA\n",
      "131       7.050920 376.682       10.23292        685.5060  76.66667  NA    NA\n",
      "132      60.723400 773.328      113.27400       1466.8437  63.66667  NA    NA\n",
      "133      18.141300 828.396       32.49140       1517.0976  69.66667  NA    NA\n",
      "134      24.668400 858.944       40.68340       1540.3527  71.00000  NA    NA\n",
      "135      28.581100 838.546       46.18510       1509.9630  75.66667  NA    NA\n",
      "136      23.794400 835.985       42.80100       1519.8494  78.33333  NA    NA\n",
      "137      34.856600 525.470       46.76380       1117.7293  46.33333  NA    NA\n",
      "138      48.117300 493.275       47.85750       1067.6989  58.00000  NA    NA\n",
      "139      69.379100 503.675       46.16510       1077.3137  67.66667  NA    NA\n",
      "140      53.065000 509.577       37.85930       1084.3612  89.00000  NA    NA\n",
      "141      27.940800 502.726       29.12500       1059.5580 116.33333  NA    NA\n",
      "142      48.111300 461.744       82.67380        986.8375  50.66667  NA    NA\n",
      "143      56.096400 460.689       90.48340        985.2905  66.66667  NA    NA\n",
      "144      60.818800 492.099       65.84260       1021.1594  70.33333  NA    NA\n",
      "145      20.633000 464.383       35.91030        990.5495  76.00000  NA    NA\n",
      "146      19.723800 480.304       34.60960       1020.1859  78.00000  NA    NA\n",
      "147      22.791400 264.494       28.67070        635.2699  73.33333  NA    NA\n",
      "148      22.318200 266.974       29.38450        628.5086  84.66667  NA    NA\n",
      "149      21.967400 267.334       29.15680        627.3463  92.00000  NA    NA\n",
      "150      20.823900 268.025       28.15430        623.5632 100.66667  NA    NA\n",
      "151      20.092300 264.588       27.55420        617.1133 107.66667  NA    NA\n",
      "152       7.338150 314.573       11.90780        660.6263  43.00000  NA    NA\n",
      "153       7.218390 320.588       11.29710        671.6519  47.00000  NA    NA\n",
      "154       7.204740 312.340       11.27930        651.4647  54.00000  NA    NA\n",
      "155       7.482510 306.440       11.48040        639.5836  55.66667  NA    NA\n",
      "156       7.186150 311.708       11.07490        651.9100  58.00000  NA    NA\n",
      "157       5.909790 281.407       11.74920        576.7573  48.00000  NA    NA\n",
      "158       6.713440 292.596       13.81540        600.5082  51.00000  NA    NA\n",
      "159       7.840000 299.700       16.24490        609.5938  56.66667  NA    NA\n",
      "160       9.623301 303.990       20.54970        616.6190  62.66667  NA    NA\n",
      "161      10.725900 306.483       21.79910        625.0700  66.66667  NA    NA\n",
      "162      23.323100 801.632       38.63980       1528.9468  57.00000  NA    NA\n",
      "163      29.757000 808.639       49.27270       1522.9988  67.33333  NA    NA\n",
      "164      31.403800 808.346       52.08070       1517.9145  71.66667  NA    NA\n",
      "165      26.760800 815.244       44.13590       1530.0352  73.33333  NA    NA\n",
      "166      31.935900 675.902       56.74470       1350.3595  75.00000  NA    NA\n",
      "167      18.696300 490.111       34.70090       1075.6740  44.33333  NA    NA\n",
      "168      22.750800 496.373       38.60650       1103.6462  50.33333  NA    NA\n",
      "169      17.078100 507.306       31.76770       1100.7223  54.33333  NA    NA\n",
      "170      17.273300 517.475       31.27470       1110.2686  56.66667  NA    NA\n",
      "171      17.301600 521.200       30.79030       1118.8320  59.33333  NA    NA\n",
      "172      49.420000 422.599       86.05520        972.4721  44.33333  NA    NA\n",
      "173      60.512000 431.383      100.04300        987.5884  48.33333  NA    NA\n",
      "174      69.639300 441.385      114.98400        995.3141  51.00000  NA    NA\n",
      "175      80.318800 452.222      131.15200       1013.2868  55.66667  NA    NA\n",
      "176      79.110300 450.123      126.31500       1001.5165  58.66667  NA    NA\n",
      "177       7.015410 423.210       16.46310        963.2222  48.00000  NA    NA\n",
      "178       9.773210 428.084       22.53630        978.6106  52.00000  NA    NA\n",
      "179      10.001200 436.093       24.15400        986.4459  56.00000  NA    NA\n",
      "180       9.421780 436.475       23.05520        985.9244  59.00000  NA    NA\n",
      "181       8.826100 440.509       25.51420        983.1218  61.33333  NA    NA\n",
      "182      10.300000 368.039       43.75110        708.1029  85.33333  NA    NA\n",
      "183       6.405920 421.370       13.79610        781.2461 204.66667  NA    NA\n",
      "184       6.305600 461.458       15.28730        836.7403 231.66667  NA    NA\n",
      "185      25.139100 334.978       45.54120        656.1197  53.33333  NA    NA\n",
      "186       6.951890 352.426       12.01920        674.4859  91.00000  NA    NA\n",
      "187      10.660300 356.824       19.91470        657.1233  61.00000  NA    NA\n",
      "188       3.927990 372.235        8.85874        680.2654  68.33333  NA    NA\n",
      "189       4.238810 375.738        7.07455        687.7213  71.33333  NA    NA\n",
      "190       4.731570 347.098        8.25031        673.3910  76.33333  NA    NA\n",
      "191       5.113200 375.202        9.13277        691.7518  82.33333  NA    NA\n",
      "192      54.053700 797.834      100.72100       1483.2932  69.33333  NA    NA\n",
      "193      53.883100 797.646       92.09360       1494.0160  75.33333  NA    NA\n",
      "194      47.141600 844.723       79.20230       1546.6088  77.66667  NA    NA\n",
      "195      37.442500 834.177       61.85600       1526.5512  84.00000  NA    NA\n",
      "196      51.762000 701.785       90.06840       1376.8435  96.33333  NA    NA\n",
      "197      24.076300 518.739       46.71330       1112.2669  54.00000  NA    NA\n",
      "198      18.792200 483.042       36.31280       1062.1483  62.66667  NA    NA\n",
      "199      69.379100 503.675       46.16510       1077.3137  75.00000  NA    NA\n",
      "200      24.176300 501.660       34.34960       1094.1425 100.33333  NA    NA\n",
      "201      14.389600 533.859       38.77030       1113.9384 124.00000  NA    NA\n",
      "202      28.230600 486.366       68.45290       1022.8000  53.00000  NA    NA\n",
      "203      30.276600 479.054       47.98700       1021.9945  72.66667  NA    NA\n",
      "204      29.436200 479.094       47.05380       1007.1708  79.00000  NA    NA\n",
      "205      29.178500 494.308       48.32240       1030.5303  85.33333  NA    NA\n",
      "206      29.387900 491.465       46.55580       1019.8470  98.00000  NA    NA\n",
      "207      48.684200 454.491      101.51800        985.7930  67.66667  NA    NA\n",
      "208      59.101600 459.341       86.16860        984.4133  94.66667  NA    NA\n",
      "209      60.819900 492.298       65.93200       1021.0601 102.33333  NA    NA\n",
      "210      51.895800 486.701       61.20210        981.2909 104.00000  NA    NA\n",
      "211      59.103200 511.141       53.00300        992.4010 109.00000  NA    NA\n",
      "212      22.268000 454.802       30.38040        869.0011  96.66667  NA    NA\n",
      "213      21.568500 453.965       30.03800        866.9346 100.33333  NA    NA\n",
      "214      22.740100 466.235       31.66450        888.3343 104.00000  NA    NA\n",
      "215      19.837300 465.926       28.53040        878.4667 111.33333  NA    NA\n",
      "216       4.751730 362.231        9.22704        709.2136  62.66667  NA    NA\n",
      "217       8.882630 362.208       16.07950        707.8368  65.00000  NA    NA\n",
      "218       5.954020 362.746       10.67330        709.8398  76.00000  NA    NA\n",
      "219       5.567240 364.893       11.03450        714.7794 121.66667  NA    NA\n",
      "220       6.196810 378.357       13.04130        741.7795 153.00000  NA    NA\n",
      "221      29.175900 334.390       39.74930        641.3334  69.00000  NA    NA\n",
      "222      32.292200 348.739       37.73410        663.7907  74.66667  NA    NA\n",
      "223      27.996600 361.831       33.20780        677.1687  81.00000  NA    NA\n",
      "224      26.129600 358.496       31.38340        671.1517  90.00000  NA    NA\n",
      "225      25.355500 371.990       30.51640        686.1154  99.33333  NA    NA\n",
      "226       4.678750 295.454       11.69160        620.2783  51.66667  NA    NA\n",
      "227       4.063160 299.207       11.08050        624.9891  69.66667  NA    NA\n",
      "228       4.302650 297.903       11.76060        621.6559 102.00000  NA    NA\n",
      "229       4.798230 302.242       13.74150        627.5745 103.00000  NA    NA\n",
      "230       4.860000 303.376       15.06540        628.3623  80.00000  NA    NA\n",
      "231      13.550900 442.335       26.84100       1014.3933  43.33333  NA    NA\n",
      "232      14.508600 447.816       27.97910       1025.4344  46.66667  NA    NA\n",
      "233      13.958200 450.365       28.09610       1024.5419  50.00000  NA    NA\n",
      "234       9.919370 456.492       22.59410       1024.5476  51.00000  NA    NA\n",
      "235      29.282000 476.238       84.94980       1036.8686  42.00000  NA    NA\n",
      "236      28.502500 454.133       64.23640       1009.4613  45.00000  NA    NA\n",
      "237      28.264300 478.190       67.55600       1025.0335  49.00000  NA    NA\n",
      "238      29.447400 494.105       67.93620       1033.0670  51.33333  NA    NA\n",
      "239      30.206300 496.542       71.13110       1024.8439  52.33333  NA    NA\n",
      "    NA..2 NA..3 NA..4 NA..5 NA..6\n",
      "1      NA    NA    NA    NA    NA\n",
      "2      NA    NA    NA    NA    NA\n",
      "3      NA    NA    NA    NA    NA\n",
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      "238    NA    NA    NA    NA    NA\n",
      "239    NA    NA    NA    NA    NA\n"
     ]
    }
   ],
   "source": [
    "data <- read.xlsx(\"dataama.xlsx\", sheetIndex = 1)\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = vc..m.min. ~ f..mm. + Bahn + Fc..N. + Stdabw..Fc..N., \n",
       "    data = data)\n",
       "\n",
       "Residuals:\n",
       "   Min     1Q Median     3Q    Max \n",
       "-80.82 -34.05 -16.77  40.17  90.67 \n",
       "\n",
       "Coefficients:\n",
       "                Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)    171.10982   12.79475  13.373   <2e-16 ***\n",
       "f..mm.         814.48782   74.01347  11.005   <2e-16 ***\n",
       "Bahn             0.97366    2.20052   0.442    0.659    \n",
       "Fc..N.          -0.42702    0.03198 -13.353   <2e-16 ***\n",
       "Stdabw..Fc..N.  -0.03999    0.10736  -0.372    0.710    \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 47.51 on 234 degrees of freedom\n",
       "Multiple R-squared:  0.4532,\tAdjusted R-squared:  0.4438 \n",
       "F-statistic: 48.48 on 4 and 234 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "input <-lm(vc..m.min. ~ f..mm.+Bahn+Fc..N.+Stdabw..Fc..N.,data)\n",
    "summary(input) # show results\n",
    "#print(head(input))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>(Intercept)</dt>\n",
       "\t\t<dd>171.10982362624</dd>\n",
       "\t<dt>f..mm.</dt>\n",
       "\t\t<dd>814.48781890767</dd>\n",
       "\t<dt>Bahn</dt>\n",
       "\t\t<dd>0.973659222381178</dd>\n",
       "\t<dt>Fc..N.</dt>\n",
       "\t\t<dd>-0.427021380292129</dd>\n",
       "\t<dt>Stdabw..Fc..N.</dt>\n",
       "\t\t<dd>-0.0399876693242438</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] 171.10982362624\n",
       "\\item[f..mm.] 814.48781890767\n",
       "\\item[Bahn] 0.973659222381178\n",
       "\\item[Fc..N.] -0.427021380292129\n",
       "\\item[Stdabw..Fc..N.] -0.0399876693242438\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   171.10982362624f..mm.\n",
       ":   814.48781890767Bahn\n",
       ":   0.973659222381178Fc..N.\n",
       ":   -0.427021380292129Stdabw..Fc..N.\n",
       ":   -0.0399876693242438\n",
       "\n"
      ],
      "text/plain": [
       "   (Intercept)         f..mm.           Bahn         Fc..N. Stdabw..Fc..N. \n",
       "  171.10982363   814.48781891     0.97365922    -0.42702138    -0.03998767 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coefficients(input) # model coefficients\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>(Intercept)</th><td>145.9021970</td><td>196.3174503</td></tr>\n",
       "\t<tr><th scope=row>f..mm.</th><td>668.6699103</td><td>960.3057275</td></tr>\n",
       "\t<tr><th scope=row>Bahn</th><td> -3.3617086</td><td>  5.3090270</td></tr>\n",
       "\t<tr><th scope=row>Fc..N.</th><td> -0.4900235</td><td> -0.3640192</td></tr>\n",
       "\t<tr><th scope=row>Stdabw..Fc..N.</th><td> -0.2514948</td><td>  0.1715194</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       "  & 2.5 \\% & 97.5 \\%\\\\\n",
       "\\hline\n",
       "\t(Intercept) & 145.9021970 & 196.3174503\\\\\n",
       "\tf..mm. & 668.6699103 & 960.3057275\\\\\n",
       "\tBahn &  -3.3617086 &   5.3090270\\\\\n",
       "\tFc..N. &  -0.4900235 &  -0.3640192\\\\\n",
       "\tStdabw..Fc..N. &  -0.2514948 &   0.1715194\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | 2.5 % | 97.5 % | \n",
       "|---|---|---|---|---|\n",
       "| (Intercept) | 145.9021970 | 196.3174503 | \n",
       "| f..mm. | 668.6699103 | 960.3057275 | \n",
       "| Bahn |  -3.3617086 |   5.3090270 | \n",
       "| Fc..N. |  -0.4900235 |  -0.3640192 | \n",
       "| Stdabw..Fc..N. |  -0.2514948 |   0.1715194 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "               2.5 %       97.5 %     \n",
       "(Intercept)    145.9021970 196.3174503\n",
       "f..mm.         668.6699103 960.3057275\n",
       "Bahn            -3.3617086   5.3090270\n",
       "Fc..N.          -0.4900235  -0.3640192\n",
       "Stdabw..Fc..N.  -0.2514948   0.1715194"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "confint(input, level=0.95) # CIs for model parameters \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>1</dt>\n",
       "\t\t<dd>58.9411752643345</dd>\n",
       "\t<dt>2</dt>\n",
       "\t\t<dd>58.1800904514906</dd>\n",
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       ":   114.038585527279189\n",
       ":   112.456727196303190\n",
       ":   112.391743816751191\n",
       ":   111.937877976245192\n",
       ":   -4.76767645219213193\n",
       ":   -7.90108074663937194\n",
       ":   -16.9506279222259195\n",
       ":   -10.0058834946129196\n",
       ":   23.8602773489612197\n",
       ":   93.0627111051601198\n",
       ":   109.61336346259199\n",
       ":   107.32465106689200\n",
       ":   101.534771096131201\n",
       ":   103.811198399455202\n",
       ":   125.699846162231203\n",
       ":   125.49313029537204\n",
       ":   133.398464132024205\n",
       ":   127.449856337518206\n",
       ":   132.577851919966207\n",
       ":   134.595438387912208\n",
       ":   138.916356782729209\n",
       ":   131.475290063101210\n",
       ":   149.917560752472211\n",
       ":   153.096212827074212\n",
       ":   44.6787038612047213\n",
       ":   46.7697503523932214\n",
       ":   41.263017173447215\n",
       ":   46.3880149487464216\n",
       ":   93.693119117377217\n",
       ":   95.3246591111628218\n",
       ":   95.6750131997717219\n",
       ":   94.9390134047209220\n",
       ":   86.2569908184774221\n",
       ":   118.361581892391222\n",
       ":   113.426621059281223\n",
       ":   111.82452007204224\n",
       ":   115.37170282797225\n",
       ":   113.135004011056226\n",
       ":   116.024876523256227\n",
       ":   115.493893896602228\n",
       ":   117.740022032599229\n",
       ":   117.023439393703230\n",
       ":   118.069910407551231\n",
       ":   121.683409749741232\n",
       ":   118.830360689387233\n",
       ":   120.737448457898234\n",
       ":   123.768378922768235\n",
       ":   115.935582318201236\n",
       ":   125.616270642538237\n",
       ":   125.918940227078238\n",
       ":   126.428214081473239\n",
       ":   132.262761346777\n",
       "\n"
      ],
      "text/plain": [
       "         1          2          3          4          5          6          7 \n",
       " 58.941175  58.180090  61.720944  52.353046  55.321575  15.942599  10.816858 \n",
       "         8          9         10         11         12         13         14 \n",
       " 10.015207  14.220243  15.386230 105.813371  98.632745  93.866997  97.320642 \n",
       "        15         16         17         18         19         20         21 \n",
       " 93.124886 122.294597 114.814581 114.623394 116.586636 110.777043 114.465103 \n",
       "        22         23         24         25         26         27         28 \n",
       "107.507738 104.215972  98.621270  98.856255 142.389586 133.205830 139.280859 \n",
       "        29         30         31         32         33         34         35 \n",
       "139.144853 129.008622 119.393371 116.217487 113.679353 111.619812 168.789117 \n",
       "        36         37         38         39         40         41         42 \n",
       "167.095274 161.906950 159.224584  62.279798  53.878914  65.930438  49.580607 \n",
       "        43         44         45         46         47         48         49 \n",
       " 58.185131  35.418733  49.647514  42.551169  14.042860   6.921392 102.787130 \n",
       "        50         51         52         53         54         55         56 \n",
       " 97.184625  92.394875  89.335261  88.388779 127.661561 114.676886 114.376692 \n",
