Lecture Overview:

• What could go wrong? (Ch. 3)
• Linearity of Regression Function
• Assumptions on error terms
• Unusual Observations

What Could go Wrong? (Ch. 3)

• We don’t know in advance whether the model is appropriate.
• It’s important to examine the aptness of the model before making inferences.
  • Model: The model structure is correct $E(Y)=\beta_0+\beta_1X$
  • Error: $\epsilon_i\sim^{iid}\mathcal{N}(0,\sigma^2)$
  • Unusual Observations: sometimes just a few observations do not fit the model. These few observations might change the choice and fit of the model.

Linearity of Regression Function

• Nonlinearity of the regression function can be studied from a scatter plot, but is not always effective.
• Residual plots
  • Residual plot against the predictor variable
  • Residual plot against the fitted values

Linearity Check

Toluca Company Example:

library("ALSM")
mydata = TolucaCompany
X = mydata$x
Y = mydata$y

mymodel = lm(Y ~ X)
residuals(mymodel)

plot(X, mymodel$residuals, col = "orange", pch = 16, ylim=c(-120,150))
abline(h = 0)