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

Using the data above calculate:

• The leverage for each observation. Are any “unusual”?

• The standardized residuals, \(r_i\).

• Show that

\[\hat{\textrm{var}}(y_{i} - \hat{y}_{(i)}) = \hat{\sigma}^2_{(i)}(1+x_i^T(\mathbf{X}_{(i)}^T\mathbf{X}_{(i)})^{-1}x_i)\]

• Using the data above, calculate \(\hat{\textrm{var}}(\hat{y})_{(i)}\) for observation 5.
• Calculate the studentized residuals for the data above.
• Calculate Cook’s Distance for the data above and plot it with the row number on the x-axis and Cook’s Distance on the y-axis.