In simple linear regression analysis, if the residual sum of squares is zero, then the coefficient of determination $r ^ { 2 }$ must be
A) -1
B) 0
C) between -1 and zero
D) 1
E) between -1 and 1

Question

Quizplus · Accepted Answer

The coefficient of determination, $r^2$, measures the proportion of the variance in the dependent variable that is predictable from the independent variable. If the residual sum of squares is zero, it means all points perfectly fit the regression line, indicating a perfect linear relationship. Therefore, $r^2$ must be 1, indicating 100% of the variance in the dependent variable is explained by the model.

In Simple Linear Regression Analysis, If the Residual Sum of Squares