       "        57         58         59         60         61         62         63 \n",
       "112.068767 109.329553 113.363864 109.437496 107.013985 106.417218 102.545817 \n",
       "        64         65         66         67         68         69         70 \n",
       "135.166306 136.835376 132.842510 131.315927 126.587118 131.699131 121.781889 \n",
       "        71         72         73         74         75         76         77 \n",
       "116.110413 112.436334 109.330758 168.009743 165.610863 163.827521 159.673885 \n",
       "        78         79         80         81         82         83         84 \n",
       "156.436478 102.172153 103.564479 109.864861 110.272888  71.128848 100.054183 \n",
       "        85         86         87         88         89         90         91 \n",
       "103.596425 106.152137 108.919679 122.075012 117.447865 119.041299 121.219291 \n",
       "        92         93         94         95         96         97         98 \n",
       "121.988793 111.354449 116.734484 116.929855 111.147572 113.425379 -26.019041 \n",
       "        99        100        101        102        103        104        105 \n",
       "-23.180620  18.025777  23.535772  38.277786  99.225551  96.653387  90.097734 \n",
       "       106        107        108        109        110        111        112 \n",
       "102.217818  99.286079 122.685886 126.501409 122.896025 124.192944 127.368436 \n",
       "       113        114        115        116        117        118        119 \n",
       "132.690763 133.814986 133.467704 131.878458 132.312694  54.674621  44.904861 \n",
       "       120        121        122        123        124        125        126 \n",
       " 50.399920  41.858841  43.443686 107.391310 104.715849 105.014492 101.123402 \n",
       "       127        128        129        130        131        132        133 \n",
       "121.956217 118.846818 117.218776 116.564821 114.029630  -6.462196  -7.580361 \n",
       "       134        135        136        137        138        139        140 \n",
       " -9.494903  -1.013455  -5.101228  91.246834 107.483185 107.324651 106.038031 \n",
       "       141        142        143        144        145        146        147 \n",
       "117.831487 134.937800 137.034627 131.367152 139.035656 129.813916  98.237184 \n",
       "       148        149        150        151        152        153        154 \n",
       "102.977634 104.398213 107.473706 110.817240 102.164690  98.672593 106.989297 \n",
       "       155        156        157        158        159        160        161 \n",
       "112.275699 108.889077 132.795492 125.293203 123.878648 122.652612 120.240648 \n",
       "       162        163        164        165        166        167        168 \n",
       "-20.800401 -13.813528 -10.484555 -12.950720  30.022762 104.985290  94.240390 \n",
       "       169        170        171        172        173        174        175 \n",
       "100.081142  98.816157  96.770169 133.752883 129.157962 128.831221 123.477718 \n",
       "       176        177        178        179        180        181        182 \n",
       "129.877171 140.590326 135.619804 134.841573 136.142021 139.553499  95.166919 \n",
       "       183        184        185        186        187        188        189 \n",
       " 80.962764  68.603930 110.587688 107.825031 118.637131 114.038586 112.456727 \n",
       "       190        191        192        193        194        195        196 \n",
       "112.391744 111.937878  -4.767676  -7.901081 -16.950628 -10.005883  23.860277 \n",
       "       197        198        199        200        201        202        203 \n",
       " 93.062711 109.613363 107.324651 101.534771 103.811198 125.699846 125.493130 \n",
       "       204        205        206        207        208        209        210 \n",
       "133.398464 127.449856 132.577852 134.595438 138.916357 131.475290 149.917561 \n",
       "       211        212        213        214        215        216        217 \n",
       "153.096213  44.678704  46.769750  41.263017  46.388015  93.693119  95.324659 \n",
       "       218        219        220        221        222        223        224 \n",
       " 95.675013  94.939013  86.256991 118.361582 113.426621 111.824520 115.371703 \n",
       "       225        226        227        228        229        230        231 \n",
       "113.135004 116.024877 115.493894 117.740022 117.023439 118.069910 121.683410 \n",
       "       232        233        234        235        236        237        238 \n",
       "118.830361 120.737448 123.768379 115.935582 125.616271 125.918940 126.428214 \n",
       "       239 \n",
       "132.262761 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fitted(input) # predicted values\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>1</dt>\n",
       "\t\t<dd>-28.9411752643345</dd>\n",
       "\t<dt>2</dt>\n",
       "\t\t<dd>-28.1800904514906</dd>\n",
       "\t<dt>3</dt>\n",
       "\t\t<dd>-31.7209440455651</dd>\n",
       "\t<dt>4</dt>\n",
       "\t\t<dd>-22.3530461591515</dd>\n",
       "\t<dt>5</dt>\n",
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       "\t<dt>6</dt>\n",
       "\t\t<dd>14.0574011123353</dd>\n",
       "\t<dt>7</dt>\n",
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       "\t<dt>8</dt>\n",
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       "\t<dt>9</dt>\n",
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       "\t<dt>10</dt>\n",
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       "\t<dt>11</dt>\n",
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       "\t<dt>12</dt>\n",
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       "\t<dt>13</dt>\n",
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       "\t<dt>14</dt>\n",
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       "\t<dt>15</dt>\n",
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       "\t<dt>16</dt>\n",
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       "\t<dt>20</dt>\n",
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       "\t\t<dd>-39.1448533632855</dd>\n",
       "\t<dt>30</dt>\n",
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       "\t<dt>31</dt>\n",
       "\t\t<dd>80.6066286488258</dd>\n",
       "\t<dt>32</dt>\n",
       "\t\t<dd>83.7825125665923</dd>\n",
       "\t<dt>33</dt>\n",
       "\t\t<dd>86.3206466709908</dd>\n",
       "\t<dt>34</dt>\n",
       "\t\t<dd>88.3801877860322</dd>\n",
       "\t<dt>35</dt>\n",
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       "\t<dt>37</dt>\n",
       "\t\t<dd>38.0930496706875</dd>\n",
       "\t<dt>38</dt>\n",
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       "\t<dt>40</dt>\n",
       "\t\t<dd>-23.8789135234117</dd>\n",
       "\t<dt>41</dt>\n",
       "\t\t<dd>-35.9304377275451</dd>\n",
       "\t<dt>42</dt>\n",
       "\t\t<dd>-19.5806068143234</dd>\n",
       "\t<dt>43</dt>\n",
       "\t\t<dd>-28.185131004036</dd>\n",
       "\t<dt>44</dt>\n",
       "\t\t<dd>-5.41873254897366</dd>\n",
       "\t<dt>45</dt>\n",
       "\t\t<dd>-19.6475138041861</dd>\n",
       "\t<dt>46</dt>\n",
       "\t\t<dd>-12.5511694765766</dd>\n",
       "\t<dt>47</dt>\n",
       "\t\t<dd>15.9571395065059</dd>\n",
       "\t<dt>48</dt>\n",
       "\t\t<dd>23.0786079015074</dd>\n",
       "\t<dt>49</dt>\n",
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       "\t<dt>51</dt>\n",
       "\t\t<dd>-32.394874840149</dd>\n",
       "\t<dt>52</dt>\n",
       "\t\t<dd>-29.3352610384567</dd>\n",
       "\t<dt>53</dt>\n",
       "\t\t<dd>-28.3887788555151</dd>\n",
       "\t<dt>54</dt>\n",
       "\t\t<dd>-67.6615610246066</dd>\n",
       "\t<dt>55</dt>\n",
       "\t\t<dd>-54.6768861927649</dd>\n",
       "\t<dt>56</dt>\n",
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       "\t\t<dd>-52.0687669735781</dd>\n",
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       "\t\t<dd>-49.3295526589752</dd>\n",
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       "\t\t<dd>34.3891369711538</dd>\n",
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       "\t\t<dd>43.5635222187957</dd>\n",
       "\t<dt>79</dt>\n",
       "\t\t<dd>-72.1721532879175</dd>\n",
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       "\t<dt>82</dt>\n",
       "\t\t<dd>-80.2728880784262</dd>\n",
       "\t<dt>83</dt>\n",
       "\t\t<dd>-11.1288482075898</dd>\n",
       "\t<dt>84</dt>\n",
       "\t\t<dd>-40.0541831952746</dd>\n",
       "\t<dt>85</dt>\n",
       "\t\t<dd>-43.5964246173571</dd>\n",
       "\t<dt>86</dt>\n",
       "\t\t<dd>-46.1521372665357</dd>\n",
       "\t<dt>87</dt>\n",
       "\t\t<dd>-48.9196786854639</dd>\n",
       "\t<dt>88</dt>\n",
       "\t\t<dd>-22.0750116704452</dd>\n",
       "\t<dt>89</dt>\n",
       "\t\t<dd>-17.4478646263812</dd>\n",
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       "\t\t<dd>-21.9887929602559</dd>\n",
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       "\t<dt>102</dt>\n",
       "\t\t<dd>-8.27778635415395</dd>\n",
       "\t<dt>103</dt>\n",
       "\t\t<dd>-39.2255514820555</dd>\n",
       "\t<dt>104</dt>\n",
       "\t\t<dd>-36.6533869082906</dd>\n",
       "\t<dt>105</dt>\n",
       "\t\t<dd>-30.0977342766366</dd>\n",
       "\t<dt>106</dt>\n",
       "\t\t<dd>-42.2178180778365</dd>\n",
       "\t<dt>107</dt>\n",
       "\t\t<dd>-39.2860794175091</dd>\n",
       "\t<dt>108</dt>\n",
       "\t\t<dd>-22.6858860492294</dd>\n",
       "\t<dt>109</dt>\n",
       "\t\t<dd>-26.501408877329</dd>\n",
       "\t<dt>110</dt>\n",
       "\t\t<dd>-22.8960246766983</dd>\n",
       "\t<dt>111</dt>\n",
       "\t\t<dd>-24.1929435436129</dd>\n",
       "\t<dt>112</dt>\n",
       "\t\t<dd>-27.3684358755695</dd>\n",
       "\t<dt>113</dt>\n",
       "\t\t<dd>67.3092368971194</dd>\n",
       "\t<dt>114</dt>\n",
       "\t\t<dd>66.1850138817631</dd>\n",
       "\t<dt>115</dt>\n",
       "\t\t<dd>66.5322963713529</dd>\n",
       "\t<dt>116</dt>\n",
       "\t\t<dd>68.121542042642</dd>\n",
       "\t<dt>117</dt>\n",
       "\t\t<dd>67.6873064027519</dd>\n",
       "\t<dt>118</dt>\n",
       "\t\t<dd>-24.674620829107</dd>\n",
       "\t<dt>119</dt>\n",
       "\t\t<dd>-14.9048610718647</dd>\n",
       "\t<dt>120</dt>\n",
       "\t\t<dd>-20.3999204965506</dd>\n",
       "\t<dt>121</dt>\n",
       "\t\t<dd>-11.8588414191661</dd>\n",
       "\t<dt>122</dt>\n",
       "\t\t<dd>-13.4436859551083</dd>\n",
       "\t<dt>123</dt>\n",
       "\t\t<dd>-7.39130995564187</dd>\n",
       "\t<dt>124</dt>\n",
       "\t\t<dd>-4.71584916286342</dd>\n",
       "\t<dt>125</dt>\n",
       "\t\t<dd>-5.01449228598571</dd>\n",
       "\t<dt>126</dt>\n",
       "\t\t<dd>-1.12340154278611</dd>\n",
       "\t<dt>127</dt>\n",
       "\t\t<dd>78.043782922517</dd>\n",
       "\t<dt>128</dt>\n",
       "\t\t<dd>81.1531815654087</dd>\n",
       "\t<dt>129</dt>\n",
       "\t\t<dd>82.7812242135144</dd>\n",
       "\t<dt>130</dt>\n",
       "\t\t<dd>83.4351788824666</dd>\n",
       "\t<dt>131</dt>\n",
       "\t\t<dd>85.9703696291405</dd>\n",
       "\t<dt>132</dt>\n",
       "\t\t<dd>36.4621955437595</dd>\n",
       "\t<dt>133</dt>\n",
       "\t\t<dd>37.5803608600041</dd>\n",
       "\t<dt>134</dt>\n",
       "\t\t<dd>39.4949025939447</dd>\n",
       "\t<dt>135</dt>\n",
       "\t\t<dd>31.0134554933249</dd>\n",
       "\t<dt>136</dt>\n",
       "\t\t<dd>35.1012281874156</dd>\n",
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       "\\end{description*}\n"
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       "           1            2            3            4            5            6 \n",
       "-28.94117526 -28.18009045 -31.72094405 -22.35304616 -25.32157461  14.05740111 \n",
       "           7            8            9           10           11           12 \n",
       " 19.18314150  19.98479332  15.77975654  14.61377022 -45.81337125 -38.63274489 \n",
       "          13           14           15           16           17           18 \n",
       "-33.86699740 -37.32064249 -33.12488564 -62.29459690 -54.81458083 -54.62339364 \n",
       "          19           20           21           22           23           24 \n",
       "-56.58663628 -50.77704270 -14.46510339  -7.50773760  -4.21597162   1.37872988 \n",
       "          25           26           27           28           29           30 \n",
       "  1.14374490 -42.38958591 -33.20582963 -39.28085945 -39.14485336  70.99137781 \n",
       "          31           32           33           34           35           36 \n",
       " 80.60662865  83.78251257  86.32064667  88.38018779  31.21088262  32.90472614 \n",
       "          37           38           39           40           41           42 \n",
       " 38.09304967  40.77541631 -32.27979750 -23.87891352 -35.93043773 -19.58060681 \n",
       "          43           44           45           46           47           48 \n",
       "-28.18513100  -5.41873255 -19.64751380 -12.55116948  15.95713951  23.07860790 \n",
       "          49           50           51           52           53           54 \n",
       "-42.78712975 -37.18462495 -32.39487484 -29.33526104 -28.38877886 -67.66156102 \n",
       "          55           56           57           58           59           60 \n",
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       "          61           62           63           64           65           66 \n",
       " -7.01398511  -6.41721793  -2.54581672 -35.16630648 -36.83537580 -32.84250999 \n",
       "          67           68           69           70           71           72 \n",
       "-31.31592713 -26.58711770  68.30086930  78.21811144  83.88958721  87.56366607 \n",
       "          73           74           75           76           77           78 \n",
       " 90.66924165  31.99025748  34.38913697  36.17247920  40.32611508  43.56352222 \n",
       "          79           80           81           82           83           84 \n",
       "-72.17215329 -73.56447867 -79.86486115 -80.27288808 -11.12884821 -40.05418320 \n",
       "          85           86           87           88           89           90 \n",
       "-43.59642462 -46.15213727 -48.91967869 -22.07501167 -17.44786463 -19.04129910 \n",
       "          91           92           93           94           95           96 \n",
       "-21.21929135 -21.98879296  88.64555107  83.26551596  83.07014471  88.85242792 \n",
       "          97           98           99          100          101          102 \n",
       " 86.57462133  56.01904075  53.18062022  11.97422319   6.46422834  -8.27778635 \n",
       "         103          104          105          106          107          108 \n",
       "-39.22555148 -36.65338691 -30.09773428 -42.21781808 -39.28607942 -22.68588605 \n",
       "         109          110          111          112          113          114 \n",
       "-26.50140888 -22.89602468 -24.19294354 -27.36843588  67.30923690  66.18501388 \n",
       "         115          116          117          118          119          120 \n",
       " 66.53229637  68.12154204  67.68730640 -24.67462083 -14.90486107 -20.39992050 \n",
       "         121          122          123          124          125          126 \n",
       "-11.85884142 -13.44368596  -7.39130996  -4.71584916  -5.01449229  -1.12340154 \n",
       "         127          128          129          130          131          132 \n",
       " 78.04378292  81.15318157  82.78122421  83.43517888  85.97036963  36.46219554 \n",
       "         133          134          135          136          137          138 \n",
       " 37.58036086  39.49490259  31.01345549  35.10122819 -31.24683431 -47.48318458 \n",
       "         139          140          141          142          143          144 \n",
       "-47.32465107 -46.03803141 -57.83148673  65.06219997  62.96537345  68.63284839 \n",
       "         145          146          147          148          149          150 \n",
       " 60.96434444  70.18608351 -68.23718350 -72.97763393 -74.39821259 -77.47370579 \n",
       "         151          152          153          154          155          156 \n",
       "-80.81724019 -42.16468958 -38.67259303 -46.98929747 -52.27569913 -48.88907667 \n",
       "         157          158          159          160          161          162 \n",
       " 67.20450830  74.70679658  76.12135238  77.34738811  79.75935229  50.80040135 \n",
       "         163          164          165          166          167          168 \n",
       " 43.81352811  40.48455499  42.95071957  -0.02276168 -44.98529022 -34.24039013 \n",
       "         169          170          171          172          173          174 \n",
       "-40.08114209 -38.81615712 -36.77016920 -33.75288290 -29.15796157 -28.83122135 \n",
       "         175          176          177          178          179          180 \n",
       "-23.47771795 -29.87717136  59.40967438  64.38019616  65.15842684  63.85797880 \n",
       "         181          182          183          184          185          186 \n",
       " 60.44650091 -35.16691853 -20.96276376  -8.60393017 -10.58768845  -7.82503120 \n",
       "         187          188          189          190          191          192 \n",
       " 81.36286877  85.96141447  87.54327280  87.60825618  88.06212202  34.76767645 \n",
       "         193          194          195          196          197          198 \n",
       " 37.90108075  46.95062792  40.00588349   6.13972265 -33.06271111 -49.61336346 \n",
       "         199          200          201          202          203          204 \n",
       "-47.32465107 -41.53477110 -43.81119840 -25.69984616 -25.49313030 -33.39846413 \n",
