Coursera's machine learning course,

Coursera_Linear Regression

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 1- Andrew NG Machine Learning Course\n",
    "## Hey all!\n",
    "This is the first task from Andrew NG course of machine learning concerning simple linear regression.\n",
    "I implemented the exercise in python but the original implementation is in MATLAB.\n",
    "feel free to review my work through tomer@nahshoh.net.\n",
    "The task is locate <a href=\"https://github.com/jdwittenauer/ipython-notebooks/blob/master/exercises/ML/ex1.pdf\">here</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.io import loadmat\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import axes3d\n",
    "from matplotlib import cm\n",
    "from pylab import *\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "df=pd.read_csv('../Exercise1/ex1/ex1data1.txt',names = [\"X\", \"Y\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.59200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.13020</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.66200</td>\n",
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       "    <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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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>8.3829</td>\n",
       "      <td>11.88600</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7.4764</td>\n",
       "      <td>4.34830</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8.5781</td>\n",
       "      <td>12.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>6.4862</td>\n",
       "      <td>6.59870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5.0546</td>\n",
       "      <td>3.81660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.7107</td>\n",
       "      <td>3.25220</td>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>14.1640</td>\n",
       "      <td>15.50500</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>5.7340</td>\n",
       "      <td>3.15510</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>8.4084</td>\n",
       "      <td>7.22580</td>\n",
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       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>5.6407</td>\n",
       "      <td>0.71618</td>\n",
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       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>5.3794</td>\n",
       "      <td>3.51290</td>\n",
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       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>6.3654</td>\n",
       "      <td>5.30480</td>\n",
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       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>5.1301</td>\n",
       "      <td>0.56077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>6.4296</td>\n",
       "      <td>3.65180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>7.0708</td>\n",
       "      <td>5.38930</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>6.1891</td>\n",
       "      <td>3.13860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>20.2700</td>\n",
       "      <td>21.76700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>5.4901</td>\n",
       "      <td>4.26300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>6.3261</td>\n",
       "      <td>5.18750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>5.5649</td>\n",
       "      <td>3.08250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>18.9450</td>\n",
       "      <td>22.63800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>12.8280</td>\n",
       "      <td>13.50100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>10.9570</td>\n",
       "      <td>7.04670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>13.1760</td>\n",
       "      <td>14.69200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>22.2030</td>\n",
       "      <td>24.14700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>10.2360</td>\n",
       "      <td>7.77540</td>\n",
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       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>5.4994</td>\n",
       "      <td>1.01730</td>\n",
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       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>20.3410</td>\n",
       "      <td>20.99200</td>\n",
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       "      <th>70</th>\n",
       "      <td>10.1360</td>\n",
       "      <td>6.67990</td>\n",
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       "      <th>71</th>\n",
       "      <td>7.3345</td>\n",
       "      <td>4.02590</td>\n",
