Py Linear regression.ipynb

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        "kernelspec": {
            "display_name": "Python 2 with Spark 2.0", 
            "language": "python", 
            "name": "python2-spark20"
        }
    }, 
    "cells": [
        {
            "metadata": {
                "scrolled": false, 
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [], 
            "execution_count": 2, 
            "source": "import numpy as np\nimport pandas as pd\nimport matplotlib.pyplot as plt\n%matplotlib inline"
        }, 
        {
            "metadata": {
                "scrolled": false, 
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [], 
            "execution_count": 3, 
            "source": "# The code was removed by DSX for sharing."
        }, 
        {
            "metadata": {
                "scrolled": false, 
                "collapsed": true
            }, 
            "cell_type": "code", 
            "outputs": [], 
            "execution_count": 4, 
            "source": "# The code was removed by DSX for sharing."
        }, 
        {
            "metadata": {
                "scrolled": false, 
                "collapsed": true
            }, 
            "cell_type": "code", 
            "outputs": [], 
            "execution_count": 5, 
            "source": "# The code was removed by DSX for sharing."
        }, 
        {
            "metadata": {
                "scrolled": false, 
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [
                {
                    "metadata": {}, 
                    "execution_count": 6, 
                    "data": {
                        "text/plain": "   Population   Profit\n0      6.1101  17.5920\n1      5.5277   9.1302\n2      8.5186  13.6620\n3      7.0032  11.8540\n4      5.8598   6.8233", 
                        "text/html": "<div>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Population</th>\n      <th>Profit</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>6.1101</td>\n      <td>17.5920</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>5.5277</td>\n      <td>9.1302</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>8.5186</td>\n      <td>13.6620</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>7.0032</td>\n      <td>11.8540</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>5.8598</td>\n      <td>6.8233</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
                    }, 
                    "output_type": "execute_result"
                }
            ], 
            "execution_count": 6, 
            "source": "import os\n\n#path = os.getcwd() + '\\data\\ex1data1.txt'\npath=data_1\ndata = pd.read_csv(path, header=None, names=['Population', 'Profit'])\ndata.head()\n"
