Day 17 - 09/27/2024

From last class

• Our assumptions should represent the data generating process as good as possible.
  
• We are working on assessing the degree of violation of our assumptions.
  
• Graphical/descriptive methods // Test methods

model checking

ASSUMPTIONS BEHIND

\[\mathbf{y} \sim \text{N}(\boldsymbol{\mu}, \sigma^2\mathbf{I}),\]

\[\boldsymbol{\mu} = \mathbf{X}\boldsymbol{\beta}.\]

• Linearity
  
• Homoscedasticity (i.e., constant variance)
  
• Residuals are iid \(\sim N(0, \sigma^2)\)
  • Independent 
  • Normally distributed
    

Live R code. A not-so-obvious example

R code

Next week

• Read chapters 4 and 5.
  
• Assignment guide is up.