{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f64907f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# CODE TO GENERATE bias_scatter.png\n",
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bf22eb4a",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array([1, 2, 3, 4, 5, 6]).reshape((-1, 1))\n",
    "y = np.array([6, 7, 8, 8, 9, 11])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b185d8b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_no_bias = LinearRegression(fit_intercept = False).fit(X, y)\n",
    "model_with_bias = LinearRegression().fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f5076cdc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "X_with_zero = np.vstack([0, X]) # Added to show the lines passing through Feature=0\n",
    "plt.scatter(X, y)\n",
    "plt.plot(X_with_zero, model_no_bias.predict(X_with_zero), color = 'b', label=\"Without bias\")\n",
    "plt.plot(X_with_zero, model_with_bias.predict(X_with_zero), color = 'r', label=\"With bias\")\n",
    "plt.ylim(ymin=0)\n",
    "plt.xlim(xmin=0, xmax=8)\n",
    "plt.xlabel(\"Feature\")\n",
    "plt.ylabel(\"Target\")\n",
    "plt.legend(loc=\"center right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e68dd023",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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