linear_regression_ML.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "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>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": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"headbrain.csv\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data[\"Head Size(cm^3)\"].values\n",
    "Y = data[\"Brain Weight(grams)\"].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean_X = np.mean(X)\n",
    "mean_Y = np.mean(Y)\n",
    "m = len(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.26342933948939945 325.57342104944223\n"
     ]
    }
   ],
   "source": [
    "numer = 0\n",
    "denom = 0\n",
    "for i in range(m):\n",
    "    numer += (X[i] - mean_X) * (Y[i] - mean_Y)\n",
    "    denom += (X[i] - mean_X) **2\n",
    "    d1 = numer/denom\n",
    "    d0 = mean_Y - (d1 * mean_X)\n",
    "print(d1, d0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "#ploting graph\n",
    "max_X = np.max(X) + 100\n",
    "min_X = np.min(X) - 100\n",
    "\n",
    "x = np.linspace(min_X, max_X, 1000)\n",
    "y = d0 + d1 * x\n",
    "\n",
    "plt.scatter(X, Y, color = \"orange\", label = \"Scatter Line\")\n",
    "plt.plot(x, y, color = \"black\", label = \"Regression Line\")\n",
    "\n",
    "plt.xlabel(\"Head Size\")\n",
    "plt.ylabel(\"Brain Size\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6315648136958643\n"
     ]
    }
   ],
   "source": [
    "#To check how good is our model by using R^2 method\n",
    "ss_t = 0\n",
    "ss_r = 0\n",
    "for i in range(m):\n",
    "    y_pred = d0 + d1 * X[i]\n",
    "    ss_t = (Y[i] - mean_Y) ** 2\n",
    "    ss_r = (Y[i] - y_pred) ** 2\n",
    "r2 = 1 - (ss_r/ss_t)\n",
    "print(r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.639311719957\n"
     ]
    }
   ],
   "source": [
    "#from inbuilt lib scikit-learn\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    "X = X.reshape((m, 1))\n",
    "reg = LinearRegression()\n",
    "reg = reg.fit(X, Y)\n",
    "Y_pred = reg.predict(X)\n",
    "r2_score = reg.score(X, Y)\n",
    "print(r2_score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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