LinearRegression.ipynb

{
 "cells":[
  {
   "cell_type":"code",
   "source":[
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from utils import *\n",
    "import copy\n",
    "import math\n",
    "%matplotlib inline"
   ],
   "execution_count":5,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"q6cIw2YNcaQJItog86PdN9"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "def load():\n",
    "    x = np.array([ 6.1101,  5.5277,  8.5186,  7.0032,  5.8598,  8.3829,  7.4764,\n",
    "         8.5781,  6.4862,  5.0546,  5.7107, 14.164 ,  5.734 ,  8.4084,\n",
    "         5.6407,  5.3794,  6.3654,  5.1301,  6.4296,  7.0708,  6.1891,\n",
    "        20.27  ,  5.4901,  6.3261,  5.5649, 18.945 , 12.828 , 10.957 ,\n",
    "        13.176 , 22.203 ,  5.2524,  6.5894,  9.2482,  5.8918,  8.2111,\n",
    "         7.9334,  8.0959,  5.6063, 12.836 ,  6.3534,  5.4069,  6.8825,\n",
    "        11.708 ,  5.7737,  7.8247,  7.0931,  5.0702,  5.8014, 11.7   ,\n",
    "         5.5416,  7.5402,  5.3077,  7.4239,  7.6031,  6.3328,  6.3589,\n",
    "         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 ,\n",
    "        10.136 ,  7.3345,  6.0062,  7.2259,  5.0269,  6.5479,  7.5386,\n",
    "         5.0365, 10.274 ,  5.1077,  5.7292,  5.1884,  6.3557,  9.7687,\n",
    "         6.5159,  8.5172,  9.1802,  6.002 ,  5.5204,  5.0594,  5.7077,\n",
    "         7.6366,  5.8707,  5.3054,  8.2934, 13.394 ,  5.4369])\n",
    "    y = np.array([17.592  ,  9.1302 , 13.662  , 11.854  ,  6.8233 , 11.886  ,\n",
    "         4.3483 , 12.     ,  6.5987 ,  3.8166 ,  3.2522 , 15.505  ,\n",
    "         3.1551 ,  7.2258 ,  0.71618,  3.5129 ,  5.3048 ,  0.56077,\n",
    "         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  ,\n",
    "        -1.22   ,  5.9966 , 12.134  ,  1.8495 ,  6.5426 ,  4.5623 ,\n",
    "         4.1164 ,  3.3928 , 10.117  ,  5.4974 ,  0.55657,  3.9115 ,\n",
    "         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 ,\n",
    "         1.4233 , -1.4211 ,  2.4756 ,  4.6042 ,  3.9624 ,  5.4141 ,\n",
    "         5.1694 , -0.74279, 17.929  , 12.054  , 17.054  ,  4.8852 ,\n",
    "         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 ,\n",
    "         6.7526 ,  2.0576 ,  0.47953,  0.20421,  0.67861,  7.5435 ,\n",
    "         5.3436 ,  4.2415 ,  6.7981 ,  0.92695,  0.152  ,  2.8214 ,\n",
    "         1.8451 ,  4.2959 ,  7.2029 ,  1.9869 ,  0.14454,  9.0551 ,\n",
    "         0.61705])\n",
    "    return x, y"
   ],
   "execution_count":7,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"yqhBCl6CL87mz3JECV6SN7"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "x_train, y_train = load()"
   ],
   "execution_count":8,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"B4waC8ZsFDL76UVbvz8XBD"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "x_train[:5]"
   ],
   "execution_count":11,
   "outputs":[
    {
     "data":{
      "text\/html":[
       
      ]
     },
     "metadata":{
      
     },
     "output_type":"display_data"
    }
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"Nw3omUhl4qWgYvXKix6bQL"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "type(x_train)"
   ],
   "execution_count":12,
   "outputs":[
    {
     "data":{
      "text\/plain":[
       "numpy.ndarray"
      ]
     },
     "metadata":{
      
