Linear_Regression_Workshop (2).ipynb

{
 "cells": [
  {
   "cell_type": "code",
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   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
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    "id": "eduw9yH3dAMz",
    "outputId": "2cf3c559-a0ee-4143-c5ca-66a81be1f135",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "!pip install ISLP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XMUK3Ua3dFtG"
   },
   "source": [
    "# Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 391
    },
    "id": "LqkqoWsic3lK",
    "outputId": "dac62f23-e318-4866-b5b3-43bd5c0d2be6"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "from matplotlib.pyplot import subplots\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.stats.outliers_influence import variance_inflation_factor as VIF\n",
    "from statsmodels.stats.anova import anova_lm\n",
    "from ISLP import load_data\n",
    "from ISLP.models import (ModelSpec as MS, summarize, poly)\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LEVc-q4hdLGF"
   },
   "source": [
    "# Loading Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 211
    },
    "id": "wNSQx3erdOdt",
    "outputId": "13e9d601-52a3-479c-a879-cfbcf90c19e4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['crim', 'zn', 'indus', 'chas', 'nox', 'rm', 'age', 'dis', 'rad', 'tax',\n",
       "       'ptratio', 'lstat', 'medv'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Loading a dataset from ISLP\n",
    "dataset = load_data(\"Boston\")\n",
    "dataset.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WQ2RLrRodOD1"
   },
   "source": [
    "# Base Simple Linear Regression to use for all the activities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 211
    },
    "id": "abTi40hEdpXX",
    "outputId": "e7dd35e0-c659-47f0-ea4a-97d1339f8694"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>const</th>\n",
       "      <th>lstat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   const  lstat\n",
       "0    1.0   4.98\n",
       "1    1.0   9.14\n",
       "2    1.0   4.03\n",
       "3    1.0   2.94"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# from the dataset we select a column to use for our x-axis\n",
    "X = dataset['lstat']\n",
    "X = sm.add_constant(X) # adding a constant term using lib, this constant term is needed for the linear regression model intercept\n",
    "X[:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 228
    },
    "id": "R7aJ-PKIdr9j",
    "outputId": "5f89345e-6a0a-406f-d57b-ab4200b1d096"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\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>coef</th>\n",
       "      <th>std err</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>34.5538</td>\n",
       "      <td>0.563</td>\n",
       "      <td>61.415</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lstat</th>\n",
       "      <td>-0.9500</td>\n",
       "      <td>0.039</td>\n",
       "      <td>-24.528</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          coef  std err       t  P>|t|\n",
       "const  34.5538    0.563  61.415    0.0\n",
       "lstat  -0.9500    0.039 -24.528    0.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# from the dataset we select a column to use for our y-axis (dependant variable)\n",
    "y = dataset['medv']\n",
    "model = sm.OLS(y, X) # Uses Ordinary Least Squares (OLS) regression from lib to fit a linear regression model (sm.OLS) with 'medv' as the dependent variable and 'lstat' (plus the constant term) as the independent variable\n",
    "results = model.fit()\n",
    "summarize(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 246
    },
    "id": "7IXPDrkzd0FT",
    "outputId": "34f78522-263c-4173-bcac-b643484704bd",
    "scrolled": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'plt' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mplt\u001b[49m\u001b[38;5;241m.\u001b[39mscatter(dataset[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlstat\u001b[39m\u001b[38;5;124m'\u001b[39m], dataset[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mmedv\u001b[39m\u001b[38;5;124m'\u001b[39m], color\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mblue\u001b[39m\u001b[38;5;124m'\u001b[39m, label\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mData points\u001b[39m\u001b[38;5;124m'\u001b[39m) \u001b[38;5;66;03m# basically plots the blue plots on the graph\u001b[39;00m\n\u001b[1;32m      3\u001b[0m lstat_line \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlinspace(dataset[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlstat\u001b[39m\u001b[38;5;124m'\u001b[39m]\u001b[38;5;241m.\u001b[39mmin(), dataset[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlstat\u001b[39m\u001b[38;5;124m'\u001b[39m]\u001b[38;5;241m.