{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "\n",
       "    /* DOWNLOAD COMPUTER MODERN FONT JUST IN CASE */\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunss.otf');\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        font-weight: bold;\n",
       "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunsx.otf');\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        font-style: oblique;\n",
       "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunsi.otf');\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        font-weight: bold;\n",
       "        font-style: oblique;\n",
       "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunso.otf');\n",
       "    }\n",
       "\n",
       "    /* GLOBAL TEXT FONT */\n",
       "    div#notebook,\n",
       "    div.output_area pre,\n",
       "    div.output_wrapper,\n",
       "    div.prompt {\n",
       "      font-family: Times new Roman, monospace !important;\n",
       "    }\n",
       "\n",
       "    /* CENTER FIGURE */\n",
       "    .output_png {\n",
       "        display: table-cell;\n",
       "        text-align: center;\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    /* LINK */\n",
       "    a {\n",
       "        color: #FF8000;\n",
       "    }\n",
       "\n",
       "    /* H1 */\n",
       "    h1 {\n",
       "        font-size: 42px !important;\n",
       "        text-align: center;\n",
       "        color: #FF8000;\n",
       "    }\n",
       "\n",
       "    /* H2 */\n",
       "    h2 {\n",
       "        font-size: 32px !important;\n",
       "    }\n",
       "\n",
       "    /* H2 */\n",
       "    h3 {\n",
       "        font-size: 24px !important;\n",
       "    }\n",
       "\n",
       "    /* H2 */\n",
       "    h4 {\n",
       "        font-size: 20px !important;\n",
       "    }\n",
       "\n",
       "    /* PARAGRAPH */\n",
       "    p {\n",
       "        font-size: 16px !important;\n",
       "        text-align: center;\n",
       "    }\n",
       "\n",
       "    /* LIST ITEM */\n",
       "    li {\n",
       "        font-size: 16px !important;\n",
       "    }\n",
       "\n",
       "</style>\n",
       "\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%run ../../common_functions/import_all.py\n",
    "\n",
    "from common_functions.setup_notebook import set_css_style, setup_matplotlib, config_ipython\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "config_ipython()\n",
    "setup_matplotlib()\n",
    "set_css_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression - an example\n",
    "\n",
    "This will use the dataset about head size and brain weight, from a 1905 Biometrika paper, see references at the bottom. The data is provided in this repo for convenience, under folder `datasets/`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('../../datasets/head_size_brain_weight.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/martina/Desktop/Mallzee/repos/plantation/venv/lib/python3.7/site-packages/ipykernel_launcher.py:10: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  # Remove the CWD from sys.path while we load stuff.\n",
      "/Users/martina/Desktop/Mallzee/repos/plantation/venv/lib/python3.7/site-packages/ipykernel_launcher.py:11: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  # This is added back by InteractiveShellApp.init_path()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11144f910>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x124609d10>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Head size (cm^3)')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Brain Weight (g)')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 379,
       "width": 622
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope of the fit:  [0.26342934]\n",
      "Intercept of the fit:  325.5734210494426\n"
     ]
    }
   ],
   "source": [
    "# Num samples\n",
    "n = df.count()['Head_size(cm^3)']\n",
    "\n",
    "# Invoking the regressor (fit the intercept as well)\n",
    "lr = LinearRegression(fit_intercept=True)\n",
    "\n",
    "# Getting x as head size columns and y as brain weight column\n",
    "# Reshaping x from (num_rows,) to (num_rows,1) for the regressor fit to work \n",
    "# (needed when using only one feature as fit method expects a matrix)\n",
    "x = df['Head_size(cm^3)'].as_matrix().reshape(n, 1)\n",
    "y = df['Brain_weight(g)'].as_matrix()\n",
    "\n",
    "# Fit the model\n",
    "fit = lr.fit(x, y)\n",
    "\n",
    "# Plot the data and the fitting line\n",
    "# Change the label index in the header_index key\n",
    "plt.scatter(x, y, color='black');\n",
    "plt.plot(x, fit.predict(x), color='blue')\n",
    "plt.xlabel('Head size (cm^3)')\n",
    "plt.ylabel('Brain Weight (g)')\n",
    "plt.savefig('linreg.png', dpi=200)\n",
    "plt.show();\n",
    "\n",
    "# Display the fitted slope and intercept of the fitting line\n",
    "print('Slope of the fit: ', fit.coef_)\n",
    "print('Intercept of the fit: ', fit.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "1. The head size and brain weight [dataset](http://users.stat.ufl.edu/~winner/data/brainhead.txt), data from R J Gladstone, A study of the brain to the size of the head, Biometrika, 4, 105-123 (1905)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
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}