In regression analysis,if the coefficient of determination is 1.0,then:
A)the sum of squares for error must be 1.0
B)the sum of squares for regression must be 1.0
C)the sum of squares for error must be 0.0
D)the sum of squares for regression must be 0.0

Question

Quizplus · Accepted Answer

The coefficient of determination, denoted by R-squared, is the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, if R-squared is 1.0, it means that all of the variance in the dependent variable is accounted for by the independent variable, and there is no error left unexplained. This implies that the sum of squares for error (SSE) must be zero, as there is no unexplained variance. Option A and B are incorrect because they refer to the sum of squares, which is a measure of variability, and does not provide information about the strength of the relationship between the variables. Option D is also incorrect because the sum of squares for regression (SSR) represents the variability explained by the independent variable and would be large if the coefficient of determination is 1.0.

In Regression Analysis,if the Coefficient of Determination Is 1