THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A professor of statistics is interested in studying the relationship between the number of hours graduate students spent studying for his comprehensive final exam and the exam score.The results of the regression analysis of hours studied on exam scores are presented below.
-If the coefficient of determination is 1.0 in a regression problem,the:
A)residual sum of squares must be 0.0.
B)error sum of squares must be 1.0.
C)regression sum of squares must be 1.0.
D)total sum of squares must be 0.0.

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A professor of statistics is interested in studying the relationship between the number of hours graduate students spent studying for his comprehensive final exam and the exam score.The results of the regression analysis of hours studied on exam scores are presented below. 
-If the coefficient of determination is 1.0 in a regression problem,the:
A)residual sum of squares must be 0.0. 
B)error sum of squares must be 1.0. 
C)regression sum of squares must be 1.0. 
D)total sum of squares must be 0.0.

Quizplus · Accepted Answer

If the coefficient of determination is 1.0, it means that all the variation in the dependent variable (exam scores in this case) is explained by the independent variable (hours studied). This implies that there is no unexplained variation or error in the regression model, so the residual sum of squares (RSS) must be 0.0. The RSS measures the amount of unexplained variation in the model, so if it's 0.0, that means there is no unexplained variation.