       "         205          206          207          208          209          210 \n",
       "-27.44985634 -32.57785192  65.40456161  61.08364322  68.52470994  50.08243925 \n",
       "         211          212          213          214          215          216 \n",
       " 46.90378717 -14.67870386 -16.76975035 -11.26301717 -16.38801495 -33.69311912 \n",
       "         217          218          219          220          221          222 \n",
       "-35.32465911 -35.67501320 -34.93901340 -26.25699082 -18.36158189 -13.42662106 \n",
       "         223          224          225          226          227          228 \n",
       "-11.82452007 -15.37170283 -13.13500401 -16.02487652 -15.49389390 -17.74002203 \n",
       "         229          230          231          232          233          234 \n",
       "-17.02343939 -18.06991041 -21.68340975 -18.83036069 -20.73744846 -23.76837892 \n",
       "         235          236          237          238          239 \n",
       "-15.93558232 -25.61627064 -25.91894023 -26.42821408 -32.26276135 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "residuals(input) # residuals\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>Sum Sq</th><th scope=col>Mean Sq</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>f..mm.</th><td>  1         </td><td>   402.1595 </td><td>   402.1595 </td><td>  0.17813982</td><td>6.733643e-01</td></tr>\n",
       "\t<tr><th scope=row>Bahn</th><td>  1         </td><td>   122.0550 </td><td>   122.0550 </td><td>  0.05406523</td><td>8.163379e-01</td></tr>\n",
       "\t<tr><th scope=row>Fc..N.</th><td>  1         </td><td>436931.8910 </td><td>436931.8910 </td><td>193.54252183</td><td>1.821578e-32</td></tr>\n",
       "\t<tr><th scope=row>Stdabw..Fc..N.</th><td>  1         </td><td>   313.2130 </td><td>   313.2130 </td><td>  0.13874025</td><td>7.098737e-01</td></tr>\n",
       "\t<tr><th scope=row>Residuals</th><td>234         </td><td>528266.6647 </td><td>  2257.5498 </td><td>          NA</td><td>          NA</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & Sum Sq & Mean Sq & F value & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tf..mm. &   1          &    402.1595  &    402.1595  &   0.17813982 & 6.733643e-01\\\\\n",
       "\tBahn &   1          &    122.0550  &    122.0550  &   0.05406523 & 8.163379e-01\\\\\n",
       "\tFc..N. &   1          & 436931.8910  & 436931.8910  & 193.54252183 & 1.821578e-32\\\\\n",
       "\tStdabw..Fc..N. &   1          &    313.2130  &    313.2130  &   0.13874025 & 7.098737e-01\\\\\n",
       "\tResiduals & 234          & 528266.6647  &   2257.5498  &           NA &           NA\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | Sum Sq | Mean Sq | F value | Pr(>F) | \n",
       "|---|---|---|---|---|\n",
       "| f..mm. |   1          |    402.1595  |    402.1595  |   0.17813982 | 6.733643e-01 | \n",
       "| Bahn |   1          |    122.0550  |    122.0550  |   0.05406523 | 8.163379e-01 | \n",
       "| Fc..N. |   1          | 436931.8910  | 436931.8910  | 193.54252183 | 1.821578e-32 | \n",
       "| Stdabw..Fc..N. |   1          |    313.2130  |    313.2130  |   0.13874025 | 7.098737e-01 | \n",
       "| Residuals | 234          | 528266.6647  |   2257.5498  |           NA |           NA | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "               Df  Sum Sq      Mean Sq     F value      Pr(>F)      \n",
       "f..mm.           1    402.1595    402.1595   0.17813982 6.733643e-01\n",
       "Bahn             1    122.0550    122.0550   0.05406523 8.163379e-01\n",
       "Fc..N.           1 436931.8910 436931.8910 193.54252183 1.821578e-32\n",
       "Stdabw..Fc..N.   1    313.2130    313.2130   0.13874025 7.098737e-01\n",
       "Residuals      234 528266.6647   2257.5498           NA           NA"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "anova(input) # anova table \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>(Intercept)</th><th scope=col>f..mm.</th><th scope=col>Bahn</th><th scope=col>Fc..N.</th><th scope=col>Stdabw..Fc..N.</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>(Intercept)</th><td>163.7056710  </td><td>  65.541897  </td><td>-13.525571092</td><td>-0.168627768 </td><td>-0.167220790 </td></tr>\n",
       "\t<tr><th scope=row>f..mm.</th><td> 65.5418973  </td><td>5477.993822  </td><td>  5.478288994</td><td>-2.108973875 </td><td>-3.557941310 </td></tr>\n",
       "\t<tr><th scope=row>Bahn</th><td>-13.5255711  </td><td>   5.478289  </td><td>  4.842300074</td><td>-0.002428778 </td><td>-0.016861959 </td></tr>\n",
       "\t<tr><th scope=row>Fc..N.</th><td> -0.1686278  </td><td>  -2.108974  </td><td> -0.002428778</td><td> 0.001022611 </td><td> 0.001054795 </td></tr>\n",
       "\t<tr><th scope=row>Stdabw..Fc..N.</th><td> -0.1672208  </td><td>  -3.557941  </td><td> -0.016861959</td><td> 0.001054795 </td><td> 0.011525233 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & (Intercept) & f..mm. & Bahn & Fc..N. & Stdabw..Fc..N.\\\\\n",
       "\\hline\n",
       "\t(Intercept) & 163.7056710   &   65.541897   & -13.525571092 & -0.168627768  & -0.167220790 \\\\\n",
       "\tf..mm. &  65.5418973   & 5477.993822   &   5.478288994 & -2.108973875  & -3.557941310 \\\\\n",
       "\tBahn & -13.5255711   &    5.478289   &   4.842300074 & -0.002428778  & -0.016861959 \\\\\n",
       "\tFc..N. &  -0.1686278   &   -2.108974   &  -0.002428778 &  0.001022611  &  0.001054795 \\\\\n",
       "\tStdabw..Fc..N. &  -0.1672208   &   -3.557941   &  -0.016861959 &  0.001054795  &  0.011525233 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | (Intercept) | f..mm. | Bahn | Fc..N. | Stdabw..Fc..N. | \n",
       "|---|---|---|---|---|\n",
       "| (Intercept) | 163.7056710   |   65.541897   | -13.525571092 | -0.168627768  | -0.167220790  | \n",
       "| f..mm. |  65.5418973   | 5477.993822   |   5.478288994 | -2.108973875  | -3.557941310  | \n",
       "| Bahn | -13.5255711   |    5.478289   |   4.842300074 | -0.002428778  | -0.016861959  | \n",
       "| Fc..N. |  -0.1686278   |   -2.108974   |  -0.002428778 |  0.001022611  |  0.001054795  | \n",
       "| Stdabw..Fc..N. |  -0.1672208   |   -3.557941   |  -0.016861959 |  0.001054795  |  0.011525233  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "               (Intercept) f..mm.      Bahn          Fc..N.      \n",
       "(Intercept)    163.7056710   65.541897 -13.525571092 -0.168627768\n",
       "f..mm.          65.5418973 5477.993822   5.478288994 -2.108973875\n",
       "Bahn           -13.5255711    5.478289   4.842300074 -0.002428778\n",
       "Fc..N.          -0.1686278   -2.108974  -0.002428778  0.001022611\n",
       "Stdabw..Fc..N.  -0.1672208   -3.557941  -0.016861959  0.001054795\n",
       "               Stdabw..Fc..N.\n",
       "(Intercept)    -0.167220790  \n",
       "f..mm.         -3.557941310  \n",
       "Bahn           -0.016861959  \n",
       "Fc..N.          0.001054795  \n",
       "Stdabw..Fc..N.  0.011525233  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vcov(input) # covariance matrix for model parameters \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\t<dt>155</dt>\n",
       "\t\t<dd>0.013503015974146</dd>\n",
       "\t<dt>156</dt>\n",
       "\t\t<dd>0.0201485536072793</dd>\n",
       "\t<dt>157</dt>\n",
       "\t\t<dd>0.0216702312800742</dd>\n",
       "\t<dt>158</dt>\n",
       "\t\t<dd>0.0139853909397614</dd>\n",
       "\t<dt>159</dt>\n",
       "\t\t<dd>0.0117742164509917</dd>\n",
       "\t<dt>160</dt>\n",
       "\t\t<dd>0.013357081877292</dd>\n",
       "\t<dt>161</dt>\n",
       "\t\t<dd>0.0195755396903109</dd>\n",
       "\t<dt>162</dt>\n",
       "\t\t<dd>0.0478452253033884</dd>\n",
       "\t<dt>163</dt>\n",
       "\t\t<dd>0.0380831101991822</dd>\n",
       "\t<dt>164</dt>\n",
       "\t\t<dd>0.0344961051304036</dd>\n",
       "\t<dt>165</dt>\n",
       "\t\t<dd>0.0381330653823796</dd>\n",
       "\t<dt>166</dt>\n",
       "\t\t<dd>0.0272762512645124</dd>\n",
       "\t<dt>167</dt>\n",
       "\t\t<dd>0.0210870970841394</dd>\n",
       "\t<dt>168</dt>\n",
       "\t\t<dd>0.0127584512610745</dd>\n",
       "\t<dt>169</dt>\n",
       "\t\t<dd>0.0136019970512981</dd>\n",
       "\t<dt>170</dt>\n",
       "\t\t<dd>0.0162879502110792</dd>\n",
       "\t<dt>171</dt>\n",
       "\t\t<dd>0.0232300983388119</dd>\n",
       "\t<dt>172</dt>\n",
       "\t\t<dd>0.0218262173105159</dd>\n",
       "\t<dt>173</dt>\n",
       "\t\t<dd>0.0181053083929999</dd>\n",
       "\t<dt>174</dt>\n",
       "\t\t<dd>0.0191531776377801</dd>\n",
       "\t<dt>175</dt>\n",
       "\t\t<dd>0.0262204503277814</dd>\n",
       "\t<dt>176</dt>\n",
       "\t\t<dd>0.0294233966623949</dd>\n",
       "\t<dt>177</dt>\n",
       "\t\t<dd>0.0331283567729262</dd>\n",
       "\t<dt>178</dt>\n",
       "\t\t<dd>0.0242106918990798</dd>\n",
       "\t<dt>179</dt>\n",
       "\t\t<dd>0.0220446461042116</dd>\n",
       "\t<dt>180</dt>\n",
       "\t\t<dd>0.025250108261581</dd>\n",
       "\t<dt>181</dt>\n",
       "\t\t<dd>0.0334729239927272</dd>\n",
       "\t<dt>182</dt>\n",
       "\t\t<dd>0.0166791129677257</dd>\n",
       "\t<dt>183</dt>\n",
       "\t\t<dd>0.0106888228678385</dd>\n",
       "\t<dt>184</dt>\n",
       "\t\t<dd>0.014149977029383</dd>\n",
       "\t<dt>185</dt>\n",
       "\t\t<dd>0.0172370214539701</dd>\n",
       "\t<dt>186</dt>\n",
       "\t\t<dd>0.0121080719426846</dd>\n",
       "\t<dt>187</dt>\n",
       "\t\t<dd>0.0188452358367619</dd>\n",
       "\t<dt>188</dt>\n",
       "\t\t<dd>0.0135158104008532</dd>\n",
       "\t<dt>189</dt>\n",
       "\t\t<dd>0.011430731690309</dd>\n",
       "\t<dt>190</dt>\n",
       "\t\t<dd>0.0132712103257513</dd>\n",
       "\t<dt>191</dt>\n",
       "\t\t<dd>0.0210499955451223</dd>\n",
       "\t<dt>192</dt>\n",
       "\t\t<dd>0.0464732213079812</dd>\n",
       "\t<dt>193</dt>\n",
       "\t\t<dd>0.0374411021987633</dd>\n",
       "\t<dt>194</dt>\n",
       "\t\t<dd>0.0386548776265421</dd>\n",
       "\t<dt>195</dt>\n",
       "\t\t<dd>0.036599773127111</dd>\n",
       "\t<dt>196</dt>\n",
       "\t\t<dd>0.0295039261437673</dd>\n",
       "\t<dt>197</dt>\n",
       "\t\t<dd>0.0184478478597397</dd>\n",
       "\t<dt>198</dt>\n",
       "\t\t<dd>0.0153663884733479</dd>\n",
       "\t<dt>199</dt>\n",
       "\t\t<dd>0.00960911921149584</dd>\n",
       "\t<dt>200</dt>\n",
       "\t\t<dd>0.0158241022350615</dd>\n",
       "\t<dt>201</dt>\n",
       "\t\t<dd>0.0230943534276581</dd>\n",
       "\t<dt>202</dt>\n",
       "\t\t<dd>0.0190855287194466</dd>\n",
       "\t<dt>203</dt>\n",
       "\t\t<dd>0.01263560652092</dd>\n",
       "\t<dt>204</dt>\n",
       "\t\t<dd>0.0119739028743406</dd>\n",
       "\t<dt>205</dt>\n",
       "\t\t<dd>0.0128259751932983</dd>\n",
       "\t<dt>206</dt>\n",
       "\t\t<dd>0.0204841651740656</dd>\n",
       "\t<dt>207</dt>\n",
       "\t\t<dd>0.0204853482457294</dd>\n",
       "\t<dt>208</dt>\n",
       "\t\t<dd>0.0145484379155574</dd>\n",
       "\t<dt>209</dt>\n",
       "\t\t<dd>0.0110565539135327</dd>\n",
       "\t<dt>210</dt>\n",
       "\t\t<dd>0.0167576793874218</dd>\n",
       "\t<dt>211</dt>\n",
       "\t\t<dd>0.024278576611866</dd>\n",
       "\t<dt>212</dt>\n",
       "\t\t<dd>0.0236848331295757</dd>\n",
       "\t<dt>213</dt>\n",
       "\t\t<dd>0.0167125352018046</dd>\n",
       "\t<dt>214</dt>\n",
       "\t\t<dd>0.016302361117199</dd>\n",
       "\t<dt>215</dt>\n",
       "\t\t<dd>0.0174482426482583</dd>\n",
       "\t<dt>216</dt>\n",
       "\t\t<dd>0.0182666609201857</dd>\n",
       "\t<dt>217</dt>\n",
       "\t\t<dd>0.0113299052807092</dd>\n",
       "\t<dt>218</dt>\n",
       "\t\t<dd>0.0105735844013041</dd>\n",
       "\t<dt>219</dt>\n",
       "\t\t<dd>0.013272154453053</dd>\n",
       "\t<dt>220</dt>\n",
       "\t\t<dd>0.0199948971796714</dd>\n",
       "\t<dt>221</dt>\n",
       "\t\t<dd>0.017636450180228</dd>\n",
       "\t<dt>222</dt>\n",
       "\t\t<dd>0.0109716788839828</dd>\n",
       "\t<dt>223</dt>\n",
       "\t\t<dd>0.00893320276245546</dd>\n",
       "\t<dt>224</dt>\n",
       "\t\t<dd>0.0116052144143867</dd>\n",
       "\t<dt>225</dt>\n",
       "\t\t<dd>0.0181693132473579</dd>\n",
       "\t<dt>226</dt>\n",
       "\t\t<dd>0.0191193692780119</dd>\n",
       "\t<dt>227</dt>\n",
       "\t\t<dd>0.0131168723031501</dd>\n",
       "\t<dt>228</dt>\n",
       "\t\t<dd>0.0115637940480771</dd>\n",
       "\t<dt>229</dt>\n",
       "\t\t<dd>0.0135230572481713</dd>\n",
       "\t<dt>230</dt>\n",
       "\t\t<dd>0.0202563855988531</dd>\n",
       "\t<dt>231</dt>\n",
       "\t\t<dd>0.0247511783361217</dd>\n",
       "\t<dt>232</dt>\n",
       "\t\t<dd>0.0168612963112735</dd>\n",
       "\t<dt>233</dt>\n",
       "\t\t<dd>0.0158898057316006</dd>\n",
       "\t<dt>234</dt>\n",
       "\t\t<dd>0.0213106170201588</dd>\n",
       "\t<dt>235</dt>\n",
       "\t\t<dd>0.0183700903126851</dd>\n",
       "\t<dt>236</dt>\n",
       "\t\t<dd>0.0123804120519223</dd>\n",
       "\t<dt>237</dt>\n",
       "\t\t<dd>0.010186217164832</dd>\n",
       "\t<dt>238</dt>\n",
       "\t\t<dd>0.0124092747288259</dd>\n",
       "\t<dt>239</dt>\n",
       "\t\t<dd>0.0195213401645488</dd>\n",
       "</dl>\n",
       "</dd>\n",
       "\t<dt>$coefficients</dt>\n",
       "\t\t<dd><table>\n",
       "<thead><tr><th></th><th scope=col>(Intercept)</th><th scope=col>f..mm.</th><th scope=col>Bahn</th><th scope=col>Fc..N.</th><th scope=col>Stdabw..Fc..N.</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>-0.6724181090</td><td> 3.4125126   </td><td> 0.123971978 </td><td>-1.131740e-03</td><td>-5.543220e-05</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>-0.4704605648</td><td> 3.3502369   </td><td> 0.058831990 </td><td>-1.119576e-03</td><td> 7.713809e-05</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>-0.3449692971</td><td> 3.6230955   </td><td>-0.002408308 </td><td>-1.169257e-03</td><td> 1.031179e-05</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>-0.0653822055</td><td> 3.0576864   </td><td>-0.049670004 </td><td>-1.062191e-03</td><td>-1.978259e-04</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 0.0666625942</td><td> 3.2004109   </td><td>-0.112841163 </td><td>-1.096979e-03</td><td> 3.962125e-04</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>-0.1332495201</td><td>-1.7298039   </td><td>-0.064176568 </td><td> 1.173997e-03</td><td> 6.224203e-04</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>-0.3260524545</td><td>-2.6929254   </td><td>-0.045835153 </td><td> 1.738124e-03</td><td> 1.260610e-03</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>-0.4847685833</td><td>-3.1808859   </td><td>-0.005467216 </td><td> 1.925948e-03</td><td> 2.374407e-03</td></tr>\n",
       "\t<tr><th scope=row>9</th><td>-0.4642442896</td><td>-2.2172929   </td><td> 0.031288094 </td><td> 1.407051e-03</td><td> 1.224074e-03</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>-0.5227096293</td><td>-2.0253454   </td><td> 0.061561838 </td><td> 1.292403e-03</td><td> 1.032389e-03</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>-1.4644685617</td><td> 0.1658913   </td><td> 0.188129618 </td><td> 6.577576e-04</td><td> 3.801773e-03</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>-0.9533501187</td><td> 0.4037236   </td><td> 0.072987999 </td><td> 3.519394e-04</td><td> 4.283263e-03</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>-0.5903573291</td><td> 0.7910759   </td><td>-0.008634254 </td><td> 1.102478e-04</td><td> 3.477392e-03</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>-0.4426263628</td><td> 0.5665459   </td><td>-0.090969515 </td><td> 2.650696e-04</td><td> 4.263969e-03</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>-0.1561810833</td><td> 0.9435480   </td><td>-0.152611614 </td><td> 4.862934e-05</td><td> 3.402848e-03</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>-0.6291444141</td><td>-7.8790574   </td><td> 0.260903107 </td><td> 2.219872e-03</td><td> 6.917447e-03</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>-0.1104679395</td><td>-5.4521609   </td><td> 0.112393851 </td><td> 1.347464e-03</td><td> 4.133907e-03</td></tr>\n",
       "\t<tr><th scope=row>18</th><td> 0.2087362247</td><td>-5.9445032   </td><td>-0.009028090 </td><td> 1.481966e-03</td><td> 6.235575e-03</td></tr>\n",
       "\t<tr><th scope=row>19</th><td> 0.5421207016</td><td>-6.6392039   </td><td>-0.133668476 </td><td> 1.718608e-03</td><td> 7.643244e-03</td></tr>\n",
       "\t<tr><th scope=row>20</th><td> 0.8560222832</td><td>-5.4828908   </td><td>-0.231726344 </td><td> 1.272007e-03</td><td> 7.348493e-03</td></tr>\n",
       "\t<tr><th scope=row>21</th><td>-0.4388966570</td><td> 0.8308475   </td><td> 0.064548054 </td><td> 4.222620e-05</td><td>-2.253022e-03</td></tr>\n",
       "\t<tr><th scope=row>22</th><td>-0.1663832611</td><td> 0.6350606   </td><td> 0.017577455 </td><td>-6.034957e-05</td><td>-1.484838e-03</td></tr>\n",
       "\t<tr><th scope=row>23</th><td>-0.0597983036</td><td> 0.5018571   </td><td> 0.001271950 </td><td>-8.130841e-05</td><td>-1.211809e-03</td></tr>\n",
       "\t<tr><th scope=row>24</th><td> 0.0082938630</td><td>-0.2113132   </td><td> 0.002478803 </td><td> 4.338437e-05</td><td> 4.966021e-04</td></tr>\n",
       "\t<tr><th scope=row>25</th><td> 0.0005391388</td><td>-0.1539081   </td><td> 0.004688660 </td><td> 2.983360e-05</td><td> 3.348748e-04</td></tr>\n",
       "\t<tr><th scope=row>26</th><td>-0.3433025707</td><td>-1.8975453   </td><td> 0.205991610 </td><td> 9.085454e-04</td><td>-1.295717e-02</td></tr>\n",
       "\t<tr><th scope=row>27</th><td> 0.5392361717</td><td> 5.6641888   </td><td> 0.048668767 </td><td>-1.449935e-03</td><td>-3.387288e-02</td></tr>\n",
       "\t<tr><th scope=row>28</th><td> 0.4483240815</td><td>-1.6439108   </td><td>-0.071499567 </td><td> 7.456213e-04</td><td>-1.074787e-02</td></tr>\n",
