Application Exercise

Show that \(E[\hat\beta|\mathbf{X}] = \beta\). Start with the equation below.

\[E[\hat{\beta}|\mathbf{X}] = E[\mathbf{I}\beta +(\mathbf{X}^T\mathbf{X})^{-1}\mathbf{X}^T\epsilon|\mathbf{X}]\]

  1. Open Rstudio Server Pro
  2. Create a new project (call it something sensible, perhaps 03-appex-expectation)
  3. Click File > New File > R Markdown
  4. Delete everything except for
---
title: "Untitled"
output: html_document
---
  1. Give your work a sensible title
  2. After adding your derivation to the file (remember you can incorporate \(\LaTeX\) by wrapping in $$), knit it.
  3. When you’ve finished, upload the .html file to Canvas