SCENARIO 13-8 It is believed that GPA (grade point average, based on a four point scale)should have a positive linear relationship with ACT scores.Given below is the Excel output for predicting GPA using ACT scores based a data set of 8 randomly chosen students from a Big-Ten university.
-Referring to Scenario 13-8, the value of the measured (observed)test statistic of the F-test for
A)may be negative.
B)is always positive.
C)is always negative.
D)has the same sign as the corresponding t test statistic.

Question

SCENARIO 13-8 It is believed that GPA (grade point average, based on a four point scale)should have a positive linear relationship with ACT scores.Given below is the Excel output for predicting GPA using ACT scores based a data set of 8 randomly chosen students from a Big-Ten university. 
-Referring to Scenario 13-8, the value of the measured (observed)test statistic of the F-test for 
A)may be negative. 
B)is always positive. 
C)is always negative. 
D)has the same sign as the corresponding t test statistic.

Quizplus · Accepted Answer

The F-test statistic is always non-negative as it is calculated as the ratio of two sample variances, which are always non-negative. Therefore, the value of the measured F-test statistic is always positive. The F-test statistic is always positive, as it measures the ratio of the explained variance to the unexplained variance in the regression model. This value can never be negative, and it is not directly related to the sign of the t-test statistic for individual coefficients in the model.

SCENARIO 13-8 It Is Believed That GPA (Grade Point Average