     },
     "output_type":"display_data"
    }
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"YKnzGkKKvgeMuRZy653YfR"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "plt.scatter(x_train, y_train, marker='*', c='r')\n",
    "\n",
    "# Set the title\n",
    "plt.title(\"Profits vs. Population per city\")\n",
    "# Set the y-axis label\n",
    "plt.ylabel('Profit in $10,000')\n",
    "# Set the x-axis label\n",
    "plt.xlabel('Population of City in 10,000s')\n",
    "plt.show()"
   ],
   "execution_count":16,
   "outputs":[
    {
     "data":{
      "image\/png":[
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\n"
      ]
     },
     "metadata":{
      "image\/png":{
       
      }
     },
     "output_type":"display_data"
    }
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"UhH9XJalbL1H85RsIsHkhS"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "def compute_cost(x, y, w, b):\n",
    "    \"\"\"\n",
    "    Compute cost\n",
    "    return total_cost\n",
    "    \"\"\"\n",
    "    m = x.shape[0]\n",
    "    cost = 0\n",
    "    for i in range(m):\n",
    "        f_wb = w * x[i] + b\n",
    "        cost += (f_wb - y[i]) ** 2\n",
    "    total_cost = (1 \/ (2 * m)) * cost\n",
    "    \n",
    "    return total_cost"
   ],
   "execution_count":21,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"v8K98AGixYJnDG3tZP0gzM"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "initial_w = 2\n",
    "initial_b = 1\n",
    "\n",
    "fcost = compute_cost(x_train, y_train, initial_w, initial_b)\n",
    "print(f'Cost for initial w : {fcost: .3f}')"
   ],
   "execution_count":25,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "Cost for initial w :  75.203\n"
     ],
     "output_type":"stream"
    }
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"S8vqM9t4tWSJoYMq8HX7hi"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "def compute_gradient(x, y, w, b):\n",
    "    \"\"\"\n",
    "    return dj_dw, dj_db\n",
    "    \"\"\"\n",
    "    m = x.shape[0]\n",
    "\n",
    "    dj_dw = 0\n",
    "    dj_db = 0\n",
    "    for i in range(m):\n",
    "        f_wb = x[i] * w + b\n",
    "        dj_dw += (f_wb - y[i]) * x[i]\n",
    "        dj_db += f_wb -y[i]\n",
    "    \n",
    "    return dj_dw \/ m, dj_db \/ m"
   ],
   "execution_count":28,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"nyDzTp1nOZk3AfRspiDF8a"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "initial_w = 0\n",
    "initial_b = 0\n",
    "\n",
    "tmp_dj_dw, tmp_dj_db = compute_gradient(x_train, y_train, initial_w, initial_b)\n",
    "print('Gradients at initial Zeros (w, b): ', tmp_dj_dw, tmp_dj_db)"
   ],
   "execution_count":29,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "Gradients at initial Zeros (w, b):  -65.32884974555672 -5.83913505154639\n"
     ],
     "output_type":"stream"
    }
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"EoWGEwmINpVw5TbfenzkWp"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "test_w = 0.2\n",
    "test_b = 0.2\n",
    "\n",
    "test_dj_dw, test_dj_db = compute_gradient(x_train, y_train, test_w, test_b)\n",
    "print('Gradients at test (w, b): ', test_dj_dw, test_dj_db)"
   ],
   "execution_count":31,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "Gradients at test (w, b):  -47.41610118114435 -4.007175051546391\n"
     ],
     "output_type":"stream"
    }
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"yd2VBm0ngC7LEYQTAwcK13"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "def gradient_descent(x, y, w_in, b_in, cost_function, gradient_function, alpha, num_iters):\n",
    "    \"\"\"\n",
    "    return w, b\n",
    "    \"\"\"\n",
    "    m = x.shape[0]\n",
    "    J_History = []\n",
    "    w_History = []\n",
    "    w = copy.deepcopy(w_in)\n",
    "    b = b_in\n",
    "\n",
    "    for i in range(num_iters):\n",
    "        dj_dw, dj_db = gradient_function(x, y, w, b)\n",
    "        w = w - (alpha * dj_dw)\n",
    "        b = b - (alpha * dj_db)\n",
    "\n",
    "        if i < 100000:\n",
    "            cost = cost_function(x, y, w, b)\n",
    "            J_History.append(cost)\n",
    "\n",
    "        if i % math.ceil(num_iters \/ 10) == 0:\n",
    "            w_History.append(w)\n",
    "            print(f'Interation {i : 4} : Cost {float(J_History[-1]) : 8.2f}')\n",
    "    return w, b, J_History, w_History"
   ],
   "execution_count":34,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"RLqQSRIDDVNYV4m3spGKAe"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "initial_w = 0\n",
    "initial_b = 0\n",
    "iterations = 1500\n",
    "alpha = 0.01\n",
    "w, b, _, _ = gradient_descent(x_train, y_train, initial_w, initial_b, compute_cost, compute_gradient, alpha, iterations)\n",
    "print('w, b found by gradient descent is: ', w, b)"
   ],
   "execution_count":36,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "Interation    0 : Cost     6.74\n",
      "Interation  150 : Cost     5.31\n",
      "Interation  300 : Cost     4.96\n",
      "Interation  450 : Cost     4.76\n",
      "Interation  600 : Cost     4.64\n",
      "Interation  750 : Cost     4.57\n",
      "Interation  900 : Cost     4.53\n",
      "Interation  1050 : Cost     4.51\n",
      "Interation  1200 : Cost     4.50\n",
      "Interation  1350 : Cost     4.49\n",
      "w, b found by gradient descent is:  1.166362350335582 -3.63029143940436\n"
     ],
     "output_type":"stream"
    }
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"BpjhSmnRNTvOu3eNJ661nQ"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "m = x_train.shape[0]\n",
    "predicted = np.zeros(m)\n",
    "\n",
    "for i in range(m):\n",
    "    predicted[i] = w * x_train[i] + b"
   ],
   "execution_count":39,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"Pq7BhfvB67Md5eKHIEvYnX"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "plt.plot(x_train, predicted, c='b')\n",
    "plt.scatter(x_train, y_train, marker='*', c='r')\n",
    "# Set the title\n",
    "plt.title(\"Profits vs. Population per city\")\n",
    "# Set the y-axis label\n",
    "plt.ylabel('Profit in $10,000')\n",
    "# Set the x-axis label\n",
    "plt.xlabel('Population of City in 10,000s')"
   ],
   "execution_count":40,
   "outputs":[
    {
     "data":{
      "text\/plain":[
       "Text(0.5, 0, 'Population of City in 10,000s')"
      ]
     },
     "metadata":{
      