        }, 
        {
            "metadata": {
                "scrolled": false, 
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [
                {
                    "metadata": {}, 
                    "execution_count": 7, 
                    "data": {
                        "text/plain": "       Population     Profit\ncount   97.000000  97.000000\nmean     8.159800   5.839135\nstd      3.869884   5.510262\nmin      5.026900  -2.680700\n25%      5.707700   1.986900\n50%      6.589400   4.562300\n75%      8.578100   7.046700\nmax     22.203000  24.147000", 
                        "text/html": "<div>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Population</th>\n      <th>Profit</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>count</th>\n      <td>97.000000</td>\n      <td>97.000000</td>\n    </tr>\n    <tr>\n      <th>mean</th>\n      <td>8.159800</td>\n      <td>5.839135</td>\n    </tr>\n    <tr>\n      <th>std</th>\n      <td>3.869884</td>\n      <td>5.510262</td>\n    </tr>\n    <tr>\n      <th>min</th>\n      <td>5.026900</td>\n      <td>-2.680700</td>\n    </tr>\n    <tr>\n      <th>25%</th>\n      <td>5.707700</td>\n      <td>1.986900</td>\n    </tr>\n    <tr>\n      <th>50%</th>\n      <td>6.589400</td>\n      <td>4.562300</td>\n    </tr>\n    <tr>\n      <th>75%</th>\n      <td>8.578100</td>\n      <td>7.046700</td>\n    </tr>\n    <tr>\n      <th>max</th>\n      <td>22.203000</td>\n      <td>24.147000</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
                    }, 
                    "output_type": "execute_result"
                }
            ], 
            "execution_count": 7, 
            "source": "data.describe()\n# print \"Total records in the dataset:\", data.count()"
        }, 
        {
            "metadata": {
                "scrolled": false, 
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [
                {
                    "metadata": {}, 
                    "execution_count": 8, 
                    "data": {
                        "text/plain": "<matplotlib.axes._subplots.AxesSubplot at 0x7f04ca7f53d0>"
                    }, 
                    "output_type": "execute_result"
                }, 
                {
                    "metadata": {}, 
                    "data": {
                        "text/plain": "<matplotlib.figure.Figure at 0x7f04caaa4a90>", 
