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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.

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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 17HP
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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.
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: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.
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
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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