tsu-nera/gradient_descent.ipynb

## gradient_descent.ipynb
{
  "cells": [
    {
      "metadata": {
        "editable": true,
        "deletable": true
      },
      "cell_type": "markdown",
      "source": "# Intro_to_the_Math_of_intelligence Challenge\nThis is the code for \"Intro - The Math of Intelligence\" by Siraj Raval on Youtube\n* https://www.youtube.com/watch?v=xRJCOz3AfYY"
    },
    {
      "metadata": {
        "editable": true,
        "deletable": true
      },
      "cell_type": "markdown",
      "source": "## Coding Challenge\nThis week's coding challenge is to implement gradient descent to find the line of best fit that predicts the relationship between 2 variables of your choice from a kaggle dataset. Bonus points for detailed documentation. Good luck! Post your github link in the youtube comments section"
    },
    {
      "metadata": {
        "editable": true,
        "deletable": true
      },
      "cell_type": "markdown",
      "source": "## Reference\n* https://github.com/llSourcell/Intro_to_the_Math_of_intelligence\n* [Linear Regression Tutorial Using Gradient Descent for Machine Learning - Machine Learning Mastery](http://machinelearningmastery.com/linear-regression-tutorial-using-gradient-descent-for-machine-learning/)\n* [Linear Regression from scratch (Gradient Descent) | Kaggle](https://www.kaggle.com/tentotheminus9/linear-regression-from-scratch-gradient-descent)\n* [An Introduction to Gradient Descent and Linear Regression](https://spin.atomicobject.com/2014/06/24/gradient-descent-linear-regression/)"
    },
    {
      "metadata": {
        "collapsed": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "markdown",
      "source": "## Kaggle Dataset: \nHouse Prices: Advanced Regression Techniques\n* https://www.kaggle.com/c/house-prices-advanced-regression-techniques/data"
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "import numpy as np\nimport pandas as pd",
      "execution_count": 1,
      "outputs": []
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "data = pd.read_csv(\"train.csv\")",
      "execution_count": 2,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "data.head()",
      "execution_count": 3,
      "outputs": [
        {
          "data": {
            "text/html": "<div>\n<style>\n    .dataframe thead tr:only-child th {\n        text-align: right;\n    }\n\n    .dataframe thead th {\n        text-align: left;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Id</th>\n      <th>MSSubClass</th>\n      <th>MSZoning</th>\n      <th>LotFrontage</th>\n      <th>LotArea</th>\n      <th>Street</th>\n      <th>Alley</th>\n      <th>LotShape</th>\n      <th>LandContour</th>\n      <th>Utilities</th>\n      <th>...</th>\n      <th>PoolArea</th>\n      <th>PoolQC</th>\n      <th>Fence</th>\n      <th>MiscFeature</th>\n      <th>MiscVal</th>\n      <th>MoSold</th>\n      <th>YrSold</th>\n      <th>SaleType</th>\n      <th>SaleCondition</th>\n      <th>SalePrice</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1</td>\n      <td>60</td>\n      <td>RL</td>\n      <td>65.0</td>\n      <td>8450</td>\n      <td>Pave</td>\n      <td>NaN</td>\n      <td>Reg</td>\n      <td>Lvl</td>\n      <td>AllPub</td>\n      <td>...</td>\n      <td>0</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>0</td>\n      <td>2</td>\n      <td>2008</td>\n      <td>WD</td>\n      <td>Normal</td>\n      <td>208500</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>2</td>\n      <td>20</td>\n      <td>RL</td>\n      <td>80.0</td>\n      <td>9600</td>\n      <td>Pave</td>\n      <td>NaN</td>\n      <td>Reg</td>\n      <td>Lvl</td>\n      <td>AllPub</td>\n      <td>...</td>\n      <td>0</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>0</td>\n      <td>5</td>\n      <td>2007</td>\n      <td>WD</td>\n      <td>Normal</td>\n      <td>181500</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>3</td>\n      <td>60</td>\n      <td>RL</td>\n      <td>68.0</td>\n      <td>11250</td>\n      <td>Pave</td>\n      <td>NaN</td>\n      <td>IR1</td>\n      <td>Lvl</td>\n      <td>AllPub</td>\n      <td>...