exercise1.ipynb

{
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  {
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   "source": [
    "# Exercise 1: Linear Regression\n",
    "\n",
    "In the first part of Exercise 1, we have been provided with a warmUpExercise in which we will be printing a 5*5 identity matrix and in the second part we have been provided with a dataset consisting of two columns. The first column is the population of a city and the second column is the profit of a food truck in that city. Remember, a negative value for profit indicates a loss.\n",
    "\n",
    "we will solve the exercise step by step.  \n",
    "\n",
    "before getting started, lets import all the important packages that we will need later on.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b070ac94",
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing the important Libraries\n",
    "\n",
    "# The OS module in Python provides functions for interacting with the operating system.\n",
    "# Used for manipulating directory path.s\n",
    "import os\n",
    "\n",
    "# Used for computations of numerical data.\n",
    "import numpy as np\n",
    "\n",
    "# Used for reading data and data manipulation\n",
    "import pandas as pd \n",
    "\n",
    "# Used for graphing data.\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# needed to plot 3-D surfaces\n",
    "from mpl_toolkits.mplot3d import Axes3D  \n",
    "\n",
    "# tells matplotlib to embed plots within the notebook\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d48001d",
   "metadata": {},
   "source": [
    "# ==================== Part 1: Basic Function ====================\n",
    "### warmUpExercise.m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "89815d53",
   "metadata": {},
   "outputs": [],
   "source": [
    "def warmUpExercise():  \n",
    "    A = np.eye(5)\n",
    "    return A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "78925c92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0.],\n",
       "       [0., 0., 1., 0., 0.],\n",
       "       [0., 0., 0., 1., 0.],\n",
       "       [0., 0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "warmUpExercise()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b095894",
   "metadata": {},
   "source": [
    "# ======================= Part 2: Plotting =======================\n",
    "\n",
    "### ex1data1.txt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f97e2f5",
   "metadata": {},
   "source": [
    "### * Linear regression with one variable"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0683163",
   "metadata": {},
   "source": [
    "### Reading and Plotting the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6ed96e03",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>6.1101</th>\n",
       "      <th>17.592</th>\n",
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       "  </thead>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.66200</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.85400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.8598</td>\n",
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       "      <th>92</th>\n",
       "      <td>5.3054</td>\n",
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       "      <th>93</th>\n",
       "      <td>8.2934</td>\n",
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       "      <th>95</th>\n",
       "      <td>5.4369</td>\n",
       "      <td>0.61705</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>96 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     6.1101    17.592\n",
       "0    5.5277   9.13020\n",
       "1    8.5186  13.66200\n",
       "2    7.0032  11.85400\n",
       "3    5.8598   6.82330\n",
       "4    8.3829  11.88600\n",
       "..      ...       ...\n",
       "91   5.8707   7.20290\n",
       "92   5.3054   1.98690\n",
       "93   8.2934   0.14454\n",
       "94  13.3940   9.05510\n",
       "95   5.4369   0.61705\n",
       "\n",
       "[96 rows x 2 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
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   ],
   "source": [
    "dataset = pd.read_csv(r'C:\\Users\\nomaniqbal\\Downloads\\notebook\\HomeworkMl\\mlclass-ex1-jin\\ex1data1.txt', sep=\",\")\n",
    "dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5c9c0625",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['6.1101', '17.592'], dtype='object')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "29d46a69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Population(10k)', 'Profit($ 10k)'], dtype='object')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Renaming columns\n",
    "dataset.rename(columns = {'6.1101':'Population(10k)', '17.592':'Profit($ 10k)'}, inplace = True)\n",