       "\t<tr><th scope=row>29</th><td> 1.0470450742</td><td> 4.2841547   </td><td>-0.144594857 </td><td>-9.215380e-04</td><td>-3.234819e-02</td></tr>\n",
       "\t<tr><th scope=row>30</th><td> 2.3682609272</td><td>-1.0635930   </td><td>-0.310368371 </td><td>-1.526466e-03</td><td> 7.502478e-03</td></tr>\n",
       "\t<tr><th scope=row>...</th><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr>\n",
       "\t<tr><th scope=row>210</th><td>-0.27895043  </td><td> 7.49467519  </td><td> 0.1124103814</td><td>-2.723601e-03</td><td>-1.467053e-03</td></tr>\n",
       "\t<tr><th scope=row>211</th><td>-0.51865234  </td><td> 7.73390725  </td><td> 0.2110091087</td><td>-2.823672e-03</td><td>-2.921352e-03</td></tr>\n",
       "\t<tr><th scope=row>212</th><td>-0.29766864  </td><td> 2.36332334  </td><td> 0.0644206668</td><td>-8.483970e-04</td><td>-7.974722e-04</td></tr>\n",
       "\t<tr><th scope=row>213</th><td>-0.24429679  </td><td> 2.47612502  </td><td> 0.0358442446</td><td>-8.891033e-04</td><td>-3.427602e-04</td></tr>\n",
       "\t<tr><th scope=row>214</th><td>-0.08258850  </td><td> 1.79338321  </td><td>-0.0003252519</td><td>-6.622894e-04</td><td>-2.138966e-04</td></tr>\n",
       "\t<tr><th scope=row>215</th><td>-0.03407635  </td><td> 2.38535692  </td><td>-0.0365977593</td><td>-8.633471e-04</td><td> 8.304982e-06</td></tr>\n",
       "\t<tr><th scope=row>216</th><td>-1.01395960  </td><td> 0.82213219  </td><td> 0.1383970232</td><td> 1.025015e-04</td><td> 3.055172e-03</td></tr>\n",
       "\t<tr><th scope=row>217</th><td>-0.83035880  </td><td> 1.05704700  </td><td> 0.0690634526</td><td> 7.325871e-05</td><td> 2.319589e-03</td></tr>\n",
       "\t<tr><th scope=row>218</th><td>-0.63172285  </td><td> 0.72384906  </td><td>-0.0090941075</td><td> 1.757909e-04</td><td> 3.621029e-03</td></tr>\n",
       "\t<tr><th scope=row>219</th><td>-0.39864557  </td><td> 0.73523662  </td><td>-0.0848378378</td><td> 1.528285e-04</td><td> 3.829505e-03</td></tr>\n",
       "\t<tr><th scope=row>220</th><td>-0.09410644  </td><td> 1.09632515  </td><td>-0.1208173128</td><td>-1.411063e-04</td><td> 2.681904e-03</td></tr>\n",
       "\t<tr><th scope=row>221</th><td>-0.59995816  </td><td> 0.16943877  </td><td> 0.0778270621</td><td> 3.364835e-04</td><td>-3.151594e-04</td></tr>\n",
       "\t<tr><th scope=row>222</th><td>-0.34179975  </td><td> 0.23427354  </td><td> 0.0274546180</td><td> 1.828483e-04</td><td>-1.087462e-04</td></tr>\n",
       "\t<tr><th scope=row>223</th><td>-0.22600870  </td><td> 0.18934865  </td><td>-0.0016564885</td><td> 1.565822e-04</td><td> 1.463360e-04</td></tr>\n",
       "\t<tr><th scope=row>224</th><td>-0.20975938  </td><td> 0.09192846  </td><td>-0.0357649845</td><td> 2.717371e-04</td><td> 4.513106e-04</td></tr>\n",
       "\t<tr><th scope=row>225</th><td>-0.09373002  </td><td> 0.11931092  </td><td>-0.0594573741</td><td> 2.086511e-04</td><td> 5.134397e-04</td></tr>\n",
       "\t<tr><th scope=row>226</th><td>-0.54275139  </td><td>-0.32384392  </td><td> 0.0653720434</td><td> 4.121326e-04</td><td> 1.571476e-03</td></tr>\n",
       "\t<tr><th scope=row>227</th><td>-0.42356645  </td><td>-0.30172725  </td><td> 0.0291856120</td><td> 3.890551e-04</td><td> 1.615519e-03</td></tr>\n",
       "\t<tr><th scope=row>228</th><td>-0.37990153  </td><td>-0.42128546  </td><td>-0.0051048970</td><td> 4.833949e-04</td><td> 1.947524e-03</td></tr>\n",
       "\t<tr><th scope=row>229</th><td>-0.25381854  </td><td>-0.31724338  </td><td>-0.0415234980</td><td> 4.336097e-04</td><td> 1.745492e-03</td></tr>\n",
       "\t<tr><th scope=row>230</th><td>-0.15961436  </td><td>-0.35582642  </td><td>-0.0837894009</td><td> 4.758687e-04</td><td> 1.899591e-03</td></tr>\n",
       "\t<tr><th scope=row>231</th><td>-0.23965583  </td><td>-3.21518365  </td><td> 0.0888027457</td><td> 9.016067e-04</td><td> 4.071986e-03</td></tr>\n",
       "\t<tr><th scope=row>232</th><td>-0.07392088  </td><td>-2.54583415  </td><td> 0.0361461046</td><td> 6.881480e-04</td><td> 3.196555e-03</td></tr>\n",
       "\t<tr><th scope=row>233</th><td> 0.03949092  </td><td>-2.93925068  </td><td>-0.0056993795</td><td> 8.132385e-04</td><td> 3.845968e-03</td></tr>\n",
       "\t<tr><th scope=row>234</th><td> 0.17287080  </td><td>-3.76448344  </td><td>-0.0598195066</td><td> 1.075962e-03</td><td> 5.378350e-03</td></tr>\n",
       "\t<tr><th scope=row>235</th><td>-0.10879571  </td><td>-1.03682319  </td><td> 0.0705515205</td><td> 2.435137e-04</td><td>-8.916755e-04</td></tr>\n",
       "\t<tr><th scope=row>236</th><td>-0.07660806  </td><td>-2.62799468  </td><td> 0.0544685461</td><td> 7.748097e-04</td><td> 4.253066e-04</td></tr>\n",
       "\t<tr><th scope=row>237</th><td> 0.08481791  </td><td>-2.62942055  </td><td>-0.0008906359</td><td> 7.778230e-04</td><td> 4.396817e-04</td></tr>\n",
       "\t<tr><th scope=row>238</th><td> 0.24641093  </td><td>-2.78633921  </td><td>-0.0585822506</td><td> 8.280412e-04</td><td> 8.446154e-04</td></tr>\n",
       "\t<tr><th scope=row>239</th><td> 0.47872814  </td><td>-3.71011107  </td><td>-0.1422947739</td><td> 1.181639e-03</td><td> 9.635637e-04</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$sigma</dt>\n",
       "\t\t<dd><dl class=dl-horizontal>\n",
       "\t<dt>1</dt>\n",
       "\t\t<dd>47.57699013149</dd>\n",
       "\t<dt>2</dt>\n",
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       "\t<dt>6</dt>\n",
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       "\t<dt>8</dt>\n",
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       "\t<dt>13</dt>\n",
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       "\t<dt>15</dt>\n",
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       "\t<dt>16</dt>\n",
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       "\t\t<dd>47.4782502371242</dd>\n",
       "\t<dt>18</dt>\n",
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       "\t<dt>26</dt>\n",
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       "\t\t<dd>47.4820421773735</dd>\n",
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       "\t<dt>101</dt>\n",
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       "\t\t<dd>47.5742675388872</dd>\n",
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       "\t\t<dd>47.5442022184557</dd>\n",
       "\t<dt>108</dt>\n",
       "\t\t<dd>47.5917439066137</dd>\n",
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       "\t<dt>111</dt>\n",
       "\t\t<dd>47.588674284583</dd>\n",
       "\t<dt>112</dt>\n",
       "\t\t<dd>47.5809042565779</dd>\n",
       "\t<dt>113</dt>\n",
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       "\t<dt>115</dt>\n",
       "\t\t<dd>47.4129122039407</dd>\n",
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       "\t\t<dd>47.5874775668037</dd>\n",
       "\t<dt>119</dt>\n",
       "\t\t<dd>47.6053430044196</dd>\n",
       "\t<dt>120</dt>\n",
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       "\t\t<dd>-27.4498563375176</dd>\n",
       "\t<dt>206</dt>\n",
       "\t\t<dd>-32.5778519199663</dd>\n",
       "\t<dt>207</dt>\n",
       "\t\t<dd>65.404561612088</dd>\n",
       "\t<dt>208</dt>\n",
       "\t\t<dd>61.0836432172714</dd>\n",
       "\t<dt>209</dt>\n",
       "\t\t<dd>68.5247099368991</dd>\n",
       "\t<dt>210</dt>\n",
       "\t\t<dd>50.0824392475277</dd>\n",
       "\t<dt>211</dt>\n",
       "\t\t<dd>46.9037871729264</dd>\n",
       "\t<dt>212</dt>\n",
       "\t\t<dd>-14.6787038612047</dd>\n",
       "\t<dt>213</dt>\n",
       "\t\t<dd>-16.7697503523932</dd>\n",
       "\t<dt>214</dt>\n",
       "\t\t<dd>-11.263017173447</dd>\n",
       "\t<dt>215</dt>\n",
       "\t\t<dd>-16.3880149487464</dd>\n",
       "\t<dt>216</dt>\n",
       "\t\t<dd>-33.693119117377</dd>\n",
       "\t<dt>217</dt>\n",
       "\t\t<dd>-35.3246591111628</dd>\n",
       "\t<dt>218</dt>\n",
       "\t\t<dd>-35.6750131997717</dd>\n",
       "\t<dt>219</dt>\n",
       "\t\t<dd>-34.9390134047209</dd>\n",
       "\t<dt>220</dt>\n",
       "\t\t<dd>-26.2569908184774</dd>\n",
       "\t<dt>221</dt>\n",
       "\t\t<dd>-18.3615818923912</dd>\n",
       "\t<dt>222</dt>\n",
       "\t\t<dd>-13.4266210592812</dd>\n",
       "\t<dt>223</dt>\n",
       "\t\t<dd>-11.8245200720398</dd>\n",
       "\t<dt>224</dt>\n",
       "\t\t<dd>-15.3717028279699</dd>\n",
       "\t<dt>225</dt>\n",
       "\t\t<dd>-13.1350040110561</dd>\n",
       "\t<dt>226</dt>\n",
       "\t\t<dd>-16.0248765232559</dd>\n",
       "\t<dt>227</dt>\n",
       "\t\t<dd>-15.4938938966024</dd>\n",
       "\t<dt>228</dt>\n",
       "\t\t<dd>-17.7400220325986</dd>\n",
       "\t<dt>229</dt>\n",
       "\t\t<dd>-17.0234393937031</dd>\n",
       "\t<dt>230</dt>\n",
       "\t\t<dd>-18.0699104075511</dd>\n",
       "\t<dt>231</dt>\n",
       "\t\t<dd>-21.683409749741</dd>\n",
       "\t<dt>232</dt>\n",
       "\t\t<dd>-18.8303606893868</dd>\n",
       "\t<dt>233</dt>\n",
       "\t\t<dd>-20.7374484578982</dd>\n",
       "\t<dt>234</dt>\n",
       "\t\t<dd>-23.7683789227678</dd>\n",
       "\t<dt>235</dt>\n",
       "\t\t<dd>-15.9355823182011</dd>\n",
       "\t<dt>236</dt>\n",
       "\t\t<dd>-25.6162706425377</dd>\n",
       "\t<dt>237</dt>\n",
       "\t\t<dd>-25.9189402270778</dd>\n",
       "\t<dt>238</dt>\n",
       "\t\t<dd>-26.4282140814733</dd>\n",
       "\t<dt>239</dt>\n",
       "\t\t<dd>-32.2627613467769</dd>\n",
       "</dl>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$hat] \\begin{description*}\n",
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       "\\item[234] 0.0213106170201588\n",
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       "\\item[236] 0.0123804120519223\n",
       "\\item[237] 0.010186217164832\n",
       "\\item[238] 0.0124092747288259\n",
       "\\item[239] 0.0195213401645488\n",
       "\\end{description*}\n",
       "\n",
       "\\item[\\$coefficients] \\begin{tabular}{r|lllll}\n",
       "  & (Intercept) & f..mm. & Bahn & Fc..N. & Stdabw..Fc..N.\\\\\n",
       "\\hline\n",
       "\t1 & -0.6724181090 &  3.4125126    &  0.123971978  & -1.131740e-03 & -5.543220e-05\\\\\n",
       "\t2 & -0.4704605648 &  3.3502369    &  0.058831990  & -1.119576e-03 &  7.713809e-05\\\\\n",
       "\t3 & -0.3449692971 &  3.6230955    & -0.002408308  & -1.169257e-03 &  1.031179e-05\\\\\n",
       "\t4 & -0.0653822055 &  3.0576864    & -0.049670004  & -1.062191e-03 & -1.978259e-04\\\\\n",
       "\t5 &  0.0666625942 &  3.2004109    & -0.112841163  & -1.096979e-03 &  3.962125e-04\\\\\n",
       "\t6 & -0.1332495201 & -1.7298039    & -0.064176568  &  1.173997e-03 &  6.224203e-04\\\\\n",
       "\t7 & -0.3260524545 & -2.6929254    & -0.045835153  &  1.738124e-03 &  1.260610e-03\\\\\n",
       "\t8 & -0.4847685833 & -3.1808859    & -0.005467216  &  1.925948e-03 &  2.374407e-03\\\\\n",
       "\t9 & -0.4642442896 & -2.2172929    &  0.031288094  &  1.407051e-03 &  1.224074e-03\\\\\n",
       "\t10 & -0.5227096293 & -2.0253454    &  0.061561838  &  1.292403e-03 &  1.032389e-03\\\\\n",
       "\t11 & -1.4644685617 &  0.1658913    &  0.188129618  &  6.577576e-04 &  3.801773e-03\\\\\n",
       "\t12 & -0.9533501187 &  0.4037236    &  0.072987999  &  3.519394e-04 &  4.283263e-03\\\\\n",
       "\t13 & -0.5903573291 &  0.7910759    & -0.008634254  &  1.102478e-04 &  3.477392e-03\\\\\n",
       "\t14 & -0.4426263628 &  0.5665459    & -0.090969515  &  2.650696e-04 &  4.263969e-03\\\\\n",
       "\t15 & -0.1561810833 &  0.9435480    & -0.152611614  &  4.862934e-05 &  3.402848e-03\\\\\n",
       "\t16 & -0.6291444141 & -7.8790574    &  0.260903107  &  2.219872e-03 &  6.917447e-03\\\\\n",
       "\t17 & -0.1104679395 & -5.4521609    &  0.112393851  &  1.347464e-03 &  4.133907e-03\\\\\n",
       "\t18 &  0.2087362247 & -5.9445032    & -0.009028090  &  1.481966e-03 &  6.235575e-03\\\\\n",
       "\t19 &  0.5421207016 & -6.6392039    & -0.133668476  &  1.718608e-03 &  7.643244e-03\\\\\n",
       "\t20 &  0.8560222832 & -5.4828908    & -0.231726344  &  1.272007e-03 &  7.348493e-03\\\\\n",
       "\t21 & -0.4388966570 &  0.8308475    &  0.064548054  &  4.222620e-05 & -2.253022e-03\\\\\n",
       "\t22 & -0.1663832611 &  0.6350606    &  0.017577455  & -6.034957e-05 & -1.484838e-03\\\\\n",
       "\t23 & -0.0597983036 &  0.5018571    &  0.001271950  & -8.130841e-05 & -1.211809e-03\\\\\n",
       "\t24 &  0.0082938630 & -0.2113132    &  0.002478803  &  4.338437e-05 &  4.966021e-04\\\\\n",
       "\t25 &  0.0005391388 & -0.1539081    &  0.004688660  &  2.983360e-05 &  3.348748e-04\\\\\n",
       "\t26 & -0.3433025707 & -1.8975453    &  0.205991610  &  9.085454e-04 & -1.295717e-02\\\\\n",
       "\t27 &  0.5392361717 &  5.6641888    &  0.048668767  & -1.449935e-03 & -3.387288e-02\\\\\n",
       "\t28 &  0.4483240815 & -1.6439108    & -0.071499567  &  7.456213e-04 & -1.074787e-02\\\\\n",
       "\t29 &  1.0470450742 &  4.2841547    & -0.144594857  & -9.215380e-04 & -3.234819e-02\\\\\n",
       "\t30 &  2.3682609272 & -1.0635930    & -0.310368371  & -1.526466e-03 &  7.502478e-03\\\\\n",
       "\t... & ... & ... & ... & ... & ...\\\\\n",
       "\t210 & -0.27895043   &  7.49467519   &  0.1124103814 & -2.723601e-03 & -1.467053e-03\\\\\n",
       "\t211 & -0.51865234   &  7.73390725   &  0.2110091087 & -2.823672e-03 & -2.921352e-03\\\\\n",
       "\t212 & -0.29766864   &  2.36332334   &  0.0644206668 & -8.483970e-04 & -7.974722e-04\\\\\n",
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       "\t224 & -0.20975938   &  0.09192846   & -0.0357649845 &  2.717371e-04 &  4.513106e-04\\\\\n",
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       "\t226 & -0.54275139   & -0.32384392   &  0.0653720434 &  4.121326e-04 &  1.571476e-03\\\\\n",
       "\t227 & -0.42356645   & -0.30172725   &  0.0291856120 &  3.890551e-04 &  1.615519e-03\\\\\n",
       "\t228 & -0.37990153   & -0.42128546   & -0.0051048970 &  4.833949e-04 &  1.947524e-03\\\\\n",
       "\t229 & -0.25381854   & -0.31724338   & -0.0415234980 &  4.336097e-04 &  1.745492e-03\\\\\n",
       "\t230 & -0.15961436   & -0.35582642   & -0.0837894009 &  4.758687e-04 &  1.899591e-03\\\\\n",
       "\t231 & -0.23965583   & -3.21518365   &  0.0888027457 &  9.016067e-04 &  4.071986e-03\\\\\n",
       "\t232 & -0.07392088   & -2.54583415   &  0.0361461046 &  6.881480e-04 &  3.196555e-03\\\\\n",
       "\t233 &  0.03949092   & -2.93925068   & -0.0056993795 &  8.132385e-04 &  3.845968e-03\\\\\n",
       "\t234 &  0.17287080   & -3.76448344   & -0.0598195066 &  1.075962e-03 &  5.378350e-03\\\\\n",
       "\t235 & -0.10879571   & -1.03682319   &  0.0705515205 &  2.435137e-04 & -8.916755e-04\\\\\n",
       "\t236 & -0.07660806   & -2.62799468   &  0.0544685461 &  7.748097e-04 &  4.253066e-04\\\\\n",
       "\t237 &  0.08481791   & -2.62942055   & -0.0008906359 &  7.778230e-04 &  4.396817e-04\\\\\n",
       "\t238 &  0.24641093   & -2.78633921   & -0.0585822506 &  8.280412e-04 &  8.446154e-04\\\\\n",
       "\t239 &  0.47872814   & -3.71011107   & -0.1422947739 &  1.181639e-03 &  9.635637e-04\\\\\n",
       "\\end{tabular}\n",
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       "\\item[93] 88.6455510706863\n",
       "\\item[94] 83.2655159619297\n",
       "\\item[95] 83.070144708084\n",
       "\\item[96] 88.8524279197395\n",
       "\\item[97] 86.5746213273435\n",
       "\\item[98] 56.0190407530017\n",
       "\\item[99] 53.1806202234805\n",
       "\\item[100] 11.9742231927179\n",
       "\\item[101] 6.46422833550639\n",
       "\\item[102] -8.27778635415395\n",
       "\\item[103] -39.2255514820555\n",
       "\\item[104] -36.6533869082906\n",
       "\\item[105] -30.0977342766366\n",
       "\\item[106] -42.2178180778365\n",
       "\\item[107] -39.2860794175091\n",
       "\\item[108] -22.6858860492294\n",
       "\\item[109] -26.501408877329\n",
       "\\item[110] -22.8960246766983\n",
       "\\item[111] -24.1929435436129\n",
       "\\item[112] -27.3684358755695\n",
       "\\item[113] 67.3092368971194\n",
       "\\item[114] 66.1850138817631\n",
       "\\item[115] 66.5322963713529\n",
       "\\item[116] 68.121542042642\n",
       "\\item[117] 67.6873064027519\n",
       "\\item[118] -24.674620829107\n",
       "\\item[119] -14.9048610718647\n",
       "\\item[120] -20.3999204965506\n",
       "\\item[121] -11.8588414191661\n",
       "\\item[122] -13.4436859551083\n",
       "\\item[123] -7.39130995564187\n",
       "\\item[124] -4.71584916286342\n",
       "\\item[125] -5.01449228598571\n",
       "\\item[126] -1.12340154278611\n",
       "\\item[127] 78.043782922517\n",
       "\\item[128] 81.1531815654087\n",
       "\\item[129] 82.7812242135144\n",
       "\\item[130] 83.4351788824666\n",
       "\\item[131] 85.9703696291405\n",
       "\\item[132] 36.4621955437595\n",
       "\\item[133] 37.5803608600041\n",
       "\\item[134] 39.4949025939447\n",
       "\\item[135] 31.0134554933249\n",
       "\\item[136] 35.1012281874156\n",
       "\\item[137] -31.2468343093123\n",
       "\\item[138] -47.4831845792399\n",
       "\\item[139] -47.3246510668899\n",
       "\\item[140] -46.0380314096748\n",
       "\\item[141] -57.8314867289442\n",
       "\\item[142] 65.0621999656128\n",
       "\\item[143] 62.965373445777\n",
       "\\item[144] 68.6328483860498\n",
       "\\item[145] 60.9643444448189\n",
       "\\item[146] 70.1860835142079\n",
       "\\item[147] -68.2371835022333\n",
       "\\item[148] -72.9776339316732\n",
       "\\item[149] -74.3982125922421\n",
       "\\item[150] -77.4737057934831\n",
       "\\item[151] -80.8172401853647\n",
       "\\item[152] -42.1646895798602\n",
       "\\item[153] -38.6725930334048\n",
       "\\item[154] -46.9892974668245\n",
       "\\item[155] -52.2756991325752\n",
       "\\item[156] -48.8890766734121\n",
       "\\item[157] 67.2045083003773\n",
