It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. 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.

Regressing GPA on ACT

Regression Statistics

Multiple R 0.7598

R Square 0.5774

Adjusted R Square 0.5069

Standard Error 0.2691

OBservations 8

ANOVA

df SS MS F Significance F

Regression 1 0.5940 0.5940 8.1986 0.0286

Residual 6 0.4347 0.0724

Total 7 1.287

Coefficients Standard Error t Stat P-Value Lower 95% Upper 95%

Intercept 0.5681 0.9284 0.6119 0.5630 -1.7036 2.8398

ACT 0.1021 0.0356 2.8633 0.0286 0.0148 0.11895

the interpretation of the coefficient of determination in this regression?

what is the predicted value of GPA when ACT = 20?

value of the measured test statistic to test whether there is any linear relationship between GPA and ACT ?

what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between GPA and ACT scores????

Do not reject the null hypothesis; hence there is insufficient evidence to show that ACT scores and GPA are linearly related.

Reject the null hypothesis; hence there is insufficient evidence to show that ACT scores and GPA are linearly related.

Do not reject the null hypothesis; hence there is sufficient evidence to show that ACT scores and GPA are linearly related.

Reject the null hypothesis; hence there is sufficient evidence to show that ACT scores and GPA are linearly related.