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       "      <th>72</th>\n",
       "      <td>6.0062</td>\n",
       "      <td>1.27840</td>\n",
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       "      <th>73</th>\n",
       "      <td>7.2259</td>\n",
       "      <td>3.34110</td>\n",
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       "      <th>74</th>\n",
       "      <td>5.0269</td>\n",
       "      <td>-2.68070</td>\n",
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       "      <th>75</th>\n",
       "      <td>6.5479</td>\n",
       "      <td>0.29678</td>\n",
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       "      <th>76</th>\n",
       "      <td>7.5386</td>\n",
       "      <td>3.88450</td>\n",
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       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>5.0365</td>\n",
       "      <td>5.70140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>10.2740</td>\n",
       "      <td>6.75260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>5.1077</td>\n",
       "      <td>2.05760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>5.7292</td>\n",
       "      <td>0.47953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>5.1884</td>\n",
       "      <td>0.20421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>6.3557</td>\n",
       "      <td>0.67861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>9.7687</td>\n",
       "      <td>7.54350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>6.5159</td>\n",
       "      <td>5.34360</td>\n",
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       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>8.5172</td>\n",
       "      <td>4.24150</td>\n",
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       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>9.1802</td>\n",
       "      <td>6.79810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>6.0020</td>\n",
       "      <td>0.92695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>5.5204</td>\n",
       "      <td>0.15200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>5.0594</td>\n",
       "      <td>2.82140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>5.7077</td>\n",
       "      <td>1.84510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>7.6366</td>\n",
       "      <td>4.29590</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",
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       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>8.2934</td>\n",
       "      <td>0.14454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>13.3940</td>\n",
       "      <td>9.05510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>5.4369</td>\n",
       "      <td>0.61705</td>\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",
       "5    8.3829  11.88600\n",
       "6    7.4764   4.34830\n",
       "7    8.5781  12.00000\n",
       "8    6.4862   6.59870\n",
       "9    5.0546   3.81660\n",
       "10   5.7107   3.25220\n",
       "11  14.1640  15.50500\n",
       "12   5.7340   3.15510\n",
       "13   8.4084   7.22580\n",
       "14   5.6407   0.71618\n",
       "15   5.3794   3.51290\n",
       "16   6.3654   5.30480\n",
       "17   5.1301   0.56077\n",
       "18   6.4296   3.65180\n",
       "19   7.0708   5.38930\n",
       "20   6.1891   3.13860\n",
       "21  20.2700  21.76700\n",
       "22   5.4901   4.26300\n",
       "23   6.3261   5.18750\n",
       "24   5.5649   3.08250\n",
       "25  18.9450  22.63800\n",
       "26  12.8280  13.50100\n",
       "27  10.9570   7.04670\n",
       "28  13.1760  14.69200\n",
       "29  22.2030  24.14700\n",
       "..      ...       ...\n",
       "67  10.2360   7.77540\n",
       "68   5.4994   1.01730\n",
       "69  20.3410  20.99200\n",
       "70  10.1360   6.67990\n",
       "71   7.3345   4.02590\n",
       "72   6.0062   1.27840\n",
       "73   7.2259   3.34110\n",
       "74   5.0269  -2.68070\n",
       "75   6.5479   0.29678\n",
       "76   7.5386   3.88450\n",
       "77   5.0365   5.70140\n",
       "78  10.2740   6.75260\n",
       "79   5.1077   2.05760\n",
       "80   5.7292   0.47953\n",
       "81   5.1884   0.20421\n",
       "82   6.3557   0.67861\n",
       "83   9.7687   7.54350\n",
       "84   6.5159   5.34360\n",
       "85   8.5172   4.24150\n",
       "86   9.1802   6.79810\n",
       "87   6.0020   0.92695\n",
       "88   5.5204   0.15200\n",
       "89   5.0594   2.82140\n",
       "90   5.7077   1.84510\n",
