4_Logistic_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "LOGISTIC REGRESSION (Binary Classification)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>bought_insurance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>22</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>25</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>47</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>52</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>46</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age  bought_insurance\n",
       "0   22                 0\n",
       "1   25                 0\n",
       "2   47                 1\n",
       "3   52                 0\n",
       "4   46                 1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insurance_df = pd.read_excel(\"ML_Algo_Datasets/Insurance.xlsx\")\n",
    "insurance_df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x15c17584550>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(insurance_df.age, insurance_df.bought_insurance, marker=\"+\", color=\"red\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# split dataset in training set and testing set \n",
    "\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(insurance_df[[\"age\"]], insurance_df.bought_insurance, train_size=0.9) # 90 percent of dataset for trainig and 10% for testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    age\n",
       "2    47\n",
       "6    55\n",
       "23   45"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    age\n",
       "19   18\n",
       "17   58\n",
       "18   19\n",
       "9    61\n",
       "1    25\n",
       "15   55\n",
       "14   49\n",
       "10   18\n",
       "20   21\n",
       "16   25\n",
       "12   27\n",
       "3    52\n",
       "11   28\n",
       "26   23\n",
       "8    62\n",
       "4    46\n",
       "5    56\n",
       "21   26\n",
       "22   40\n",
       "25   54\n",
       "0    22\n",
       "13   29\n",
       "24   50\n",
       "7    60"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "Model = LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LogisticRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LogisticRegression.html\">?<span>Documentation for LogisticRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LogisticRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1], dtype=int64)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\utkarsh.alpuria\\Desktop\\My Work\\Python\\Python ML\\Python ML Algorithm\\.ml_algo_py_venv\\lib\\site-packages\\sklearn\\base.py:493: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0, 1], dtype=int64)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Model.predict([[18], [45]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6666666666666666"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.17845576, 0.82154424],\n",
       "       [0.05565772, 0.94434228],\n",
       "       [0.23134372, 0.76865628]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Model.predict_proba(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "LOGISTIC REGRESSION (Multiclass Classification)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import load_digits  # 1797 images of hand written numbers in 8x8 pxl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "digits = load_digits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['DESCR', 'data', 'feature_names', 'frame', 'images', 'target', 'target_names']"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  5., 13.,  9.,  1.,  0.,  0.,  0.,  0., 13., 15., 10.,\n",
       "       15.,  5.,  0.,  0.,  3., 15.,  2.,  0., 11.,  8.,  0.,  0.,  4.,\n",
       "       12.,  0.,  0.,  8.,  8.,  0.,  0.,  5.,  8.,  0.,  0.,  9.,  8.,\n",
       "        0.,  0.,  4., 11.,  0.,  1., 12.,  7.,  0.,  0.,  2., 14.,  5.,\n",
       "       10., 12.,  0.,  0.,  0.,  0.,  6., 13., 10.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  5., 13.,  9.,  1.,  0.,  0.],\n",
       "       [ 0.,  0., 13., 15., 10., 15.,  5.,  0.],\n",
       "       [ 0.,  3., 15.,  2.,  0., 11.,  8.,  0.],\n",
       "       [ 0.,  4., 12.,  0.,  0.,  8.,  8.,  0.],\n",
       "       [ 0.,  5.,  8.,  0.,  0.,  9.,  8.,  0.],\n",
       "       [ 0.,  4., 11.,  0.,  1., 12.,  7.,  0.],\n",
       "       [ 0.,  2., 14.,  5., 10., 12.,  0.,  0.],\n",
       "       [ 0.,  0.,  6., 13., 10.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.images[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.gray()\n",
    "for i in range(3):\n",
    "    plt.matshow(digits.images[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.target[:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(digits.data, digits.target, test_size=0.2) # 20% for test and 80% for training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1437"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "360"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "model = LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\utkarsh.alpuria\\Desktop\\My Work\\Python\\Python ML\\Python ML Algorithm\\.ml_algo_py_venv\\lib\\site-packages\\sklearn\\linear_model\\_logistic.py:469: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
      "\n",
      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
      "Please also refer to the documentation for alternative solver options:\n",
      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
      "  n_iter_i = _check_optimize_result(\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-2 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-2 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-2 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-2 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-2 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LogisticRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LogisticRegression.html\">?<span>Documentation for LogisticRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LogisticRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9583333333333334"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x15c331bc490>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(digits.images[64])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.target[64]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict([digits.data[64]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(digits.data[0:3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}