Question

A business statistics professor at a college 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. Use the accompanying data to complete parts a through c below.

Score   GPA   Hours   Absences   Gender
68   2.55   3.00   0   0
69   2.22   4.00   3   0
70   2.60   2.50   1   0
71   3.09   0.50   0   1
74   3.08   6.00   4   1
77   2.80   3.50   6   0
77   3.34   1.50   0   0
78   2.98   3.00   3   1
78   2.99   2.00   3   1
79   2.81   2.50   2   1
79   2.80   4.50   0   1
82   3.47   7.00   1   0
83   3.19   3.00   1   0
84   3.10   3.00   4   0
84   3.18   5.50   0   1
84   2.98   2.00   0   0
84   2.71   4.00   1   1
85   3.20   4.50   3   0
85   3.75   2.00   0   1
85   3.57   3.50   2   0
86   2.87   6.00   1   1
86   3.09   6.50   1   0
86   3.20   5.00   3   1
87   3.89   7.50   4   0
87   3.55   4.00   0   1
89   3.31   6.50   1   1
89   3.66   5.00   0   1
90   2.90   3.50   1   0
90   3.41   6.00   1   0
91   3.28   4.50   2   0
91   3.74   7.00   0   0
92   3.91   6.00   2   1
92   3.95   5.00   0   0
92   3.54   6.50   1   0
93   3.02   4.00   2   1
94   3.26   6.50   0   1
98   2.88   3.50   0   0
99   3.78   5.00   1   0
100   3.46   6.50   1   1
100   3.00   7.00   0   0

a. Use technology to check for the presence of multicollinearity.

Find the variance inflation factor (VIF) for each independent variable. Use x1=GPA, x2=Hours, x3=Absences,and x4=Gender , where x4=1 if the gender is male, and x4=0 otherwise.

Independent Variable		VIF
GPA	(x1 )
Hours	(x2 )
Absences	(x3 )
Gender	(x4 )

Is there multicollinearity?

A. Yes, because at least one of the VIFs is greater than or equal to 5.0.

B. No, because at least one of the VIFs is greater than or equal to 5.0.

C. No, because none of the VIFs are greater than or equal to 5.0.

D. Yes, because none of the VIFs are greater than or equal to 5.0.

b. If multicollinearity is present, take the necessary steps to eliminate it.

What is necessary to eliminate any multicollinearity? Select all that apply.

A.Remove the independent variable

x1

(GPAGPA ).

Your answer is not correct.

B. Remove the independent variable x2 (Hours).

C. Remove the independent variable x3 (Absences).

D.Remove the independent variable x4 (Gender).

E. Since no multicollinearity is present, no steps are necessary.

c. Perform a general stepwise regression using

alphaαequals=0.10

for the p-value to enter and to remove independent variables from the regression model.

What is the resulting regression equation? Use x1=GPA, x2=Hours, x3=Absences, and x4=Gender, where x4=1 if the gender is male, and x4=0 otherwise. Note that the coefficient is 0 for any variable that was removed or is not significant.

y=(_)+(_)x1+(_)x2+(_)x3+(_)x4

Answer 1

Regression Analysis: Score versus GPA, Hours, Absences, Gender

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	4	1274.25	318.562	7.97	0.000
GPA	1	292.24	292.242	7.32	0.010
Hours	1	362.46	362.457	9.07	0.005
Absences	1	108.85	108.851	2.72	0.108
Gender	1	3.06	3.055	0.08	0.784
Error	35	1398.15	39.947
Total	39	2672.40

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
6.32038	47.68%	41.70%	31.30%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	54.62	8.55	6.39	0.000
GPA	7.52	2.78	2.70	0.010	1.22
Hours	1.860	0.618	3.01	0.005	1.19
Absences	-1.150	0.697	-1.65	0.108	1.04
Gender	-0.56	2.01	-0.28	0.784	1.00

Regression Equation

Score

=

54.62 + 7.52 GPA + 1.860 Hours - 1.150 Absences - 0.56 Gender

Fits and Diagnostics for Unusual Observations

Obs	Score	Fit	Resid	Std Resid
37	98.00	82.79	15.21	2.53	R

a) C. No, because none of the VIFs are greater than or equal to 5.0.

b) Since no multicollinearity is present, no steps are necessary.

c)