    "dataset=pd.DataFrame(np.array([[6.1101, 17.592]]), columns=['Population(10k)','Profit($ 10k)']).append(dataset, ignore_index=True)\n",
    "dataset.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b607b344",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Population(10k)</th>\n",
       "      <th>Profit($ 10k)</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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       "      <td>5.5277</td>\n",
       "      <td>9.13020</td>\n",
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       "      <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",
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       "      <th>4</th>\n",
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       "      <th>93</th>\n",
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       "      <th>96</th>\n",
       "      <td>5.4369</td>\n",
       "      <td>0.61705</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>97 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Population(10k)  Profit($ 10k)\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]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "a5842b55",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X= 97\n",
      "[ 6.1101  5.5277  8.5186  7.0032  5.8598  8.3829  7.4764  8.5781  6.4862\n",
      "  5.0546  5.7107 14.164   5.734   8.4084  5.6407  5.3794  6.3654  5.1301\n",
      "  6.4296  7.0708  6.1891 20.27    5.4901  6.3261  5.5649 18.945  12.828\n",
      " 10.957  13.176  22.203   5.2524  6.5894  9.2482  5.8918  8.2111  7.9334\n",
      "  8.0959  5.6063 12.836   6.3534  5.4069  6.8825 11.708   5.7737  7.8247\n",
      "  7.0931  5.0702  5.8014 11.7     5.5416  7.5402  5.3077  7.4239  7.6031\n",
      "  6.3328  6.3589  6.2742  5.6397  9.3102  9.4536  8.8254  5.1793 21.279\n",
      " 14.908  18.959   7.2182  8.2951 10.236   5.4994 20.341  10.136   7.3345\n",
      "  6.0062  7.2259  5.0269  6.5479  7.5386  5.0365 10.274   5.1077  5.7292\n",
      "  5.1884  6.3557  9.7687  6.5159  8.5172  9.1802  6.002   5.5204  5.0594\n",
      "  5.7077  7.6366  5.8707  5.3054  8.2934 13.394   5.4369]\n",
      "Y= 97\n",
      "[17.592    9.1302  13.662   11.854    6.8233  11.886    4.3483  12.\n",
      "  6.5987   3.8166   3.2522  15.505    3.1551   7.2258   0.71618  3.5129\n",
      "  5.3048   0.56077  3.6518   5.3893   3.1386  21.767    4.263    5.1875\n",
      "  3.0825  22.638   13.501    7.0467  14.692   24.147   -1.22     5.9966\n",
      " 12.134    1.8495   6.5426   4.5623   4.1164   3.3928  10.117    5.4974\n",
      "  0.55657  3.9115   5.3854   2.4406   6.7318   1.0463   5.1337   1.844\n",
      "  8.0043   1.0179   6.7504   1.8396   4.2885   4.9981   1.4233  -1.4211\n",
      "  2.4756   4.6042   3.9624   5.4141   5.1694  -0.74279 17.929   12.054\n",
      " 17.054    4.8852   5.7442   7.7754   1.0173  20.992    6.6799   4.0259\n",
      "  1.2784   3.3411  -2.6807   0.29678  3.8845   5.7014   6.7526   2.0576\n",
      "  0.47953  0.20421  0.67861  7.5435   5.3436   4.2415   6.7981   0.92695\n",
      "  0.152    2.8214   1.8451   4.2959   7.2029   1.9869   0.14454  9.0551\n",
      "  0.61705]\n"
     ]
    }
   ],
   "source": [
    "X = dataset.iloc[:,0].values\n",
    "y = dataset.iloc[:,1].values\n",
    "print(\"X=\", X.size)\n",
    "print(X)\n",
    "m = y.size # no. of training example (labels)\n",
    "print(\"Y=\", m)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce5c5c1d",
   "metadata": {},
   "source": [
    "### Plotting the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "fa948a59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Population of City in 10,000s')"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14,7))\n",
    "\n",
    "# 'ro' option refers to the markers(red circles), 'ms' refers to marker size while 'mec' property refers to the marker edge color.\n",
    "plt.plot(X, y, 'ro', ms=10, mec='b')\n",
    "plt.ylabel('Profit in $10,000')\n",
    "plt.xlabel('Population of City in 10,000s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9872469",
   "metadata": {},
   "source": [
    "# =================== Part 3: Gradient descent ===================\n",
    "### Gradient Descent\n",
    "As we have learned from the course that Gradient descent is an optimization algorithm used to find the values of parameters (coefficients) of a function (f) that minimizes a cost function (cost) and the cost function or Sum of Squeared Errors(SSE) is a measure of how far away our hypothesis is from the optimal hypothesis. \n",
    "\n",
    "In this part, we will fit the linear regression parameters $θ$ to our dataset using gradient descent.\n",
    "\n",
    "The objective of linear regression is to minimize the cost function  \n",
    "\n",
    "$J(\\theta) = \\frac{1}{2m} \\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)}) - y^{(i)}\\right)^2$  \n",
