Regression Continued.ipynb

{
    "nbformat_minor": 1, 
    "cells": [
        {
            "source": "## Polynomial Regression", 
            "cell_type": "markdown", 
            "metadata": {}
        }, 
        {
            "source": "import matplotlib.pyplot as plt\nimport pandas as pd\nimport pylab as pl\nimport numpy as np\n%matplotlib inline", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [], 
            "execution_count": 1
        }, 
        {
            "source": "!wget -O FuelConsumption.csv https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/FuelConsumptionCo2.csv", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "stream", 
                    "name": "stdout", 
                    "text": "--2019-07-14 05:40:46--  https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/FuelConsumptionCo2.csv\nResolving s3-api.us-geo.objectstorage.softlayer.net (s3-api.us-geo.objectstorage.softlayer.net)... 67.228.254.193\nConnecting to s3-api.us-geo.objectstorage.softlayer.net (s3-api.us-geo.objectstorage.softlayer.net)|67.228.254.193|:443... connected.\nHTTP request sent, awaiting response... 200 OK\nLength: 72629 (71K) [text/csv]\nSaving to: \u2018FuelConsumption.csv\u2019\n\n100%[======================================>] 72,629      --.-K/s   in 0.004s  \n\n2019-07-14 05:40:46 (18.2 MB/s) - \u2018FuelConsumption.csv\u2019 saved [72629/72629]\n\n"
                }
            ], 
            "execution_count": 2
        }, 
        {
            "source": "df = pd.read_csv(\"FuelConsumption.csv\")\n\n# take a look at the dataset\ndf.head()", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "execute_result", 
                    "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>MODELYEAR</th>\n      <th>MAKE</th>\n      <th>MODEL</th>\n      <th>VEHICLECLASS</th>\n      <th>ENGINESIZE</th>\n      <th>CYLINDERS</th>\n      <th>TRANSMISSION</th>\n      <th>FUELTYPE</th>\n      <th>FUELCONSUMPTION_CITY</th>\n      <th>FUELCONSUMPTION_HWY</th>\n      <th>FUELCONSUMPTION_COMB</th>\n      <th>FUELCONSUMPTION_COMB_MPG</th>\n      <th>CO2EMISSIONS</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>2014</td>\n      <td>ACURA</td>\n      <td>ILX</td>\n      <td>COMPACT</td>\n      <td>2.0</td>\n      <td>4</td>\n      <td>AS5</td>\n      <td>Z</td>\n      <td>9.9</td>\n      <td>6.7</td>\n      <td>8.5</td>\n      <td>33</td>\n      <td>196</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>2014</td>\n      <td>ACURA</td>\n      <td>ILX</td>\n      <td>COMPACT</td>\n      <td>2.4</td>\n      <td>4</td>\n      <td>M6</td>\n      <td>Z</td>\n      <td>11.2</td>\n      <td>7.7</td>\n      <td>9.6</td>\n      <td>29</td>\n      <td>221</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>2014</td>\n      <td>ACURA</td>\n      <td>ILX HYBRID</td>\n      <td>COMPACT</td>\n      <td>1.5</td>\n      <td>4</td>\n      <td>AV7</td>\n      <td>Z</td>\n      <td>6.0</td>\n      <td>5.8</td>\n      <td>5.9</td>\n      <td>48</td>\n      <td>136</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>2014</td>\n      <td>ACURA</td>\n      <td>MDX 4WD</td>\n      <td>SUV - SMALL</td>\n      <td>3.5</td>\n      <td>6</td>\n      <td>AS6</td>\n      <td>Z</td>\n      <td>12.7</td>\n      <td>9.1</td>\n      <td>11.1</td>\n      <td>25</td>\n      <td>255</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>2014</td>\n      <td>ACURA</td>\n      <td>RDX AWD</td>\n      <td>SUV - SMALL</td>\n      <td>3.5</td>\n      <td>6</td>\n      <td>AS6</td>\n      <td>Z</td>\n      <td>12.1</td>\n      <td>8.7</td>\n      <td>10.6</td>\n      <td>27</td>\n      <td>244</td>\n    </tr>\n  </tbody>\n</table>\n</div>", 
                        "text/plain": "   MODELYEAR   MAKE       MODEL VEHICLECLASS  ENGINESIZE  CYLINDERS  \\\n0       2014  ACURA         ILX      COMPACT         2.0          4   \n1       2014  ACURA         ILX      COMPACT         2.4          4   \n2       2014  ACURA  ILX HYBRID      COMPACT         1.5          4   \n3       2014  ACURA     MDX 4WD  SUV - SMALL         3.5          6   \n4       2014  ACURA     RDX AWD  SUV - SMALL         3.5          6   \n\n  TRANSMISSION FUELTYPE  FUELCONSUMPTION_CITY  FUELCONSUMPTION_HWY  \\\n0          AS5        Z                   9.9                  6.7   \n1           M6        Z                  11.2                  7.7   \n2          AV7        Z                   6.0                  5.8   \n3          AS6        Z                  12.7                  9.1   \n4          AS6        Z                  12.1                  8.7   \n\n   FUELCONSUMPTION_COMB  FUELCONSUMPTION_COMB_MPG  CO2EMISSIONS  \n0                   8.5                        33           196  \n1                   9.6                        29           221  \n2                   5.9                        48           136  \n3                  11.1                        25           255  \n4                  10.6                        27           244  "
