The variance of Yi is given by
A) + var(Xi)+ var(ui).
B)the variance of ui.
C) var(Xi)+ var(ui).
D)the variance of the residuals.

Question

The variance of Yi is given by
A) + var(Xi)+ var(ui). 
B)the variance of ui. 
C) var(Xi)+ var(ui). 
D)the variance of the residuals.

Quizplus · Accepted Answer

The formula for variance of Y is Var(Yi) = Var(a + bXi + ui) = Var(bXi + ui) since a is a constant. This can then be expanded using the properties of variance to get Var(Yi) = b^2Var(Xi) + Var(ui) since Var(aX) = a^2Var(X) and Cov(X,Y) = 0 when X and Y are independent. Therefore, the formula given in option C is the correct expression for the variance of Yi. Options A, B, and D are either incorrect or incomplete.

The Variance of Yi Is Given by