TABLE 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 Table 13-8, the value of the measured (observed) test statistic of the F-test for H₀: β₁ = 0 vs. H₁: β₁ ≠ 0
A) may be negative.
B) is always positive.
C) is always negative.
D) has the same sign as the corresponding t test statistic.

Question

TABLE 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 Table 13-8, the value of the measured (observed) test statistic of the F-test for H₀: β₁ = 0 vs. H₁: β₁ ≠ 0
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-statistic is always positive and represents the ratio of the explained variance to the unexplained variance. A negative value for this statistic would not make sense in the context of linear regression. The sign of the F-statistic is not necessarily the same as the corresponding t-test statistic, which tests the significance of individual coefficients, whereas the F-test tests the overall significance of the model.

TABLE 13-8 It Is Believed That GPA (Grade Point Average, Based on Based