{
 "cells": [
  {
   "metadata": {},
   "cell_type": "raw",
   "source": "",
   "id": "be6244de7cfcd701"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-29T05:29:36.933911Z",
     "start_time": "2024-08-29T05:29:36.504648Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "\n",
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 2 * np.random.rand(m,1)\n",
    "y = 4 + 3 * X + np.random.randn(m, 1)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.show()"
   ],
   "id": "3c81f81deea2c2a1",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 1
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-29T05:29:36.949411Z",
     "start_time": "2024-08-29T05:29:36.947675Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "3d9c6a63a93d52df",
   "outputs": [],
   "execution_count": null
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-29T05:29:37.321995Z",
     "start_time": "2024-08-29T05:29:37.039844Z"
    }
   },
   "cell_type": "code",
   "source": [
    "from sklearn.preprocessing import add_dummy_feature\n",
    "\n",
    "X_b = add_dummy_feature(X)\n",
    "theta_best = np.linalg.inv(X_b.T @ X_b) "
   ],
   "id": "4671b023cffc6931",
   "outputs": [],
   "execution_count": 2
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-29T05:29:37.331207Z",
     "start_time": "2024-08-29T05:29:37.329659Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "b084f1c82ff7bf4b",
   "outputs": [],
   "execution_count": null
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-29T05:29:37.377406Z",
     "start_time": "2024-08-29T05:29:37.375500Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "6aae850feb410978",
   "outputs": [],
   "execution_count": null
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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