linear_models.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3f3e3698-4321-43d9-855c-149a3950a280",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f15ec7a2-a1ea-4c4d-9be0-1837b879224b",
   "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": "code",
   "execution_count": 39,
   "id": "ee732cec-e690-48dc-8bed-f33ef0f26bf0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "X = 2 * np.random.rand(100, 1)\n",
    "y = 4 + 3 * X + np.random.randn(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "bbc157ee-101e-414a-88b3-d5901c6bf362",
   "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": [
    "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": 41,
   "id": "c972e1d2-37fd-4bcb-adff-abc2fe497ff9",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_b = np.c_[np.ones((100, 1)), X]  # add x0 = 1 to each instance\n",
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "7ab8a9be-0ce6-4abd-9109-c36f9161f2a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.61308771],\n",
       "       [3.35788041]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "bbedb503-fa18-44d5-bd87-0e9f30d8fdca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.61308771],\n",
       "       [10.32884852]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = np.c_[np.ones((2, 1)), X_new]  # add x0 = 1 to each instance\n",
    "y_predict = X_new_b.dot(theta_best)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "7d5e308c-16a1-4a2a-9b91-58d317723ad5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "5bf33f10-7827-4b94-b34d-55d4ed3c9c94",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "400245ae-3049-4a85-8580-4c8f1201229c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([3.61308771]), array([[3.35788041]]))"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression().fit(X,y)\n",
    "lin_reg.intercept_ , lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "6df22f8a-8ab9-4f60-a868-bb614756c767",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.61308771],\n",
       "       [10.32884852]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "964dbaf1-e49c-4250-b907-1b3719e0a0fa",
   "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",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}