       "\\item[158] 74.7067965784163\n",
       "\\item[159] 76.1213523802898\n",
       "\\item[160] 77.3473881132242\n",
       "\\item[161] 79.7593522925035\n",
       "\\item[162] 50.8004013528654\n",
       "\\item[163] 43.8135281051894\n",
       "\\item[164] 40.4845549891936\n",
       "\\item[165] 42.95071957483\n",
       "\\item[166] -0.0227616760484058\n",
       "\\item[167] -44.9852902162501\n",
       "\\item[168] -34.2403901288758\n",
       "\\item[169] -40.0811420869461\n",
       "\\item[170] -38.8161571217332\n",
       "\\item[171] -36.7701691991191\n",
       "\\item[172] -33.752882897192\n",
       "\\item[173] -29.1579615675667\n",
       "\\item[174] -28.8312213527824\n",
       "\\item[175] -23.4777179484271\n",
       "\\item[176] -29.8771713630698\n",
       "\\item[177] 59.4096743841536\n",
       "\\item[178] 64.380196161197\n",
       "\\item[179] 65.158426839965\n",
       "\\item[180] 63.8579787976962\n",
       "\\item[181] 60.4465009088271\n",
       "\\item[182] -35.166918533862\n",
       "\\item[183] -20.9627637565567\n",
       "\\item[184] -8.60393017107383\n",
       "\\item[185] -10.5876884499848\n",
       "\\item[186] -7.8250311985195\n",
       "\\item[187] 81.3628687659742\n",
       "\\item[188] 85.9614144727206\n",
       "\\item[189] 87.5432728036967\n",
       "\\item[190] 87.6082561832486\n",
       "\\item[191] 88.0621220237555\n",
       "\\item[192] 34.7676764521921\n",
       "\\item[193] 37.9010807466394\n",
       "\\item[194] 46.9506279222259\n",
       "\\item[195] 40.0058834946129\n",
       "\\item[196] 6.13972265103877\n",
       "\\item[197] -33.0627111051601\n",
       "\\item[198] -49.6133634625903\n",
       "\\item[199] -47.3246510668899\n",
       "\\item[200] -41.5347710961307\n",
       "\\item[201] -43.8111983994553\n",
       "\\item[202] -25.699846162231\n",
       "\\item[203] -25.49313029537\n",
       "\\item[204] -33.398464132024\n",
       "\\item[205] -27.4498563375176\n",
       "\\item[206] -32.5778519199663\n",
       "\\item[207] 65.404561612088\n",
       "\\item[208] 61.0836432172714\n",
       "\\item[209] 68.5247099368991\n",
       "\\item[210] 50.0824392475277\n",
       "\\item[211] 46.9037871729264\n",
       "\\item[212] -14.6787038612047\n",
       "\\item[213] -16.7697503523932\n",
       "\\item[214] -11.263017173447\n",
       "\\item[215] -16.3880149487464\n",
       "\\item[216] -33.693119117377\n",
       "\\item[217] -35.3246591111628\n",
       "\\item[218] -35.6750131997717\n",
       "\\item[219] -34.9390134047209\n",
       "\\item[220] -26.2569908184774\n",
       "\\item[221] -18.3615818923912\n",
       "\\item[222] -13.4266210592812\n",
       "\\item[223] -11.8245200720398\n",
       "\\item[224] -15.3717028279699\n",
       "\\item[225] -13.1350040110561\n",
       "\\item[226] -16.0248765232559\n",
       "\\item[227] -15.4938938966024\n",
       "\\item[228] -17.7400220325986\n",
       "\\item[229] -17.0234393937031\n",
       "\\item[230] -18.0699104075511\n",
       "\\item[231] -21.683409749741\n",
       "\\item[232] -18.8303606893868\n",
       "\\item[233] -20.7374484578982\n",
       "\\item[234] -23.7683789227678\n",
       "\\item[235] -15.9355823182011\n",
       "\\item[236] -25.6162706425377\n",
       "\\item[237] -25.9189402270778\n",
       "\\item[238] -26.4282140814733\n",
       "\\item[239] -32.2627613467769\n",
       "\\end{description*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$hat\n",
       ":   1\n",
       ":   0.02019689302756682\n",
       ":   0.01425502837822793\n",
       ":   0.01179242167612274\n",
       ":   0.01606889903838175\n",
       ":   0.02223854346973486\n",
       ":   0.0315967437504447\n",
       ":   0.02765799384160178\n",
       ":   0.02765837500541489\n",
       ":   0.026957181255281210\n",
       ":   0.03289604316781111\n",
       ":   0.018057591017588312\n",
       ":   0.012816480797210713\n",
       ":   0.010663918776278514\n",
       ":   0.013420530080185115\n",
       ":   0.019658922965122316\n",
       ":   0.020635142601753517\n",
       ":   0.012196081665917118\n",
       ":   0.011354991527374219\n",
       ":   0.014533921990928320\n",
       ":   0.020919804320363421\n",
       ":   0.021883650693448422\n",
       ":   0.018092397107185823\n",
       ":   0.024080099186263724\n",
       ":   0.034594765845283725\n",
       ":   0.033220534367127426\n",
       ":   0.039190265408924927\n",
       ":   0.15724003908908828\n",
       ":   0.028591729724227729\n",
       ":   0.12430819019737830\n",
       ":   0.021016732869436431\n",
       ":   0.031458137828635132\n",
       ":   0.018705009576111533\n",
       ":   0.016356017630595434\n",
       ":   0.026940224688476235\n",
       ":   0.033560434817747736\n",
       ":   0.023736694035630437\n",
       ":   0.022466381246552238\n",
       ":   0.026714400786433439\n",
       ":   0.019716563392986740\n",
       ":   0.015093532048241\n",
       ":   0.011306819398695142\n",
       ":   0.016724815393618343\n",
       ":   0.022059621948615544\n",
       ":   0.02513940974622445\n",
       ":   0.015606745730758446\n",
       ":   0.015630748355836547\n",
       ":   0.026267332656186748\n",
       ":   0.035642824956604549\n",
       ":   0.018450667557932250\n",
       ":   0.012698835420644751\n",
       ":   0.010874055346612352\n",
       ":   0.013256820280606853\n",
       ":   0.018892689934894154\n",
       ":   0.023165730305310755\n",
       ":   0.015488341862574656\n",
       ":   0.013615346833577257\n",
       ":   0.016295940615832158\n",
       ":   0.023460231982017659\n",
       ":   0.022710212704596560\n",
       ":   0.022719349955632461\n",
       ":   0.0098925057964734462\n",
       ":   0.014166478408285163\n",
       ":   0.027597889044989764\n",
       ":   0.021754563020908865\n",
       ":   0.019980215210654566\n",
       ":   0.023381712846784567\n",
       ":   0.02668987920335468\n",
       ":   0.051495268585266769\n",
       ":   0.025458268095926170\n",
       ":   0.026540548191199771\n",
       ":   0.022274335512499772\n",
       ":   0.021100743169164973\n",
       ":   0.022511227307587674\n",
       ":   0.036240302279520875\n",
       ":   0.029703599954526576\n",
       ":   0.019170264390981677\n",
       ":   0.019980441765334578\n",
       ":   0.024630947782917679\n",
       ":   0.011890897807926580\n",
       ":   0.0096726463372186781\n",
       ":   0.011702963510795482\n",
       ":   0.01807339284699883\n",
       ":   0.01844318679354384\n",
       ":   0.011729268318232885\n",
       ":   0.010178830882185986\n",
       ":   0.013022404260460787\n",
       ":   0.020051649068686788\n",
       ":   0.02023245636051289\n",
       ":   0.01131233295336190\n",
       ":   0.0095693287771732491\n",
       ":   0.012094072012987892\n",
       ":   0.018685791846507493\n",
       ":   0.018078235986128294\n",
       ":   0.012822126974299595\n",
       ":   0.010892130148164696\n",
       ":   0.0113922869274797\n",
       ":   0.018328638327788898\n",
       ":   0.051170748020761299\n",
       ":   0.0438353051155142100\n",
       ":   0.022413028801218101\n",
       ":   0.0227162469061851102\n",
       ":   0.0252293359932228103\n",
       ":   0.0190883623212341104\n",
       ":   0.0126426990134916105\n",
       ":   0.010209608746786106\n",
       ":   0.0170874411865991107\n",
       ":   0.0241203377226941108\n",
       ":   0.0247351608235762109\n",
       ":   0.0145714113432733110\n",
       ":   0.0178857138308024111\n",
       ":   0.0175885012705044112\n",
       ":   0.024792722053507113\n",
       ":   0.0232043356616999114\n",
       ":   0.0158759506992823115\n",
       ":   0.0133270253586709116\n",
       ":   0.0134071846323969117\n",
       ":   0.0197812289373825118\n",
       ":   0.021659260433771119\n",
       ":   0.0172821138404015120\n",
       ":   0.014037015282542121\n",
       ":   0.0186109862760628122\n",
       ":   0.0249430539892123123\n",
       ":   0.0173616319776621124\n",
       ":   0.0117466099617099125\n",
       ":   0.0103296596431147126\n",
       ":   0.0125688065199542127\n",
       ":   0.0180011107104763128\n",
       ":   0.0137988462387237129\n",
       ":   0.0117613925732342130\n",
       ":   0.0143100022885164131\n",
       ":   0.0208538707799959132\n",
       ":   0.046532470626197133\n",
       ":   0.035717254765533134\n",
       ":   0.0343997231263672135\n",
       ":   0.0329842739350838136\n",
       ":   0.0414895078101973137\n",
       ":   0.0170232411665542138\n",
       ":   0.0109440696752163139\n",
       ":   0.00960911921149584140\n",
       ":   0.0104780646079519141\n",
       ":   0.018643161759595142\n",
       ":   0.0217681284099242143\n",
       ":   0.0174161389282632144\n",
       ":   0.0110371638175179145\n",
       ":   0.0175030633159761146\n",
       ":   0.0221000412593042147\n",
       ":   0.0185019798435406148\n",
       ":   0.0119403076706646149\n",
       ":   0.00979346316992125150\n",
       ":   0.0117088858954323151\n",
       ":   0.0181234364519357152\n",
       ":   0.0178818427237655153\n",
       ":   0.011737751050208154\n",
       ":   0.0104986424839759155\n",
       ":   0.013503015974146156\n",
       ":   0.0201485536072793157\n",
       ":   0.0216702312800742158\n",
       ":   0.0139853909397614159\n",
       ":   0.0117742164509917160\n",
       ":   0.013357081877292161\n",
       ":   0.0195755396903109162\n",
       ":   0.0478452253033884163\n",
       ":   0.0380831101991822164\n",
       ":   0.0344961051304036165\n",
       ":   0.0381330653823796166\n",
       ":   0.0272762512645124167\n",
       ":   0.0210870970841394168\n",
       ":   0.0127584512610745169\n",
       ":   0.0136019970512981170\n",
       ":   0.0162879502110792171\n",
       ":   0.0232300983388119172\n",
       ":   0.0218262173105159173\n",
       ":   0.0181053083929999174\n",
       ":   0.0191531776377801175\n",
       ":   0.0262204503277814176\n",
       ":   0.0294233966623949177\n",
       ":   0.0331283567729262178\n",
       ":   0.0242106918990798179\n",
       ":   0.0220446461042116180\n",
       ":   0.025250108261581181\n",
       ":   0.0334729239927272182\n",
       ":   0.0166791129677257183\n",
       ":   0.0106888228678385184\n",
       ":   0.014149977029383185\n",
       ":   0.0172370214539701186\n",
       ":   0.0121080719426846187\n",
       ":   0.0188452358367619188\n",
       ":   0.0135158104008532189\n",
       ":   0.011430731690309190\n",
       ":   0.0132712103257513191\n",
       ":   0.0210499955451223192\n",
       ":   0.0464732213079812193\n",
       ":   0.0374411021987633194\n",
       ":   0.0386548776265421195\n",
       ":   0.036599773127111196\n",
       ":   0.0295039261437673197\n",
       ":   0.0184478478597397198\n",
       ":   0.0153663884733479199\n",
       ":   0.00960911921149584200\n",
       ":   0.0158241022350615201\n",
       ":   0.0230943534276581202\n",
       ":   0.0190855287194466203\n",
       ":   0.01263560652092204\n",
       ":   0.0119739028743406205\n",
       ":   0.0128259751932983206\n",
       ":   0.0204841651740656207\n",
       ":   0.0204853482457294208\n",
       ":   0.0145484379155574209\n",
       ":   0.0110565539135327210\n",
       ":   0.0167576793874218211\n",
       ":   0.024278576611866212\n",
       ":   0.0236848331295757213\n",
       ":   0.0167125352018046214\n",
       ":   0.016302361117199215\n",
       ":   0.0174482426482583216\n",
       ":   0.0182666609201857217\n",
       ":   0.0113299052807092218\n",
       ":   0.0105735844013041219\n",
       ":   0.013272154453053220\n",
       ":   0.0199948971796714221\n",
       ":   0.017636450180228222\n",
       ":   0.0109716788839828223\n",
       ":   0.00893320276245546224\n",
       ":   0.0116052144143867225\n",
       ":   0.0181693132473579226\n",
       ":   0.0191193692780119227\n",
       ":   0.0131168723031501228\n",
       ":   0.0115637940480771229\n",
       ":   0.0135230572481713230\n",
       ":   0.0202563855988531231\n",
       ":   0.0247511783361217232\n",
       ":   0.0168612963112735233\n",
       ":   0.0158898057316006234\n",
       ":   0.0213106170201588235\n",
       ":   0.0183700903126851236\n",
       ":   0.0123804120519223237\n",
       ":   0.010186217164832238\n",
       ":   0.0124092747288259239\n",
       ":   0.0195213401645488\n",
       "\n",
       "\n",
       "$coefficients\n",
       ":   \n",
       "| <!--/--> | (Intercept) | f..mm. | Bahn | Fc..N. | Stdabw..Fc..N. | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | -0.6724181090 |  3.4125126    |  0.123971978  | -1.131740e-03 | -5.543220e-05 | \n",
       "| 2 | -0.4704605648 |  3.3502369    |  0.058831990  | -1.119576e-03 |  7.713809e-05 | \n",
       "| 3 | -0.3449692971 |  3.6230955    | -0.002408308  | -1.169257e-03 |  1.031179e-05 | \n",
       "| 4 | -0.0653822055 |  3.0576864    | -0.049670004  | -1.062191e-03 | -1.978259e-04 | \n",
       "| 5 |  0.0666625942 |  3.2004109    | -0.112841163  | -1.096979e-03 |  3.962125e-04 | \n",
       "| 6 | -0.1332495201 | -1.7298039    | -0.064176568  |  1.173997e-03 |  6.224203e-04 | \n",
       "| 7 | -0.3260524545 | -2.6929254    | -0.045835153  |  1.738124e-03 |  1.260610e-03 | \n",
       "| 8 | -0.4847685833 | -3.1808859    | -0.005467216  |  1.925948e-03 |  2.374407e-03 | \n",
       "| 9 | -0.4642442896 | -2.2172929    |  0.031288094  |  1.407051e-03 |  1.224074e-03 | \n",
       "| 10 | -0.5227096293 | -2.0253454    |  0.061561838  |  1.292403e-03 |  1.032389e-03 | \n",
       "| 11 | -1.4644685617 |  0.1658913    |  0.188129618  |  6.577576e-04 |  3.801773e-03 | \n",
       "| 12 | -0.9533501187 |  0.4037236    |  0.072987999  |  3.519394e-04 |  4.283263e-03 | \n",
       "| 13 | -0.5903573291 |  0.7910759    | -0.008634254  |  1.102478e-04 |  3.477392e-03 | \n",
       "| 14 | -0.4426263628 |  0.5665459    | -0.090969515  |  2.650696e-04 |  4.263969e-03 | \n",
       "| 15 | -0.1561810833 |  0.9435480    | -0.152611614  |  4.862934e-05 |  3.402848e-03 | \n",
       "| 16 | -0.6291444141 | -7.8790574    |  0.260903107  |  2.219872e-03 |  6.917447e-03 | \n",
       "| 17 | -0.1104679395 | -5.4521609    |  0.112393851  |  1.347464e-03 |  4.133907e-03 | \n",
       "| 18 |  0.2087362247 | -5.9445032    | -0.009028090  |  1.481966e-03 |  6.235575e-03 | \n",
       "| 19 |  0.5421207016 | -6.6392039    | -0.133668476  |  1.718608e-03 |  7.643244e-03 | \n",
       "| 20 |  0.8560222832 | -5.4828908    | -0.231726344  |  1.272007e-03 |  7.348493e-03 | \n",
       "| 21 | -0.4388966570 |  0.8308475    |  0.064548054  |  4.222620e-05 | -2.253022e-03 | \n",
       "| 22 | -0.1663832611 |  0.6350606    |  0.017577455  | -6.034957e-05 | -1.484838e-03 | \n",
       "| 23 | -0.0597983036 |  0.5018571    |  0.001271950  | -8.130841e-05 | -1.211809e-03 | \n",
       "| 24 |  0.0082938630 | -0.2113132    |  0.002478803  |  4.338437e-05 |  4.966021e-04 | \n",
       "| 25 |  0.0005391388 | -0.1539081    |  0.004688660  |  2.983360e-05 |  3.348748e-04 | \n",
       "| 26 | -0.3433025707 | -1.8975453    |  0.205991610  |  9.085454e-04 | -1.295717e-02 | \n",
       "| 27 |  0.5392361717 |  5.6641888    |  0.048668767  | -1.449935e-03 | -3.387288e-02 | \n",
       "| 28 |  0.4483240815 | -1.6439108    | -0.071499567  |  7.456213e-04 | -1.074787e-02 | \n",
       "| 29 |  1.0470450742 |  4.2841547    | -0.144594857  | -9.215380e-04 | -3.234819e-02 | \n",
       "| 30 |  2.3682609272 | -1.0635930    | -0.310368371  | -1.526466e-03 |  7.502478e-03 | \n",
       "| ... | ... | ... | ... | ... | ... | \n",
       "| 210 | -0.27895043   |  7.49467519   |  0.1124103814 | -2.723601e-03 | -1.467053e-03 | \n",
       "| 211 | -0.51865234   |  7.73390725   |  0.2110091087 | -2.823672e-03 | -2.921352e-03 | \n",
       "| 212 | -0.29766864   |  2.36332334   |  0.0644206668 | -8.483970e-04 | -7.974722e-04 | \n",
       "| 213 | -0.24429679   |  2.47612502   |  0.0358442446 | -8.891033e-04 | -3.427602e-04 | \n",
       "| 214 | -0.08258850   |  1.79338321   | -0.0003252519 | -6.622894e-04 | -2.138966e-04 | \n",
       "| 215 | -0.03407635   |  2.38535692   | -0.0365977593 | -8.633471e-04 |  8.304982e-06 | \n",
       "| 216 | -1.01395960   |  0.82213219   |  0.1383970232 |  1.025015e-04 |  3.055172e-03 | \n",
       "| 217 | -0.83035880   |  1.05704700   |  0.0690634526 |  7.325871e-05 |  2.319589e-03 | \n",
       "| 218 | -0.63172285   |  0.72384906   | -0.0090941075 |  1.757909e-04 |  3.621029e-03 | \n",
       "| 219 | -0.39864557   |  0.73523662   | -0.0848378378 |  1.528285e-04 |  3.829505e-03 | \n",
       "| 220 | -0.09410644   |  1.09632515   | -0.1208173128 | -1.411063e-04 |  2.681904e-03 | \n",
       "| 221 | -0.59995816   |  0.16943877   |  0.0778270621 |  3.364835e-04 | -3.151594e-04 | \n",
       "| 222 | -0.34179975   |  0.23427354   |  0.0274546180 |  1.828483e-04 | -1.087462e-04 | \n",
       "| 223 | -0.22600870   |  0.18934865   | -0.0016564885 |  1.565822e-04 |  1.463360e-04 | \n",
       "| 224 | -0.20975938   |  0.09192846   | -0.0357649845 |  2.717371e-04 |  4.513106e-04 | \n",
       "| 225 | -0.09373002   |  0.11931092   | -0.0594573741 |  2.086511e-04 |  5.134397e-04 | \n",
       "| 226 | -0.54275139   | -0.32384392   |  0.0653720434 |  4.121326e-04 |  1.571476e-03 | \n",
       "| 227 | -0.42356645   | -0.30172725   |  0.0291856120 |  3.890551e-04 |  1.615519e-03 | \n",
       "| 228 | -0.37990153   | -0.42128546   | -0.0051048970 |  4.833949e-04 |  1.947524e-03 | \n",
       "| 229 | -0.25381854   | -0.31724338   | -0.0415234980 |  4.336097e-04 |  1.745492e-03 | \n",
