Linear_Regression_in_Python_using_Statsmodels_GeeksForGeeks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "74fd5938-f7aa-4a18-9f81-cd37e1c85be8",
   "metadata": {},
   "source": [
    "# Linear Regression in Python using Statsmodels\n",
    "https://www.geeksforgeeks.org/linear-regression-in-python-using-statsmodels/"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d88c404-2a17-4130-baf2-ec9d63120ece",
   "metadata": {},
   "source": [
    "## Import packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d90342a5-c66f-4003-b6a8-9f8fb3ab9ff9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.formula.api as smf\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8509c6a4-fc22-4aeb-8704-0ce016f192d5",
   "metadata": {},
   "source": [
    "## Loading data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "3aa4f865-cbc4-496c-b750-f566fa6f4b33",
   "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>Gender</th>\n",
       "      <th>Age Range</th>\n",
       "      <th>Head Size(cm^3)</th>\n",
       "      <th>Brain Weight(grams)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4512</td>\n",
       "      <td>1530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3738</td>\n",
       "      <td>1297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4261</td>\n",
       "      <td>1335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3777</td>\n",
       "      <td>1282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4177</td>\n",
       "      <td>1590</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Gender  Age Range  Head Size(cm^3)  Brain Weight(grams)\n",
       "0       1          1             4512                 1530\n",
       "1       1          1             3738                 1297\n",
       "2       1          1             4261                 1335\n",
       "3       1          1             3777                 1282\n",
       "4       1          1             4177                 1590"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('./Data/headbrain.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28c86c5a-dda1-4391-8aa7-2cf34b866bf8",
   "metadata": {},
   "source": [
    "### Visualizing the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "7c4f30ec-7e44-430f-b4a1-9c8ff9f4ab6a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\x-20a\\anaconda3\\lib\\site-packages\\seaborn\\_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot('Head Size(cm^3)', 'Brain Weight(grams)', data=df)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af9d9485-3332-4d05-9f35-6205e4c03daf",
   "metadata": {},
   "source": [
    "## Setting a hypothesis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5dbdd27-d651-4e33-afd8-2ce365c2baa3",
   "metadata": {},
   "source": [
    "**Null hypothesis (H0):** There is no relationship between head size and brain weight.\\\n",
    "**Alternative hypothesis (Ha):** There is a relationship between head size and brain weight."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7e7534f-20b6-43da-b338-c05d7c106391",
   "metadata": {},
   "source": [
    "## Fitting the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "25dd4620-63ee-4a86-8198-009bd1adca70",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.rename(columns={'Head Size(cm^3)': 'Head_size',\n",
    "        'Brain Weight(grams)': 'Brain_weight'}, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "3f7e488d-4e06-4be8-a8ee-b66a90e2ce6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = smf.ols(formula='Head_size ~ Brain_weight', data=df).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2c7529b1-676e-4b5f-9727-d4e4d0e0e568",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              Head_size   R-squared:                       0.639\n",
      "Model:                            OLS   Adj. R-squared:                  0.638\n",
      "Method:                 Least Squares   F-statistic:                     416.5\n",
      "Date:                Sat, 08 Jul 2023   Prob (F-statistic):           5.96e-54\n",
      "Time:                        15:16:09   Log-Likelihood:                -1613.4\n",
      "No. Observations:                 237   AIC:                             3231.\n",
      "Df Residuals:                     235   BIC:                             3238.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "================================================================================\n",
      "                   coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------\n",
      "Intercept      520.6101    153.215      3.398      0.001     218.759     822.461\n",
      "Brain_weight     2.4269      0.119     20.409      0.000       2.193       2.661\n",
      "==============================================================================\n",
      "Omnibus:                        2.687   Durbin-Watson:                   1.726\n",
      "Prob(Omnibus):                  0.261   Jarque-Bera (JB):                2.321\n",
      "Skew:                           0.207   Prob(JB):                        0.313\n",
      "Kurtosis:                       3.252   Cond. No.                     1.38e+04\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.38e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7ecf0a6-ea8c-4f08-b7a8-2650e20ed5a4",
   "metadata": {},
   "source": [
    "## Description of some of the terms in the table:\n",
    "**R- squared value:** R-squared value ranges between 0 and 1. An R-squared of 100 percent indicates that all changes in the dependent variable are completely explained by changes in the independent variable(s). if we get 1 as an r-squared value it means there’s a perfect fit. In our example, the r-squared value is 0.638.\n",
    "\\\n",
    "**F- statistic:** The F statistic simply compares the combined effect of all variables. In simplest terms, reject the null hypothesis if your alpha level is greater than your p-value.\n",
    "\\\n",
    "**coef:** the coefficients of the independent variables in the regression equation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a623d4c5-d0d4-4f88-9c5c-cbf674354f81",
   "metadata": {},
   "source": [
    "## Our predictions:\n",
    "If we take our significance level (alpha) to be 0.05, we reject the null hypothesis and accept the alternative hypothesis as p<0.05. so, we can say that there is a relationship between head size and brain weight."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1bbd257e-2c42-45c7-90da-7eeabeb51cc0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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