Multicollinearity: What Happens if the
Regressors Are Correlated?
You should know the formulas:
VIF =
1
1 – r2
23
(8)
var( ˆ 2) = 2
P
x22
i
VIF (9)
var( ˆ 3) = 2
P
x23
i
VIF (10)
1. Why does the classical linear model assume that there is no multicollinearity
among the explanatory variables? What is the consequence of perfect
multicollinearity for the regression coefficients and their standard errors?
Of less than perfect multicollinearity? (
2. What are the practical consequences of high multicollinearity?
3. What is the Variance-Inflating Factor ( VIF)? What d oes t he Variance-
Inflating Factor show? How is the Variance-Inflating Factor used to
detect multicollinearity?
4. Give three ways to detect multicollinearity (
5. Explain how transformation of variables can sometimes address the problem
of multicollinearity. Give two examples of possible transformations.
Heteroscedasticity: What Happens if the Error
Variance Is Nonconstant?
1. Illustrate the nature of homoscedasticity and heteroscedasticity in two
diagrams.
2. Give three (out of seven) reasons for heteroscedasticity. Briefly
explain.
3. What happens to ordinary least squares estimators and their variances in
the presence of heteroscedasticity?