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1tQvjML2SZBSstwIQ9LH1YW1j41Q2Nk7l9OkVfwEBDt1uA/UrkzxQVT9dVetJ3pzkfzm8\nsoChbRechRWmnQ9rwBB2mkOdqqokV5N8QZLPzWgW9bnW2sOHXBvMlWn6M/XNLRlXr67k4sX1m8JK\nsrk5CjB7rXV19WyuXl3J5ubo+sLCuayurh/krwAAE7NjoG6ttar61dbaZyW5NIGaYO7cKsAOFapv\nFZwPyvLy8mMBPUlWV/VPczB8WAOGsGOgHntLVX1ua+1Nh1oNzKmDWvk9bAcZVpaXl6fu92P2+bAG\nDGG3gfrzk7ywqt6V5K8zavtok5ryAUzWrYKzsMIs8GENmLTdjs27a7vjrbV3H3hF2/98Y/M40qZx\njNw09XQDwKQc+E6JVfVRSb4lybOTPJjkta21D/eqch8EauaBAAsAwzuMQP0LST6U5LeSfFmSd7fW\nXtKryn0QqAEAmITDCNQPjqd7pKqOJ3lja+1EvzL3TqAGAGASDmOnxA9tXRii1QMAAKbdTivUf5vR\nVI9kNNljIcnf5PEpH0869ApjhRoAgMnYzwr1bcfmtdY+ol9JAABwtO3U8gEAANyGQA0AAD0I1AAA\n0INADQAAPQjUAADQg0ANAAA9CNQAANCDQA0AAD0I1AAA0INADQAAPQjUAADQw0QCdVW9tqoeqarf\nv+7YnVV1uareUVVdVT15ErUAkHRdl6WlM1laOpOu64YuB2CmTWqF+nVJlm869l1J/q/W2qcl+fUk\n3z2hWgDmWtd1OX16JRsbp7KxcSqnT68I1QA9VGttMj+o6q4kr2+tffb4+tuTvKC19khVPTPJldba\np9/ivm1SdQIcdUtLZ7KxcSrJyvjIek6evJTLl+8fsiyAqVBVaa3VXu4zZA/1x7XWHkmS1trDSZ4+\nYC0AALAvx4cuYLfOnz//2OXFxcUsLi4OVgvALFtdPZurV1eyuTm6vrBwLqur68MWBTCQK1eu5MqV\nK70eY8iWj7clWbyu5eM3WmufcYv7avkAOEBd12Vt7UKSUcBeXr75NBeA+bSflo9JBupPzihQf9b4\n+n1JPtBau6+qziW5s7X2Xbe4r0ANAMChm9pAXVU/m2QxyVOTPJLkniT/Jsm/SvKJSf4kyde01v7i\nFvcXqAEAOHRTG6j7EqgBAJiEWZvyAQAAM0+gBgCAHgRqAADoQaAGAIAeBGrmRtd1WVo6k6WlM+m6\nbuhyAIAjQqBmLnRdl9OnV7KxcSobG6dy+vSKUA375MMpwI2MzWMuLC2dycbGqSQr4yPrOXnyUi5f\nvn/IsmDmbH043dy8L8lo2/KLF9fttAgcGfsZm3f8sIoB4OhZW7swDtOjD6ebm6NjAjUwzwRq5sLq\n6tlcvbqSzc3R9YWFc1ldXR+2KADgSNDywdzoui5raxeSjAK2FTXYOy0fwFFn63EADp0Pp8BRJlAD\nAEAP+wnUxuYBAEAPAjUAAPQgUAMAQA8CNQAA9CBQAwBADwI1AAD0IFADDKTruiwtncnS0pl0XTd0\nOQDskznUAAOw4yDAdLKxC8CMWFo6k42NU0lWxkfWc/LkpVy+fP+QZQHMPRu7ANxEWwUAh+340AUA\nHJab2yquXl2ZmraK1dWzuXp1JZubo+sLC+eyuro+bFEA7IuWD+DImva2iq7rsrZ2IckoYE9D0AeY\nd/tp+bBCDcyUoxRCl5eXZ7p+AEYEamBm7LWFQ1sFAJOg5QOYGftp4ThKK9oAHD4tHwA30VYBwGEz\nNg+uY8Tajabt+VhdPZuFhXNJ1pOsj1s4zg5dFgBzTssHjNm57kbT+nxo4QDgMNkpEXqY9hFrk+b5\neCJhHuDo00MNcEimeZMYAIYlUMOYEWs38nzcaG3twjhMj1bsNzdHxwRqAJyUCGPLy8t52ctenKc8\n5RV5ylNekZe97MVzHZaWl5dz8eKozePkyUsHtho7bSc6AkBfeqhhbFpPwtvJTn2909T3O9RzfBDP\nway+PgDYGyclQg+zeBLeTiFv2kLgpJ7j6wP0C15wIvfe+2MH8hxM04cTAA6HkxJhCkwydO3U1zuP\nfb83f4j4tV9bzbVrazmI58AmMQBsR6CGsYM4CW+WJ0FM4oPAJE50vPlDxLVrrznQxweAmwnUMLZ1\nEt7joXLvQXjSK8I7BdTdBthJfRA4iOd4756XY8e+Pdeuja7N+7QSAA6eHmo4QEP0YR/ESYmz2D9+\nK9v1jb/sZS/OG97wliR6nwG4PSclwsCm7STA3TpKgTpx8iAA+ydQwxSYxTA3qx8EAOCgCdTAvs3i\nBwEAOGgCNQAA9LCfQG3rcTgkttgGgPlghRoOgZ5kAJhNWj5gShy1qRkAMC+0fDA3tFMcHs8tAOyN\nnRKZObOwvfckttg+DLPw3ALAtNHywcyZlXaKWRxDNyvPLQAclv20fFihhp5uFZyXl5dnIkQDAP3o\noWbmrK6ezcLCuSTrSdbH7RRnB6llq0ViY+NUNjZO5fTplV59x0P3Lw/93A79+w9hHn9ngKNGywcz\naVraKbZrkXjOc34iT3vaM/Zc27SM2hvquZ2W33+S5vF3Bph2xubBhJ04sZgHHvjGPB6oX5qq16a1\nH0myt4A07/3L8/j7z+PvDDDtjM2DCfvLv/zTJN+WrRaJ5HXjML2SZLTyuLXae9RpXQBgXg1+UmJV\nvSvJ/5vkWpIPtdY+b9iKmBVDt310XZd3vvP/SfKiJK9J8odJ7tz3483qqL3kYMbtzfLvv1/z+DsD\nHEWDt3xU1X9M8tzW2p/f5jZaPrjBNPSebvfn+qoX5yM/8qPy6KM/tK+6+nxIGPIDxkG1Lgz9IWkI\n8/g7A0yzWR2bV9F6wh6trV0Yh+lRgNvcHB0bOozcffeJvPKV331dQNpbyN/vqL2jsiHLPI4anMff\nGeComYZA3ZJ0VdWSXGit/cTQBcFubPfn+le