    "\n",
    "where the hypothesis $h_\\theta(x)$ is given by the linear model  \n",
    "$h_\\theta(x) = \\theta^Tx = \\theta_0 + \\theta_1 x_1$  \n",
    "\n",
    "Recall that the parameters of our model are the $\\theta_j$ values. These are the values we will adjust to minimize cost $J(\\theta)$. One way to do this is to use the batch gradient descent algorithm. In batch gradient descent, each iteration performs the update  \n",
    "$\\theta_j = \\theta_j - \\alpha \\frac{1}{m} \\sum_{i=1}^m \\left( h_\\theta(x^{(i)}) - y^{(i)}\\right)x_j^{(i)} \\qquad \\text{simultaneously update } \\theta_j \\text{ for all } j$\n",
    "\n",
    "With each step of gradient descent, our parameters $\\theta_j$ come closer to the optimal values that will achieve the lowest cost J($\\theta$).,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "bdbcccd0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# adding the intercept\n",
    "# X and Y are rank 1 arrays. rank 1 array's shape = (m, ) where as rank 2 array's shape = (m,1). \n",
    "# When operating on arrays its good to convert rank 1 arrays to rank 2 arrays because rank 1 arrays often give unexpected \n",
    "# results. To convert rank 1 to rank 2 array we use someArray[:,np.newaxis].\n",
    "X = X[:, np.newaxis]\n",
    "y = y[:, np.newaxis]\n",
    "\n",
    "#initializing theta value into 0\n",
    "theta = np.zeros([2,1])\n",
    "iterations = 1500\n",
    "alpha = 0.01\n",
    "ones = np.ones((m,1))\n",
    "X = np.hstack((ones, X)) # adding the intercept term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "16c82662",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       [ 1.    ,  5.4369]])"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f57280dd",
   "metadata": {},
   "source": [
    "# Computing the cost $J(\\theta)$\n",
    "\n",
    "Now we will be computing the cost and the gradient descent. First we will compute the cost function and then find optimal parameters using gradient descent.\n",
    "\n",
    "As we perform gradient descent to learn minimize the cost function $J(\\theta)$, it is helpful to monitor the convergence by computing the cost. In this section, we will implement a function to calculate $J(\\theta)$ so we can check the convergence of our gradient descent implementation.\n",
    "\n",
    "our next task is to complete the code for the function computeCost using gradient descent which computes $J(\\theta)$. As we are doing this, remember that the variables  X and y  are not scalar values. X is a matrix whose rows represent the examples from the training set and y is a vector whose each elemennt represent the value at a given row of X."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "a3d74463",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32.072733877455676\n"
     ]
    }
   ],
   "source": [
    "# cost function\n",
    "def computeCost(X, y, theta):\n",
    "    temp = np.dot(X, theta) - y\n",
    "    return np.sum(np.power(temp, 2)) / (2*m)\n",
    "J = computeCost(X, y, theta)\n",
    "print(J)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a6dd36e",
   "metadata": {},
   "source": [
    "# Finding the optimal parameters using Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "9e3d1035",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-3.63029144]\n",
      " [ 1.16636235]]\n"
     ]
    }
   ],
   "source": [
    "def gradientDescent(X, y, theta, alpha, iterations):\n",
    "    for _ in range(iterations):\n",
    "        temp = np.dot(X, theta) - y\n",
    "        temp = np.dot(X.T, temp)\n",
    "        theta = theta - (alpha/m) * temp\n",
    "    return theta\n",
    "theta = gradientDescent(X, y, theta, alpha, iterations)\n",
    "print(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "4ec92c83",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.483388256587726\n"
     ]
    }
   ],
   "source": [
    "# We now have the optimized value of theta, lets Use this value in the above cost function and compare both the values.\n",
    "J = computeCost(X, y, theta)\n",
    "print(J)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7aad7794",
   "metadata": {},
   "source": [
    "We got a value of 4.483 which is much better than 32.07"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bffe682",
   "metadata": {},
   "source": [
    "# Plot showing the best fit line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "61f3ebb6",
   "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": [
    "plt.scatter(X[:,1], y)\n",
    "plt.xlabel('Population of City in 10,000s')\n",
    "plt.ylabel('Profit in $10,000s')\n",
    "plt.plot(X[:,1], np.dot(X, theta))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "ff4e2229",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For population size of 35,000 profit = [4519.7678677]\n",
