A business statistics professor would like to develop a regression model to predict the final exam scores for students based on their current GPAs, the number of hours they studied for the exam, the number of times they were absent during the semester, and their genders. The data for these variables are given in the accompanying table. Complete parts a through d below.
Score GPA Hours
87 3.75 2.0 0 Female
77 3.20 4.5 3 Male
82 3.16 5.0 3 Male
79 3.35 1.5 0 Female
76 2.75 3.5 6 Female
87 3.04 6.5 1 Female
77 2.53 3.0 0 Male
86 2.92 6.0 1 Female
71 2.99 2.0 3 Female
94 3.89 7.5 4 Male
76 2.98 3.0 3 Female
78 2.25 4.0 3 Male
a. Using technology, construct a regression model using all of the independent variables. (Let variable Gen be the dummy variable for gender. Assign a 1 to a male.)Complete the regression equation for the model below, where y=Score,x1=GPA,x2=Hours,x3=Absences,and x4=Gen.
ModifyingAbove y= ___ + ( )x1 + ( ) x2 + ( ) x3 + ( ) x4
(Round to two decimal places as needed.)
b. Interpret the meaning of the regression coefficient for the dummy variable.
c. A test for the significance of the overall regression model shows that it is significant using α=0.10. Using the p-values, identify which independent variables are significant with α=0.10.
d. Construct a regression model using only the significant variables found in part c and predict the average class score for a student who studied 3.5
hours for the class, missed three classes during the semester, has a current GPA of 3.89 , and is female.
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