                    }, 
                    "execution_count": 3, 
                    "metadata": {}
                }
            ], 
            "execution_count": 3
        }, 
        {
            "source": "cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\ncdf.head()", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "execute_result", 
                    "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>ENGINESIZE</th>\n      <th>CYLINDERS</th>\n      <th>FUELCONSUMPTION_COMB</th>\n      <th>CO2EMISSIONS</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>2.0</td>\n      <td>4</td>\n      <td>8.5</td>\n      <td>196</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>2.4</td>\n      <td>4</td>\n      <td>9.6</td>\n      <td>221</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1.5</td>\n      <td>4</td>\n      <td>5.9</td>\n      <td>136</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>3.5</td>\n      <td>6</td>\n      <td>11.1</td>\n      <td>255</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>3.5</td>\n      <td>6</td>\n      <td>10.6</td>\n      <td>244</td>\n    </tr>\n  </tbody>\n</table>\n</div>", 
                        "text/plain": "   ENGINESIZE  CYLINDERS  FUELCONSUMPTION_COMB  CO2EMISSIONS\n0         2.0          4                   8.5           196\n1         2.4          4                   9.6           221\n2         1.5          4                   5.9           136\n3         3.5          6                  11.1           255\n4         3.5          6                  10.6           244"
                    }, 
                    "execution_count": 4, 
                    "metadata": {}
                }
            ], 
            "execution_count": 4
        }, 
        {
            "source": "plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS,  color='blue')\nplt.xlabel(\"Engine size\")\nplt.ylabel(\"Emission\")\nplt.show()", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "display_data", 
                    "data": {
                        "image/png": "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\n", 
                        "text/plain": "<Figure size 432x288 with 1 Axes>"
                    }, 
                    "metadata": {
                        "needs_background": "light"
                    }
                }
            ], 
            "execution_count": 67
        }, 
        {
            "source": "msk = np.random.rand(len(df)) < 0.8\ntrain = cdf[msk]\ntest = cdf[~msk]", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [], 
            "execution_count": 68
        }, 
        {
            "source": "train.shape", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "execute_result", 
                    "data": {
                        "text/plain": "(867, 4)"
                    }, 
                    "execution_count": 69, 
                    "metadata": {}
                }
            ], 
            "execution_count": 69
        }, 
        {
            "source": "test.shape", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "execute_result", 
                    "data": {
                        "text/plain": "(200, 4)"
                    }, 
                    "execution_count": 70, 
                    "metadata": {}
                }
            ], 
            "execution_count": 70
        }, 
        {
            "source": "cdf.shape", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "execute_result", 
                    "data": {
                        "text/plain": "(1067, 4)"
                    }, 
                    "execution_count": 71, 
                    "metadata": {}
                }
            ], 
            "execution_count": 71
        }, 
        {
            "source": "from sklearn.preprocessing import PolynomialFeatures\nfrom sklearn import linear_model\ntrain_x = np.asanyarray(train[['ENGINESIZE']])\ntrain_y = np.asanyarray(train[['CO2EMISSIONS']])\n\ntest_x = np.asanyarray(test[['ENGINESIZE']])\ntest_y = np.asanyarray(test[['CO2EMISSIONS']])\n\n\npoly = PolynomialFeatures(degree=3)\ntrain_x_poly = poly.fit_transform(train_x)\ntrain_x_poly", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "execute_result", 
                    "data": {
                        "text/plain": "array([[ 1.   ,  2.   ,  4.   ,  8.   ],\n       [ 1.   ,  2.4  ,  5.76 , 13.824],\n       [ 1.   ,  1.5  ,  2.25 ,  3.375],\n       ...,\n       [ 1.   ,  3.   ,  9.   , 27.   ],\n       [ 1.   ,  3.2  , 10.24 , 32.768],\n       [ 1.   ,  3.2  , 10.24 , 32.768]])"
                    }, 
