Gradient+Descent+Practice+Question+Solution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>Sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>16.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "      <td>17.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      TV  Radio  Newspaper  Sales\n",
       "0  230.1   37.8       69.2   22.1\n",
       "1   44.5   39.3       45.1   10.4\n",
       "2   17.2   45.9       69.3   12.0\n",
       "3  151.5   41.3       58.5   16.5\n",
       "4  180.8   10.8       58.4   17.9"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "ad = pd.read_csv('advertising.csv')\n",
    "ad.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>Sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.967425</td>\n",
       "      <td>0.979066</td>\n",
       "      <td>1.774493</td>\n",
       "      <td>1.319009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.194379</td>\n",
       "      <td>1.080097</td>\n",
       "      <td>0.667903</td>\n",
       "      <td>-0.895268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.512360</td>\n",
       "      <td>1.524637</td>\n",
       "      <td>1.779084</td>\n",
       "      <td>-0.592461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.051919</td>\n",
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       "      <td>1.283185</td>\n",
       "      <td>0.259184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.393196</td>\n",
       "      <td>-0.839507</td>\n",
       "      <td>1.278593</td>\n",
       "      <td>0.524140</td>\n",
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      ],
      "text/plain": [
       "         TV     Radio  Newspaper     Sales\n",
       "0  0.967425  0.979066   1.774493  1.319009\n",
       "1 -1.194379  1.080097   0.667903 -0.895268\n",
       "2 -1.512360  1.524637   1.779084 -0.592461\n",
       "3  0.051919  1.214806   1.283185  0.259184\n",
       "4  0.393196 -0.839507   1.278593  0.524140"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ad = (ad - ad.mean())/ad.std()\n",
    "ad.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Putting feature variable to X\n",
    "X = ad[['TV','Radio','Newspaper']]\n",
    "# Putting response variable to y\n",
    "y = ad['Sales']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'DataFrame' object has no attribute 'reindex_axis'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-7-bde00f6af9fc>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'intercept'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mX\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mreindex_axis\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'intercept'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'TV'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'Radio'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'Newspaper'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\pandas\\core\\generic.py\u001b[0m in \u001b[0;36m__getattr__\u001b[1;34m(self, name)\u001b[0m\n\u001b[0;32m   5463\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_info_axis\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_can_hold_identifiers_and_holds_name\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mname\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   5464\u001b[0m                 \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mname\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 5465\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mobject\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__getattribute__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mname\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   5466\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   5467\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m__setattr__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mname\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mstr\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m->\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'DataFrame' object has no attribute 'reindex_axis'"
     ]
    }
   ],
   "source": [
    "X['intercept'] = 1\n",
    "X = X.reindex_axis(['intercept','TV','Radio','Newspaper'], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>intercept</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.967425</td>\n",
       "      <td>0.979066</td>\n",
       "      <td>1.774493</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.194379</td>\n",
       "      <td>1.080097</td>\n",
       "      <td>0.667903</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.512360</td>\n",
       "      <td>1.524637</td>\n",
       "      <td>1.779084</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.051919</td>\n",
       "      <td>1.214806</td>\n",
       "      <td>1.283185</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.393196</td>\n",
       "      <td>-0.839507</td>\n",
       "      <td>1.278593</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         TV     Radio  Newspaper  intercept\n",