\u001b[39mmax()) \u001b[38;5;66;03m# creates a list of numbers evenly spaced between min and max \u001b[39;00m\n\u001b[1;32m      5\u001b[0m \u001b[38;5;66;03m# IMPORTANT\u001b[39;00m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;66;03m# results.params['const'] retrieves the estimated coefficient (parameter) of the constant term from the linear regression model {hence B_0}\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;66;03m# results.params['lstat'] retrieves the estimated coefficient of the 'lstat' variable from the linear regression model {hence B_1}\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[38;5;66;03m# It essentially represents the regression line or line of best fit based on the model's coefficients and the range of 'lstat' values\u001b[39;00m\n\u001b[1;32m     11\u001b[0m \u001b[38;5;66;03m# RECALL: this is essentially the equation we just learnt y^ = B_0 + B_1*x\u001b[39;00m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'plt' is not defined"
     ]
    }
   ],
   "source": [
    "plt.scatter(dataset['lstat'], dataset['medv'], color='blue', label='Data points') # basically plots the blue plots on the graph\n",
    "\n",
    "lstat_line = np.linspace(dataset['lstat'].min(), dataset['lstat'].max()) # creates a list of numbers evenly spaced between min and max \n",
    "\n",
    "# IMPORTANT\n",
    "# results.params['const'] retrieves the estimated coefficient (parameter) of the constant term from the linear regression model {hence B_0}\n",
    "# results.params['lstat'] retrieves the estimated coefficient of the 'lstat' variable from the linear regression model {hence B_1}\n",
    "# results.params['const'] + results.params['lstat'] * lstat_line computes the predicted 'medv' values based on the linear regression equation {hence B_1 * x}\n",
    "# This line calculates the values for the 'medv' variable using the coefficients obtained from the regression results and the 'lstat' values in lstat_line\n",
    "# It essentially represents the regression line or line of best fit based on the model's coefficients and the range of 'lstat' values\n",
    "# RECALL: this is essentially the equation we just learnt y^ = B_0 + B_1*x\n",
    "medv_line = results.params['const'] + results.params['lstat'] * lstat_line\n",
    "\n",
    "plt.plot(lstat_line, medv_line, color='red', label='Line of best fit') # plotting best fit by plotting the 'lstat_line' values along the x-axis against the 'medv_line' values along the y-axis\n",
    "\n",
    "plt.xlabel('LSTAT')\n",
    "plt.ylabel('MEDV')\n",
    "plt.title('Scatter plot with line of best fit')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['AtBat', 'Hits', 'HmRun', 'Runs', 'RBI', 'Walks', 'Years', 'CAtBat',\n",
       "       'CHits', 'CHmRun', 'CRuns', 'CRBI', 'CWalks', 'League', 'Division',\n",
       "       'PutOuts', 'Assists', 'Errors', 'Salary', 'NewLeague'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this time we're gonna use another dataset from ISLP\n",
    "# TODO: import the dataset Hitters (Hint -- look at the Loading Dataset section)\n",
    "new_dataset = 0\n",
    "new_dataset.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\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>const</th>\n",
       "      <th>CRuns</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>828</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   const  CRuns\n",
       "0    1.0     30\n",
       "1    1.0    321\n",
       "2    1.0    224\n",
       "3    1.0    828"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_2 = 0 # TODO: set the column CRuns as the independent variable along the x-axis\n",
    "X_2 = 0 # add a constant term using lib, this constant term is needed for the linear regression model intercept\n",
    "X_2[:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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>coef</th>\n",
       "      <th>std err</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>87.9649</td>\n",
       "      <td>3.675</td>\n",
       "      <td>23.935</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CRuns</th>\n",
       "      <td>0.0364</td>\n",
       "      <td>0.008</td>\n",
       "      <td>4.852</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          coef  std err       t  P>|t|\n",
       "const  87.9649    3.675  23.935    0.0\n",
       "CRuns   0.0364    0.008   4.852    0.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_2 = 0 # TODO: set the column Hits as the dependent variable along the y-axis\n",
    "second_model = 0 # TODO: Use Ordinary Least Squares (OLS) regression from lib to fit a linear regression model\n",
    "second_results = 0 # TODO: replace\n",
    "summarize(0) # TODO: replace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: calculate the linear regression and plot the graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_3 = 0 # TODO: set the column Walks as the independent variable along the x-axis\n",