       "91   7.6366   4.29590\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": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great, we loaded the data. X will represent the population of the city, and Y will represent the profits we've made. Let's plot the data to see what we're talking about here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Profit in 10,000$')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2dcbf8191d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = df.sort_values('X', ascending=True)\n",
    "ax = df.plot.scatter(x = \"X\", y=\"Y\",title='City population vs. profit')\n",
    "ax.set_xlabel(\"City Population in 10,000\")\n",
    "ax.set_ylabel(\"Profit in 10,000$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, we plotted the data after sorting it. We can see the data is not entirely balanced since there are many small cities but much less larger cities, this could harm us down the road. for fitting the linear regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def computecost(X, y, theta):\n",
    "    m = X.shape[0]\n",
    "    J = np.sum((np.square((X * theta.T) - y)) / (2 * m))\n",
    "    return J"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check the cost function we wrote:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = np.array([1, 1])\n",
    "xx = np.array([3, 2])\n",
    "yy = np.array([1,2])\n",
    "computecost(xx, yy, theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Playing with it a bit shows ok results. Let's add a bias column to our data for theta0 parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<bound method NDFrame.head of     Bias        X         Y\n",
       "74     1   5.0269  -2.68070\n",
       "77     1   5.0365   5.70140\n",
       "9      1   5.0546   3.81660\n",
       "89     1   5.0594   2.82140\n",
       "46     1   5.0702   5.13370\n",
       "79     1   5.1077   2.05760\n",
       "17     1   5.1301   0.56077\n",
       "61     1   5.1793  -0.74279\n",
       "81     1   5.1884   0.20421\n",
       "30     1   5.2524  -1.22000\n",
       "93     1   5.3054   1.98690\n",
       "51     1   5.3077   1.83960\n",
       "15     1   5.3794   3.51290\n",
       "40     1   5.4069   0.55657\n",
       "96     1   5.4369   0.61705\n",
       "22     1   5.4901   4.26300\n",
       "68     1   5.4994   1.01730\n",
       "88     1   5.5204   0.15200\n",
       "1      1   5.5277   9.13020\n",
       "49     1   5.5416   1.01790\n",
       "24     1   5.5649   3.08250\n",
       "37     1   5.6063   3.39280\n",
       "57     1   5.6397   4.60420\n",
       "14     1   5.6407   0.71618\n",
       "90     1   5.7077   1.84510\n",
       "10     1   5.7107   3.25220\n",
       "80     1   5.7292   0.47953\n",
       "12     1   5.7340   3.15510\n",
       "43     1   5.7737   2.44060\n",
       "47     1   5.8014   1.84400\n",
       "..   ...      ...       ...\n",
       "66     1   8.2951   5.74420\n",
       "5      1   8.3829  11.88600\n",
       "13     1   8.4084   7.22580\n",
       "85     1   8.5172   4.24150\n",
       "2      1   8.5186  13.66200\n",
       "7      1   8.5781  12.00000\n",
       "60     1   8.8254   5.16940\n",
       "86     1   9.1802   6.79810\n",
       "32     1   9.2482  12.13400\n",
       "58     1   9.3102   3.96240\n",
       "59     1   9.4536   5.41410\n",
       "83     1   9.7687   7.54350\n",
       "70     1  10.1360   6.67990\n",
       "67     1  10.2360   7.77540\n",
       "78     1  10.2740   6.75260\n",
       "27     1  10.9570   7.04670\n",
       "48     1  11.7000   8.00430\n",
       "42     1  11.7080   5.38540\n",
       "26     1  12.8280  13.50100\n",
       "38     1  12.8360  10.11700\n",
       "28     1  13.1760  14.69200\n",
       "95     1  13.3940   9.05510\n",
       "11     1  14.1640  15.50500\n",
       "63     1  14.9080  12.05400\n",
       "25     1  18.9450  22.63800\n",
       "64     1  18.9590  17.05400\n",
       "21     1  20.2700  21.76700\n",
       "69     1  20.3410  20.99200\n",
       "62     1  21.2790  17.92900\n",
       "29     1  22.2030  24.14700\n",
       "\n",
       "[97 rows x 3 columns]>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.insert(0, 'Bias', 1)\n",
    "df.head"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "seperation = df.shape[1]\n",
    "X = df.iloc[:,0:seperation-1]\n",
    "y = df.iloc[:,seperation-1:seperation]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((97, 2), (97, 1), (1, 2))"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#turning to matrices for cost function multiplication\n",
    "X = np.matrix(X.values)\n",
    "y = np.matrix(y.values)\n",
    "theta = np.matrix(np.array([0,0]))\n",
    "X.shape, y.shape, theta.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see we have 97 rows and 2 columns for training (97 samples  for x0=1 and x1=City Population).\n",