+cv1AA9JuVy+H/oChdQGAeTYNgfqLWmsPV9XTk2xU\n1dtaa1dvvtH58+cfu7y4uJjFxcXJVcjUmYYAt7y8nIsX1/e9Gr2TWVp1PuznAgAOy5UrV3LlypVe\njzF4D/X1quqeJH/VWnv1Tcf1UPMER733dC99ydPQUw4AR8HM9VBX1UcnOdZa+2BVfUySpSTfO2RN\nzI4+rRVHLYxbIQaA4Qy6Ql1Vn5LkYkZ91MeT/MvW2g9sczsr1ByYWVnNPeg6j9qHCAA4DHZKhF2Y\npd3pDioEz8qHCAAY2sy1fAC3d1ATQ4aeAgIAR5n5z8yd1dWzWVg4l63twkcTQs4OXdaedF2XEycW\n89SnPjsnTjw/XdfZ+hsABqLlg7lwc+tEkpntJ+66LqdOff1juzEmL83x45s5duyjb7lD40G0fOjB\nBmAe6KGGbRy1/uHtesCT/ynJ9+d2feF9tzU/Ss8hANyKHmrYhv7hke36sWdlJ0YAmGYCNcyIrfD7\n/vf/WY4ff0k+/OGt72y1fHxnHn10dGQ3O0dOw06M2kgAOAoEao68adimfDt7CZM3h9877vjOfOqn\nruXP//xvcuedH5cnPenpST6c5HV52tOeuquNXfay6nwYz+E0BHoAOAgCNTNpL2F0GncR3GuYvDn8\nPvpo8vf//qWsrp7N6dMr+eM//mdJDq+3+TCeQ20kABwVAjUzZz8rmwc1z/mgHFSY7PM4e111nrbn\nEACmhTnUzJwbQ+QoWG+tnA7pMOdAH8bs7K1V55MnL+XkyUsTb7c4CvPAASCxQg0HYq+r5vtZHb5V\ny0Wf3uYhV52nsRUHAPbDHGpmzm5nIk9ygsR2s6FvngN9s4Oqz6QMADg4NnZhbuwUIie9Ecl+AjUA\nMH0Eahi7XcA9jBXdwwrwVp8BYLLslAg7OKzZx4fRD2xOMwDMBivUHEm3WjFeW7vwhJXrpzzlFXnu\ncz9n6laAtZEAwOTtZ4Xa2DyOpL2MhPvABxaysfG+fPmX//e59957d3zswxyPBwDMHivUzJV77703\nL3/5Wq5d++Hxke9Ici3JjyRJjh379vzqr/7cLcP3JE92nPSJlQCAkxLhth4PqC9M8ttJ3pHkY5J8\nf3bbVjHpNgwnJQLAZDkpEW7j5m26Rzv0fceAFe3Mdt8AMP0EambSQa3cfuqnflLe+c5vz7Vro+s7\n7TS41x0OAYCjT8sHM2e/vcW3ul+SPYVzbRgAcHTpoWYu9OljFoYBgNvRQw070JMMABw0c6iZOaur\nZ7OwcC6jkwrXx33MZydeh3nUAECi5YMZddCtG3t9PDOiAeBo0kMN+7CfcGxbcAA4mvRQwz7cPJ96\nc3N0zGozALAbAjXsg3nUAMAWLR/MvT5zrY3gA4CjRQ81c+egQq1wDAAkAjVz5qB2PgQA2CJQM1e2\nm7TxnOf8RN7+9j/adfvGdivTVqsBYH6Z8sHce/e7H971xI6bV7h/7df+ST7lU56V97znPXn00R9J\nkly9umK+NABwWwI1M2u7SRt33vnx+cAHbrzd+9//Z9ve/+ZxedeuJX/8x6/J6H+LZyZZNkIPANiR\nrceZWcvLy7l4cbShysmTl3Lx4nqe9KSPSfLSbG1LPrr84T086t9L8qokFw6+YADgSLJCzUxbXl6+\nYfV41Pv8BUkujY+s5GlPe+e29715hTs5l1EIfzjJ+5Ksmy8NAOzICjVHyurq2Sws/EySU0lOZWHh\nZ7K6enbb226tcD/nOa/LsWOrSV6Y5OHcccd35jnP+YjHVr21ewAAt2PKB0fOfqZ09JnsYSoIABwd\nxubBhO13l0UAYDrtJ1Br+YDb6LouS0tnsrR0Jl3XPeH7N04KGQXrrdVqAGA+OCkRbuHm1WczqQGA\n7QjUcAs3z6nebib1drOwTQUBgPmi5YO50HVdTpxYzFOf+uycOPH8bds39mO7Wdh9V7B3ajMBAKaL\nkxI58rquy6lTX59HH/2h8ZGX5o47PpxLl37+tuF3dL+vzaOPfnqS5I473r7jfQ6iVic5AsBwnJQI\n21hbuzAO0yvjr1fl0Uc/fZcnD35kkm8Zf33kIVY54iRHAJg9AjXcws1B/NFHf0i4BQCeQKDmyFtd\nPZs77vjOjLYVX0/y0hw//ra8//2PHEif8kH2PI92etzaAn1r6/Ptd3oEAKaDKR/Mhc/8zH+QP/qj\nl6e1D+UZz/j4vOc978kDD3xTkluPw9vNBI+DHq23dZLj4zsv6p8GgGnnpERm2k7bft977715+cvX\ncu3aDycZheJP//Rnj8P0yvhWoykdly/fv+fHX1o6k42NU7t6LABg+u3npEQr1MysnVaHu67Ly1/+\nw+Mw/fgs6Xe/+xXXP0qS1+TNb/7TdF33hMC8vLxshRgAuC2Bmpm108Yra2sXcu3af/mE+91117Oy\nuXkum5sPZtSr/Kp84APJ6dN7b9ewsQsAIFBzxD0vybnHrh079u155St/LknydV/3rfnAB16V2+2E\nuJNb9Tzv1CoCABwdAjUz68bV4Qdz7NhP5/3v/68ea914/PsvTPKaHDv2h/m+71t9LNw+97mfk42N\n/nXc3BZy0CcqAgDTzUmJzLSu6/Ld3/2K/N7vPXTDiYdbAfb6leIXvOBE3vCGtyTJY6PoDmNXwlk/\nUdHqOgDzbCZPSqyqL03yIxnNxH5ta+2+gUtihiwvL497