</td>\n      <td>0</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>0</td>\n      <td>9</td>\n      <td>2008</td>\n      <td>WD</td>\n      <td>Normal</td>\n      <td>223500</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>4</td>\n      <td>70</td>\n      <td>RL</td>\n      <td>60.0</td>\n      <td>9550</td>\n      <td>Pave</td>\n      <td>NaN</td>\n      <td>IR1</td>\n      <td>Lvl</td>\n      <td>AllPub</td>\n      <td>...</td>\n      <td>0</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>0</td>\n      <td>2</td>\n      <td>2006</td>\n      <td>WD</td>\n      <td>Abnorml</td>\n      <td>140000</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>5</td>\n      <td>60</td>\n      <td>RL</td>\n      <td>84.0</td>\n      <td>14260</td>\n      <td>Pave</td>\n      <td>NaN</td>\n      <td>IR1</td>\n      <td>Lvl</td>\n      <td>AllPub</td>\n      <td>...</td>\n      <td>0</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>0</td>\n      <td>12</td>\n      <td>2008</td>\n      <td>WD</td>\n      <td>Normal</td>\n      <td>250000</td>\n    </tr>\n  </tbody>\n</table>\n<p>5 rows × 81 columns</p>\n</div>",
            "text/plain": "   Id  MSSubClass MSZoning  LotFrontage  LotArea Street Alley LotShape  \\\n0   1          60       RL         65.0     8450   Pave   NaN      Reg   \n1   2          20       RL         80.0     9600   Pave   NaN      Reg   \n2   3          60       RL         68.0    11250   Pave   NaN      IR1   \n3   4          70       RL         60.0     9550   Pave   NaN      IR1   \n4   5          60       RL         84.0    14260   Pave   NaN      IR1   \n\n  LandContour Utilities    ...     PoolArea PoolQC Fence MiscFeature MiscVal  \\\n0         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n1         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n2         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n3         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n4         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n\n  MoSold YrSold  SaleType  SaleCondition  SalePrice  \n0      2   2008        WD         Normal     208500  \n1      5   2007        WD         Normal     181500  \n2      9   2008        WD         Normal     223500  \n3      2   2006        WD        Abnorml     140000  \n4     12   2008        WD         Normal     250000  \n\n[5 rows x 81 columns]"
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "x = data['GrLivArea'].values\ny = data['SalePrice'].values",
      "execution_count": 4,
      "outputs": []
    },
    {
      "metadata": {
        "editable": true,
        "deletable": true
      },
      "cell_type": "markdown",
      "source": "## Plotting points"
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "import matplotlib.pyplot as plt\nplt.scatter(x, y, color='green')\nplt.show()",
      "execution_count": 5,
      "outputs": [
        {
          "data": {
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ucCyJyD5ptqLdB3ZPmhyXZEZ1XHqPw6OH+eYz35z2WdpxtcJSa4uaUS7Vljho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\nAElFTkSuQmCC\n",
            "text/plain": "<matplotlib.figure.Figure at 0x7fcdc828c7b8>"
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "editable": true,
        "deletable": true
      },
      "cell_type": "markdown",
      "source": "## Gradient Descent"
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "initial_b = 0\ninitial_m = 1.0",
      "execution_count": 6,
      "outputs": []
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "def calcurate_mean_squared_error(x, y, b, m):\n    total_error = 0\n    n = y.size\n    for i in range(n):\n        prediction = m*x[i] + b\n        total_error += (y[i] - prediction)**2\n    return (1/n) * total_error",
      "execution_count": 7,
      "outputs": []
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "def step_gradient(x, y, b, m, learning_rate):\n    m_grad = 0\n    b_grad = 0\n    n = y.size\n    \n    #Computes the gradients\n    for i in range(n):\n        # Partial derivative for m\n        m_grad += -(2/n) * x[i] * (y[i] - ((m*x[i]) + b))\n        # Partial derivative for b\n        b_grad += -(2/n) * (y[i] - (m*x[i]) + b)\n        \n    # update m and b\n    m = m - (learning_rate * m_grad)\n    b = b - (learning_rate * b_grad)    \n    return b, m",
      "execution_count": 8,
      "outputs": []