       "| 230 | -0.15961436   | -0.35582642   | -0.0837894009 |  4.758687e-04 |  1.899591e-03 | \n",
       "| 231 | -0.23965583   | -3.21518365   |  0.0888027457 |  9.016067e-04 |  4.071986e-03 | \n",
       "| 232 | -0.07392088   | -2.54583415   |  0.0361461046 |  6.881480e-04 |  3.196555e-03 | \n",
       "| 233 |  0.03949092   | -2.93925068   | -0.0056993795 |  8.132385e-04 |  3.845968e-03 | \n",
       "| 234 |  0.17287080   | -3.76448344   | -0.0598195066 |  1.075962e-03 |  5.378350e-03 | \n",
       "| 235 | -0.10879571   | -1.03682319   |  0.0705515205 |  2.435137e-04 | -8.916755e-04 | \n",
       "| 236 | -0.07660806   | -2.62799468   |  0.0544685461 |  7.748097e-04 |  4.253066e-04 | \n",
       "| 237 |  0.08481791   | -2.62942055   | -0.0008906359 |  7.778230e-04 |  4.396817e-04 | \n",
       "| 238 |  0.24641093   | -2.78633921   | -0.0585822506 |  8.280412e-04 |  8.446154e-04 | \n",
       "| 239 |  0.47872814   | -3.71011107   | -0.1422947739 |  1.181639e-03 |  9.635637e-04 | \n",
       "\n",
       "\n",
       "\n",
       "$sigma\n",
       ":   1\n",
       ":   47.576990131492\n",
       ":   47.57921171991263\n",
       ":   47.56962095053474\n",
       ":   47.59264044817395\n",
       ":   47.58596915776\n",
       ":   47.60633485854717\n",
       ":   47.59847278059768\n",
       ":   47.59701689490179\n",
       ":   47.603997997838610\n",
       ":   47.605578988561211\n",
       ":   47.519104011862112\n",
       ":   47.547347036075613\n",
       ":   47.563254840224114\n",
       ":   47.55186405467915\n",
       ":   47.56506288191316\n",
       ":   47.436620632281117\n",
       ":   47.478250237124218\n",
       ":   47.479323732469419\n",
       ":   47.468869070038320\n",
       ":   47.496702686769321\n",
       ":   47.605890291175522\n",
       ":   47.612945007971723\n",
       ":   47.614711352299124\n",
       ":   47.615443437898225\n",
       ":   47.615471195611926\n",
       ":   47.531173205058827\n",
       ":   47.556531177202928\n",
       ":   47.54389269494529\n",
       ":   47.536605542778530\n",
       ":   47.382957020473331\n",
       ":   47.312231102279832\n",
       ":   47.292050006584733\n",
       ":   47.272904676737434\n",
       ":   47.25237462416735\n",
       ":   47.570084661053236\n",
       ":   47.565523754350137\n",
       ":   47.548585251198438\n",
       ":   47.538482029364739\n",
       ":   47.567603657950140\n",
       ":   47.589433492594341\n",
       ":   47.556648145224342\n",
       ":   47.597956064665543\n",
       ":   47.578908644598244\n",
       ":   47.614174724694545\n",
       ":   47.597855825119646\n",
       ":   47.608319297286747\n",
       ":   47.603745549916348\n",
       ":   47.590634415471649\n",
       ":   47.531399740385350\n",
       ":   47.552373833953551\n",
       ":   47.567692891657252\n",
       ":   47.576211536934953\n",
       ":   47.578497268023254\n",
       ":   47.403844761835355\n",
       ":   47.478482637591556\n",
       ":   47.480243293439757\n",
       ":   47.491160031789658\n",
       ":   47.503096816229859\n",
       ":   47.607295657586760\n",
       ":   47.611424668726461\n",
       ":   47.613292821713662\n",
       ":   47.613649551043263\n",
       ":   47.615231794021364\n",
       ":   47.558524784101465\n",
       ":   47.553094657224366\n",
       ":   47.565730903880167\n",
       ":   47.570101209676568\n",
       ":   47.581933536262369\n",
       ":   47.399307797727870\n",
       ":   47.331439691731771\n",
       ":   47.290031793610272\n",
       ":   47.261213395947673\n",
       ":   47.2349814280374\n",
       ":   47.567652572081675\n",
       ":   47.560571219130776\n",
       ":   47.555372872368177\n",
       ":   47.540690258123878\n",
       ":   47.527762824879779\n",
       ":   47.377361996772280\n",
       ":   47.368615457851981\n",
       ":   47.323774688942282\n",
       ":   47.318858331347183\n",
       ":   47.609845266687184\n",
       ":   47.542313934125785\n",
       ":   47.528914677188586\n",
       ":   47.518170954571287\n",
       ":   47.505344699893688\n",
       ":   47.593111612809889\n",
       ":   47.601653304340790\n",
       ":   47.59903119576491\n",
       ":   47.594987216667792\n",
       ":   47.593321518341193\n",
       ":   47.253492101004394\n",
       ":   47.297953673442595\n",
       ":   47.3000660263296\n",
       ":   47.254263157824497\n",
       ":   47.270183081260598\n",
       ":   47.466242399424899\n",
       ":   47.4820421773735100\n",
       ":   47.6089216682029101\n",
       ":   47.6136051537787102\n",
       ":   47.6123640259624103\n",
       ":   47.544787068267104\n",
       ":   47.5541702133566105\n",
       ":   47.5742675388872106\n",
       ":   47.5337393354841107\n",
       ":   47.5442022184557108\n",
       ":   47.5917439066137109\n",
       ":   47.5834011382621110\n",
       ":   47.5914700879243111\n",
       ":   47.588674284583112\n",
       ":   47.5809042565779113\n",
       ":   47.4060401604927114\n",
       ":   47.4145059788801115\n",
       ":   47.4129122039407116\n",
       ":   47.4030774491115117\n",
       ":   47.4044163771977118\n",
       ":   47.5874775668037119\n",
       ":   47.6053430044196120\n",
       ":   47.5965061303468121\n",
       ":   47.6090735793069122\n",
       ":   47.6071778728261123\n",
       ":   47.6130264947522124\n",
       ":   47.6145179816752125\n",
       ":   47.6143871016173126\n",
       ":   47.615474576057127\n",
       ":   47.3351751132061128\n",
       ":   47.3136134147824129\n",
       ":   47.3019873994243130\n",
       ":   47.2961708190047131\n",
       ":   47.274122923812132\n",
       ":   47.55264935364133\n",
       ":   47.5494804364182134\n",
       ":   47.542673287301135\n",
       ":   47.5706848264381136\n",
       ":   47.5575656036132137\n",
       ":   47.5707465632108138\n",
       ":   47.5126847222405139\n",
       ":   47.5135089236184140\n",
       ":   47.5189016372551141\n",
       ":   47.4616921504357142\n",
       ":   47.4201102712986143\n",
       ":   47.4333394425044144\n",
       ":   47.4003869180026145\n",
       ":   47.4447409207788146\n",
       ":   47.3879637107596147\n",
       ":   47.4012448229783148\n",
       ":   47.3719901625083149\n",
       ":   47.3629410388786150\n",
       ":   47.3410318556655151\n",
       ":   47.3147928324837152\n",
       ":   47.5338791953787153\n",
       ":   47.5472808360973154\n",
       ":   47.5148607329004155\n",
       ":   47.4905235900893156\n",
       ":   47.5054717771458157\n",
       ":   47.4070211966041158\n",
       ":   47.3597499491094159\n",
       ":   47.3505403914221160\n",
       ":   47.3414704535046161\n",
       ":   47.3222036452723162\n",
       ":   47.4932254602469163\n",
       ":   47.525508845126164\n",
       ":   47.5389655583957165\n",
       ":   47.529018244393166\n",
       ":   47.615532152903167\n",
       ":   47.5222737795877168\n",
       ":   47.5619816551431169\n",
       ":   47.5420759607416170\n",
       ":   47.5464545098443171\n",
       ":   47.5531085209197172\n",
       ":   47.5630138672479173\n",
       ":   47.5764936954669174\n",
       ":   47.5773232697659175\n",
       ":   47.5900149815987176\n",
       ":   47.5740650708299177\n",
       ":   47.4507299098503178\n",
       ":   47.4237140561794179\n",
       ":   47.4194750568339180\n",
       ":   47.4266178184011181\n",
       ":   47.444856040907182\n",
       ":   47.5588172301504183\n",
       ":   47.5955095559311184\n",
       ":   47.6121479164633185\n",
       ":   47.6103912384472186\n",
       ":   47.6127387269293187\n",
       ":   47.3104802095095188\n",
       ":   47.2767424765509189\n",
       ":   47.2648561500242190\n",
       ":   47.2636759024923191\n",
       ":   47.2571713065473192\n",
       ":   47.5583652738813193\n",
       ":   47.5482270163331194\n",
       ":   47.5120796822758195\n",
       ":   47.5406034644845196\n",
       ":   47.6137816163141197\n",
       ":   47.5653143331543198\n",
       ":   47.5027338031178199\n",
       ":   47.5135089236184200\n",
       ":   47.5364684882021201\n",
       ":   47.526900804954202\n",
       ":   47.5851769277857203\n",
       ":   47.5858586166994204\n",
       ":   47.5646246219735205\n",
       ":   47.5811202624633206\n",
       ":   47.5666757465195207\n",
       ":   47.4183030900175208\n",
       ":   47.444585638027209\n",
       ":   47.4010616709903210\n",
       ":   47.5004253512723211\n",
       ":   47.5138090808302212\n",
       ":   47.6055850836952213\n",
       ":   47.6026408706298214\n",
       ":   47.6097199867956215\n",
       ":   47.603211944624216\n",
       ":   47.563389635672217\n",
       ":   47.5586167971338218\n",
       ":   47.5575259204012219\n",
       ":   47.5597437873564220\n",
       ":   47.5838166691544221\n",
       ":   47.6000624038241222\n",
       ":   47.6073167971423223\n",
       ":   47.6091736200584224\n",
       ":   47.6047569084861225\n",
       ":   47.607612173314226\n",
       ":   47.6037318922637227\n",
       ":   47.6045681302408228\n",
       ":   47.6011808995327229\n",
       ":   47.6022907889419230\n",
       ":   47.6005099779085231\n",
       ":   47.5937999475676232\n",
       ":   47.5992751145924233\n",
       ":   47.5958341743301234\n",
       ":   47.5895103145247235\n",
       ":   47.6038719577516236\n",
       ":   47.5855789116105237\n",
       ":   47.5849346740356238\n",
       ":   47.5836484193397239\n",
       ":   47.5676637978479\n",
       "\n",
       "\n",
       "$wt.res\n",
       ":   1\n",
       ":   -28.94117526433452\n",
       ":   -28.18009045149063\n",
       ":   -31.72094404556514\n",
       ":   -22.35304615915155\n",
       ":   -25.32157461083736\n",
       ":   14.05740111233537\n",
       ":   19.18314150442948\n",
       ":   19.98479332173019\n",
       ":   15.779756539448210\n",
       ":   14.613770217005411\n",
       ":   -45.813371249161712\n",
       ":   -38.632744894868413\n",
       ":   -33.866997400526814\n",
       ":   -37.320642492193315\n",
       ":   -33.124885635161116\n",
       ":   -62.294596904853217\n",
       ":   -54.814580828461618\n",
       ":   -54.623393635289219\n",
       ":   -56.586636281472420\n",
       ":   -50.777042700443121\n",
       ":   -14.465103392441422\n",
       ":   -7.5077376045644723\n",
       ":   -4.2159716227503924\n",
       ":   1.3787298831113625\n",
       ":   1.1437449016993226\n",
       ":   -42.389585911822127\n",
       ":   -33.20582963168928\n",
       ":   -39.280859454401729\n",
       ":   -39.144853363285530\n",
       ":   70.991377810200831\n",
       ":   80.606628648825832\n",
       ":   83.782512566592333\n",
       ":   86.320646670990834\n",
       ":   88.380187786032235\n",
       ":   31.210882621428436\n",
       ":   32.904726142267237\n",
       ":   38.093049670687538\n",
       ":   40.775416310255539\n",
       ":   -32.279797504266240\n",
       ":   -23.878913523411741\n",
       ":   -35.930437727545142\n",
       ":   -19.580606814323443\n",
       ":   -28.18513100403644\n",
       ":   -5.4187325489736645\n",
       ":   -19.647513804186146\n",
       ":   -12.551169476576647\n",
       ":   15.957139506505948\n",
       ":   23.078607901507449\n",
       ":   -42.787129754908750\n",
       ":   -37.184624954736751\n",
       ":   -32.39487484014952\n",
       ":   -29.335261038456753\n",
       ":   -28.388778855515154\n",
       ":   -67.661561024606655\n",
       ":   -54.676886192764956\n",
       ":   -54.3766918058557\n",
       ":   -52.068766973578158\n",
       ":   -49.329552658975259\n",
       ":   -13.363863736789760\n",
       ":   -9.4374960297797361\n",
       ":   -7.0139851069529662\n",
       ":   -6.4172179257245163\n",
       ":   -2.5458167162018664\n",
       ":   -35.166306477930465\n",
       ":   -36.835375800390566\n",
       ":   -32.842509987378667\n",
       ":   -31.315927128410568\n",
       ":   -26.587117703181469\n",
       ":   68.300869295898970\n",
       ":   78.218111439801171\n",
       ":   83.889587213825572\n",
       ":   87.563666068563173\n",
       ":   90.669241649207374\n",
       ":   31.990257482440975\n",
       ":   34.389136971153876\n",
       ":   36.172479201088177\n",
       ":   40.326115075041278\n",
       ":   43.563522218795779\n",
       ":   -72.172153287917580\n",
       ":   -73.564478671346481\n",
       ":   -79.864861145394582\n",
       ":   -80.272888078426283\n",
       ":   -11.128848207589884\n",
       ":   -40.054183195274685\n",
       ":   -43.596424617357186\n",
       ":   -46.152137266535787\n",
       ":   -48.919678685463988\n",
       ":   -22.075011670445289\n",
       ":   -17.447864626381290\n",
       ":   -19.041299104493191\n",
       ":   -21.219291353166492\n",
       ":   -21.988792960255993\n",
       ":   88.645551070686394\n",
       ":   83.265515961929795\n",
       ":   83.07014470808496\n",
       ":   88.852427919739597\n",
       ":   86.574621327343598\n",
       ":   56.019040753001799\n",
       ":   53.1806202234805100\n",
       ":   11.9742231927179101\n",
       ":   6.46422833550639102\n",
       ":   -8.27778635415395103\n",
       ":   -39.2255514820555104\n",
       ":   -36.6533869082906105\n",
       ":   -30.0977342766366106\n",
       ":   -42.2178180778365107\n",
       ":   -39.2860794175091108\n",
       ":   -22.6858860492294109\n",
       ":   -26.501408877329110\n",
       ":   -22.8960246766983111\n",
       ":   -24.1929435436129112\n",
       ":   -27.3684358755695113\n",
       ":   67.3092368971194114\n",
       ":   66.1850138817631115\n",
       ":   66.5322963713529116\n",
       ":   68.121542042642117\n",
       ":   67.6873064027519118\n",
       ":   -24.674620829107119\n",
       ":   -14.9048610718647120\n",
       ":   -20.3999204965506121\n",
       ":   -11.8588414191661122\n",
       ":   -13.4436859551083123\n",
       ":   -7.39130995564187124\n",
       ":   -4.71584916286342125\n",
       ":   -5.01449228598571126\n",
       ":   -1.12340154278611127\n",
       ":   78.043782922517128\n",
       ":   81.1531815654087129\n",
       ":   82.7812242135144130\n",
       ":   83.4351788824666131\n",
       ":   85.9703696291405132\n",
       ":   36.4621955437595133\n",
       ":   37.5803608600041134\n",
       ":   39.4949025939447135\n",
       ":   31.0134554933249136\n",
       ":   35.1012281874156137\n",
       ":   -31.2468343093123138\n",
       ":   -47.4831845792399139\n",
       ":   -47.3246510668899140\n",
       ":   -46.0380314096748141\n",
       ":   -57.8314867289442142\n",
       ":   65.0621999656128143\n",
       ":   62.965373445777144\n",
       ":   68.6328483860498145\n",
       ":   60.9643444448189146\n",
       ":   70.1860835142079147\n",
       ":   -68.2371835022333148\n",
       ":   -72.9776339316732149\n",
       ":   -74.3982125922421150\n",
       ":   -77.4737057934831151\n",
       ":   -80.8172401853647152\n",
       ":   -42.1646895798602153\n",
       ":   -38.6725930334048154\n",
       ":   -46.9892974668245155\n",
       ":   -52.2756991325752156\n",
       ":   -48.8890766734121157\n",
       ":   67.2045083003773158\n",
       ":   74.7067965784163159\n",
       ":   76.1213523802898160\n",
       ":   77.3473881132242161\n",
       ":   79.7593522925035162\n",
       ":   50.8004013528654163\n",
       ":   43.8135281051894164\n",
       ":   40.4845549891936165\n",
       ":   42.95071957483166\n",
       ":   -0.0227616760484058167\n",
       ":   -44.9852902162501168\n",
       ":   -34.2403901288758169\n",
       ":   -40.0811420869461170\n",
       ":   -38.8161571217332171\n",
       ":   -36.7701691991191172\n",
       ":   -33.752882897192173\n",
       ":   -29.1579615675667174\n",
       ":   -28.8312213527824175\n",
       ":   -23.4777179484271176\n",
       ":   -29.8771713630698177\n",
       ":   59.4096743841536178\n",
       ":   64.380196161197179\n",
       ":   65.158426839965180\n",
       ":   63.8579787976962181\n",
       ":   60.4465009088271182\n",
       ":   -35.166918533862183\n",
       ":   -20.9627637565567184\n",
       ":   -8.60393017107383185\n",
       ":   -10.5876884499848186\n",
       ":   -7.8250311985195187\n",
       ":   81.3628687659742188\n",
       ":   85.9614144727206189\n",
       ":   87.5432728036967190\n",
       ":   87.6082561832486191\n",
       ":   88.0621220237555192\n",
       ":   34.7676764521921193\n",
       ":   37.9010807466394194\n",
       ":   46.9506279222259195\n",
       ":   40.0058834946129196\n",
       ":   6.13972265103877197\n",
       ":   -33.0627111051601198\n",
       ":   -49.6133634625903199\n",
       ":   -47.3246510668899200\n",
       ":   -41.5347710961307201\n",
       ":   -43.8111983994553202\n",
       ":   -25.699846162231203\n",
       ":   -25.49313029537204\n",
       ":   -33.398464132024205\n",
       ":   -27.4498563375176206\n",
       ":   -32.5778519199663207\n",
       ":   65.404561612088208\n",
       ":   61.0836432172714209\n",
       ":   68.5247099368991210\n",
       ":   50.0824392475277211\n",
       ":   46.9037871729264212\n",
       ":   -14.6787038612047213\n",
       ":   -16.7697503523932214\n",
       ":   -11.263017173447215\n",
       ":   -16.3880149487464216\n",
       ":   -33.693119117377217\n",
       ":   -35.3246591111628218\n",
       ":   -35.6750131997717219\n",
       ":   -34.9390134047209220\n",
       ":   -26.2569908184774221\n",
       ":   -18.3615818923912222\n",
       ":   -13.4266210592812223\n",
       ":   -11.8245200720398224\n",
       ":   -15.3717028279699225\n",
       ":   -13.1350040110561226\n",
       ":   -16.0248765232559227\n",
       ":   -15.4938938966024228\n",