       "0  0.967425  0.979066   1.774493          1\n",
       "1 -1.194379  1.080097   0.667903          1\n",
       "2 -1.512360  1.524637   1.779084          1\n",
       "3  0.051919  1.214806   1.283185          1\n",
       "4  0.393196 -0.839507   1.278593          1"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "X = np.array(X)\n",
    "y = np.array(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Theta needed to be changed with the number of response varaible used.\n",
    "theta = np.matrix(np.array([0,0,0,0])) \n",
    "alpha = 0.01\n",
    "iterations = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def compute_cost(X, y, theta):\n",
    "    return np.sum(np.square(np.matmul(X, theta) - y)) / (2 * len(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent_multi(X, y, theta, alpha, iterations):\n",
    "    theta = np.zeros(X.shape[1])\n",
    "    m = len(X)\n",
    "    gdm_df = pd.DataFrame( columns = ['Bets','cost'])\n",
    "\n",
    "    for i in range(iterations):\n",
    "        gradient = (1/m) * np.matmul(X.T, np.matmul(X, theta) - y)\n",
    "        theta = theta - alpha * gradient\n",
    "        cost = compute_cost(X, y, theta)\n",
    "        gdm_df.loc[i] = [theta,cost]\n",
    "\n",
    "    return gdm_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "        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>Bets</th>\n",
       "      <th>cost</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>[0.008967018737358192, 0.0034788294152263105, ...</td>\n",
       "      <td>0.488054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>[0.0178420325875863, 0.0069126167187037926, 0....</td>\n",
       "      <td>0.478812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>[0.026626000134855474, 0.010301976346834421, 0...</td>\n",
       "      <td>0.469770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>[0.03531986978687297, 0.013647514202632952, 0....</td>\n",
       "      <td>0.460923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>[0.043924579885335935, 0.016949827774590004, 0...</td>\n",
       "      <td>0.452267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>[0.884604822565373, 0.3004142619643607, 0.0016...</td>\n",
       "      <td>0.048461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>[0.8846052708861454, 0.3004157861185134, 0.001...</td>\n",
       "      <td>0.048461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>[0.884605714844278, 0.30041730067213385, 0.001...</td>\n",
       "      <td>0.048461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>[0.8846061544823369, 0.3004188056851351, 0.001...</td>\n",
       "      <td>0.048461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>[0.8846065898424722, 0.30042030121706104, 0.00...</td>\n",
       "      <td>0.048461</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                  Bets      cost\n",
       "0    [0.008967018737358192, 0.0034788294152263105, ...  0.488054\n",
       "1    [0.0178420325875863, 0.0069126167187037926, 0....  0.478812\n",
       "2    [0.026626000134855474, 0.010301976346834421, 0...  0.469770\n",
       "3    [0.03531986978687297, 0.013647514202632952, 0....  0.460923\n",
       "4    [0.043924579885335935, 0.016949827774590004, 0...  0.452267\n",
       "..                                                 ...       ...\n",
       "995  [0.884604822565373, 0.3004142619643607, 0.0016...  0.048461\n",
       "996  [0.8846052708861454, 0.3004157861185134, 0.001...  0.048461\n",
       "997  [0.884605714844278, 0.30041730067213385, 0.001...  0.048461\n",
       "998  [0.8846061544823369, 0.3004188056851351, 0.001...  0.048461\n",
       "999  [0.8846065898424722, 0.30042030121706104, 0.00...  0.048461\n",
       "\n",
       "[1000 rows x 2 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient_descent_multi(X, y, theta, alpha, iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([ 8.84606590e-01,  3.00420301e-01,  1.63040417e-03, -5.55372415e-16])\n",
      " 0.04846087144244533]\n"
     ]
    }
   ],
   "source": [
    "print(gradient_descent_multi(X, y, theta, alpha, iterations).values[999])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='index'>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "gradient_descent_multi(X, y, theta, alpha, iterations).reset_index().plot.line(x='index', y=['cost'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# import LinearRegression from sklearn\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# Representing LinearRegression as lr(Creating LinearRegression Object)\n",
    "lr = LinearRegression()\n",
    "\n",
    "#You don't need to specify an object to save the result because 'lr' will take the results of the fitted model.\n",
    "lr.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-5.585064192018886e-16\n",
      "[0.88465106 0.30065466 0.00138348 0.        ]\n"
     ]
    }
   ],
   "source": [
    "print(lr.intercept_)\n",
    "print(lr.coef_)"
   ]
  }
 ],
 "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}