LogisticRegressionWithHeartDataset.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Age</th>\n",
       "      <th>Sex</th>\n",
       "      <th>ChestPain</th>\n",
       "      <th>RestBP</th>\n",
       "      <th>Chol</th>\n",
       "      <th>Fbs</th>\n",
       "      <th>RestECG</th>\n",
       "      <th>MaxHR</th>\n",
       "      <th>ExAng</th>\n",
       "      <th>Oldpeak</th>\n",
       "      <th>Slope</th>\n",
       "      <th>Ca</th>\n",
       "      <th>Thal</th>\n",
       "      <th>AHD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>63</td>\n",
       "      <td>1</td>\n",
       "      <td>typical</td>\n",
       "      <td>145</td>\n",
       "      <td>233</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>150</td>\n",
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       "      <td>2.3</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>fixed</td>\n",
       "      <td>No</td>\n",
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       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>67</td>\n",
       "      <td>1</td>\n",
       "      <td>asymptomatic</td>\n",
       "      <td>160</td>\n",
       "      <td>286</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
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       "      <td>1.5</td>\n",
       "      <td>2</td>\n",
       "      <td>3.0</td>\n",
       "      <td>normal</td>\n",
       "      <td>Yes</td>\n",
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       "      <th>2</th>\n",
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       "      <td>67</td>\n",
       "      <td>1</td>\n",
       "      <td>asymptomatic</td>\n",
       "      <td>120</td>\n",
       "      <td>229</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>129</td>\n",
       "      <td>1</td>\n",
       "      <td>2.6</td>\n",
       "      <td>2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>reversable</td>\n",
       "      <td>Yes</td>\n",
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       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>37</td>\n",
       "      <td>1</td>\n",
       "      <td>nonanginal</td>\n",
       "      <td>130</td>\n",
       "      <td>250</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>187</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>normal</td>\n",
       "      <td>No</td>\n",
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       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "      <td>nontypical</td>\n",
       "      <td>130</td>\n",
       "      <td>204</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>172</td>\n",
       "      <td>0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>normal</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  Age  Sex     ChestPain  RestBP  Chol  Fbs  RestECG  MaxHR  \\\n",
       "0           1   63    1       typical     145   233    1        2    150   \n",
       "1           2   67    1  asymptomatic     160   286    0        2    108   \n",
       "2           3   67    1  asymptomatic     120   229    0        2    129   \n",
       "3           4   37    1    nonanginal     130   250    0        0    187   \n",
       "4           5   41    0    nontypical     130   204    0        2    172   \n",
       "\n",
       "   ExAng  Oldpeak  Slope   Ca        Thal  AHD  \n",
       "0      0      2.3      3  0.0       fixed   No  \n",
       "1      1      1.5      2  3.0      normal  Yes  \n",
       "2      1      2.6      2  2.0  reversable  Yes  \n",
       "3      0      3.5      3  0.0      normal   No  \n",
       "4      0      1.4      1  0.0      normal   No  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('Heart.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['typical', 'asymptomatic', 'nonanginal', 'nontypical'],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['ChestPain'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['fixed', 'normal', 'reversable', nan], dtype=object)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Thal'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"ChestPainx\"]= df.ChestPain.replace({\"typical\": 1, \"asymptomatic\": 2, \"nonanginal\": 3, \"nontypical\": 4})\n",
    "df[\"Thalx\"] = df.Thal.replace({\"fixed\": 1, \"normal\":2, \"reversable\":3})\n",
    "df[\"AHD\"] = df.AHD.replace({\"Yes\": 1, \"No\":0})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>3.0</td>\n",
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       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
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       "      <td>2.6</td>\n",
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       "      <td>nonanginal</td>\n",
       "      <td>130</td>\n",
       "      <td>250</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>187</td>\n",
       "      <td>0</td>\n",
       "      <td>3.5</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>normal</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
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       "      <td>1</td>\n",
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       "      <td>0</td>\n",
       "      <td>nontypical</td>\n",
       "      <td>130</td>\n",
       "      <td>204</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>172</td>\n",
       "      <td>0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>normal</td>\n",
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       "      <td>2</td>\n",
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      ],
      "text/plain": [
       "   00  Unnamed: 0  Age  Sex     ChestPain  RestBP  Chol  Fbs  RestECG  MaxHR  \\\n",
       "0   1           1   63    1       typical     145   233    1        2    150   \n",
       "1   1           2   67    1  asymptomatic     160   286    0        2    108   \n",
       "2   1           3   67    1  asymptomatic     120   229    0        2    129   \n",
       "3   1           4   37    1    nonanginal     130   250    0        0    187   \n",
       "4   1           5   41    0    nontypical     130   204    0        2    172   \n",
       "\n",
       "   ExAng  Oldpeak  Slope   Ca        Thal  AHD  ChestPainx  Thalx  \n",
       "0      0      2.3      3  0.0       fixed    0           1      1  \n",
       "1      1      1.5      2  3.0      normal    1           2      2  \n",
       "2      1      2.6      2  2.0  reversable    1           2      3  \n",
       "3      0      3.5      3  0.0      normal    0           3      2  \n",
