---
title: "Econ 425T Homework 5"
subtitle: "Due Mar 8, 2023 @ 11:59PM"
author: "YOUR NAME and UID"
date: "`r format(Sys.time(), '%d %B, %Y')`"
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## ISL Exercise 9.7.1 (10pts)

## ISL Exercise 9.7.2 (10pts)

## Support vector machines (SVMs) on the `Carseats` data set (30pts)

Follow the machine learning workflow to train support vector classifier (same as SVM with linear kernel), SVM with polynomial kernel (tune the degree and regularization parameter $C$), and SVM with radial kernel (tune the scale parameter $\gamma$ and regularization parameter $C$) for classifying `Sales<=8` versus `Sales>8`. Use the same seed as in your HW4 for the initial test/train split and compare the final test AUC and accuracy to those methods you tried in HW4.

## Bonus (10pts)

Let
$$
f(X) = \beta_0 + \beta_1 X_1 + \cdots + \beta_p X_p = \beta_0 + \beta^T X. 
$$
Then $f(X)=0$ defines a hyperplane in $\mathbb{R}^p$. Show that $f(x)$ is proportional to the signed distance of a point $x$ to the hyperplane $f(X) = 0$.