Lecture Overview:

• Some inference questions with the housing data
• Multicollinearity and it effects (Ch 7.6)
• Polynomial regression models

Some inference questions with the housing data (will be in lecture 7 r code)

mod3 = lm(log(price) ~ size + bed + bath)
summary(mod3)

Some inference questions on this full model:

$X_1$: size

$X_2$: bedroom

$X_3$: bathroom

The estimated model

$\hat{Y}=12.35+0.400X_1-0.058X_2+0.051X_3$

Q1: Construct a 95% confidence interval on $\beta_!$:

confint(mod3)

##                      2.5 %         97.5 %
## (Intercept)    12.28897274    12.36184027
## size            0.38336891     0.41667762
## bed            -0.07114635    -0.04584463
## bath            0.03236653     0.06909401

Q2: Construct Bonferroni 95% joint confidence interval on $\beta_1,\beta_2,\beta_3$

$1-3\alpha=0.95, where~~\alpha=0.016667$