     },
     "output_type":"display_data"
    },
    {
     "data":{
      "image\/png":[
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\n"
      ]
     },
     "metadata":{
      "image\/png":{
       
      }
     },
     "output_type":"display_data"
    }
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"HNj1lKI3dw5IEnTXSIDa5F"
    }
   }
  },
  {
   "cell_type":"markdown",
   "source":[
    "Your final values of $w,b$ can also be used to make predictions on profits. Let's predict what the profit would be in areas of 35,000 and 70,000 people. \n",
    "\n",
    "- The model takes in population of a city in 10,000s as input. \n",
    "\n",
    "- Therefore, 35,000 people can be translated into an input to the model as `np.array([3.5])`\n",
    "\n",
    "- Similarly, 70,000 people can be translated into an input to the model as `np.array([7.])`"
   ],
   "attachments":{
    
   },
   "metadata":{
    "datalore":{
     "type":"MD",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"g7rG9LgNy1u1R4HXYvjyI2"
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "predict1 = 3.5 * w + b\n",
    "print(f'For population = 35,000, we predict a profit of ${predict1*10000:.2f}')\n",
    "predict2 = 7.0 * w + b\n",
    "print(f'For population = 70,000, we predict a profit of ${predict2*10000:.2f}')"
   ],
   "execution_count":45,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "For population = 35,000, we predict a profit of $4519.77\n",
      "For population = 70,000, we predict a profit of $45342.45\n"
     ],
     "output_type":"stream"
    }
   ],
   "metadata":{
    "datalore":{
     "type":"CODE",
     "hide_input_from_viewers":false,
     "hide_output_from_viewers":false,
     "node_id":"JUTo7mQg7InmTcwhZiMASF"
    }
   }
  }
 ],
 "metadata":{
  "kernelspec":{
   "display_name":"Python",
   "language":"python",
   "name":"python"
  },
  "datalore":{
   "version":1,
   "computation_mode":"JUPYTER",
   "package_manager":"pip",
   "base_environment":"default",
   "packages":[
    
   ]
  }
 },
 "nbformat":4,
 "nbformat_minor":4
}