If one was estimating a simple regression of Earnings (Y) on Height of individuals (X), and got a coefficient on the Height variable of 30, what would the intercept be if you added 3 inches to every individual in the sample but kept their earnings the same?
A) 30
B) Above 30, but not enough information to tell exactly.
C) Below 30, but not enough information to tell exactly.
D) None of these choices are correct.

Question

Quizplus · Accepted Answer

The intercept in a regression equation represents the expected value of the dependent variable (Y, which is Earnings in this case) when all independent variables (X, which is Height in this case) are equal to zero. Adding 3 inches to every individual's height without changing their earnings would shift the regression line horizontally, not vertically. This means the slope (coefficient on the Height variable) would remain the same, but the intercept would change to reflect the new relationship between height and earnings. However, without knowing the original intercept or the specific distribution of heights and earnings, we cannot determine the exact new value of the intercept, only that it would change to maintain the same earnings at the new heights. Therefore, the correct answer is that none of the provided choices accurately describe the change in the intercept.

If One Was Estimating a Simple Regression of Earnings (Y)