pR+f2nF968bW161WjY2ou5HVdQDYu0ED\ndVUdS/LPk3xJkvcleVNV/XJr7e1D1sXRc6sTGC9fvv/Aw+Isn6i404meAMATDb1C/XlJ/rC19u4k\nqaqfT/IVSQRqdm3aAqzNWQBgvgwdqD8hyXuuu/7ejEI27NpuAuykQ/eszq+etg8nADALBj0psaq+\nOslSa+3s+PoLk3xua+0lN92u3XPPPY9dX1xczOLi4iRL5Qhwst3ueJ4AmCdXrlzJlStXHrv+vd/7\nvXs+KXHoQP0FSc631r50fP27krSbT0w05QMAgEnYz5SPY4dVzC69Kcmzq+quqrojydcmuTRwTQAA\nsGuD9lC31v62qv7HJJfz+Ni8tw1ZEwAA7IWNXQAAYGwWWz4AAGCmCdQAANCDQM2R0HVdlpbOZGnp\nTLquG7ocAGCO6KFm5nVdl9OnV8ZbZo82I7l40e6EAMDe7aeHWqBm5i0tncnGxqkkK+Mj6zl58lIu\nX75/yLIAgBnkpEQAAJiwQedQw0FYXT2bq1dXsrk5ur6wcC6rq+vDFgUAzA0tHxwJXddlbe1CklHA\n1j8NAOwogGvzAAAIT0lEQVSHHmrmnmANAPQhUDPXTPsAAPpyUiJzbW3twjhMryQZBeut1erDZAY2\nAMw3JyVCDzevil+9umJVHADmjEDNkTHEtI8bV8WTzc3RMYEaAOaHQM2Rsby8nIsX1687KdFKMQBw\n+JyUCD04ERIAjhZTPmAARvUBwNEhUAMAQA/G5gEAwIQJ1AAA0INADQAAPQjUAADQg0ANAAA9CNQA\nANCDQA0AAD0I1AAA0INADQAAPQjUzKSu67K0dCZLS2fSdd3Q5QAAc8zW48ycruty+vRKNjfvS5Is\nLJzLxYvrWV5eHrgyAGDW7WfrcYGambO0dCYbG6eSrIyPrOfkyUu5fPn+IcsCAI6A/QRqLR8AANDD\n8aELgL1aXT2bq1dXsrk5ur6wcC6rq+vDFgUAzC0tH8ykruuytnYhyShg658GAA6CHmoAAOhBDzUA\nAEyYQA0AAD0I1AAA0INADQAAPQjUAADQg0ANAAA9CNQAANCDQA0AAD0I1AAA0INADQAAPQjUAADQ\ng0ANAAA9CNQAANCDQA0AAD0I1AAA0INADQAAPQjUAADQg0ANAAA9CNQAANCDQA0AAD0I1AAA0INA\nDQAAPQwWqKvqnqp6b1W9Zfz1pUPVwmy6cuXK0CUwhbwu2I7XBdvxuuCgDL1C/erW2onx178buBZm\njDdCtuN1wXa8LtiO1wUHZehAXQP/fAAA6GXoQP2tVfXWqvrJqnrywLUAAMCeVWvt8B68aiPJM64/\nlKQleVmS30ny/tZaq6rvT/LxrbUX3eJxDq9IAAC4TmttT10Uhxqod11E1V1JXt9a++yhawEAgL0Y\ncsrHM6+7+lVJ/mCoWgAAYL+OD/izf7Cq7k5yLcm7knzzgLUAAMC+TEXLBwAAzKqhp3zcVlV9aVW9\nvar+Q1WdG7oepkNVvauqfq+qHqiqNw5dD8OpqtdW1SNV9fvXHbuzqi5X1TuqqjNBaL7c4jVhI7E5\nV1XPqqpfr6qHqurBqvqn4+PeL+bYNq+LF4+P7/k9Y2pXqKvqWJL/kORLkrwvyZuSfG1r7e2DFsbg\nquo/Jnlua+3Ph66FYVXV85N8MMm/2DqpuaruS/JnrbUfHH8Qv7O19l1D1snk3OI1cU+Sv2qtvXrQ\n4hjM+LytZ7bW3lpVH5vkzUm+Isk3xvvF3LrN6+IfZ4/vGdO8Qv15Sf6wtfbu1tqHkvx8Rr8kVKb7\ntcuEtNauJrn5g9VXJFkfX15P8pUTLYpB3eI1kdhIbK611h5urb11fPmDSd6W5FnxfjHXbvG6+ITx\nt/f0njHNoeQTkrznuuvvzeO/JPOtJemq6k1V9U1DF8PU+bjW2iPJ6M0yydMHrofpYCMxkiRV9clJ\n7s5oP4xneL8gueF18bvjQ3t6z5jmQL3dJ4Pp7E9h0r6otfZfJ/nyjF7wzx+6IGCq/XiST22t3Z3k\n4SRaP+bU+M/6v5TkJeMVSbmC7V4Xe37PmOZA/d4kn3Td9Wdl1EvNnBuvIqS19qdJLmbUHgRbHqmq\nZySP9cf9p4HrYWCttT9tj58w9BNJPnfIehhGVR3PKDT9H621Xx4f9n4x57Z7XeznPWOaA/Wbkjy7\nqu6qqjuSfG2SSwPXxMCq6qPHnyRTVR+TZCk2BZp3lRv/onUpyTeML68k+eWb78CRd8NrwkZijP1U\nkodaaz963THvFzzhdbGf94ypnfKRjMbmJfnRjIL/a1trPzBwSQysqj4lo1XpltHGRP/S62J+VdXP\nJllM8tQkjyS5J8m/SfKvknxikj9J8jWttb8YqkYm6xaviS/OqDfysY3EtvpmmQ9V9bwkv5nkwYz+\n/WhJvifJG5P8YrxfzKXbvC6+Lnt8z5jqQA0AANNumls+AABg6gnUAADQg0ANAAA9CNQAANCDQA0A\nAD0I1AAA0INADTBhVfW3VfWWqnqwqn6hqj7qgB9/pap+bIfbvKCqvvC6699cVS88yDoA5oVADTB5\nf91aO9Fa+6wkH0ryLYfwM3baZGAxyRc9duPW/vfW2s8cQh0AR55ADTCs30ry7CSpqu8Yr1r/flW9\nZHzsrqp6W1X9TFU9VFW/uLWiXVXvrKqnjC8/t6p+4+YHr6p/VFW/