                    "execution_count": 72, 
                    "metadata": {}
                }
            ], 
            "execution_count": 72
        }, 
        {
            "source": "clf = linear_model.LinearRegression()\ntrain_y_ = clf.fit(train_x_poly, train_y)\n# The coefficients\nprint ('Coefficients: ', clf.coef_)\nprint ('Intercept: ',clf.intercept_)", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "stream", 
                    "name": "stdout", 
                    "text": "Coefficients:  [[ 0.         37.30751358  2.28407606 -0.33141921]]\nIntercept:  [120.75649241]\n"
                }
            ], 
            "execution_count": 73
        }, 
        {
            "source": "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\nXX = np.arange(0.0, 10.0, 0.1)\nyy = clf.intercept_[0]+ clf.coef_[0][1]*XX+ clf.coef_[0][2]*np.power(XX, 2)+ clf.coef_[0][3]*np.power(XX, 3)\nplt.plot(XX, yy, '-r' )\nplt.xlabel(\"Engine size\")\nplt.ylabel(\"Emission\")", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "execute_result", 
                    "data": {
                        "text/plain": "Text(0, 0.5, 'Emission')"
                    }, 
                    "execution_count": 77, 
                    "metadata": {}
                }, 
                {
                    "output_type": "display_data", 
                    "data": {
                        "image/png": "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\n", 
                        "text/plain": "<Figure size 432x288 with 1 Axes>"
                    }, 
                    "metadata": {
                        "needs_background": "light"
                    }
                }
            ], 
            "execution_count": 77
        }, 
        {
            "source": "from sklearn.metrics import r2_score\n\ntest_x_poly = poly.fit_transform(test_x)\ntest_y_ = clf.predict(test_x_poly)\n\nprint(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y_ - test_y)))\nprint(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y_ - test_y) ** 2))\nprint(\"R2-score: %.2f\" % r2_score(test_y_ , test_y) )", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "stream", 
                    "name": "stdout", 
                    "text": "Mean absolute error: 24.17\nResidual sum of squares (MSE): 1028.73\nR2-score: 0.68\n"
                }
            ], 
            "execution_count": 75
        }, 
        {
            "source": "## Non-Linear Regression", 
            "cell_type": "markdown", 
            "metadata": {}
        }, 
        {
            "source": "### Quadratic Equation", 
            "cell_type": "markdown", 
            "metadata": {}
        }, 
        {
            "source": "x = np.arange(-5.0, 5.0, 0.1)\n\n##You can adjust the slope and intercept to verify the changes in the graph\n\ny = np.power(x,2)\ny_noise = 2 * np.random.normal(size=x.size)\nydata = y + y_noise\nplt.plot(x, ydata,  'bo')\nplt.plot(x,y, 'r') \nplt.ylabel('Dependent Variable')\nplt.xlabel('Indepdendent Variable')\nplt.show()", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "display_data", 
                    "data": {
                        "image/png": "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\n", 
                        "text/plain": "<Figure size 432x288 with 1 Axes>"
                    }, 
                    "metadata": {
                        "needs_background": "light"
                    }
                }
            ], 
            "execution_count": 80
        }, 
        {
            "source": "### Exponential", 
            "cell_type": "markdown", 
            "metadata": {}
        }, 
        {
            "source": "X = np.arange(-5.0, 5.0, 0.1)\n\n##You can adjust the slope and intercept to verify the changes in the graph\n\nY= np.exp(X)\n\nplt.plot(X,Y) \nplt.ylabel('Dependent Variable')\nplt.xlabel('Indepdendent Variable')\nplt.show()", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "display_data", 
                    "data": {
                        "image/png": "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\n", 
                        "text/plain": "<Figure size 432x288 with 1 Axes>"
                    }, 
                    "metadata": {
                        "needs_background": "light"
                    }
                }
            ], 
            "execution_count": 81
        }, 
        {
            "source": "### Logarithmic", 
            "cell_type": "markdown", 
            "metadata": {}
        }, 
        {
            "source": "X = np.arange(-5.0, 5.0, 0.1)\n\nY = np.log(X)\n\nplt.plot(X,Y) \nplt.ylabel('Dependent Variable')\nplt.xlabel('Indepdendent Variable')\nplt.show()", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "stream", 
