Question

A teacher wants to develop a model to predict a student’s grade on the final exam from the number of hours spent studying for the final exam and the student’s GPA at the university. The data (for 22 students) follows below.

       PREDICTOR                 COEF             STDEV                       P-VALUE

       Constant                         -1.30               1.429                          0.405

       Hours                              .0793              .0759                          0.344

       GPA                                1.11               .7543                          0.202

       ANOVA

       SOURCE                                    SS                               DF                   MS                  F                                              

       Regression                                 5.0040            

                                                

       Error                                            1.1548            

       TOTAL    

(a) What is the student’s expected grade if she has a 2.7 GPA and she studies 12 hours for this test?

(b) Interpret the slope coefficient for the variable Hours.

(c) Use the p-value approach to see if GPA is linearly related to the dependent variable? Use alpha = .05. Please include all test parts.

(d) Fill in all missing parts of the ANOVA table.

Answer 1

Solution:

(a) What is the student’s expected grade if she has a 2.7 GPA and she studies 12 hours for this test?

Answer:

  

(b) Interpret the slope coefficient for the variable Hours.

Answer: The slope coefficient for the variable hours is 0.0759. It means for every one hour increase in Hours, the grade is going to increase by 0.0759 unit keeping the GPA score constant

(c) Use the p-value approach to see if GPA is linearly related to the dependent variable? Use alpha = .05. Please include all test parts.

Answer: Since the p-value for the GPA coefficient is 0.202 which is greater than the significance level, therefore, we fail to reject the null hypothesis and conclude there is no significant linear relationship between GPA and Grade

(d) Fill in all missing parts of the ANOVA table.

Source	SS	DF	MS	F
Regression	5.004	2	2.502	41.16557
Error	1.1548	19	0.060779
Total	6.1588	21