Var(uᵢ | X₁ᵢ, X₂ᵢ) = 6 and var(X₁ᵢ) = 2.
A random sample of size n = 300 is drawn from the population. Assume that X₁ᵢ and X₂ᵢ are uncorrelated.
(a) Compute the variance of ^β₁.
(b) Assume that Corr(X₁ᵢ, X₂ᵢ) = 0.9. Compute the variance of ^β₁.
(c) Comment on the following statement:
"When X₁ᵢ and X₂ᵢ are correlated, the variance of ^β₁ is larger than it would be if X₁ᵢ and X₂ᵢ were uncorrelated. Thus, if you are interested in β₁, it is best to leave X₂ out of the regression if it is correlated with X₁."