In multiple regression analysis, when the response surface (the graphical depiction of the regression equation) hits every single point, the sum of squares for error SSE = 0, the standard error of estimate = 0, and the coefficient of determination = 1.

Question

In multiple regression analysis, when the response surface (the graphical depiction of the regression equation) hits every single point, the sum of squares for error SSE = 0, the standard error of estimate  = 0, and the coefficient of determination  = 1.

Quizplus · Accepted Answer

If the response surface hits every single point, this implies that the regression equation is a perfect fit for the data, meaning there is no error between the predicted values and the actual values. Therefore, SSE = 0, and the coefficient of determination, R-squared, equals 1. Additionally, the standard error of estimate, which measures the variation of the actual values around the predicted values, would be 0 in this scenario.

In Multiple Regression Analysis, When the Response Surface (The Graphical