       "4      0      1.4      1  0.0      normal    0           4      2  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.concat([pd.Series(1, index = df.index, name = '00'), df], axis=1)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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       "      <th>Age</th>\n",
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       "      <td>2.6</td>\n",
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       "      <td>130</td>\n",
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       "      <td>187</td>\n",
       "      <td>0</td>\n",
       "      <td>3.5</td>\n",
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       "      <td>3</td>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "      <td>130</td>\n",
       "      <td>204</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>172</td>\n",
       "      <td>0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
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       "      <td>2</td>\n",
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      ],
      "text/plain": [
       "   00  Age  Sex  RestBP  Chol  Fbs  RestECG  MaxHR  ExAng  Oldpeak  Slope  \\\n",
       "0   1   63    1     145   233    1        2    150      0      2.3      3   \n",
       "1   1   67    1     160   286    0        2    108      1      1.5      2   \n",
       "2   1   67    1     120   229    0        2    129      1      2.6      2   \n",
       "3   1   37    1     130   250    0        0    187      0      3.5      3   \n",
       "4   1   41    0     130   204    0        2    172      0      1.4      1   \n",
       "\n",
       "    Ca  AHD  ChestPainx  Thalx  \n",
       "0  0.0    0           1      1  \n",
       "1  3.0    1           2      2  \n",
       "2  2.0    1           2      3  \n",
       "3  0.0    0           3      2  \n",
       "4  0.0    0           4      2  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = df.drop(columns=[\"Unnamed: 0\", \"ChestPain\", \"Thal\"])\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "y= df[\"AHD\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = [0.5]*len(X.columns)\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hypothesis(X, theta):\n",
    "    z = np.dot(theta, X.T)\n",
    "    return 1/(1+np.exp(-(z))) - 0.0000001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(X, y, theta):\n",
    "    y1 = hypothesis(X, theta)\n",
    "    return -(1/len(X)) * np.sum(y*np.log(y1) + (1-y)*np.log(1-y1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(X, y, theta, alpha, epochs):\n",
    "    m =len(X)\n",
    "    J = [cost(X, y, theta)] \n",
    "    for i in range(0, epochs):\n",
    "        h = hypothesis(X, theta)\n",
    "        for i in range(0, len(X.columns)):\n",
    "            theta[i] -= (alpha/m) * np.sum((h-y)*X.iloc[:, i])\n",
    "        J.append(cost(X, y, theta))\n",
    "    return J, theta    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\User\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "L, theta = gradient_descent(X, y, theta, 0.03, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(X, y, theta, alpha, epochs):\n",
    "    J, th = gradient_descent(X, y, theta, alpha, epochs) \n",
    "    h = hypothesis(X, theta)\n",
    "    for i in range(len(h)):\n",
    "        h[i]=1 if h[i]>=0.5 else 0\n",
    "    y = list(y)\n",
    "    acc = np.sum([y[i] == h[i] for i in range(len(y))])/len(y)\n",
    "    return J, acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\User\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: overflow encountered in exp\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "C:\\Users\\User\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([8.683149218644948, -0.0, 8.683149218644948, -0.0], 0.5387205387205387)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(X, y, theta, 0.03, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\User\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "C:\\Users\\User\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: overflow encountered in exp\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "theta = [0.5]*len(X.columns)\n",
    "J, acc = predict(X, y, theta, 0.01, 20000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6262626262626263"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize = (12, 8))\n",
    "plt.scatter(range(0, len(J)), J)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\User\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "theta = [0.5]*len(X.columns)\n",
    "J, acc = predict(X, y, theta, 0.0005, 5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6127946127946128"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize = (12, 8))\n",
    "plt.scatter(range(0, len(J)), J)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\User\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "theta = [0.5]*len(X.columns)\n",
    "J, acc = predict(X, y, theta, 0.0001, 15000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8316498316498316"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize = (12, 8))\n",
    "plt.scatter(range(0, len(J)), J)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\User\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "theta = [0.5]*len(X.columns)\n",
    "J, acc = predict(X, y, theta, 0.0001, 20000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8417508417508418"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\User\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "theta = [0.5]*len(X.columns)\n",
    "J, acc = predict(X, y, theta, 0.0001, 25000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize = (12, 8))\n",
    "plt.scatter(range(0, len(J)), J)\n",
    "plt.xlabel(\"Epochs\")\n",
    "plt.ylabel(\"Cost\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8484848484848485"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize = (12, 8))\n",
    "plt.scatter(range(0, len(J)), J)\n",
    "plt.xlabel(\"Epochs\")\n",
    "plt.ylabel(\"Cost\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\User\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "theta = [0.5]*len(X.columns)\n",
    "J, acc = predict(X, y, theta, 0.0001, 5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8181818181818182"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize = (12, 8))\n",
    "plt.scatter(range(0, len(J)), J)\n",
    "plt.show()"
   ]
  },
  {
   "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}