U1VvrqrLVfX0qroroxD/beOV\n8udV1T1V9R3j+9xdVf++qt5aVfdX1ZPHx3+jqn6gqn63qt4+3mUMYO4J1ACTV0lSVceTfFmSB6vq\nRJKVJJ+b5AuTfFNVfc749p+W5J+31v5Bkr9K8j+Mj9+8Cr3dqvRvtda+oLX23CS/kOSftdbeneQ1\nSX54vFL+2zfdZz3Jd7bW7k7yBxlt373lI1prn5/k25Oc3+PvDXAkCdQAk7dQVW9J8sYk70ry2iTP\nT3Kxtfb/tdb+Osm/TvLfjG//J6213xlf/pnxbZNxMN/BJ1ZVV1W/n+SlST7zdjeuqicleXJr7er4\n0HqSf3jdTf71+L9vTnLXLn4+wJF3fOgCAObQ37TWTlx/oKp2E463bK1EfziPL4zc6sTGH0vyqtba\n/1lVL8iNq823crta/vP4v38b/4YAJLFCDTCE7QLrbyb5yqr6qKr6mCSnM+qvTpJPqqrPH1/+J0m2\nVo/fmeS548tnbvGznpTkfePLK9cd/6vx927QWvvLJB+4rj/665O8YQ+/B8DcEagBJu8Jvc6ttQeS\n/HSSNyX590kutNZ+b/ztdyT51qp6KMmdSf638fHvS/K/VtUbM1qt3s73JvmlqnpTkj+97vjrk5ze\nOinxppq+IcmrquqtST5n/HO2q3unSSIAc6Fa834IMK3GEzl+ZTxiD4ApZIUaYPpZ+QCYYlaoAQCg\nByvUAADQg0ANAAA9CNQAANCDQA0AAD0I1AAA0MP/D5PKYD0EvUN6AAAAAElFTkSuQmCC\n"
                    }, 
                    "output_type": "display_data"
                }
            ], 
            "execution_count": 8, 
            "source": "data.plot(kind='scatter', x='Population', y='Profit', figsize=(12,8))"
        }, 
        {
            "metadata": {
                "scrolled": false, 
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [], 
            "execution_count": 9, 
            "source": "def computeCost(X, y, theta):\n    inner = np.power(((X * theta.T) - y), 2)\n    return np.sum(inner) / (2 * len(X))"
        }, 
        {
            "metadata": {
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [
                {
                    "metadata": {}, 
                    "execution_count": 12, 
                    "data": {
                        "text/plain": "   Ones  Population   Profit\n0     1      6.1101  17.5920\n1     1      5.5277   9.1302\n2     1      8.5186  13.6620\n3     1      7.0032  11.8540\n4     1      5.8598   6.8233", 
                        "text/html": "<div>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Ones</th>\n      <th>Population</th>\n      <th>Profit</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1</td>\n      <td>6.1101</td>\n      <td>17.5920</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1</td>\n      <td>5.5277</td>\n      <td>9.1302</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1</td>\n      <td>8.5186</td>\n      <td>13.6620</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1</td>\n      <td>7.0032</td>\n      <td>11.8540</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1</td>\n      <td>5.8598</td>\n      <td>6.8233</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
                    }, 
                    "output_type": "execute_result"
                }
            ], 
            "execution_count": 12, 
            "source": "data.insert(0, 'Ones', 1)"
        }, 