    "X_3 = 0 # add a constant term using lib, this constant term is needed for the linear regression model intercept\n",
    "X_3[:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_3 = 0 # TODO: set the column  as the dependent variable along the y-axis\n",
    "third_model = 0 # TODO: Use Ordinary Least Squares (OLS) regression from lib to fit a linear regression model\n",
    "third_results = 0 # TODO: replace\n",
    "summarize(0) # TODO: replace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: calculate the linear regression and plot the graph\n",
    "# TODO: name the graph something unique"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1ZgEJWbPKG7u"
   },
   "source": [
    "# Standard Error and Confidence Intervals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "B5dEy_2RQHvz"
   },
   "source": [
    "Standard Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "NNO2Y55eeUxj",
    "outputId": "cff92025-00e8-4d42-9d07-3ca942498fed"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const    0.563\n",
       "lstat    0.039\n",
       "Name: std err, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating S.E using lib\n",
    "summarize(results)['std err']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "Wg7spDInOqqR"
   },
   "outputs": [],
   "source": [
    "# Get the residuals\n",
    "e_terms = results.resid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "-pQEzW3dOqqS",
    "outputId": "f9f26835-5cdd-45b2-ea04-38210906a142"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 0  # TODO - hint: number of observations\n",
    "p = 0  # TODO - hint: number of parameters estimated (intercept and slope)\n",
    "SSR = 0 # TODO\n",
    "sigma_squared = 0 # TODO\n",
    "sigma_squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "4fo1GJwgOqqS",
    "outputId": "52657cad-78db-4d11-84fb-e8cb9c870c61"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 0)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# y_hat = beta_0_hat + beta_1_hat*x\n",
    "# Calculate the sum of squares of the differences from the mean of 'lstat'\n",
    "lstat_mean = 0 # TODO\n",
    "sum_squares = 0 # TODO\n",
    "\n",
    "# Calculate SE(beta_1_hat) - the standard error of the slope\n",
    "SE_beta_1_hat = 0 # TODO\n",
    "\n",
    "# Calculate SE(beta_0_hat) - the standard error of the intercept\n",
    "SE_beta_0_hat = 0 # TODO\n",
    "\n",
    "SE_beta_1_hat, SE_beta_0_hat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zmojB4r6QMaX"
   },
   "source": [
    "Confidence Intervals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 112
    },
    "id": "oSQ-6lRJQN8P",
    "outputId": "94d5c379-5016-4133-dcce-2c814d58f8a6"
   },
   "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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>33.448457</td>\n",
       "      <td>35.659225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lstat</th>\n",
       "      <td>-1.026148</td>\n",
       "      <td>-0.873951</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               0          1\n",
       "const  33.448457  35.659225\n",
       "lstat  -1.026148  -0.873951"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Using the library\n",
    "results.conf_int()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "fk0n12ABQick",
    "outputId": "b8dccf8c-e9af-449b-9df3-629703e7cabb"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((0, 0), (0, 0))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating it manually\n",
    "beta_0_hat = results.params[0]\n",
    "beta_1_hat = results.params[1]\n",
    "\n",
    "beta_0_min_val = 0 # TODO\n",
    "beta_0_max_val = 0 # TODO\n",
    "\n",
    "\n",
    "beta_1_min_val = 0 # TODO\n",
    "beta_1_max_val = 0 # TODO\n",
    "\n",
    "((beta_0_min_val, beta_0_max_val), (beta_1_min_val, beta_1_max_val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hypothesis Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Null Hypothesis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# H₀: The data is normally distributed.\n",
    "# H₁: The data is not normally distributed\n",
    "# Assume that α=0.05. If the p-value is >0.05, it can be said that data is normally distributed.n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### t-statistic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate the t-statistic for beta_hat_1\n",
    "t_stat_beta_1 = 0 # TODO: use formula (beta_hat_1 - 0) / SE(beta_hat_1)\n",
    "t_stat_beta_1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p-value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate the degrees of freedom\n",
    "degrees_freedom = # TODO (Hint -- Two parameters intercept and slope)\n",
    "\n",
    "# Calculate the p-value for beta_1_hat\n",
    "p_value_beta_1 = 0 # TODO: use formula p = 2×(1−cdf(∣t-statistic∣))\n",
    "# HINT: look into stats.t.cdf() from the scipy lib\n",
    "p_value_beta_1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bM8yekHhSNOD"
   },
