{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Homework 8.1: Lasso and Ridge regression on the Advertising data set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this homework you will perform lasso and ridge regression on the advertising data set.\n",
    "The following cell imports the data set (adjust the path as necessary)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "adv = pd.read_csv('./datasets/Advertising.csv', index_col=0)\n",
    "X = adv.values[:,0:3]\n",
    "y = adv.values[:,3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Perform both lasso and ridge regression on the data.\n",
    "Read the documentation for the functions `RidgeCV` and `LassoCV` from `sklearn.linear_model`.\n",
    "These functions select the regularization parameter by cross-validation, as we did by hand in Problem 8.\n",
    "Use 5-fold cross-validation and the following range for $\\alpha$: `np.logspace(-4,4,100)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Compute the $R^2$-scores for both lasso and ridge regression. Which coefficients are selected by the lasso?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: At the end of Exercise 3 and in the lecture, we noticed that there may exist interactions or higher order variations among the predictor variables.\n",
    "Use the function `PolynomialFeatures` from `sklearn.preprocessing` to add quadratic terms as well as interaction terms between the predictors. How does this improve your $R^2$-score?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}