      "For population size of 70,000 profit = [45342.45012945]\n"
     ]
    }
   ],
   "source": [
    "# Predict values for population sizes of 35,000 and 70,000\n",
    "predict1 = np.dot([1, 3.5], theta)\n",
    "print('For population size of 35,000 profit =', predict1*10000)\n",
    "\n",
    "predict2 = np.dot([1, 7], theta)\n",
    "print('For population size of 70,000 profit =', predict2*10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "654b19a4",
   "metadata": {},
   "source": [
    "# ============= Part 4: Visualizing J(theta_0, theta_1) =============\n",
    "\n",
    "###  Visualizing J(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "cf639efe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.92, 'Surface')"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# grid over which we will calculate J\n",
    "theta0_vals = np.linspace(-10, 10, 100)\n",
    "theta1_vals = np.linspace(-1, 4, 100)\n",
    "\n",
    "# initialize J_vals to a matrix of 0's\n",
    "J_vals = np.zeros((theta0_vals.shape[0], theta1_vals.shape[0]))\n",
    "\n",
    "# Fill out J_vals\n",
    "for i, theta0 in enumerate(theta0_vals):\n",
    "    for j, theta1 in enumerate(theta1_vals):\n",
    "        J_vals[i, j] = computeCost(X, y, [theta0, theta1])\n",
    "        \n",
    "# Because of the way meshgrids work in the surf command, we need to\n",
    "# transpose J_vals before calling surf, or else the axes will be flipped\n",
    "J_vals = J_vals.T\n",
    "\n",
    "# surface plot\n",
    "fig = plt.figure(figsize=(20, 10))\n",
    "ax = fig.add_subplot(121, projection='3d')\n",
    "ax.plot_surface(theta0_vals, theta1_vals, J_vals, cmap='viridis')\n",
    "plt.xlabel('theta0')\n",
    "plt.ylabel('theta1')\n",
    "plt.title('Surface')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "id": "3f477c20",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-157-20addea855a9>:5: UserWarning: No contour levels were found within the data range.\n",
      "  plt.contour(theta0_vals, theta1_vals, J_vals, linewidths=2, cmap='viridis', levels=np.logspace(-2, 3, 20))\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# contour plot\n",
    "# Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100\n",
    "fig = plt.figure(figsize=(20, 10))\n",
    "ax = plt.subplot(122)\n",
    "plt.contour(theta0_vals, theta1_vals, J_vals, linewidths=2, cmap='viridis', levels=np.logspace(-2, 3, 20))\n",
    "plt.xlabel('theta0')\n",
    "plt.ylabel('theta1')\n",
    "plt.plot(theta[0], theta[1], 'ro', ms=10, lw=2)\n",
    "plt.title('Contour, showing minimum')\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0e87462",
   "metadata": {},
   "source": [
    "# * Linear regression with multiple variables\n",
    "\n",
    "### ex1data2.txt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19cb51b0",
   "metadata": {},
   "source": [
    "Now, we will implement linear regression with multiple variables (also called Multivariate Linear Regression).\n",
    "The file ex1data2.txt contains a training set of housing prices in Portland, Oregon. The first column is the size of the house (in square feet), the second column is the number of bedrooms, and the third column is the price of the house."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "id": "ed7ff19c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2104</td>\n",
       "      <td>3</td>\n",
       "      <td>399900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1600</td>\n",
       "      <td>3</td>\n",
       "      <td>329900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2400</td>\n",
       "      <td>3</td>\n",
       "      <td>369000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1416</td>\n",
       "      <td>2</td>\n",
       "      <td>232000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3000</td>\n",
       "      <td>4</td>\n",
       "      <td>539900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0  1       2\n",
       "0  2104  3  399900\n",
       "1  1600  3  329900\n",
       "2  2400  3  369000\n",
       "3  1416  2  232000\n",
       "4  3000  4  539900"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "data = pd.read_csv(r'C:\\Users\\nomaniqbal\\Downloads\\notebook\\HomeworkMl\\mlclass-ex1-jin\\ex1data2.txt', sep = ',', header = None)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "id": "732252f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data.iloc[:,0:2] # read first two columns into X\n",
    "y = data.iloc[:,2] # read the third column into y\n",
    "m = len(y) # no. of training samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "id": "ffddc506",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['size', 'bedrooms', 'price'], dtype='object')"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Renaming columns\n",
