LinearRegression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Taking in data\n",
    "column_label = ['X','Y']\n",
    "data = pd.read_csv('ex1data1.txt',names = column_label)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <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>6.1101</td>\n",
       "      <td>17.59200</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.13020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.66200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.85400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.82330</td>\n",
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       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>5.8707</td>\n",
       "      <td>7.20290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>5.3054</td>\n",
       "      <td>1.98690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>8.2934</td>\n",
       "      <td>0.14454</td>\n",
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       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>13.3940</td>\n",
       "      <td>9.05510</td>\n",
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       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>5.4369</td>\n",
       "      <td>0.61705</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "<p>97 rows × 2 columns</p>\n",
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      "text/plain": [
       "          X         Y\n",
       "0    6.1101  17.59200\n",
       "1    5.5277   9.13020\n",
       "2    8.5186  13.66200\n",
       "3    7.0032  11.85400\n",
       "4    5.8598   6.82330\n",
       "..      ...       ...\n",
       "92   5.8707   7.20290\n",
       "93   5.3054   1.98690\n",
       "94   8.2934   0.14454\n",
       "95  13.3940   9.05510\n",
       "96   5.4369   0.61705\n",
       "\n",
       "[97 rows x 2 columns]"
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     "execution_count": 30,
     "metadata": {},
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   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      6.1101\n",
       "1      5.5277\n",
       "2      8.5186\n",
       "3      7.0032\n",
       "4      5.8598\n",
       "       ...   \n",
       "92     5.8707\n",
       "93     5.3054\n",
       "94     8.2934\n",
       "95    13.3940\n",
       "96     5.4369\n",
       "Name: X, Length: 97, dtype: float64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = data['X']\n",
    "y = data['Y']\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = np.ones(len(x))\n",
    "x0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "new = pd.DataFrame([x0,x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>6.1101</td>\n",
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       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
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       "      <td>1.0</td>\n",
       "      <td>8.5186</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>7.0032</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>5.8598</td>\n",
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       "      <th>...</th>\n",
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       "      <th>92</th>\n",
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       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>1.0</td>\n",
       "      <td>5.3054</td>\n",
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       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>1.0</td>\n",
       "      <td>8.2934</td>\n",
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       "      <th>95</th>\n",
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       "      <th>96</th>\n",
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       "      <td>5.4369</td>\n",
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       "<p>97 rows × 2 columns</p>\n",
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      "text/plain": [
       "      0        1\n",
       "0   1.0   6.1101\n",
       "1   1.0   5.5277\n",
       "2   1.0   8.5186\n",
       "3   1.0   7.0032\n",
       "4   1.0   5.8598\n",
       "..  ...      ...\n",
       "92  1.0   5.8707\n",
       "93  1.0   5.3054\n",
       "94  1.0   8.2934\n",
       "95  1.0  13.3940\n",
       "96  1.0   5.4369\n",
       "\n",
       "[97 rows x 2 columns]"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new = new.T\n",
    "m = len(new)\n",
    "new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.0\n",
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     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Initializing theta and assigning a learning rate (alpha)\n",
    "theta = np.zeros(len(new.columns))\n",
    "theta = pd.Series(theta)\n",
    "alpha = 0.01\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "#The cost function is a representation of the error\n",
    "def cost_func(X,y,theta):\n",
    "    return (1/len(X))*sum((X.dot(theta) - y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Gradient is the derivative of the cost function and allows us to reach a global minimum\n",
    "def gradient(X,y,theta):\n",
    "    return X.T.dot((X.dot(theta) - y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "How many iterations do you want the program to do?: 1500\n"
     ]
    }
   ],
   "source": [
    "iterations = int(input(\"How many iterations do you want the program to do?: \"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
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   "outputs": [
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     "name": "stdout",
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      "dtype: float64\n",
      "0   -3.627886\n",
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      "dtype: float64\n",
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      "dtype: float64\n",
      "0   -3.628851\n",
      "1    1.166218\n",
      "dtype: float64\n",
      "0   -3.629332\n",
      "1    1.166266\n",
      "dtype: float64\n",
      "0   -3.629812\n",
      "1    1.166314\n",
      "dtype: float64\n",
      "0   -3.630291\n",
      "1    1.166362\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "#More iterations = Better the accuracy\n",
    "for i in range(1500):\n",
    "    theta = theta - alpha * (1/m) * gradient(new,y,theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-5.83913505154639\n",
      "0.04785701531752992\n"
     ]
    }
   ],
   "source": [
    "#TESTING using the initial theta.\n",
    "temp = np.zeros(len(new.columns))\n",
    "print(cost_func(new,y,temp))\n",
    "print(cost_func(new,y,theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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