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "def gradient_descent_runner(x, y, initial_b, initial_m, learning_rate, num_iterations):\n    b = initial_b\n    m = initial_m\n    past_errors = []\n    for i in range(num_iterations):\n        b, m = step_gradient(x, y, b, m, learning_rate)\n        if(i % 100) == 0:\n            error = calcurate_mean_squared_error(x, y, b, m)\n            past_errors.append(error)\n            print('Error after', i, 'iterations:', error)\n    return b, m, past_errors",
      "execution_count": 9,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "num_iterations = 1000\nlearning_late = 0.0001\nprint(\"Starting gradient descent at b = {0}, m = {1}, error = {2}\".format(\n    initial_b, initial_m, \n    calcurate_mean_squared_error(x, y, initial_b, initial_m)))\nprint(\"Running...\")\n[b, m, errors] = gradient_descent_runner(x, y, initial_b, \n                                 initial_m, learning_late, num_iterations)\nprint(\"After {0} iterations b = {1}, m = {2}, error = {3}\".format(\n    num_iterations, b, m, calcurate_mean_squared_error(x, y, b, m)))",
      "execution_count": 10,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": "Starting gradient descent at b = 0, m = 1.0, error = 38434358058.74041\nRunning...\nError after 0 iterations: 9.29730669048e+15\n"
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": "/home/tsu-nera/anaconda3/envs/dlnd/lib/python3.6/site-packages/ipykernel_launcher.py:6: RuntimeWarning: overflow encountered in double_scalars\n  \n/home/tsu-nera/anaconda3/envs/dlnd/lib/python3.6/site-packages/ipykernel_launcher.py:9: RuntimeWarning: overflow encountered in double_scalars\n  if __name__ == '__main__':\n/home/tsu-nera/anaconda3/envs/dlnd/lib/python3.6/site-packages/ipykernel_launcher.py:14: RuntimeWarning: invalid value encountered in double_scalars\n  \n"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": "Error after 100 iterations: inf\nError after 200 iterations: nan\nError after 300 iterations: nan\nError after 400 iterations: nan\nError after 500 iterations: nan\nError after 600 iterations: nan\nError after 700 iterations: nan\nError after 800 iterations: nan\nError after 900 iterations: nan\nAfter 1000 iterations b = nan, m = nan, error = nan\n"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "num_iterations = 1000\nlearning_late = 0.000000385\nprint(\"Starting gradient descent at b = {0}, m = {1}, error = {2}\".format(\n    initial_b, initial_m, \n    calcurate_mean_squared_error(x, y, initial_b, initial_m)))\nprint(\"Running...\")\n[b, m, errors] = gradient_descent_runner(x, y, initial_b, \n                                 initial_m, learning_late, num_iterations)\nprint(\"After {0} iterations b = {1}, m = {2}, error = {3}\".format(\n    num_iterations, b, m, calcurate_mean_squared_error(x, y, b, m)))",
      "execution_count": 11,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": "Starting gradient descent at b = 0, m = 1.0, error = 38434358058.74041\nRunning...\nError after 0 iterations: 37099009446.5\nError after 100 iterations: 3890785241.57\nError after 200 iterations: 3191853393.25\nError after 300 iterations: 3177142423.56\nError after 400 iterations: 3176832204.37\nError after 500 iterations: 3176825076.72\nError after 600 iterations: 3176824328.14\nError after 700 iterations: 3176823713.73\nError after 800 iterations: 3176823102.06\nError after 900 iterations: 3176822490.38\nAfter 1000 iterations b = 1.6038367299354666, m = 118.06815503968734, error = 3176821884.722309\n"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "plt.scatter(x, y, color='green')\nlx = np.linspace(0,6000) \nly = lx*m + b\nplt.plot(lx,ly,\"r-\")\nplt.show()",
      "execution_count": 12,
      "outputs": [
        {
          "data": {
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9gI+Dzt3iynq449DyOueo6gFgN5Ab5VrG1GGpyVPYiy96actnzIDzzvNmRU2ZYplo05Tf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\n0DDGGOObBQ1jjDG+WdAwxhjj2/8HMdTrOVdTAa4AAAAASUVORK5CYII=\n",
            "text/plain": "<matplotlib.figure.Figure at 0x7fcdf0ad3898>"
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "editable": true,
        "deletable": true
      },
      "cell_type": "markdown",
      "source": "## Standardization(Feature Scaling)\n* [Feature scaling - Wikipedia](https://en.wikipedia.org/wiki/Feature_scaling)"
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "norm_x = (x - x.mean()) / x.std()",