    "For y we have 97 samples of equivelant profits.\n",
    "and we have the learned parameters vector theta which composed of theta 0 (the bias term) and theta 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32.072733877455676"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computecost(X,y,theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great, exactly what we expected  fromt the exercise.　Now let's build the gradient descent function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientDescent(X, y, theta, alpha, num_iters):\n",
    "    parameters = int(theta.ravel().shape[1])\n",
    "    cost_history= np.zeros(num_iters)\n",
    "    temp_theta = np.zeros(theta.shape)\n",
    "    temp_theta= np.matrix(temp_theta)\n",
    "    for i in range(num_iters):\n",
    "        e = (X * theta.T) - y # calculating just one -avoiding redundancy\n",
    "        for j in range(parameters):\n",
    "            temp_theta[0,j] = theta[0,j] - ((alpha / len(X)) * np.sum(np.multiply(e, X[:,j])))\n",
    "        theta = temp_theta\n",
    "        cost_history[i] = computecost(X, y, theta)\n",
    "        \n",
    "    return theta, cost_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(24.47289936878686, 19.08057847001107)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learning_rate = 0.001\n",
    "iters = 14\n",
    "theta = np.matrix(np.array([0,0]))\n",
    "theta, cost = gradientDescent(X, y, theta, learning_rate, iters)\n",
    "cost[1], cost[3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, we can see that the cost is descending, So now let's draw the hypothesis we got with the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0.04572468, 0.55590616]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a list of values in the best fit line\n",
    "abline_values = [theta[0,1]* i + theta[0,0] for i in X[:,1]]\n",
    "abline_values = [float(i) for i in abline_values]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Profit in 10,000$')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2dcbf77bfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = df.plot.scatter(x = \"X\", y=\"Y\",title='City population vs. profit')\n",
    "plt.plot(X[:,1], abline_values, 'g')\n",
    "ax.set_xlabel(\"City Population in 10,000\")\n",
    "ax.set_ylabel(\"Profit in 10,000$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, so we have our new hypothesis drawn.let's try to have more iteration and get a better fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "iters = 800\n",
    "theta, cost = gradientDescent(X, y, theta, learning_rate, iters)\n",
    "# Create a list of values in the best fit line\n",
    "abline_values = [theta[0,1]* i + theta[0,0] for i in X[:,1]]\n",
    "abline_values = [float(i) for i in abline_values]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Profit in 10,000$')"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2dcbf8866a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = df.plot.scatter(x = \"X\", y=\"Y\",title='City population vs. profit')\n",
    "plt.plot(X[:,1], abline_values, 'g')\n",
    "ax.set_xlabel(\"City Population in 10,000\")\n",
    "ax.set_ylabel(\"Profit in 10,000$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks better, Now let's try to visualize J(theta), the cost function as a function of theta(0) and theta(1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "def visualize_cost():\n",
    "    theta0_vals = np.linspace(-10, 10, 100);\n",
    "    theta1_vals = np.linspace(-1, 4, 100);\n",
    "    J_vals = np.zeros((len(theta0_vals), len(theta1_vals)));\n",
    "    # Fill out J_vals\n",
    "    for i in range (0,len(theta0_vals)):\n",
    "        for j in range (0,len(theta1_vals)):\n",
    "          t = np.matrix([theta0_vals[i], theta1_vals[j]])\n",
    "          J_vals[i,j] = computecost(X, y, t)\n",
    "    # now let's build the contours and plot them\n",
    "    plt.figure()\n",
    "    cp = plt.contour(theta0_vals, theta1_vals, J_vals)\n",
    "    plt.clabel(cp, inline=True, fontsize=10)\n",
    "    plt.xlabel('theta0')\n",
    "    plt.ylabel('theta1')\n",
    "    plt.show()\n",
    "    return "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2dcbfe05668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize_cost()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OK, this is it for now,\n",
    "<br>\n",
    "For comments please send to my mail: tomer@nahshoh.net\n",
    "<br>\n",
    "Thank you!\n",
    "<br>\n",
    "Tomer Nahshon"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (myenv)",
   "language": "python",
   "name": "myenv"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}