Linear Regression 101.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "from builtins import range\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "data=pd.read_csv('data_1d.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        vertical-align: middle;\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>95.724162</td>\n",
       "      <td>197.179636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>35.757619</td>\n",
       "      <td>67.590670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>28.816847</td>\n",
       "      <td>60.854133</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>99.958481</td>\n",
       "      <td>196.907397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>66.809748</td>\n",
       "      <td>125.311128</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           x           Y\n",
       "0  95.724162  197.179636\n",
       "1  35.757619   67.590670\n",
       "2  28.816847   60.854133\n",
       "3  99.958481  196.907397\n",
       "4  66.809748  125.311128"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.array(data.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y=np.array(data.Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, Y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "deno = x.dot(x) - x.mean() * x.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = (x.dot(Y) - Y.mean()*x.sum())/deno"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = (Y.mean() * x.dot(x) - x.mean() * x.dot(Y))/deno"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_hat = a*x + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, Y)\n",
    "plt.plot(x, Y_hat)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1=Y-Y_hat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "d2=Y-Y.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "r2=1-d1.dot(d1) / d2.dot(d2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9911838202948865\n"
     ]
    }
   ],
   "source": [
    "print(r2)"
   ]
  },
  {
   "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}