In multiple regression analysis,which one of the following is the appropriate notation for error (residual)?
A) $y _ {i } - \bar { y }$
B) $y _ { i } - \hat { y } _ { i }$
C) $\hat { y } _ { i } - \bar { y }$
D) $\bar { y } - \hat { y } _ { i }$
E)None of these

Question

Quizplus · Accepted Answer

The error or residual in multiple regression analysis is the difference between the actual value of the dependent variable and the predicted value (based on the independent variables). Therefore, the appropriate notation for error is the difference between the observed dependent variable (y) and the predicted value of y, represented by the fitted value (ŷ). This is option B: yᵢ - ŷᵢ. Option A represents the deviation of each observation from the mean, which is not the same as the residual, while options C and D represent the difference between two estimates, which is not a residual. Therefore, the correct answer is B.

In Multiple Regression Analysis,which One of the Following Is the Appropriate