2010 practice question 7

[[email protected]]

Hi David,
Could you help with my question below?

Question: Which of the following statements about the ordinary least squares regression model (or simple regression model) with one independent variable are correct?

i. In the ordinary least squares (OLS) model, the random error term is assumed to have zero mean and constant variance.
ii. In the OLS model, the variance of the independent variable is assumed to be positively correlated with the variance of the error term.
iii. In the OLS model, it is assumed that the correlation between the dependent variable and the random error term is zero.
iv. In the OLS model, the variance of the dependent variable is assumed to be constant.

a. i, ii, iii, and iv
b. ii and iv only
c. i and iv only
d. i, ii, and iii only
The answer is c.
My question is for iii. Why is it incorrect? Isn't it one of the requirements of the regression model? If the errors and y are correlated, the variance of errors can't be constant then since it may vary with y. Am I right?

 

[David Harper CFA FRM]

Hi ldcn,

Yes, agreed, while perhaps not a technical CLRM assumption, per Gujarati's 6.24 PROOF, the errors and the predicted Y are uncorrelated. Looks like a blatant mistake in the Q&A.

But i really like how you used logic to implicate heteroskedasticity, that's the way to own the regression!! David