Question

3. The University Secretary wants to determine how University grade point average, GPA (highest being 4.0) of a sample of students from the University depends on a student’s high school GPA (HS), age of a student (A), achievement test score (AS), average number of lectures skipped each week (S), gender of a student (where M=1 if a student is male or 0 otherwise), computer or PC ownership of a student (where PC=1 if a student owns a computer or 0 otherwise), the means of transport to school (drive, bicycle or walk; where D=1 if a student drives to campus or 0 otherwise, B=1 if a student bicycles to campus or 0 otherwise), and finally, the subject major of the student (finance, human resource, marketing and accounting; where F=1 if a student majors in finance or 0 otherwise, HR=1 if a student majors in human resource or 0 otherwise, MR=1 if a student majors in marketing or 0 otherwise). Use the correlation matrix and dummy regression output to answer the questions.

	GPA	HS	A	AS	S	M	PC	D	B	F	HR	MR
GPA	1.00
HS	0.41	1.00
A	-0.02	-0.26	1.00
AS	0.21	0.35	-0.08	1.00
S	-0.26	-0.09	-0.08	0.12	1.00
M	-0.08	-0.21	0.04	0.18	0.20	1.00
PC	0.22	0.04	-0.09	0.04	-0.21	-0.07	1.00
D	-0.11	-0.19	0.27	-0.20	0.26	-0.08	0.02	1.00
B	0.08	0.14	-0.05	0.16	-0.13	0.13	-0.10	-0.38	1.00
F	0.08	0.12	-0.22	0.18	0.06	0.04	0.08	-0.08	-0.11	1.00
HR	0.08	0.17	-0.49	0.08	0.06	0.05	-0.04	-0.11	0.07	-0.12	1.00
MR	-0.10	-0.19	0.37	-0.11	-0.05	0.02	0.05	0.08	0.01	-0.15	-0.79	1.00

1. Which 2 pairs of variables are most correlated with the regress and?
2. Which 3 pairs of variables are mostly multicollinear?
3. Identify 3 pairs of variables that are most correlated.

Answer 1

Answer:

a. The regressand is University grade point average, GPA. To find the variables most correlated with this, we need to see the absolute values of the correlations of the first column of the correlation matrix. We see the correlation with HS (.41) and S (-.26) are highest in absolute value. So, the two variables most correlated with GPA are high school GPA (HS) and the average number of lectures skipped each week (S).

b. To find pairs of multicollinear variables while regressing GPA, we need to see the high correlations (in absolute value) except for the first column. 3 pairs of multicollinear variables are,

1. HR (a student majors in human resource) and MR (a student majors in marketing) (-.79)

2. HR (a student majors in human resource) and A (age of a student) (-.49)

3. B (a student bicycles to campus) and D (a student drives to campus) (-.38)

To find the most correlated variables we need to see the high correlations (in absolute value) of the whole correlation matrix.

1. HR (a student majors in human resource) and MR (a student majors in marketing) (-.79)

2. HR (a student majors in human resource) and A (age of a student) (-.49)

3. high school GPA (HS) and University grade point average (GPA) (.41).

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