      "execution_count": 13,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "num_iterations = 3000\nlearning_late = 0.0001\nprint(\"Starting gradient descent at b = {0}, m = {1}, error = {2}\".format(\n    initial_b, initial_m, \n    calcurate_mean_squared_error(norm_x, y, initial_b, initial_m)))\nprint(\"Running...\")\n[b, m, errors] = gradient_descent_runner(norm_x, y, initial_b, \n                                 initial_m, learning_late, num_iterations)\nprint(\"After {0} iterations b = {1}, m = {2}, error = {3}\".format(\n    num_iterations, b, m, calcurate_mean_squared_error(norm_x, y, b, m)))",
      "execution_count": 14,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": "Starting gradient descent at b = 0, m = 1.0, error = 39039155157.5263\nRunning...\nError after 0 iterations: 39024796868.7\nError after 100 iterations: 37591675380.6\nError after 200 iterations: 36164517438.6\nError after 300 iterations: 34744277941.7\nError after 400 iterations: 33331988271.7\nError after 500 iterations: 31928759264.1\nError after 600 iterations: 30535784333.6\nError after 700 iterations: 29154342758.0\nError after 800 iterations: 27785803128.3\nError after 900 iterations: 26431626968.9\nError after 1000 iterations: 25093372536.5\nError after 1100 iterations: 23772698802.4\nError after 1200 iterations: 22471369626.5\nError after 1300 iterations: 21191258129.9\nError after 1400 iterations: 19934351272.8\nError after 1500 iterations: 18702754647.8\nError after 1600 iterations: 17498697494.5\nError after 1700 iterations: 16324537945.6\nError after 1800 iterations: 15182768513.2\nError after 1900 iterations: 14076021824.8\nError after 2000 iterations: 13007076618.1\nError after 2100 iterations: 11978864006.6\nError after 2200 iterations: 10994474025.2\nError after 2300 iterations: 10057162467.2\nError after 2400 iterations: 9170358025.52\nError after 2500 iterations: 8337669749.07\nError after 2600 iterations: 7562894827.6\nError after 2700 iterations: 6850026718.21\nError after 2800 iterations: 6203263627.23\nError after 2900 iterations: 5627017362.03\nAfter 3000 iterations b = 148718.94016599742, m = 25393.306845628165, error = 5130545732.32363\n"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "plt.plot(errors)\nplt.show()",
      "execution_count": 15,
      "outputs": [
        {
          "data": {
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+36xXyAfaJR3n7pwb65xLds4lx8fHX8qvFpEgERUZwc3JVfnmD+14vncDDh8/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\n34XSAAAAAElFTkSuQmCC\n",
            "text/plain": "<matplotlib.figure.Figure at 0x7fcdc828cda0>"
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "plt.scatter(norm_x, y, color='green')\nlx = np.linspace(-3,8)\nly = lx*m + b\nplt.plot(lx,ly,\"r-\")\nplt.show()",
      "execution_count": 16,
      "outputs": [
        {
          "data": {
            "image/png": 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U3d20eTO0t3vprjNndq8Ce955XlqsyUnW0jAJ4Xer1kwLGJDcOu1q2cWGXRui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\nAAAAAElFTkSuQmCC\n",
            "text/plain": "<matplotlib.figure.Figure at 0x7fcdc4361dd8>"
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "editable": true,
        "deletable": true
      },
      "cell_type": "markdown",
      "source": "## Delete outlier\n* [python - Is there a numpy builtin to reject outliers from a list - Stack Overflow](https://stackoverflow.com/questions/11686720/is-there-a-numpy-builtin-to-reject-outliers-from-a-list)"
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": true
      },
      "cell_type": "code",
      "source": "def reject_outliers(x, y):\n    m = 2\n    retx, rety = [], []\n    u = np.mean(x)\n    s = np.std(x)\n    for i in range(x.size):\n        if (u - m * s < x[i] < u + m * s):\n            retx.append(x[i])\n            rety.append(y[i])\n    return np.array(retx), np.array(rety)",
      "execution_count": 17,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": true
      },
      "cell_type": "code",
      "source": "x2, y2 = reject_outliers(x, y)",
      "execution_count": 18,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "x2.size",
      "execution_count": 19,
      "outputs": [
        {
          "data": {
            "text/plain": "1401"