                    "name": "stderr", 
                    "text": "/opt/conda/envs/Python36/lib/python3.6/site-packages/ipykernel/__main__.py:3: RuntimeWarning: invalid value encountered in log\n  app.launch_new_instance()\n"
                }, 
                {
                    "output_type": "display_data", 
                    "data": {
                        "image/png": "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\n", 
                        "text/plain": "<Figure size 432x288 with 1 Axes>"
                    }, 
                    "metadata": {
                        "needs_background": "light"
                    }
                }
            ], 
            "execution_count": 82
        }, 
        {
            "source": "### Sigmoid", 
            "cell_type": "markdown", 
            "metadata": {}
        }, 
        {
            "source": "X = np.arange(-5.0, 5.0, 0.1)\n\n\nY = 1-4/(1+np.power(3, X-2))\n\nplt.plot(X,Y) \nplt.ylabel('Dependent Variable')\nplt.xlabel('Indepdendent Variable')\nplt.show()", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "display_data", 
                    "data": {
                        "image/png": "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\n", 
                        "text/plain": "<Figure size 432x288 with 1 Axes>"
                    }, 
                    "metadata": {
                        "needs_background": "light"
                    }
                }
            ], 
            "execution_count": 83
        }, 
        {
            "source": "## Non-Linear Regression Implementation", 
            "cell_type": "markdown", 
            "metadata": {}
        }, 
        {
            "source": "import numpy as np\nimport pandas as pd\n\n#downloading dataset\n!wget -nv -O china_gdp.csv https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/china_gdp.csv\n    \ndf = pd.read_csv(\"china_gdp.csv\")\ndf.head(10)", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "stream", 
                    "name": "stdout", 
                    "text": "2019-07-14 06:27:01 URL:https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/china_gdp.csv [1218/1218] -> \"china_gdp.csv\" [1]\r\n"
                }, 
                {
                    "output_type": "execute_result", 
                    "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>Year</th>\n      <th>Value</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1960</td>\n      <td>5.918412e+10</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1961</td>\n      <td>4.955705e+10</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1962</td>\n      <td>4.668518e+10</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1963</td>\n      <td>5.009730e+10</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1964</td>\n      <td>5.906225e+10</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>1965</td>\n      <td>6.970915e+10</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>1966</td>\n      <td>7.587943e+10</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>1967</td>\n      <td>7.205703e+10</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>1968</td>\n      <td>6.999350e+10</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>1969</td>\n      <td>7.871882e+10</td>\n    </tr>\n  </tbody>\n</table>\n</div>", 
                        "text/plain": "   Year         Value\n0  1960  5.918412e+10\n1  1961  4.955705e+10\n2  1962  4.668518e+10\n3  1963  5.009730e+10\n4  1964  5.906225e+10\n5  1965  6.970915e+10\n6  1966  7.587943e+10\n7  1967  7.205703e+10\n8  1968  6.999350e+10\n9  1969  7.871882e+10"
                    }, 
                    "execution_count": 84, 
                    "metadata": {}
                }
            ], 
            "execution_count": 84
        }, 
        {
            "source": "plt.figure(figsize=(8,5))\nx_data, y_data = (df[\"Year\"].values, df[\"Value\"].values)\nplt.plot(x_data, y_data, 'ro')\nplt.ylabel('GDP')\nplt.xlabel('Year')\nplt.show()", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "display_data", 
                    "data": {
                        "image/png": "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\n", 
                        "text/plain": "<Figure size 576x360 with 1 Axes>"
                    }, 
                    "metadata": {
                        "needs_background": "light"
                    }
                }
            ], 
            "execution_count": 85
        }, 
        {
            "source": "X = np.arange(-5.0, 5.0, 0.1)\nY = 1.0 / (1.0 + np.exp(-X))\n\nplt.plot(X,Y) \nplt.ylabel('Dependent Variable')\nplt.xlabel('Indepdendent Variable')\nplt.show()", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "display_data", 
                    "data": {