   "source": [
    "# RSE, R^2 and F-Statistic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2T4BAxZaXAps"
   },
   "source": [
    "### RSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "0IiynYXuSTrf",
    "outputId": "7b4036e3-0b97-43df-8f29-94daf6b29df8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19472.381418326437"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# RSS using lib\n",
    "np.sum(results.resid**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "zVyj5fW6UIl7",
    "outputId": "d1e6f1b2-7a5d-4382-b546-891a98ebef39"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating RSS manually\n",
    "beta_0_hat = results.params[0]\n",
    "beta_1_hat = results.params[1]\n",
    "x = None # TODO\n",
    "y = None # TODO\n",
    "y_hat = None # TODO\n",
    "RSS = 0 # TODO\n",
    "RSS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "fA1KtfVeWwqY",
    "outputId": "0fe76997-1636-4d6c-e96f-51490d26a9fe"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.215760405398068"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# RSE using lib\n",
    "np.sqrt(results.mse_resid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "0Jog7PgFWEKK",
    "outputId": "cd6d891c-aa57-406f-fbd7-de820e5d413c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating RSE manually\n",
    "n = 0 # TODO\n",
    "RSE = 0 # TODO\n",
    "RSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gY7jG9hqW88C"
   },
   "source": [
    "### R-squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "J3k9JDcrWUhy",
    "outputId": "5d336701-daa7-4d46-a18c-baead7b9aa13"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5441462975864799"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# R-squared using lib\n",
    "results.rsquared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "6Wke4rJLXTXM",
    "outputId": "4bcb3fe6-8c05-4432-e14f-22a5c6091188"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating R squared manually\n",
    "\n",
    "# Calculating TSS\n",
    "y_mean = 0 # TODO\n",
    "TSS = 0 # TODO\n",
    "\n",
    "# Calculating R-squared\n",
    "r_squared = 0 #TODO\n",
    "\n",
    "r_squared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "c-yfznNtUIFm"
   },
   "source": [
    "### F-statistic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "OvUdArtTYpPO",
    "outputId": "963526fc-3ba8-4257-829d-a5d5c5ff6266"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "601.6178711098955"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating it manually\n",
    "results.fvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "GOadTApmYckv"
   },
   "outputs": [],
   "source": [
    "p = 0  # TODO - number of predictors including the intercept\n",
    "n = 0  # TODO - number of observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Hm1deb0TYgT7",
    "outputId": "d2c52527-433c-4c2b-9bee-0195e86f7998"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_value = 0 # TODO\n",
    "f_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# imports\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from the dataset we select multiple columns to use for our x-axis (independent variables)\n",
    "X = dataset[['lstat', 'age']]\n",
    "X = 0 # add a constant term using lib, this constant term is needed for the linear regression model intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: set the dependent variable along the y-axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the coefficients from the fitted model\n",
    "coef = results.params\n",
    "\n",
    "# Generate coordinates for the plane using lstat and age values\n",
    "lstat_vals = 0 # TODO: Use Ordinary Least Squares (OLS) regression from lib to fit a linear regression model, only 100 intervals\n",
    "age_vals = 0 # TODO: Use Ordinary Least Squares (OLS) regression from lib to fit a linear regression model, only 100 intervals\n",
    "lstat_vals, age_vals = np.meshgrid(lstat_vals, age_vals)\n",
    "medv_vals = coef[0] + coef[1] * lstat_vals + coef[2] * age_vals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a 3D plot\n",
    "fig = plt.figure(figsize=(10, 8))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "# Plot the data points\n",
    "ax.scatter(dataset['lstat'], dataset['age'], dataset['medv'], color='blue', label='Data points')\n",
    "\n",
    "# Plot the fitted plane\n",
    "ax.plot_surface(lstat_vals, age_vals, medv_vals, alpha=0.5, cmap='viridis')\n",
    "\n",
    "# Set labels and title\n",
    "ax.set_xlabel('LSTAT')\n",
    "ax.set_ylabel('AGE')\n",
    "ax.set_zlabel('MEDV')\n",
    "ax.set_title('3D Scatter plot with fitted plane')\n",
    "\n",
    "# Show the plot\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "B_f1RtafaBhb"
   },
   "source": [
    "## Polynomial Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wsCyoDa8gKaT"
   },
   "source": [
    "TODO: in the below cell, make your dataframe look like this when you print out the first 4 records\n",