    "data.rename(columns = {0:'size', 1:'bedrooms', 2:'price'}, inplace = True)\n",
    "data.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "id": "65ac6a5f",
   "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>size</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2104</td>\n",
       "      <td>3</td>\n",
       "      <td>399900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1600</td>\n",
       "      <td>3</td>\n",
       "      <td>329900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2400</td>\n",
       "      <td>3</td>\n",
       "      <td>369000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1416</td>\n",
       "      <td>2</td>\n",
       "      <td>232000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3000</td>\n",
       "      <td>4</td>\n",
       "      <td>539900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   size  bedrooms   price\n",
       "0  2104         3  399900\n",
       "1  1600         3  329900\n",
       "2  2400         3  369000\n",
       "3  1416         2  232000\n",
       "4  3000         4  539900"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "eadae109",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "47"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "064969bb",
   "metadata": {},
   "source": [
    "# ================ Part 1: Feature Normalization ================\n",
    "### Feature Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "d4eedfad",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Subtract the mean value of each feature from the dataset.\n",
    "# After subtracting the mean, additionally scale (divide) the feature values by their respective “standard deviations.”\n",
    "X = (X - np.mean(X))/np.std(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29610e1e",
   "metadata": {},
   "source": [
    "### Adding the intercept term and initializing parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "5f41d1ee",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-164-f74fcb530f43>:6: FutureWarning: Support for multi-dimensional indexing (e.g. `obj[:, None]`) is deprecated and will be removed in a future version.  Convert to a numpy array before indexing instead.\n",
      "  y = y[:,np.newaxis]\n"
     ]
    }
   ],
   "source": [
    "ones = np.ones((m,1))\n",
    "X = np.hstack((ones, X))\n",
    "alpha = 0.01\n",
    "num_iters = 400\n",
    "theta = np.zeros((3,1))\n",
    "y = y[:,np.newaxis]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6fbdb98",
   "metadata": {},
   "source": [
    "# ================ Part 2: Gradient Descent ================\n",
    "\n",
    "### Computing the cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "00c688dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "65591548106.45744\n"
     ]
    }
   ],
   "source": [
    "def computeCostMulti(X, y, theta):\n",
    "    temp = np.dot(X, theta) - y\n",
    "    return np.sum(np.power(temp, 2)) / (2*m)\n",
    "J = computeCostMulti(X, y, theta)\n",
    "print(J)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b25a993d",
   "metadata": {},
   "source": [
    "### Finding the optimal parameters using Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "68795a9e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[334302.06399328]\n",
      " [ 99411.44947359]\n",
      " [  3267.01285407]]\n"
     ]
    }
   ],
   "source": [
    "def gradientDescentMulti(X, y, theta, alpha, iterations):\n",
    "    m = len(y)\n",
    "    for _ in range(iterations):\n",
    "        temp = np.dot(X, theta) - y\n",
    "        temp = np.dot(X.T, temp)\n",
    "        theta = theta - (alpha/m) * temp\n",
    "    return theta\n",
    "theta = gradientDescentMulti(X, y, theta, alpha, num_iters)\n",
    "print(theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5836b9e1",
   "metadata": {},
   "source": [
    "since we got the optimized value of theta . we will use this value in the above cost function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "4f8ce1f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2105448288.6292474\n"
     ]
    }
   ],
   "source": [
    "J = computeCostMulti(X, y, theta)\n",
    "print(J)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd80b2fb",
   "metadata": {},
   "source": [
    "This this give us the value of 2105448288.6292474 which is much better than 65591548106.45744"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "b1ebde76",
   "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": [
    "# Drawing and plotting model\n",
    "plot = \"bedrooms\"\n",
    "plt.scatter(data[plot], data[\"price\"])\n",
    "plt.xlabel(plot)\n",
    "plt.ylabel(\"Prices\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e134c1c5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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