notebooks/linear-regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from scipy import stats\n",
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load titanic train dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_ds = pd.read_csv('../data/titanic/train.csv', delimiter=',')\n",
    "\n",
    "# Excluding age with NaN, filter fare in range(100, 400)\n",
    "train_ds = train_ds[(~train_ds['Age'].isnull()) & (train_ds['Fare'] < 400) & (train_ds['Fare'] > 100)]\n",
    "\n",
    "ages = train_ds['Age']\n",
    "fares = train_ds['Fare']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lr_model(a, b, ages):\n",
    "    return a * ages + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data preview"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "27     19.00\n",
      "88     23.00\n",
      "118    24.00\n",
      "195    58.00\n",
      "215    31.00\n",
      "268    58.00\n",
      "269    35.00\n",
      "297     2.00\n",
      "299    50.00\n",
      "305     0.92\n",
      "Name: Age, dtype: float64 45\n"
     ]
    }
   ],
   "source": [
    "print(ages[:10], len(ages))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "27     263.0000\n",
      "88     263.0000\n",
      "118    247.5208\n",
      "195    146.5208\n",
      "215    113.2750\n",
      "268    153.4625\n",
      "269    135.6333\n",
      "297    151.5500\n",
      "299    247.5208\n",
      "305    151.5500\n",
      "Name: Fare, dtype: float64 45\n"
     ]
    }
   ],
   "source": [
    "print(fares[:10], len(fares))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11eb6b588>]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "fig, ax = plt.subplots()\n",
    "ax.scatter(ages, fares, alpha=0.6)\n",
    "ax.set_xlabel(r'Age', fontsize=13)\n",
    "ax.set_ylabel(r'Fare', fontsize=13)\n",
    "ax.set_title('Age and Fare change')\n",
    "\n",
    "# a, b is calculated by running following command\n",
    "#\n",
    "# $ python algorithm/linear_regression.py data/titanic/train.csv\n",
    "#\n",
    "a, b = 1.3877787807814457e-16, 151.49999999999568\n",
    "\n",
    "hypothesis_fares = lr_model(a, b, ages)\n",
    "plt.plot(ages, hypothesis_fares, 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy version of linear regression (least-squares solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.lstsq.html#numpy.linalg.lstsq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.20436845912321858 173.93816467002722\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11e9d0e48>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "A = np.vstack([ages, np.ones(len(ages))]).T\n",
    "a, b = np.linalg.lstsq(A, fares, rcond=None)[0]\n",
    "print(a, b)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.plot(ages, fares, 'o', label='Original data', markersize=10)\n",
    "plt.plot(ages, a * ages + b, 'r', label='Fitted line')\n",
    "ax.set_xlabel(r'Age', fontsize=13)\n",
    "ax.set_ylabel(r'Fare', fontsize=13)\n",
    "ax.set_title('Age and Fare change')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scipy version of linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.linregress.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r-squared: 0.0030440317055870783\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11ea37e80>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "np.random.seed(12345678)\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(ages, fares)\n",
    "\n",
    "# To get coefficient of determination (r_squared)\n",
    "print(\"r-squared:\", r_value**2)\n",
    "\n",
    "plt.plot(ages, fares, 'o', label='original data')\n",
    "plt.plot(ages, intercept + slope * ages, 'r', label='fitted line')\n",
    "plt.legend()"
   ]
  },
  {
   "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}