Application Exercise

1. Open Rstudio Server Pro
2. Create a new project
3. Click File > New File > R Markdown
4. Delete everything except for

---
title: "Untitled"
output: html_document
---

5. Give your work a sensible title
6. When you’ve finished, upload the .html file to Canvas

• In R, find a design matrix X where it is not possible to calculate \(\hat\beta\)

solve(t(X) %*% X) %*% t(X) %*% y

• Calculate the determinant of the following matrices in R using the det() function:

\[\mathbf{A} = \begin{bmatrix} 1 & 2 \\ 4 & 5 \end{bmatrix}\]

\[\mathbf{B} = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 6 & 9 \\ 2 & 5 & 7\end{bmatrix}\] * Are these both invertible?

• Find \(\hat\beta\) that minimizes this:

\[(\mathbf{y}-\mathbf{X}\beta)^T(\mathbf{y}-\mathbf{X}\beta)+\lambda\beta^T\beta\]