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9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. a) What is heteroscedasticity? (b) Why is heteroscedasticity a problem? c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance).

9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. a) What is heteroscedasticity? (b) Why is heteroscedasticity a problem? c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance).

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. a) What is heteroscedasticity? (b) Why is heteroscedasticity a problem? c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance).
9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. SUMMARY OUTPUT Regression Statistics Multiple R 0.588 R Square 0.346 Adjusted R Square 0.044 Standard Error 4.55 Observations 20 ANOVA df SS MS Significance F Regression 142.0 23.7 1.15 0.391 Residual 13 268.8 20.7 Total 19 410.8 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 86.8 25.9 3.4 0.0 30.9 142.8 % of Classes Under 20 -0.171 0.205 -0.838 0.417 -0.613 0.271 % of Classes of 50 or More -0.266 0.387 -0.688 0.503 -1.102 0.570 -0.127 0.099 -1.276 0.224 -0.341 0.088 Acceptance Rate 1st-Year Students in Top 10% of HS Class 0.116 0.089 1.304 0.215 -0.076 0.308 2.075 4.018 0.516 0.614 -6.607 10.756 Academic Reputation Score -0.532 0.408 -1.305 0.215 -1.413 0.349 Student/Faculty Ratio
Transcribed Image Text:9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. SUMMARY OUTPUT Regression Statistics Multiple R 0.588 R Square 0.346 Adjusted R Square 0.044 Standard Error 4.55 Observations 20 ANOVA df SS MS Significance F Regression 142.0 23.7 1.15 0.391 Residual 13 268.8 20.7 Total 19 410.8 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 86.8 25.9 3.4 0.0 30.9 142.8 % of Classes Under 20 -0.171 0.205 -0.838 0.417 -0.613 0.271 % of Classes of 50 or More -0.266 0.387 -0.688 0.503 -1.102 0.570 -0.127 0.099 -1.276 0.224 -0.341 0.088 Acceptance Rate 1st-Year Students in Top 10% of HS Class 0.116 0.089 1.304 0.215 -0.076 0.308 2.075 4.018 0.516 0.614 -6.607 10.756 Academic Reputation Score -0.532 0.408 -1.305 0.215 -1.413 0.349 Student/Faculty Ratio
SUMMARY OUTPUT Regression Statistics Multiple R 0.821 R Square 0.673 Adjusted R Square 0.564 Standard Error 2.52 Observations 25 ANOVA df F Significance F SS MS Regression 6. 236.32 39.39 6.18 0.0012 Residual 18 114.64 6.37 Total 24 350.96 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 70.26 10.59 6.63 0.00 48.01 92.51 0.021 0.087 0,241 0.812 -0.161 0.203 % of Classes Under 20 -0.013 0.221 -0.060 0.953 -0.478 0.452 % of Classes of 50 or More -0.159 0.055 -2,907 0.009 -0.274 -0.044 Acceptance Rate 1st-Year Students in Top 10% of HS 0.142 0.090 1.589 0.129 -0.046 0.330 Class 1.278 1.947 0.656 0.520 -2.812 5.368 Academic Reputation Score 0.688 0.268 2.563 0.020 0.124 1.251 Student/Faculty Ratio a) What is heteroscedasticity? b) Why is heteroscedasticity a problem?
Transcribed Image Text:SUMMARY OUTPUT Regression Statistics Multiple R 0.821 R Square 0.673 Adjusted R Square 0.564 Standard Error 2.52 Observations 25 ANOVA df F Significance F SS MS Regression 6. 236.32 39.39 6.18 0.0012 Residual 18 114.64 6.37 Total 24 350.96 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 70.26 10.59 6.63 0.00 48.01 92.51 0.021 0.087 0,241 0.812 -0.161 0.203 % of Classes Under 20 -0.013 0.221 -0.060 0.953 -0.478 0.452 % of Classes of 50 or More -0.159 0.055 -2,907 0.009 -0.274 -0.044 Acceptance Rate 1st-Year Students in Top 10% of HS 0.142 0.090 1.589 0.129 -0.046 0.330 Class 1.278 1.947 0.656 0.520 -2.812 5.368 Academic Reputation Score 0.688 0.268 2.563 0.020 0.124 1.251 Student/Faculty Ratio a) What is heteroscedasticity? b) Why is heteroscedasticity a problem?
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