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 which condition must hold?
A) The sum of squared residuals must equal zero.
B) The sum of absolute residuals must equal zero.
C) The sum of the residuals for the observations with Finished Basements (=1) must be zero.
D) The correlation between the residuals and Home Prices must be equal to zero.

Question

Quizplus · Accepted Answer

In multiple regression analysis, one of the moment conditions for the ordinary least squares (OLS) estimator to be the best linear unbiased estimator (BLUE) is that the sum of the residuals (differences between observed and predicted values) for any subset of the data (such as those observations with a finished basement) must be orthogonal to the regressors, which implies their sum should be zero. This ensures that the model does not systematically over or underpredict for any particular group within the dataset.

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