        {
            "metadata": {
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [
                {
                    "metadata": {}, 
                    "execution_count": 13, 
                    "data": {
                        "text/plain": "    Profit\n0  17.5920\n1   9.1302\n2  13.6620\n3  11.8540\n4   6.8233", 
                        "text/html": "<div>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Profit</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>17.5920</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>9.1302</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>13.6620</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>11.8540</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>6.8233</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
                    }, 
                    "output_type": "execute_result"
                }
            ], 
            "execution_count": 13, 
            "source": "# set X (training data) and y (target variable)\ncols = data.shape[1]\nx = data.iloc[:,0:cols-1]\ny = data.iloc[:,cols-1:cols]\nx.head()\ny.head()"
        }, 
        {
            "metadata": {
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [], 
            "execution_count": 15, 
            "source": "x = np.matrix(x.values)\ny = np.matrix(y.values)\ntheta = np.matrix(np.array([0,0]))"
        }, 
        {
            "metadata": {
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [
                {
                    "metadata": {}, 
                    "execution_count": 16, 
                    "data": {
                        "text/plain": "32.072733877455676"
                    }, 
                    "output_type": "execute_result"
                }
            ], 
            "execution_count": 16, 
            "source": "computeCost(x, y, theta)"
        }, 
        {
            "metadata": {
                "collapsed": true
            }, 
            "cell_type": "code", 
            "outputs": [], 
            "execution_count": 17, 
            "source": "def gradientDescent(X, y, theta, alpha, iters):\n    temp = np.matrix(np.zeros(theta.shape))\n    parameters = int(theta.ravel().shape[1])\n    cost = np.zeros(iters)\n    \n    for i in range(iters):\n        error = (X * theta.T) - y\n        \n        for j in range(parameters):\n            term = np.multiply(error, X[:,j])\n            temp[0,j] = theta[0,j] - ((alpha / len(X)) * np.sum(term))\n            \n        theta = temp\n        cost[i] = computeCost(X, y, theta)\n        \n    return theta, cost"
        }, 
        {
            "metadata": {
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [
                {
                    "metadata": {}, 
