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.
-Which of the following statements must be true,if the regression sum of squares (SSR)is 83.6?
A)The correlation coefficient is 0.95
B)The slope of the regression line is positive.
C)The error sum of squares (SS
E)is larger than or equal to 83.6
D)The total sum of squares (SS
T)is larger than or equal to 83.6

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. 
-Which of the following statements must be true,if the regression sum of squares (SSR)is 83.6?
A)The correlation coefficient is 0.95 
B)The slope of the regression line is positive. 
C)The error sum of squares (SS
E)is larger than or equal to 83.6 
D)The total sum of squares (SS
T)is larger than or equal to 83.6

Quizplus · Accepted Answer

The total sum of squares (SST) represents the variation in the response variable and is always larger than or equal to SSR. Therefore, if SSR is 83.6, then SST must be larger than or equal to 83.6. Option A and B cannot be determined based on just the SSR value. Option C is false since SSE always represents the unexplained or leftover variation after accounting for variation due to the regression model, and should be smaller than SSR in a well-fitting model.