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "plt.scatter(x2, y2, color='green')\nplt.show()",
      "execution_count": 20,
      "outputs": [
        {
          "data": {
            "image/png": 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81pjQMNoCF9/3ZZllzPNJ4Jmvgtn27LaS/qGjfOV9T51cNlf9m6sSvmCMi3Oo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\nojcQlZ0AAAAASUVORK5CYII=\n",
            "text/plain": "<matplotlib.figure.Figure at 0x7fcdc828c4a8>"
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true,
        "editable": true,
        "deletable": true
      },
      "cell_type": "code",
      "source": "x2 = (x2 - x2.mean()) / x2.std()",
      "execution_count": 21,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "num_iterations = 3000\nlearning_late = 0.0001\nprint(\"Starting gradient descent at b = {0}, m = {1}, error = {2}\".format(\n    initial_b, initial_m, \n    calcurate_mean_squared_error(x2, y2, initial_b, initial_m)))\nprint(\"Running...\")\n[b, m, errors] = gradient_descent_runner(x2, y2, initial_b, \n                                 initial_m, learning_late, num_iterations)\nprint(\"After {0} iterations b = {1}, m = {2}, error = {3}\".format(\n    num_iterations, b, m, calcurate_mean_squared_error(x2, y2, b, m)))",
      "execution_count": 22,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": "Starting gradient descent at b = 0, m = 1.0, error = 35066480010.58602\nRunning...\nError after 0 iterations: 35053480651.8\nError after 100 iterations: 33755402109.6\nError after 200 iterations: 32461594862.6\nError after 300 iterations: 31172994901.3\nError after 400 iterations: 29890607268.2\nError after 500 iterations: 28615508892.5\nError after 600 iterations: 27348851563.6\nError after 700 iterations: 26091865051.1\nError after 800 iterations: 24845860373.9\nError after 900 iterations: 23612233226.7\nError after 1000 iterations: 22392467568.0\nError after 1100 iterations: 21188139377.2\nError after 1200 iterations: 20000920587.0\nError after 1300 iterations: 18832583196.7\nError after 1400 iterations: 17685003576.7\nError after 1500 iterations: 16560166967.2\nError after 1600 iterations: 15460172183.4\nError after 1700 iterations: 14387236532.2\nError after 1800 iterations: 13343700950.3\nError after 1900 iterations: 12332035372.0\nError after 2000 iterations: 11354844336.2\nError after 2100 iterations: 10414872842.9\nError after 2200 iterations: 9515012467.38\nError after 2300 iterations: 8658307744.34\nError after 2400 iterations: 7847962832.45\nError after 2500 iterations: 7087348470.01\nError after 2600 iterations: 6380009234.44\nError after 2700 iterations: 5729671117.42\nError after 2800 iterations: 5140249428.81\nError after 2900 iterations: 4615857042.68\nAfter 3000 iterations b = 143285.9124730132, m = 20762.383465645886, error = 4165005460.5867414\n"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "plt.plot(errors)\nplt.show()",
      "execution_count": 23,
      "outputs": [
        {
          "data": {
            "image/png": 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lTm4bnciPuw97XZZI0FO4yxUL9c0RP+nx1hw8nsXtryfySdJ2r8sSCWoKdykwbWtFM2tY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\nEoAU7iIiAUjhLiISgBTuIiIB6P8AuoBx3tqDFKQAAAAASUVORK5CYII=\n",
            "text/plain": "<matplotlib.figure.Figure at 0x7fcdc42c75c0>"
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "plt.scatter(x2, y2, color='green')\nlx = np.linspace(-3,8) \nly = lx*m + b\nplt.plot(lx,ly,\"r-\")\nplt.show()",
      "execution_count": 24,
      "outputs": [
        {
          "data": {
            "image/png": 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BQ0omr3954bDR+wh6CrPc/bnwqeeBWeHjM4HtscMOhG0D4ePU9uiYZwHcfdDM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\n",
            "text/plain": "<matplotlib.figure.Figure at 0x7fcdc44ca4e0>"
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true,
        "editable": true,
        "deletable": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "plt.scatter(x2, y2, color='green')\nlx = np.linspace(-3,3)  \nly = lx*m + b\nplt.plot(lx,ly,\"r-\")\nplt.show()",
      "execution_count": 25,
      "outputs": [
        {
          "data": {
            "image/png": 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