Question

When the predictor variable is coded so that barx=0 and the normal error regression model (2.1) applies, are b ₀ and b₁ independent?

a. Yes
b. No
c. Not enough information
d. Depends on the sample size

Answer 1

When the mean of the predictor variable is zero, the OLS regression model coefficients b₀ and b₁ are independent of each other. Option A is correct.

Step-by-step explanation:

When the predictor (independent) variable is coded so that the mean of the predictor variable (Õ) is zero, the ordinary least squares (OLS) regression model coefficients b₀ (intercept) and b₁ (slope) are supposed to be uncorrelated, meaning they are independent of each other.

This independence arises because with Õ = 0, the sum of the cross-products of the predictor variable and the errors equals zero, which implies that b₀, which estimates the expected value of the dependent variable when the predictor is at its mean, is not influenced by the value of b₁, which estimates the change in the dependent variable per unit change in the predictor variable. Therefore, the answer to the question is (a) Yes.