Math Solutions

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

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
  1. State the regression equation.
  2. Interpret the meaning of b 0 and b 1 in this problem.
  3. What is the predicted average value of GPA when ACT = 32?
  4. At the 0.05 level of significance, is there evidence of a linear relationship between the GPA and ACT?
  5. Construct a 95% confidence interval estimate of the population slope β 1 . Interpret the confidence interval estimate.
  6. How useful do you think this regression model is for predicting GPA?

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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