Suppose you're running a multiple regression of Home Prices on two treatment variables, City, which is a binary variable for whether or not the home is located in a city or not, and Finished Basement, which is a binary variable for whether or not the home has a finished basement. If you solve for the multiple regression using the moment conditions all of the following conditions must hold except for what?
A) The sum of residuals must equal zero.
B) The correlation between the residuals and Home Prices must be equal to zero.
C) The correlation between the residuals and City must be equal to zero.
D) The correlation between the residuals and Finished Basement must be equal to zero.

Question

Quizplus · Accepted Answer

In multiple regression analysis, the sum of residuals is indeed expected to equal zero (A), and the residuals should not be correlated with the independent variables (C and D), ensuring that the model accounts for the variability in the dependent variable related to those predictors. However, the correlation between the residuals and the dependent variable (Home Prices) (B) does not need to be zero. The residuals represent the error or the part of the dependent variable not explained by the model, so they are inherently related to the dependent variable but not in a way that would result in a zero correlation by necessity.

Suppose You're Running a Multiple Regression of Home Prices on Two