You are using OLS to fit a regression equation. True or false, and explain:

(a) If you exclude a variable from the equation, but the excluded variable is orthogonal to the other variables in the equation, you won’t bias the estimated coefficients of the remaining variables.

(b) If you exclude a variable from the equation, and the excluded variable isn’t orthogonal to the other variables, your estimates are going to be biased.

(c) If you put an extra variable into the equation, you won’t bias the estimated coefficients—as long as the error term remains independent of the explanatory variables.

(d) If you put an extra variable into the equation, you are likely to bias the estimated coefficients—if the error term is dependent on that extra variable.