A business statistics professor would like to develop a regression model to pred
ID: 3360998 • Letter: A
Question
A business statistics professor would like to develop a regression model to predict the final class scores for students based on their current GPAs, the number of hours they studied for the class, 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 Absences Gender
90 3.22 4.5 2 Male
91 3.00 7.0 0 Female
82 3.08 6.0 4 Male
80 3.25 3.0 1 Female
96 3.93 6.0 2 Female
90 3.60 6.5 1 Female
99 4.00 5.0 0 Male
84 3.18 5.5 0 Female
85 2.98 4.0 2 Male
78 2.95 2.0 0 Male
82 3.15 3.0 4 Female
76 2.71 4.0 1 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 =0.10. Using the p-values, identify which independent variables are significant with =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.
Explanation / Answer
a.)
Regression Analysis: Score versus GPA, Hours, Absences, Gender_Male
The regression equation is
Score = 34.4 + 13.2 GPA + 1.77 Hours - 0.440 Absences + 2.10 Gender_Male
b) If Gender is Male then the Score will be increase 2.10 since its regression coefficient is 2.10
If Gender is female then the score is no change
c)
Analysis of Variance
Source DF SS MS F P
Regression 4 467.13 116.78 8.53 0.008
Residual Error 7 95.79 13.68
Total 11 562.92
The P-value of regression is 0.008 < alpha 0.05 so we reject H0
Thus we conclude that the regression equation is best fit to the given data
c)
From the given data
Predictor Coef SE Coef T P
Constant 36.540 9.571 3.82 0.007
GPA 13.182 3.085 4.27 0.004
Hours 1.7666 0.7900 2.24 0.060
Absences -0.4401 0.7768 -0.57 0.589
Gender_Female -2.097 2.277 -0.92 0.388
The p-value of GPA and HOurs are < alpha 0.10, so they are significant
i.e. Those population regression coefficient are not equal to zero
d)
The predicted score is
Score = 34.4 + 13.2 (3.89) + 1.77 (3.5)- 0.440 (3) + 2.10 (0) =43.943
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