--- 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')" format: html: theme: cosmo number-sections: true toc: true toc-depth: 4 toc-location: left code-fold: false engine: knitr knitr: opts_chunk: fig.align: 'center' # fig.width: 6 # fig.height: 4 message: FALSE cache: false --- ## 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 $f(X) = 0$.