    "\n",
    "![image.png](data:image/png;base64,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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "AyCfeEqLaFsP"
   },
   "outputs": [],
   "source": [
    "# TODO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "nDr6lzA3cDGv"
   },
   "outputs": [],
   "source": [
    "y = dataset['medv']\n",
    "model = sm.OLS(y, X)\n",
    "results = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 112
    },
    "id": "a3Po2LqJcIP8",
    "outputId": "f305e89b-121e-4594-c5f8-a58d790ab4e9"
   },
   "outputs": [
    {
     "data": {
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       "      const buttonEl =\n",
       "        document.querySelector('#df-e2261824-735c-4e4a-9a6e-9ad267684667 button.colab-df-convert');\n",
       "      buttonEl.style.display =\n",
       "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
       "\n",
       "      async function convertToInteractive(key) {\n",
       "        const element = document.querySelector('#df-e2261824-735c-4e4a-9a6e-9ad267684667');\n",
       "        const dataTable =\n",
       "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
       "                                                    [key], {});\n",
       "        if (!dataTable) return;\n",
       "\n",
       "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
       "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
       "          + ' to learn more about interactive tables.';\n",
       "        element.innerHTML = '';\n",
       "        dataTable['output_type'] = 'display_data';\n",
       "        await google.colab.output.renderOutput(dataTable, element);\n",
       "        const docLink = document.createElement('div');\n",
       "        docLink.innerHTML = docLinkHtml;\n",
       "        element.appendChild(docLink);\n",
       "      }\n",
       "    </script>\n",
       "  </div>\n",
       "\n",
       "\n",
       "<div id=\"df-e3058760-e7de-4c09-8e3a-2f8d594ecd0a\">\n",
       "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-e3058760-e7de-4c09-8e3a-2f8d594ecd0a')\"\n",
       "            title=\"Suggest charts\"\n",
       "            style=\"display:none;\">\n",
       "\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
       "     width=\"24px\">\n",
       "    <g>\n",
       "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
       "    </g>\n",
       "</svg>\n",
       "  </button>\n",
       "\n",
       "<style>\n",
       "  .colab-df-quickchart {\n",
       "      --bg-color: #E8F0FE;\n",
       "      --fill-color: #1967D2;\n",
       "      --hover-bg-color: #E2EBFA;\n",
       "      --hover-fill-color: #174EA6;\n",
       "      --disabled-fill-color: #AAA;\n",
       "      --disabled-bg-color: #DDD;\n",
       "  }\n",
       "\n",
       "  [theme=dark] .colab-df-quickchart {\n",
       "      --bg-color: #3B4455;\n",
       "      --fill-color: #D2E3FC;\n",
       "      --hover-bg-color: #434B5C;\n",
       "      --hover-fill-color: #FFFFFF;\n",
       "      --disabled-bg-color: #3B4455;\n",
       "      --disabled-fill-color: #666;\n",
       "  }\n",
       "\n",
       "  .colab-df-quickchart {\n",
       "    background-color: var(--bg-color);\n",
       "    border: none;\n",
       "    border-radius: 50%;\n",
       "    cursor: pointer;\n",
       "    display: none;\n",
       "    fill: var(--fill-color);\n",
       "    height: 32px;\n",
       "    padding: 0;\n",
       "    width: 32px;\n",
       "  }\n",
       "\n",
       "  .colab-df-quickchart:hover {\n",
       "    background-color: var(--hover-bg-color);\n",
       "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
       "    fill: var(--button-hover-fill-color);\n",
       "  }\n",
       "\n",
       "  .colab-df-quickchart-complete:disabled,\n",
       "  .colab-df-quickchart-complete:disabled:hover {\n",
       "    background-color: var(--disabled-bg-color);\n",
       "    fill: var(--disabled-fill-color);\n",
       "    box-shadow: none;\n",
       "  }\n",
       "\n",
       "  .colab-df-spinner {\n",
       "    border: 2px solid var(--fill-color);\n",
       "    border-color: transparent;\n",
       "    border-bottom-color: var(--fill-color);\n",
       "    animation:\n",
       "      spin 1s steps(1) infinite;\n",
       "  }\n",
       "\n",
       "  @keyframes spin {\n",
       "    0% {\n",
       "      border-color: transparent;\n",
       "      border-bottom-color: var(--fill-color);\n",
       "      border-left-color: var(--fill-color);\n",
       "    }\n",
       "    20% {\n",
       "      border-color: transparent;\n",
       "      border-left-color: var(--fill-color);\n",
       "      border-top-color: var(--fill-color);\n",
       "    }\n",
       "    30% {\n",
       "      border-color: transparent;\n",
       "      border-left-color: var(--fill-color);\n",
