{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e74eea63-24c7-4bba-9cf1-3a0799c1a13f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Python ≥3.5 is required\n",
    "import sys\n",
    "assert sys.version_info >= (3, 5)\n",
    "\n",
    "# Scikit-Learn ≥0.20 is required\n",
    "import sklearn\n",
    "assert sklearn.__version__ >= \"0.20\"\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "mpl.rc('axes', labelsize=14)\n",
    "mpl.rc('xtick', labelsize=12)\n",
    "mpl.rc('ytick', labelsize=12)\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"training_linear_models\"\n",
    "IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID)\n",
    "os.makedirs(IMAGES_PATH, exist_ok=True)\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
    "    path = os.path.join(IMAGES_PATH, fig_id + \".\" + fig_extension)\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format=fig_extension, dpi=resolution)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0e4cb91-b959-4b4c-a8f8-8c6b91a1407f",
   "metadata": {},
   "source": [
    "A linear model makes a prediction by simply computing a weighted sum of the input features, plus a constant called the _bias term_ (also called the _intercept term_)\n",
    "\n",
    "$$ \\hat{y} = h_{\\boldsymbol{θ}}(\\boldsymbol{x}) = \\boldsymbol{θ} · \\boldsymbol{x}  = θ_0 + θ_1x_1 + θ_2x_2 + \\ldots + θ_nx_n$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a7a27aef-62d9-46f7-8876-42669ccb1ce8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure generated_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = 2 * np.random.rand(100, 1)\n",
    "y = 4 + 3 * X + np.random.randn(100, 1)\n",
    "\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "save_fig(\"generated_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c562d2dc-3c69-4707-85de-4a60843abde0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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