Scikit-learn LinearRegression vs Numpy Polyfit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scikit-learn LinearRegression vs Numpy Polyfit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "x = [9, 28, 38, 58, 88, 98, 108, 118, 128, 138, 148, 158, 168, 178, 188, 198, 208, 218, 228, 238, 278, 288, 298]\n",
    "y = [51, 80, 112, 294, 286, 110, 59, 70, 56, 70, 104, 59, 59, 72, 87, 99, 64, 60, 74, 151, 157, 57, 83]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.title(\"Test data observation\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def error(f, x, y):\n",
    "    return sp.sum((f(x)-y)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy.polyfit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "fx = np.linspace(min(x), max(x), 100) # x-axis data points\n",
    "f1 = np.polyfit(x, y, 1)\n",
    "f2 = np.polyfit(x, y, 2)\n",
    "f3 = np.polyfit(x, y, 3)\n",
    "f4 = np.polyfit(x, y, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ -0.1605313  125.77023172]\n",
      "[ 7.97183228e-04 -4.07809516e-01  1.39787684e+02]\n",
      "[ 3.89638135e-05 -1.74165800e-02  1.88213131e+00  7.84214050e+01]\n",
      "[-1.07313899e-06  7.02970734e-04 -1.50591781e-01  1.13179608e+01\n",
      " -7.54496044e+01]\n"
     ]
    }
   ],
   "source": [
    "print(f1)\n",
    "print(f2)\n",
    "print(f3)\n",
    "print(f4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: [-0.1605313]\n",
      "Intercept: 125.77023172322039\n",
      "Error: 92743.77449407903\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: [ 0.00079718 -0.40780952]\n",
      "Intercept: 139.7876843734297\n",
      "Error: 92025.81182290475\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: [ 3.89638135e-05 -1.74165800e-02  1.88213131e+00]\n",
      "Intercept: 78.4214049819388\n",
      "Error: 82768.48920722329\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: [-1.07313899e-06  7.02970734e-04 -1.50591781e-01  1.13179608e+01]\n",
      "Intercept: -75.44960440261413\n",
      "Error: 51070.95819968556\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for coefs in [f1, f2, f3, f4]:\n",
    "    f = np.poly1d(coefs)\n",
    "    print('Coefficients: {}'.format(coefs[:-1]))\n",
    "    print('Intercept: {}'.format(coefs[-1]))\n",
    "    print('Error: {}'.format(error(f, x, y)))\n",
    "\n",
    "    fitted_curve = np.poly1d(coefs)(fx)\n",
    "    plt.scatter(x, y, label=\"observed\")\n",
    "    plt.plot(fx, fitted_curve, c=\"red\", label=\"fitted\")\n",
    "    plt.grid()\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scikit-learn.LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.pipeline import Pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.1605313]\n",
      "125.77023172322043\n",
      "92743.77449407903\n"
     ]
    }
   ],
   "source": [
    "poly1d = PolynomialFeatures(degree=1)\n",
    "X1 = poly1d.fit_transform(np.array(x).reshape(-1, 1))\n",
    "linear_reg_1d = LinearRegression()\n",
    "linear_reg_1d.fit(X1, y)\n",
    "print(linear_reg_1d.coef_[1:])\n",
    "print(linear_reg_1d.intercept_)\n",
    "print(np.linalg.norm(y - linear_reg_1d.predict(X1)) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.40780952  0.00079718]\n",
      "139.78768437342626\n",
      "92025.81182290474\n"
     ]
    }
   ],
   "source": [
    "poly2d = PolynomialFeatures(degree=2)\n",
    "X2 = poly2d.fit_transform(np.array(x).reshape(-1, 1))\n",
    "linear_reg_2d = LinearRegression()\n",
    "linear_reg_2d.fit(X2, y)\n",
    "print(linear_reg_2d.coef_[1:])\n",
    "print(linear_reg_2d.intercept_)\n",
    "print(np.linalg.norm(y - linear_reg_2d.predict(X2)) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.88213131e+00 -1.74165800e-02  3.89638135e-05]\n",
      "78.42140498235423\n",
      "82768.4892072233\n"
     ]
    }
   ],
   "source": [
    "poly3d = PolynomialFeatures(degree=3)\n",
    "X3 = poly3d.fit_transform(np.array(x).reshape(-1, 1))\n",
    "linear_reg_3d = LinearRegression()\n",
    "linear_reg_3d.fit(X3, y)\n",
    "print(linear_reg_3d.coef_[1:])\n",
    "print(linear_reg_3d.intercept_)\n",
    "print(np.linalg.norm(y - linear_reg_3d.predict(X3)) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.13179615e+01 -1.50591791e-01  7.02970776e-04 -1.07313906e-06]\n",
      "-75.44961766310675\n",
      "51070.958199685454\n"
     ]
    }
   ],
   "source": [
    "poly4d = PolynomialFeatures(degree=4)\n",
    "X4 = poly4d.fit_transform(np.array(x).reshape(-1, 1))\n",
    "linear_reg_4d = LinearRegression()\n",
    "linear_reg_4d.fit(X4, y)\n",
    "print(linear_reg_4d.coef_[1:])\n",
    "print(linear_reg_4d.intercept_)\n",
    "print(np.linalg.norm(y - linear_reg_4d.predict(X4)) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regression_line(model, coefs, intercept, X_):\n",
    "    print('Coefficients: {}'.format(coefs))\n",
    "    print('Intercept: {}'.format(intercept))\n",
    "    print('Error: {}'.format(np.linalg.norm(y - model.predict(X_)) ** 2))\n",
    "\n",
    "    plt.scatter(x, y, label=\"observed\")\n",
    "    plt.plot(x, model.predict(X_), c='red', label=\"fitted\")\n",
    "    plt.grid()\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: [-0.1605313]\n",
      "Intercept: 125.77023172322043\n",
      "Error: 92743.77449407903\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "regression_line(linear_reg_1d, linear_reg_1d.coef_[1:], linear_reg_1d.intercept_, X1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: [-0.40780952  0.00079718]\n",
      "Intercept: 139.78768437342626\n",
      "Error: 92025.81182290474\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "regression_line(linear_reg_2d, linear_reg_2d.coef_[1:], linear_reg_2d.intercept_, X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: [ 1.88213131e+00 -1.74165800e-02  3.89638135e-05]\n",
      "Intercept: 78.42140498235423\n",
      "Error: 82768.4892072233\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "regression_line(linear_reg_3d, linear_reg_3d.coef_[1:], linear_reg_3d.intercept_, X3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: [ 1.13179615e+01 -1.50591791e-01  7.02970776e-04 -1.07313906e-06]\n",
      "Intercept: -75.44961766310675\n",
      "Error: 51070.958199685454\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "regression_line(linear_reg_4d, linear_reg_4d.coef_[1:], linear_reg_4d.intercept_, X4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}