                    "execution_count": 18, 
                    "data": {
                        "text/plain": "matrix([[-3.24140214,  1.1272942 ]])"
                    }, 
                    "output_type": "execute_result"
                }
            ], 
            "execution_count": 18, 
            "source": "alpha = 0.01\niters = 1000\ng, cost = gradientDescent(x, y, theta, alpha, iters)\ng"
        }, 
        {
            "metadata": {
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [
                {
                    "metadata": {}, 
                    "execution_count": 19, 
                    "data": {
                        "text/plain": "4.5159555030789118"
                    }, 
                    "output_type": "execute_result"
                }
            ], 
            "execution_count": 19, 
            "source": "computeCost(x, y, g)"
        }, 
        {
            "metadata": {
                "collapsed": false
            }, 
            "cell_type": "code", 
            "outputs": [
                {
                    "metadata": {}, 
                    "execution_count": 20, 
                    "data": {
                        "text/plain": "<matplotlib.text.Text at 0x7f04ca2fee10>"
                    }, 
                    "output_type": "execute_result"
                }, 
                {
                    "metadata": {}, 
                    "data": {
                        "text/plain": "<matplotlib.figure.Figure at 0x7f04ca354990>", 
                        "image/png": 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OhY03TpbD22mntKtSAxmoJUmScmHSJDjrLFi0CP7yF+jdO+2K1EgM1JIkSU3p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\n8iFJLc2sWXDOOfDoo0mLx0k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NPProo7GoaP3sOW+KRUXrL1P3ym6v6/2q9emnMf7udzF2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\n"
                    }, 
                    "output_type": "display_data"
                }
            ], 
            "execution_count": 20, 
            "source": "x = np.linspace(data.Population.min(), data.Population.max(), 100)\nf = g[0, 0] + (g[0, 1] * x)\n\nfig, ax = plt.subplots(figsize=(12,8))\nax.plot(x, f, 'r', label='Prediction')\nax.scatter(data.Population, data.Profit, label='Traning Data')\nax.legend(loc=2)\nax.set_xlabel('Population')\nax.set_ylabel('Profit')\nax.set_title('Predicted Profit vs. Population Size')"
        }, 
        {
            "metadata": {
                "collapsed": true
            }, 
            "cell_type": "code", 
            "outputs": [], 
            "execution_count": null, 
            "source": ""
        }
    ], 
    "nbformat": 4, 
    "nbformat_minor": 0
}