       "      border-top-color: var(--fill-color);\n",
       "      border-right-color: var(--fill-color);\n",
       "    }\n",
       "    40% {\n",
       "      border-color: transparent;\n",
       "      border-right-color: var(--fill-color);\n",
       "      border-top-color: var(--fill-color);\n",
       "    }\n",
       "    60% {\n",
       "      border-color: transparent;\n",
       "      border-right-color: var(--fill-color);\n",
       "    }\n",
       "    80% {\n",
       "      border-color: transparent;\n",
       "      border-right-color: var(--fill-color);\n",
       "      border-bottom-color: var(--fill-color);\n",
       "    }\n",
       "    90% {\n",
       "      border-color: transparent;\n",
       "      border-bottom-color: var(--fill-color);\n",
       "    }\n",
       "  }\n",
       "</style>\n",
       "\n",
       "  <script>\n",
       "    async function quickchart(key) {\n",
       "      const quickchartButtonEl =\n",
       "        document.querySelector('#' + key + ' button');\n",
       "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
       "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
       "      try {\n",
       "        const charts = await google.colab.kernel.invokeFunction(\n",
       "            'suggestCharts', [key], {});\n",
       "      } catch (error) {\n",
       "        console.error('Error during call to suggestCharts:', error);\n",
       "      }\n",
       "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
       "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
       "    }\n",
       "    (() => {\n",
       "      let quickchartButtonEl =\n",
       "        document.querySelector('#df-e3058760-e7de-4c09-8e3a-2f8d594ecd0a button');\n",
       "      quickchartButtonEl.style.display =\n",
       "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
       "    })();\n",
       "  </script>\n",
       "</div>\n",
       "    </div>\n",
       "  </div>\n"
      ],
      "text/plain": [
       "          coef  std err       t  P>|t|\n",
       "const  34.5538    0.563  61.415    0.0\n",
       "lstat  -0.9500    0.039 -24.528    0.0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summarize(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "kxQyFtg8cQ-C",
    "outputId": "b6a924f1-c4d7-47bd-8a2e-fe6d08491008"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const    34.553841\n",
       "lstat    -0.950049\n",
       "dtype: float64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "id": "nwkPGQsWcSNS",
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "KeyError",
     "evalue": "'lstat_2'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/pandas/core/indexes/base.py:3802\u001b[0m, in \u001b[0;36mIndex.get_loc\u001b[0;34m(self, key, method, tolerance)\u001b[0m\n\u001b[1;32m   3801\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m-> 3802\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_engine\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_loc\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcasted_key\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   3803\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mKeyError\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m err:\n",
      "File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/pandas/_libs/index.pyx:138\u001b[0m, in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
      "File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/pandas/_libs/index.pyx:165\u001b[0m, in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
      "File \u001b[0;32mpandas/_libs/hashtable_class_helper.pxi:5745\u001b[0m, in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n",
      "File \u001b[0;32mpandas/_libs/hashtable_class_helper.pxi:5753\u001b[0m, in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;31mKeyError\u001b[0m: 'lstat_2'",
      "\nThe above exception was the direct cause of the following exception:\n",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[25], line 9\u001b[0m\n\u001b[1;32m      5\u001b[0m lstat_line \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlinspace(dataset[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlstat\u001b[39m\u001b[38;5;124m'\u001b[39m]\u001b[38;5;241m.\u001b[39mmin(), dataset[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlstat\u001b[39m\u001b[38;5;124m'\u001b[39m]\u001b[38;5;241m.\u001b[39mmax(), \u001b[38;5;241m100\u001b[39m)\n\u001b[1;32m      7\u001b[0m \u001b[38;5;66;03m# Calculate the corresponding medv values using the regression results\u001b[39;00m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;66;03m# Include the quadratic term in the prediction\u001b[39;00m\n\u001b[0;32m----> 9\u001b[0m medv_line \u001b[38;5;241m=\u001b[39m results\u001b[38;5;241m.\u001b[39mparams[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mconst\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m+\u001b[39m results\u001b[38;5;241m.