       ":   -17.7400220325986229\n",
       ":   -17.0234393937031230\n",
       ":   -18.0699104075511231\n",
       ":   -21.683409749741232\n",
       ":   -18.8303606893868233\n",
       ":   -20.7374484578982234\n",
       ":   -23.7683789227678235\n",
       ":   -15.9355823182011236\n",
       ":   -25.6162706425377237\n",
       ":   -25.9189402270778238\n",
       ":   -26.4282140814733239\n",
       ":   -32.2627613467769\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$hat\n",
       "          1           2           3           4           5           6 \n",
       "0.020196893 0.014255028 0.011792422 0.016068899 0.022238543 0.031596744 \n",
       "          7           8           9          10          11          12 \n",
       "0.027657994 0.027658375 0.026957181 0.032896043 0.018057591 0.012816481 \n",
       "         13          14          15          16          17          18 \n",
       "0.010663919 0.013420530 0.019658923 0.020635143 0.012196082 0.011354992 \n",
       "         19          20          21          22          23          24 \n",
       "0.014533922 0.020919804 0.021883651 0.018092397 0.024080099 0.034594766 \n",
       "         25          26          27          28          29          30 \n",
       "0.033220534 0.039190265 0.157240039 0.028591730 0.124308190 0.021016733 \n",
       "         31          32          33          34          35          36 \n",
       "0.031458138 0.018705010 0.016356018 0.026940225 0.033560435 0.023736694 \n",
       "         37          38          39          40          41          42 \n",
       "0.022466381 0.026714401 0.019716563 0.015093532 0.011306819 0.016724815 \n",
       "         43          44          45          46          47          48 \n",
       "0.022059622 0.025139410 0.015606746 0.015630748 0.026267333 0.035642825 \n",
       "         49          50          51          52          53          54 \n",
       "0.018450668 0.012698835 0.010874055 0.013256820 0.018892690 0.023165730 \n",
       "         55          56          57          58          59          60 \n",
       "0.015488342 0.013615347 0.016295941 0.023460232 0.022710213 0.022719350 \n",
       "         61          62          63          64          65          66 \n",
       "0.009892506 0.014166478 0.027597889 0.021754563 0.019980215 0.023381713 \n",
       "         67          68          69          70          71          72 \n",
       "0.026689879 0.051495269 0.025458268 0.026540548 0.022274336 0.021100743 \n",
       "         73          74          75          76          77          78 \n",
       "0.022511227 0.036240302 0.029703600 0.019170264 0.019980442 0.024630948 \n",
       "         79          80          81          82          83          84 \n",
       "0.011890898 0.009672646 0.011702964 0.018073393 0.018443187 0.011729268 \n",
       "         85          86          87          88          89          90 \n",
       "0.010178831 0.013022404 0.020051649 0.020232456 0.011312333 0.009569329 \n",
       "         91          92          93          94          95          96 \n",
       "0.012094072 0.018685792 0.018078236 0.012822127 0.010892130 0.011392287 \n",
       "         97          98          99         100         101         102 \n",
       "0.018328638 0.051170748 0.043835305 0.022413029 0.022716247 0.025229336 \n",
       "        103         104         105         106         107         108 \n",
       "0.019088362 0.012642699 0.010209609 0.017087441 0.024120338 0.024735161 \n",
       "        109         110         111         112         113         114 \n",
       "0.014571411 0.017885714 0.017588501 0.024792722 0.023204336 0.015875951 \n",
       "        115         116         117         118         119         120 \n",
       "0.013327025 0.013407185 0.019781229 0.021659260 0.017282114 0.014037015 \n",
       "        121         122         123         124         125         126 \n",
       "0.018610986 0.024943054 0.017361632 0.011746610 0.010329660 0.012568807 \n",
       "        127         128         129         130         131         132 \n",
       "0.018001111 0.013798846 0.011761393 0.014310002 0.020853871 0.046532471 \n",
       "        133         134         135         136         137         138 \n",
       "0.035717255 0.034399723 0.032984274 0.041489508 0.017023241 0.010944070 \n",
       "        139         140         141         142         143         144 \n",
       "0.009609119 0.010478065 0.018643162 0.021768128 0.017416139 0.011037164 \n",
       "        145         146         147         148         149         150 \n",
       "0.017503063 0.022100041 0.018501980 0.011940308 0.009793463 0.011708886 \n",
       "        151         152         153         154         155         156 \n",
       "0.018123436 0.017881843 0.011737751 0.010498642 0.013503016 0.020148554 \n",
       "        157         158         159         160         161         162 \n",
       "0.021670231 0.013985391 0.011774216 0.013357082 0.019575540 0.047845225 \n",
       "        163         164         165         166         167         168 \n",
       "0.038083110 0.034496105 0.038133065 0.027276251 0.021087097 0.012758451 \n",
       "        169         170         171         172         173         174 \n",
       "0.013601997 0.016287950 0.023230098 0.021826217 0.018105308 0.019153178 \n",
       "        175         176         177         178         179         180 \n",
       "0.026220450 0.029423397 0.033128357 0.024210692 0.022044646 0.025250108 \n",
       "        181         182         183         184         185         186 \n",
       "0.033472924 0.016679113 0.010688823 0.014149977 0.017237021 0.012108072 \n",
       "        187         188         189         190         191         192 \n",
       "0.018845236 0.013515810 0.011430732 0.013271210 0.021049996 0.046473221 \n",
       "        193         194         195         196         197         198 \n",
       "0.037441102 0.038654878 0.036599773 0.029503926 0.018447848 0.015366388 \n",
       "        199         200         201         202         203         204 \n",
       "0.009609119 0.015824102 0.023094353 0.019085529 0.012635607 0.011973903 \n",
       "        205         206         207         208         209         210 \n",
       "0.012825975 0.020484165 0.020485348 0.014548438 0.011056554 0.016757679 \n",
       "        211         212         213         214         215         216 \n",
       "0.024278577 0.023684833 0.016712535 0.016302361 0.017448243 0.018266661 \n",
       "        217         218         219         220         221         222 \n",
       "0.011329905 0.010573584 0.013272154 0.019994897 0.017636450 0.010971679 \n",
       "        223         224         225         226         227         228 \n",
       "0.008933203 0.011605214 0.018169313 0.019119369 0.013116872 0.011563794 \n",
       "        229         230         231         232         233         234 \n",
       "0.013523057 0.020256386 0.024751178 0.016861296 0.015889806 0.021310617 \n",
       "        235         236         237         238         239 \n",
       "0.018370090 0.012380412 0.010186217 0.012409275 0.019521340 \n",
       "\n",
       "$coefficients\n",
       "      (Intercept)        f..mm.          Bahn        Fc..N. Stdabw..Fc..N.\n",
       "1   -0.6724181090  3.412513e+00  1.239720e-01 -1.131740e-03  -5.543220e-05\n",
       "2   -0.4704605648  3.350237e+00  5.883199e-02 -1.119576e-03   7.713809e-05\n",
       "3   -0.3449692971  3.623095e+00 -2.408308e-03 -1.169257e-03   1.031179e-05\n",
       "4   -0.0653822055  3.057686e+00 -4.967000e-02 -1.062191e-03  -1.978259e-04\n",
       "5    0.0666625942  3.200411e+00 -1.128412e-01 -1.096979e-03   3.962125e-04\n",
       "6   -0.1332495201 -1.729804e+00 -6.417657e-02  1.173997e-03   6.224203e-04\n",
       "7   -0.3260524545 -2.692925e+00 -4.583515e-02  1.738124e-03   1.260610e-03\n",
       "8   -0.4847685833 -3.180886e+00 -5.467216e-03  1.925948e-03   2.374407e-03\n",
       "9   -0.4642442896 -2.217293e+00  3.128809e-02  1.407051e-03   1.224074e-03\n",
       "10  -0.5227096293 -2.025345e+00  6.156184e-02  1.292403e-03   1.032389e-03\n",
       "11  -1.4644685617  1.658913e-01  1.881296e-01  6.577576e-04   3.801773e-03\n",
       "12  -0.9533501187  4.037236e-01  7.298800e-02  3.519394e-04   4.283263e-03\n",
       "13  -0.5903573291  7.910759e-01 -8.634254e-03  1.102478e-04   3.477392e-03\n",
       "14  -0.4426263628  5.665459e-01 -9.096952e-02  2.650696e-04   4.263969e-03\n",
       "15  -0.1561810833  9.435480e-01 -1.526116e-01  4.862934e-05   3.402848e-03\n",
       "16  -0.6291444141 -7.879057e+00  2.609031e-01  2.219872e-03   6.917447e-03\n",
       "17  -0.1104679395 -5.452161e+00  1.123939e-01  1.347464e-03   4.133907e-03\n",
       "18   0.2087362247 -5.944503e+00 -9.028090e-03  1.481966e-03   6.235575e-03\n",
       "19   0.5421207016 -6.639204e+00 -1.336685e-01  1.718608e-03   7.643244e-03\n",
       "20   0.8560222832 -5.482891e+00 -2.317263e-01  1.272007e-03   7.348493e-03\n",
       "21  -0.4388966570  8.308475e-01  6.454805e-02  4.222620e-05  -2.253022e-03\n",
       "22  -0.1663832611  6.350606e-01  1.757746e-02 -6.034957e-05  -1.484838e-03\n",
       "23  -0.0597983036  5.018571e-01  1.271950e-03 -8.130841e-05  -1.211809e-03\n",
       "24   0.0082938630 -2.113132e-01  2.478803e-03  4.338437e-05   4.966021e-04\n",
       "25   0.0005391388 -1.539081e-01  4.688660e-03  2.983360e-05   3.348748e-04\n",
       "26  -0.3433025707 -1.897545e+00  2.059916e-01  9.085454e-04  -1.295717e-02\n",
       "27   0.5392361717  5.664189e+00  4.866877e-02 -1.449935e-03  -3.387288e-02\n",
       "28   0.4483240815 -1.643911e+00 -7.149957e-02  7.456213e-04  -1.074787e-02\n",
       "29   1.0470450742  4.284155e+00 -1.445949e-01 -9.215380e-04  -3.234819e-02\n",
       "30   2.3682609272 -1.063593e+00 -3.103684e-01 -1.526466e-03   7.502478e-03\n",
       "31   1.8334526152 -8.090355e+00 -2.053750e-01  5.613433e-04   2.644319e-02\n",
       "32   1.4162558494 -6.452486e+00 -1.649590e-02  1.705642e-04   1.866537e-02\n",
       "33   0.9415040915 -5.639689e+00  1.776952e-01 -7.042649e-06   1.392385e-02\n",
       "34   0.3096069139 -7.827941e+00  3.700753e-01  6.463088e-04   1.950382e-02\n",
       "35   0.4169334716  8.045788e+00 -5.577484e-02 -2.935570e-03  -7.915393e-03\n",
       "36   0.0433640572  4.418368e+00 -5.268275e-03 -1.901944e-03   4.723676e-03\n",
       "37  -0.2097934229  5.022580e+00  7.859645e-02 -2.084623e-03   4.260188e-03\n",
       "38  -0.4884763876  5.496147e+00  1.756063e-01 -2.217885e-03   3.313170e-03\n",
       "39  -0.7569718205  3.827407e+00  1.392334e-01 -1.220288e-03  -8.378334e-04\n",
       "40  -0.3816112048  3.050363e+00  5.006312e-02 -1.054676e-03   1.617376e-05\n",
       "41  -0.4288942917  3.510257e+00 -4.383921e-03 -1.088164e-03   1.052771e-03\n",
       "42  -0.0532952028  2.675819e+00 -4.401909e-02 -9.539057e-04   1.918711e-04\n",
       "43   0.0496379782  3.156703e+00 -1.268980e-01 -1.069213e-03   1.294372e-03\n",
       "44   0.0300196912  3.796600e-01  2.407454e-02 -3.216143e-04   3.612270e-05\n",
       "45   0.1998115929  1.151392e+00  4.502398e-02 -9.712542e-04  -8.440047e-04\n",
       "46   0.2257659569  1.012476e+00  2.082794e-03 -7.395219e-04  -8.379554e-04\n",
       "47  -0.4489249859 -1.787319e+00  3.388548e-02  1.293759e-03  -3.228675e-04\n",
       "48  -0.8334921600 -2.990001e+00  1.002582e-01  2.073133e-03  -3.901643e-04\n",
       "49  -1.3549507364  2.273027e-01  1.750346e-01  5.363452e-04   4.143163e-03\n",
       "50  -0.9072307639  5.241524e-01  7.046178e-02  2.762023e-04   4.007146e-03\n",
       "51  -0.5588121565  8.084026e-01 -8.406154e-03  6.972339e-05   3.457546e-03\n",
       "52  -0.3057558772  9.774565e-01 -7.083147e-02 -4.717692e-05   3.047618e-03\n",
       "53  -0.1006544557  1.310207e+00 -1.293423e-01 -1.614870e-04   2.075903e-03\n",
       "54  -0.7791887975 -1.003783e+01  2.799882e-01  2.995652e-03   1.013119e-02\n",
       "55  -0.1652951012 -6.684282e+00  1.063460e-01  1.695588e-03   8.360111e-03\n",
       "56   0.1785341169 -6.614130e+00 -1.250141e-02  1.667614e-03   8.630020e-03\n",
       "57   0.5130478936 -6.229675e+00 -1.257464e-01  1.511138e-03   8.935502e-03\n",
       "58   0.8178338673 -5.818258e+00 -2.286790e-01  1.343410e-03   9.246179e-03\n",
       "59  -0.4007932787  8.544176e-01  5.998583e-02  7.879209e-06  -2.280732e-03\n",
       "60  -0.2064486233  9.155595e-01  2.291673e-02 -1.004751e-04  -2.379450e-03\n",
       "61  -0.1202779886  3.634696e-01 -2.402738e-05  6.452177e-06  -5.505223e-04\n",
       "62  -0.0650353483  4.448165e-01 -1.344253e-02 -2.766721e-05  -8.229524e-04\n",
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       "221 -0.5999581609  1.694388e-01  7.782706e-02  3.364835e-04  -3.151594e-04\n",
       "222 -0.3417997545  2.342735e-01  2.745462e-02  1.828483e-04  -1.087462e-04\n",
       "223 -0.2260087011  1.893486e-01 -1.656488e-03  1.565822e-04   1.463360e-04\n",
       "224 -0.2097593822  9.192846e-02 -3.576498e-02  2.717371e-04   4.513106e-04\n",
       "225 -0.0937300184  1.193109e-01 -5.945737e-02  2.086511e-04   5.134397e-04\n",
       "226 -0.5427513859 -3.238439e-01  6.537204e-02  4.121326e-04   1.571476e-03\n",
       "227 -0.4235664510 -3.017272e-01  2.918561e-02  3.890551e-04   1.615519e-03\n",
       "228 -0.3799015254 -4.212855e-01 -5.104897e-03  4.833949e-04   1.947524e-03\n",
       "229 -0.2538185386 -3.172434e-01 -4.152350e-02  4.336097e-04   1.745492e-03\n",
       "230 -0.1596143564 -3.558264e-01 -8.378940e-02  4.758687e-04   1.899591e-03\n",
       "231 -0.2396558264 -3.215184e+00  8.880275e-02  9.016067e-04   4.071986e-03\n",
       "232 -0.0739208789 -2.545834e+00  3.614610e-02  6.881480e-04   3.196555e-03\n",
       "233  0.0394909167 -2.939251e+00 -5.699380e-03  8.132385e-04   3.845968e-03\n",
       "234  0.1728707996 -3.764483e+00 -5.981951e-02  1.075962e-03   5.378350e-03\n",
       "235 -0.1087957149 -1.036823e+00  7.055152e-02  2.435137e-04  -8.916755e-04\n",
       "236 -0.0766080553 -2.627995e+00  5.446855e-02  7.748097e-04   4.253066e-04\n",
       "237  0.0848179074 -2.629421e+00 -8.906359e-04  7.778230e-04   4.396817e-04\n",
       "238  0.2464109256 -2.786339e+00 -5.858225e-02  8.280412e-04   8.446154e-04\n",
       "239  0.4787281377 -3.710111e+00 -1.422948e-01  1.181639e-03   9.635637e-04\n",
       "\n",
       "$sigma\n",
       "       1        2        3        4        5        6        7        8 \n",
       "47.57699 47.57921 47.56962 47.59264 47.58597 47.60633 47.59847 47.59702 \n",
       "       9       10       11       12       13       14       15       16 \n",
       "47.60400 47.60558 47.51910 47.54735 47.56325 47.55186 47.56506 47.43662 \n",
       "      17       18       19       20       21       22       23       24 \n",
       "47.47825 47.47932 47.46887 47.49670 47.60589 47.61295 47.61471 47.61544 \n",
       "      25       26       27       28       29       30       31       32 \n",
       "47.61547 47.53117 47.55653 47.54389 47.53661 47.38296 47.31223 47.29205 \n",
       "      33       34       35       36       37       38       39       40 \n",
       "47.27290 47.25237 47.57008 47.56552 47.54859 47.53848 47.56760 47.58943 \n",
       "      41       42       43       44       45       46       47       48 \n",
       "47.55665 47.59796 47.57891 47.61417 47.59786 47.60832 47.60375 47.59063 \n",
       "      49       50       51       52       53       54       55       56 \n",
       "47.53140 47.55237 47.56769 47.57621 47.57850 47.40384 47.47848 47.48024 \n",
       "      57       58       59       60       61       62       63       64 \n",
       "47.49116 47.50310 47.60730 47.61142 47.61329 47.61365 47.61523 47.55852 \n",
       "      65       66       67       68       69       70       71       72 \n",
       "47.55309 47.56573 47.57010 47.58193 47.39931 47.33144 47.29003 47.26121 \n",
       "      73       74       75       76       77       78       79       80 \n",
       "47.23498 47.56765 47.56057 47.55537 47.54069 47.52776 47.37736 47.36862 \n",
       "      81       82       83       84       85       86       87       88 \n",
       "47.32377 47.31886 47.60985 47.54231 47.52891 47.51817 47.50534 47.59311 \n",
       "      89       90       91       92       93       94       95       96 \n",
       "47.60165 47.59903 47.59499 47.59332 47.25349 47.29795 47.30007 47.25426 \n",
       "      97       98       99      100      101      102      103      104 \n",
       "47.27018 47.46624 47.48204 47.60892 47.61361 47.61236 47.54479 47.55417 \n",
       "     105      106      107      108      109      110      111      112 \n",
       "47.57427 47.53374 47.54420 47.59174 47.58340 47.59147 47.58867 47.58090 \n",
       "     113      114      115      116      117      118      119      120 \n",
       "47.40604 47.41451 47.41291 47.40308 47.40442 47.58748 47.60534 47.59651 \n",
       "     121      122      123      124      125      126      127      128 \n",
       "47.60907 47.60718 47.61303 47.61452 47.61439 47.61547 47.33518 47.31361 \n",
       "     129      130      131      132      133      134      135      136 \n",
       "47.30199 47.29617 47.27412 47.55265 47.54948 47.54267 47.57068 47.55757 \n",
       "     137      138      139      140      141      142      143      144 \n",
       "47.57075 47.51268 47.51351 47.51890 47.46169 47.42011 47.43334 47.40039 \n",
       "     145      146      147      148      149      150      151      152 \n",
       "47.44474 47.38796 47.40124 47.37199 47.36294 47.34103 47.31479 47.53388 \n",