                        "image/png": "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\n", 
                        "text/plain": "<Figure size 432x288 with 1 Axes>"
                    }, 
                    "metadata": {
                        "needs_background": "light"
                    }
                }
            ], 
            "execution_count": 86
        }, 
        {
            "source": "def sigmoid(x, Beta_1, Beta_2):\n     y = 1 / (1 + np.exp(-Beta_1*(x-Beta_2)))\n     return y", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [], 
            "execution_count": 129
        }, 
        {
            "source": "beta_1 = 0.3\nbeta_2 = 1990.0\n\n#logistic function\nY_pred = sigmoid(x_data, beta_1 , beta_2)\n\n#plot initial prediction against datapoints\nplt.plot(x_data, Y_pred*15000000000000.)\nplt.plot(x_data, y_data, 'ro')", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "execute_result", 
                    "data": {
                        "text/plain": "[<matplotlib.lines.Line2D at 0x7fe866bc6a20>]"
                    }, 
                    "execution_count": 130, 
                    "metadata": {}
                }, 
                {
                    "output_type": "display_data", 
                    "data": {
                        "image/png": "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\n", 
                        "text/plain": "<Figure size 432x288 with 1 Axes>"
                    }, 
                    "metadata": {
                        "needs_background": "light"
                    }
                }
            ], 
            "execution_count": 130
        }, 
        {
            "source": "# Lets normalize our data\nxdata =x_data/max(x_data)\nydata =y_data/max(y_data)", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [], 
            "execution_count": 131
        }, 
        {
            "source": "from scipy.optimize import curve_fit\npopt, pcov = curve_fit(sigmoid, xdata, ydata)\n#print the final parameters\nprint(\" beta_1 = %f, beta_2 = %f\" % (popt[0], popt[1]))", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "stream", 
                    "name": "stdout", 
                    "text": " beta_1 = 690.453017, beta_2 = 0.997207\n"
                }
            ], 
            "execution_count": 132
        }, 
        {
            "source": "x = np.linspace(1960, 2015, 55)\nx = x/max(x)\nplt.figure(figsize=(8,5))\ny = sigmoid(x, popt[0], popt[1])\nplt.plot(xdata, ydata, 'ro', label='data')\nplt.plot(x,y, linewidth=3.0, label='fit')\nplt.legend(loc='best')\nplt.ylabel('GDP')\nplt.xlabel('Year')\nplt.show()", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "display_data", 
                    "data": {
                        "image/png": "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\n", 
                        "text/plain": "<Figure size 576x360 with 1 Axes>"
                    }, 
                    "metadata": {
                        "needs_background": "light"
                    }
                }
            ], 
            "execution_count": 133
        }, 
        {
            "source": "# split data into train/test\nmsk = np.random.rand(len(df)) < 0.8\ntrain_x = xdata[msk]\ntest_x = xdata[~msk]\ntrain_y = ydata[msk]\ntest_y = ydata[~msk]\n\n# build the model using train set\npopt, pcov = curve_fit(sigmoid, train_x, train_y)\n\n# predict using test set\ny_hat = sigmoid(test_x, *popt)\n\n# evaluation\nprint(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\nprint(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\nfrom sklearn.metrics import r2_score\nprint(\"R2-score: %.2f\" % r2_score(y_hat , test_y) )", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [
                {
                    "output_type": "stream", 
                    "name": "stdout", 
                    "text": "Mean absolute error: 0.03\nResidual sum of squares (MSE): 0.00\nR2-score: 0.95\n"
                }
            ], 
            "execution_count": 134
        }, 
        {
            "source": "", 
            "cell_type": "code", 
            "metadata": {}, 
            "outputs": [], 
            "execution_count": null
        }
    ], 
    "metadata": {
        "kernelspec": {
            "display_name": "Python 3.6", 
            "name": "python3", 
            "language": "python"
        }, 
        "language_info": {
            "mimetype": "text/x-python", 
            "nbconvert_exporter": "python", 
            "version": "3.6.8", 
            "name": "python", 
            "pygments_lexer": "ipython3", 
            "file_extension": ".py", 
            "codemirror_mode": {
                "version": 3, 
                "name": "ipython"
            }
        }
    }, 
    "nbformat": 4
}