\u001b[39mparams[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlstat\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m*\u001b[39m lstat_line \u001b[38;5;241m+\u001b[39m \u001b[43mresults\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mparams\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mlstat_2\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m]\u001b[49m \u001b[38;5;241m*\u001b[39m lstat_line\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m\n\u001b[1;32m     11\u001b[0m \u001b[38;5;66;03m# Plot the quadratic curve\u001b[39;00m\n\u001b[1;32m     12\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(lstat_line, medv_line, color\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mred\u001b[39m\u001b[38;5;124m'\u001b[39m, label\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mQuadratic fit\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
      "File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/pandas/core/series.py:981\u001b[0m, in \u001b[0;36mSeries.__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m    978\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_values[key]\n\u001b[1;32m    980\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m key_is_scalar:\n\u001b[0;32m--> 981\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_get_value\u001b[49m\u001b[43m(\u001b[49m\u001b[43mkey\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    983\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m is_hashable(key):\n\u001b[1;32m    984\u001b[0m     \u001b[38;5;66;03m# Otherwise index.get_value will raise InvalidIndexError\u001b[39;00m\n\u001b[1;32m    985\u001b[0m     \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m    986\u001b[0m         \u001b[38;5;66;03m# For labels that don't resolve as scalars like tuples and frozensets\u001b[39;00m\n",
      "File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/pandas/core/series.py:1089\u001b[0m, in \u001b[0;36mSeries._get_value\u001b[0;34m(self, label, takeable)\u001b[0m\n\u001b[1;32m   1086\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_values[label]\n\u001b[1;32m   1088\u001b[0m \u001b[38;5;66;03m# Similar to Index.get_value, but we do not fall back to positional\u001b[39;00m\n\u001b[0;32m-> 1089\u001b[0m loc \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mindex\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_loc\u001b[49m\u001b[43m(\u001b[49m\u001b[43mlabel\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   1090\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mindex\u001b[38;5;241m.\u001b[39m_get_values_for_loc(\u001b[38;5;28mself\u001b[39m, loc, label)\n",
      "File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/pandas/core/indexes/base.py:3804\u001b[0m, in \u001b[0;36mIndex.get_loc\u001b[0;34m(self, key, method, tolerance)\u001b[0m\n\u001b[1;32m   3802\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_engine\u001b[38;5;241m.\u001b[39mget_loc(casted_key)\n\u001b[1;32m   3803\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mKeyError\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m err:\n\u001b[0;32m-> 3804\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mKeyError\u001b[39;00m(key) \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01merr\u001b[39;00m\n\u001b[1;32m   3805\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m:\n\u001b[1;32m   3806\u001b[0m     \u001b[38;5;66;03m# If we have a listlike key, _check_indexing_error will raise\u001b[39;00m\n\u001b[1;32m   3807\u001b[0m     \u001b[38;5;66;03m#  InvalidIndexError. Otherwise we fall through and re-raise\u001b[39;00m\n\u001b[1;32m   3808\u001b[0m     \u001b[38;5;66;03m#  the TypeError.\u001b[39;00m\n\u001b[1;32m   3809\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_check_indexing_error(key)\n",
      "\u001b[0;31mKeyError\u001b[0m: 'lstat_2'"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot of the data points\n",
    "plt.scatter(dataset['lstat'], dataset['medv'], color='blue', label='Data points')\n",
    "\n",
    "# Generate a range of values for lstat to plot the curve\n",
    "lstat_line = np.linspace(dataset['lstat'].min(), dataset['lstat'].max(), 100)\n",
    "\n",
    "# Calculate the corresponding medv values using the regression results\n",
    "# Include the quadratic term in the prediction\n",
    "medv_line = results.params['const'] + results.params['lstat'] * lstat_line + results.params['lstat_2'] * lstat_line**2\n",
    "\n",
    "# Plot the quadratic curve\n",
    "plt.plot(lstat_line, medv_line, color='red', label='Quadratic fit')\n",
    "\n",
    "# Label the axes and add a title\n",
    "plt.xlabel('LSTAT')\n",
    "plt.ylabel('MEDV')\n",
    "plt.title('Scatter plot with quadratic fit')\n",
    "\n",
    "# Show the legend\n",
    "plt.legend()\n",
    "\n",
    "# Display the plot\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}