In multiple regression, 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 $S _ { \varepsilon }$ = 0, and the coefficient of determination $R ^ { 2 }$ = 1.

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When the regression surface perfectly fits all data points, there is no error in prediction, leading to SSE = 0, $S _ { \varepsilon }$ = 0, and $R ^ { 2 }$ = 1, indicating a perfect fit.

In Multiple Regression, When the Response Surface (The Graphical Depiction SεS _ { \varepsilon }Sε​

In Multiple Regression, When the Response Surface (The Graphical Depiction $S _ { \varepsilon }$