10) The following results are from a regression where the dependent variable is COST OF COLLEGE and the independent variables are TYPE OF SCHOOL which is a dummy variable = 0 for public schools and = 1 for private schools, FIRST QUARTILE SAT which is the average score of students in the top quartile of SAT’s, THIRD QUARTILE SAT which is the average score of students in the 3rd quartile, and ROOM AND BOARD which is the cost of room and board at the school. The first set of results includes all the independent variables whereas the second set of results excludes the THIRD QUARTILE SAT variable. a) Based on these two sets of data, does there appear that multicollinearity is a problem (specifically, does it appear that THIRD QUARTILE SAT is highly collinear with the other independent variables? Explain. b) Calculate the VIF for THIRD QUARTILE SAT. c) Based on the VIF, do you think that multicollinearity is a problem? Explain.
10) The following results are from a regression where the dependent variable is COST OF COLLEGE and the independent variables are TYPE OF SCHOOL which is a dummy variable = 0 for public schools and = 1 for private schools, FIRST QUARTILE SAT which is the average score of students in the top quartile of SAT’s, THIRD QUARTILE SAT which is the average score of students in the 3rd quartile, and ROOM AND BOARD which is the cost of room and board at the school. The first set of results includes all the independent variables whereas the second set of results excludes the THIRD QUARTILE SAT variable. a) Based on these two sets of data, does there appear that multicollinearity is a problem (specifically, does it appear that THIRD QUARTILE SAT is highly collinear with the other independent variables? Explain. b) Calculate the VIF for THIRD QUARTILE SAT. c) Based on the VIF, do you think that multicollinearity is a problem? Explain.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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10) The following results are from a regression where the dependent variable is COST OF COLLEGE and the independent variables are TYPE OF SCHOOL which is a dummy variable = 0 for public schools and = 1 for private schools, FIRST QUARTILE SAT which is the average score of students in the top quartile of SAT’s, THIRD QUARTILE SAT which is the average score of students in the 3rd quartile, and ROOM AND BOARD which is the cost of room and board at the school. The first set of results includes all the independent variables whereas the second set of results excludes the THIRD QUARTILE SAT variable.
a) Based on these two sets of data, does there appear that multicollinearity is a problem (specifically, does it appear that THIRD QUARTILE SAT is highly collinear with the other independent variables? Explain.
b) Calculate the VIF for THIRD QUARTILE SAT.
c) Based on the VIF, do you think that multicollinearity is a problem? Explain.
Transcribed Image Text:a)
Based on these two sets of data, does there appear that multicollinearity is a problem (specifically,
does it appear that THIRD QUARTILE SAT is highly collinear with the other independent
variables? Explain
Below is the regression of THIRD QUARTILE SAT on the other independent variables.
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
0.991
0.982
0.981
17.23
Observations
80
ANOVA
df
SS
MS
Significance F
F
Regression
Residual
3
1220536
406845
1370.0
4.8462E-66
76
22570
297
Total
79
1243106
Coefficients
290.96
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
Type of School
First quartile SAT
19.50
14.92
0.00
252.13
329.79
-15.569
5.811
-2.679
0.009
-27.142
-3.995
0.926
0.016
56.146
0.000
0.893
0.959
Room and Board
-0.001
0.002
-0.316
0,753
-0,004
0.003
b) Calculate the VIF for THIRD QUARTILE SAT.
c)
Based on the VIF, do you think that multicollinearity is a problem? Explain.
Transcribed Image Text:Regression Statistics
Multiple R
R Square
Adjusted R Square
0.913
0.834
0.825
Standard Error
2808
Observations
80
ANOVA
df
SS
Significance F
1.87182E-28
MS
F
Regression
4
2968537592
742134398
94.14
Residual
75
591268812
7883584
Total
79
3559806404
Coefficients
Standard Error
Upper 95%
6723.72
t Stat
P-value
Lower 95%
Intercept
Type of School
First quartile SAT
Third quartile SAT
-5822.16
6297.80
-0.92
0.36
-18368.03
8220.71
990.49
8.30
0.00
6247.56
10193.86
27.32
17.51
1.56
0.12
-7.56
62.21
-8.61
18.69
-0.46
0.65
-45,84
28.62
Room and Board
0.20
0.31
0.65
0.52
-0.42
0.83
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
0.913
0.833
0.827
Standard Error
2793
Observations
80
ANOVA
Significance F
1.69212E-29
SS
MS
F
Sp
3
Regression
2966863325
988954442
126.8
Residual
76
592943079
7801883
Total
79
3559806404
Coefficients
Standard Error
I Stat
P-value
Lower 95%
Upper 95%
-8328.17
3160.19
-2.64
0,01
-14622.24
-2034.10
Intercept
Type of School
First quartile SAT
10230.69
24.67
8354.80
941.87
8,87
0.001
6478.91
19.35
2.67
7.24
0.001
14.03
0,21
0.31
0.67
0.50
-0.41
0.83
Room and Board
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