       "     153      154      155      156      157      158      159      160 \n",
       "47.54728 47.51486 47.49052 47.50547 47.40702 47.35975 47.35054 47.34147 \n",
       "     161      162      163      164      165      166      167      168 \n",
       "47.32220 47.49323 47.52551 47.53897 47.52902 47.61553 47.52227 47.56198 \n",
       "     169      170      171      172      173      174      175      176 \n",
       "47.54208 47.54645 47.55311 47.56301 47.57649 47.57732 47.59001 47.57407 \n",
       "     177      178      179      180      181      182      183      184 \n",
       "47.45073 47.42371 47.41948 47.42662 47.44486 47.55882 47.59551 47.61215 \n",
       "     185      186      187      188      189      190      191      192 \n",
       "47.61039 47.61274 47.31048 47.27674 47.26486 47.26368 47.25717 47.55837 \n",
       "     193      194      195      196      197      198      199      200 \n",
       "47.54823 47.51208 47.54060 47.61378 47.56531 47.50273 47.51351 47.53647 \n",
       "     201      202      203      204      205      206      207      208 \n",
       "47.52690 47.58518 47.58586 47.56462 47.58112 47.56668 47.41830 47.44459 \n",
       "     209      210      211      212      213      214      215      216 \n",
       "47.40106 47.50043 47.51381 47.60559 47.60264 47.60972 47.60321 47.56339 \n",
       "     217      218      219      220      221      222      223      224 \n",
       "47.55862 47.55753 47.55974 47.58382 47.60006 47.60732 47.60917 47.60476 \n",
       "     225      226      227      228      229      230      231      232 \n",
       "47.60761 47.60373 47.60457 47.60118 47.60229 47.60051 47.59380 47.59928 \n",
       "     233      234      235      236      237      238      239 \n",
       "47.59583 47.58951 47.60387 47.58558 47.58493 47.58365 47.56766 \n",
       "\n",
       "$wt.res\n",
       "           1            2            3            4            5            6 \n",
       "-28.94117526 -28.18009045 -31.72094405 -22.35304616 -25.32157461  14.05740111 \n",
       "           7            8            9           10           11           12 \n",
       " 19.18314150  19.98479332  15.77975654  14.61377022 -45.81337125 -38.63274489 \n",
       "          13           14           15           16           17           18 \n",
       "-33.86699740 -37.32064249 -33.12488564 -62.29459690 -54.81458083 -54.62339364 \n",
       "          19           20           21           22           23           24 \n",
       "-56.58663628 -50.77704270 -14.46510339  -7.50773760  -4.21597162   1.37872988 \n",
       "          25           26           27           28           29           30 \n",
       "  1.14374490 -42.38958591 -33.20582963 -39.28085945 -39.14485336  70.99137781 \n",
       "          31           32           33           34           35           36 \n",
       " 80.60662865  83.78251257  86.32064667  88.38018779  31.21088262  32.90472614 \n",
       "          37           38           39           40           41           42 \n",
       " 38.09304967  40.77541631 -32.27979750 -23.87891352 -35.93043773 -19.58060681 \n",
       "          43           44           45           46           47           48 \n",
       "-28.18513100  -5.41873255 -19.64751380 -12.55116948  15.95713951  23.07860790 \n",
       "          49           50           51           52           53           54 \n",
       "-42.78712975 -37.18462495 -32.39487484 -29.33526104 -28.38877886 -67.66156102 \n",
       "          55           56           57           58           59           60 \n",
       "-54.67688619 -54.37669181 -52.06876697 -49.32955266 -13.36386374  -9.43749603 \n",
       "          61           62           63           64           65           66 \n",
       " -7.01398511  -6.41721793  -2.54581672 -35.16630648 -36.83537580 -32.84250999 \n",
       "          67           68           69           70           71           72 \n",
       "-31.31592713 -26.58711770  68.30086930  78.21811144  83.88958721  87.56366607 \n",
       "          73           74           75           76           77           78 \n",
       " 90.66924165  31.99025748  34.38913697  36.17247920  40.32611508  43.56352222 \n",
       "          79           80           81           82           83           84 \n",
       "-72.17215329 -73.56447867 -79.86486115 -80.27288808 -11.12884821 -40.05418320 \n",
       "          85           86           87           88           89           90 \n",
       "-43.59642462 -46.15213727 -48.91967869 -22.07501167 -17.44786463 -19.04129910 \n",
       "          91           92           93           94           95           96 \n",
       "-21.21929135 -21.98879296  88.64555107  83.26551596  83.07014471  88.85242792 \n",
       "          97           98           99          100          101          102 \n",
       " 86.57462133  56.01904075  53.18062022  11.97422319   6.46422834  -8.27778635 \n",
       "         103          104          105          106          107          108 \n",
       "-39.22555148 -36.65338691 -30.09773428 -42.21781808 -39.28607942 -22.68588605 \n",
       "         109          110          111          112          113          114 \n",
       "-26.50140888 -22.89602468 -24.19294354 -27.36843588  67.30923690  66.18501388 \n",
       "         115          116          117          118          119          120 \n",
       " 66.53229637  68.12154204  67.68730640 -24.67462083 -14.90486107 -20.39992050 \n",
       "         121          122          123          124          125          126 \n",
       "-11.85884142 -13.44368596  -7.39130996  -4.71584916  -5.01449229  -1.12340154 \n",
       "         127          128          129          130          131          132 \n",
       " 78.04378292  81.15318157  82.78122421  83.43517888  85.97036963  36.46219554 \n",
       "         133          134          135          136          137          138 \n",
       " 37.58036086  39.49490259  31.01345549  35.10122819 -31.24683431 -47.48318458 \n",
       "         139          140          141          142          143          144 \n",
       "-47.32465107 -46.03803141 -57.83148673  65.06219997  62.96537345  68.63284839 \n",
       "         145          146          147          148          149          150 \n",
       " 60.96434444  70.18608351 -68.23718350 -72.97763393 -74.39821259 -77.47370579 \n",
       "         151          152          153          154          155          156 \n",
       "-80.81724019 -42.16468958 -38.67259303 -46.98929747 -52.27569913 -48.88907667 \n",
       "         157          158          159          160          161          162 \n",
       " 67.20450830  74.70679658  76.12135238  77.34738811  79.75935229  50.80040135 \n",
       "         163          164          165          166          167          168 \n",
       " 43.81352811  40.48455499  42.95071957  -0.02276168 -44.98529022 -34.24039013 \n",
       "         169          170          171          172          173          174 \n",
       "-40.08114209 -38.81615712 -36.77016920 -33.75288290 -29.15796157 -28.83122135 \n",
       "         175          176          177          178          179          180 \n",
       "-23.47771795 -29.87717136  59.40967438  64.38019616  65.15842684  63.85797880 \n",
       "         181          182          183          184          185          186 \n",
       " 60.44650091 -35.16691853 -20.96276376  -8.60393017 -10.58768845  -7.82503120 \n",
       "         187          188          189          190          191          192 \n",
       " 81.36286877  85.96141447  87.54327280  87.60825618  88.06212202  34.76767645 \n",
       "         193          194          195          196          197          198 \n",
       " 37.90108075  46.95062792  40.00588349   6.13972265 -33.06271111 -49.61336346 \n",
       "         199          200          201          202          203          204 \n",
       "-47.32465107 -41.53477110 -43.81119840 -25.69984616 -25.49313030 -33.39846413 \n",
       "         205          206          207          208          209          210 \n",
       "-27.44985634 -32.57785192  65.40456161  61.08364322  68.52470994  50.08243925 \n",
       "         211          212          213          214          215          216 \n",
       " 46.90378717 -14.67870386 -16.76975035 -11.26301717 -16.38801495 -33.69311912 \n",
       "         217          218          219          220          221          222 \n",
       "-35.32465911 -35.67501320 -34.93901340 -26.25699082 -18.36158189 -13.42662106 \n",
       "         223          224          225          226          227          228 \n",
       "-11.82452007 -15.37170283 -13.13500401 -16.02487652 -15.49389390 -17.74002203 \n",
       "         229          230          231          232          233          234 \n",
       "-17.02343939 -18.06991041 -21.68340975 -18.83036069 -20.73744846 -23.76837892 \n",
       "         235          236          237          238          239 \n",
       "-15.93558232 -25.61627064 -25.91894023 -26.42821408 -32.26276135 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "influence(input) # regression diagnostics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Cj8ZF2aCR2E1VilXiHtbcGpyhSsy2/W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\nAcAAhAQAAxASAAxASAAwACEBwMD/pynisCgqPfQAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# diagnostic plots \n",
    "layout(matrix(c(1,2,3,4),2,2)) # optional 4 graphs/page \n",
    "plot(input)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Res.Df</th><th scope=col>RSS</th><th scope=col>Df</th><th scope=col>Sum of Sq</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>235      </td><td>528708.6 </td><td>NA       </td><td>       NA</td><td>       NA</td><td>     NA  </td></tr>\n",
       "\t<tr><td>236      </td><td>528972.3 </td><td>-1       </td><td>-263.6944</td><td>0.1172067</td><td>0.73239  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllll}\n",
       " Res.Df & RSS & Df & Sum of Sq & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\t 235       & 528708.6  & NA        &        NA &        NA &      NA  \\\\\n",
       "\t 236       & 528972.3  & -1        & -263.6944 & 0.1172067 & 0.73239  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Res.Df | RSS | Df | Sum of Sq | F | Pr(>F) | \n",
       "|---|---|\n",
       "| 235       | 528708.6  | NA        |        NA |        NA |      NA   | \n",
       "| 236       | 528972.3  | -1        | -263.6944 | 0.1172067 | 0.73239   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Res.Df RSS      Df Sum of Sq F         Pr(>F) \n",
       "1 235    528708.6 NA        NA        NA      NA\n",
       "2 236    528972.3 -1 -263.6944 0.1172067 0.73239"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compare models\n",
    "input1 <-lm(vc..m.min. ~ f..mm.+Fc..N.+Stdabw..Fc..N.,data)\n",
    "input2 <-lm(vc..m.min. ~ f..mm.+Fc..N.,data)\n",
    "anova(input1, input2)\n",
    "#input1 <- lm(y ~ x1 + x2 + x3 + x4, data=mydata)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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T9rDnViUKMSInmMtRxrJHFHmX//rDvUjQCRdi3Cfyxm2Vca/9tKoOEQdgaRvMVq\nkinI490DaIFIvmI7y3SptLtLiOQrBxBJRQwFiOQr1hPstH8a7x9BBSJ5i+38UiCSot4dInmL\n9fRSYdJ2P+M0DiJ5jPXkUmHS7gFkIBKsQYNKGjxCJFiFhu5dVfieOiESrEKDSa1fn9kpBkSC\nlWgwqRnHPqUjEqxGhUo7R4BIsB5EQiQQQEOThEj7FAGSaBhy4BhplyJAlNP+KiHSLkWAMLuL\nxHmkXYoAafZvk9rBbFsgIoEYakTaIQZEAkGUqIRI2xUBVlAh0h4hIBJIouI4CZE2LAIsocAk\nRNqwCLCEApE4RtqwCLDG/ioh0nZFgDU0nFDiPNJWRYBF9hdpcxAJ5FHQJG0NIoEFNPTutgWR\nwApHM2lTkZ7Xi0m5RE9bRYAaEEl+k4xPaGrOVooARRyrTdpQpMgE91d26/0ITGSjCFDFkVTa\nUKTAvKrbLxPYKAJ0gUjCm+TbmaE7YkWALg7UJNEigUUQSXaTjOQY6fHObnGMdByOotKWw9/n\nxqhd+LFSBGjjKKdmtz2PFGXnkYLLlfNIx+EYJjGzASxzjDYJkcA6iCS1SZNbaMzlYbUI0Ib/\nKm1+HqkYcRgdtEMk7/C+e7e1SJGJPnH8jszt++kGC4sArSCSyCb5dumGgcnGvT8mtFEEqMV3\nk7YWqWxsmCJ0NDwfvNtapL9SJKYIHQ6vVdpUpMv19jD35OYnYorQEUGklZvk29UDCcYETBE6\nIB43SVueR3q9brfLJRtyiEY9QiRvQaRVmygsAvYBkdZsorAI2InaI69k2kOk3+dbEclf2mN3\n3qiESLA1VXvkk0mIBLvgW5OESLALvnXuEAl2AZEQCSRAJIa/QQDPhu4QCXbCr1FwRIKdQCT5\nKHYoAvbHJ5UQCfbEG5UQCfYEkayCSIfBF5MQCXYFkWyCSAcCkeyBSIfCA48QCfYHkWyBSAfD\ndY0QCUAERAIQAJEABEAkAAEQCfTh4NgDIoE2nBwNRyTQBiKJgUgHxs0ZQ4gEykAkORDpwCCS\nHIh0ZFz0CJFAHYgkBiIdG+c0QiQAERAJQABEAhAAkQAEQCQAARAJQABEAhAAkcAB9J9YQiQQ\nwG6iuzDVAZFgNbYTHZGWgkhOYTnRnZgOjkiwFtuJjkiLQSSXQKQYkWA91hPdAY8QCdbDYAMi\ngQD2E127RogEIuhPdNsgEoAAiAQgACIBCIBIIM0hD5gQCWRxYazaAogEsiCSxU0UFgF2qKY5\nHEwlRAJREMnmJgqLADucTsdUCZFAloOahEggy+l0SJUQCaRBJGubKCwCrHHIJgmRQB5EsrSJ\nwiLAIohkadYx0GUAAAuUSURBVBOFRYBVjuYRIoEdEMnGJgqLANscSSNEgg04glKIBJY5RicP\nkcAyiCS3icIiYCMOMhCOSGAXRBLcRGERsBGIJLiJwiJgKw7hESKBbWqRfNYJkcA6lUYet0yI\nBBvh97ESIsE2eD7ogEiwDZ5fWoFIsA2IJLCJwiJga/w2CZFgIxBp/SYKi4DNQaTVmygsAnbA\nX48QCTYEkVZuorAI2AVPNUIkABEQCUAARAIQAJEABEAkAAEQCUAARAIQAJEABEAkAAEQCUAA\nRAIQAJEABEAkAAEQCUAARAIQAJEABEAkAAEQCUAARAIQAJEABEAkAAEQCUAARAIQAJEABEAk\nAAEQCUAARAIQAJEABEAkAAEQCUAARAIQYFORnteLSblET1tFAOzChiJ9QlNztlIEwE5sKFJk\ngvsru/V+BCayUQTATmwoUmBe1e2XCWwUAbATG4pkzNAdsSIAdoIWCUCAbY+RHu/sFsdI4Btb\nDn+fG6N24cdKEQD7sO15pCg7jxRcrpxHAr9gZgOAAIgEIABThAAEYIoQgABMEQIQgBOyAAIw\nRQhAAFokAAGYIgQgAFOEAATQM0XINFlcBMAuMLMBQABEAhAAkQAEQCQAARAJQIBNZzZMHphD\nJHCMDUW6zRAJwDG2Eyl+BeMXT+yGCw2gCzE6EaSeGJdH8hqfGLQbeup2GBdidCJIPTGuiOTW\nmLeqCD11O4wLMToRpJ4Y9UQihQvvyIUYnQhST4x6IpHChXfkQoxOBKknRj2RSOHCO3IhRieC\n1BPj6kjUTe7WFk8fLsToRJB6YkSkPXAhRieC1BMjIu2BCzE6EaSeGBFpD1yI0Ykg9cSISHvg\nQoxOBKknRkTaAxdidCJIPTHqiQTAYRAJQABEAhAAkQAEQCQAARAJQABEAhAAkQAEQCQAARAJ\nQABEAhAAkQAEQCQAARAJQABEAhAAkQAE8EykKDBBNPrT0HvSXKFdZ6S3Mh8a4WmLtIxRV236\nJVL+U+vh3mEM8Gp89DojfZXXOzfC0xZpGaOy2vRKpKcJXvErMD0/s66Bl7mUN3VGmgSU50Mj\nPG2RVjEqq02vRIrMI/n3bq57B9LPrQ5MZaQ3cy57SnV4yiKtY1RWm16JdDHvuPVVpYubuZU3\nVUZqonIpm0Z4yiKtY1RWm16JVFSxuoWNCi7m8ZccE6c3VUb66saV/lEWaR2jstpUUj8yaKjQ\nES750XH6S4daI1UvUtwQSVVt6qkfATRU6AjG3OP4E6VdEq2ROiSSstrUUz8CaKjQn3zSYVqt\nkTokUo6a2tRTPwIECir0N2l4WiMtAmqEpy/SdihaYtRTPwLkozdvLSNMA6Sft9ZIW6N273rU\nTlOk3yJpiNErka7Z+YSH0p9bT74400ks2eetNdIiSRvh6Yu0ajVV1aZXImk4wz1ClH7Sn+zs\nodZI9c9sqGJUVpteiRSH1YioRj5BFl72vak00rLb1AhPXaRFjMpq0y+RPtks4L2jGCQNL7xV\nNxVGWorUCE9dpM0Y9dSmXyIB7AQiAQiASAACIBKAAIgEIAAiAQiASAACIBKAAIgEIAAiAQiA\nSAACIBKAAIgEIAAiAQiASAACIBKAAIgEIAAiAQiASAACIBKAAIgEIAAiAQiASAACIBKAAIgE\nIAAiAQiASAACIBKAAIgEIAAiAQiASAACIBKAAIgEIAAiacCUFL9H98gefQy9eHxX0sHBFKh2\nDXRECrNPJRz4bBBJI1S7BjrZn98dUgKRNEK1awCRnIdq10Aj+5ObeSev6OrF8S00Qf7j3XEU\nmKj+VW8TZn9D84kfF1P8rHd1nBV3t36cjTkPHHfBWhBJA2MiXbIb5/S5c3rrUr34bN7Jv+/k\nuWt+hBXFXyLVW9/y19w2fWPHAZE0UI81fLUoD3P+xJ+zSZqSuwle8SuoRLqba/LvNXnKmHt6\n93v7xtaBeaWvCfd4fwcAkTQwItIl6bil3bhLevMZp25Un1lmRT2417N9Y2tj6NZZBJE00O7a\ntUTqnmJqvvgv6du9sw5d/H5czz0iNbaOkl7h67XZWzoaiKSBhSI9k75dlDVT54EWrbF1fE06\nhSZ4b/amjgUiaWBUpO6rGo8EYfpf2jSFt8e7V6RmMY8o5BjJEoikgRGRLvWhTX7z2XhxZG7Z\ngEP2UEekZ36M1Dkw4jSTJahXDXyJ9I7Lf7OhuviWDhc8OqN2mTvZaIJJ+nev+hgpNLd0qM60\ntg7zkT1aJDsgkgY6IoXJsUz5b3H4kx3bZCeF/pqNSpifYIqKI6Fnvv2tPt9Ub32vXgIWQCQN\ndER6hqlC+b/Z3ATzl48RXJszG1LuRdctsev8fOSj3Pnr/uqZDcXW2cwGPLIEIgEIgEgAAiAS\ngACIBCAAIgEIgEgAAiASgACIBCAAIgEI4LxIA7MwHxe7++/n85df7y1FPqvnazrCrJiaV1IM\nvOAxfbefKEwCKhaBGA5pYoRLYrvovD7RU5He2VxOe/sfIJ0MdxUqOC8859V9eME+RpI1mLzb\nT5DvK/h01t2zJtJXbB+j8pIqT0U6S7YL0zHCH3L+5qJ8Zmr34Vn7GH1BIf+E3f6Zc/IO3+e0\n3TUSIi2ILToPvXpP/BTpLtYgzWP11T79+djd7Xgxc3PamDD3v++VXzvLKvbzddGgNZG+Y/uk\n14OowwuRkv+vJrhmlxNkTVF4bi/7li4Id+42Fl9b9T5aXB90yR77FcpXL6Vnbz1ltt/N9928\nf9Nauy7K4+mLbCyn++vhZS49G/7YWfVm68X2uhFG6eWFf1ns+bHOX+cqjmWxnTVeU+WJSNnC\nbo9zsbjbM1u9rV72Lb8qJ/h0t2xv1f9ovv/s0OCXSb0idffWV2b73XzdjbK301q7Lrsy6dYf\n2YhIA/VQJPgEkaLygo5apHqxve8Iz+kqYOmL//I3Wx7xrIvtpvGiKk9EOn/Sq9myf4P0406P\nzutl3+7pM3/dxO1u1f9oY//dL8LIhNnw1aOxy6/ounvrKzMe2oGpUzNurV1XxtMXWf8+TFYj\n/fVQtN4TRErTPYyejacai+21IswfvSf1f4/LQYN797toWWwv0ZFRITwRKf/Sehf3z3lPvlr2\nLVsQ7vP9ddjeqv/R5v7b22ffueErSYFWMKNl9JdZvvZrDKu4f341Homb8XQjG96HiYfrIf2S\nv00KKPnW+EsbjkdV6vdie3mEj+zRS94jeCYN1KvsI/SUMC+2T3fwRQOeiFTeat6vl33rP6bt\nbtX/aHf/je0f2ToJJj8KiPteMhDZwP76JEj/fQR5X6a1dl1/ZIP76A+vfjQ9kpwkUsLzGpQX\ntVf7zP90Iqy+1ZIuQtIYvb8EWBjbxKGMTVEY0jxGRKqWfbMjUtaju4fNfsYqkXoeK+6+sgxs\nr103HNnwMdJIPTyra9NHAyp45d3Kxgvqw6WuSI/kUwjCOAyLXp5AbIhkgRGRqmXf7Ig0uMuR\nMpaJlP3trF0nLFLStXr9Dqi691V2b4T5HxM+ky+byHzCr5MSC2NDJAv0pWdxjFQt+3Ye7H+7\nIdKnHPWI14k0Vg9vE/4O6FL8mEUdUHOxvVaE+ZFTOnQdmb/kNY/k37+4w7LYOEayQV96RsX4\naLns2y0dEYp6RoTi71RUKNKnmEjQWrtuiUhj9ZANXv8KKPHlllTo85wf/6dDB4/mqF0jwvzR\nQrL0UzA9q/gvi+3JqJ0F+tLzWQ6zFsu+Nc5RNF76ldS9j3b2P25T/y7HRPq1v5w09M7adZMV\nbz45Ug/pGZ/fAZVBpNVarLtXL7bXijAd3MvPpcb5OsnnorUZ+i6ZHtuV80gW6E3PsGj7y2Xf\nsp9ieHde5IxIQZT1VDtr1y0RaaQeyiHsH+3u6y/J6XM2aFCuu1cvtteKMKpmXFyzFuRatCOD\njfLk2JjZsBkPnTOEQYK3yh968lOkvWZ/wwYw+3tD5K5HAmVwPdKmPL6GWsEP/jR27PwVCWBT\nEAlAAEQCEOB/Dd1xeGdhbuwAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Matrix Scatterplot\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NgdECG18xFYEtHRERESRwJBACFpZARDhCSMgd0xHTikbRZDhHRMhw2JFSNIIiRA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\nAAGEBAj4Dz0vG3fYxBdwAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Matrix Scatterplot\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pF28bUXIp6eGOmgXIkkfh3J0/O1e3xt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\nSUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Matrix Scatterplot\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2BAEN0mHU6kVuHzba2UiBzGo9okZSKNetTcapJVpOqDf5MTDXPR3FCa/RiF79ZY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\ngP+rbBLXuTBfXwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Matrix Scatterplot\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot matrix of all variables.\n",
    "plot(input, pch=16, col=\"blue\", main=\"Matrix Scatterplot\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}