Application Exercise Derive the Hat Matrix

In the Derive the Hat Matrix video, I derive the hat matrix. I skip a few steps when taking the derivative of \((y-\mathbf{X}\beta)^T(y-\mathbf{X}\beta)\). Fill in these steps and derive the hat matrix here (using \(\LaTeX\)). Don’t remember all of the \(\LaTeX\) symbols? Here is a cheat sheet.

Start with the sum of squared residuals:

\[\sum\epsilon^2 = \epsilon^T\epsilon = (y-\mathbf{X}\beta)^T(y-\mathbf{X}\beta)\]

1. Open Rstudio Server Pro
2. Create a new project (call it something sensible, perhaps 02-appex-hat-matrix)
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. After adding your derivation to the file (remember you can incorporate \(\LaTeX\) by wrapping in $$), knit it.
7. When you’ve finished, upload the .html file to Canvas