Solutions Statistics

It is believed that GPA (grade point average, based on a four point scale) should have a positive li

Question: 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 from regressing GPA on ACT scores using 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 1.0287
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 0.1895

(a) State the regression equation.

(b) Interpret the meaning of b0 and b1 in this problem.

(c) What is the predicted average value of GPA when ACT = 32?

(d) At the 0.05 level of significance, is there evidence of a linear relationship between the GPA and ACT?

(e) Construct a 95% confidence interval estimate of the population slope β1. Interpret the confidence interval estimate.

(f) How useful do you think this regression model is for predicting GPA?

Price: $2.99
See Answer: The solution file consists of 2 pages
Deliverables: Word Document


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