Question

BUS 3700. Quiz 9. 11/7/2019 Name: For a random list of universities, the following variables were noted: graduation rate", faculty ratio", and "alumni giving rate". A partial set of data is shown below: University Graduation Rate % of Classes Under 20 Student/Faculty Ratio of classes under 20 students", "student Alumni Giving Rate 79 08 A linear regression model was created to explain the "alumni giving rate" (-y) based on the other 3 variables. The results are: SUMMARY OUTPUT Regression Statistics Multiple R 0.836625 R Square 0.699941 Adjusted R Square 0.679482 Standard Error 7.609725 Observations ANOVA df SS MS F Significance F Regression 3 5 943.531 1981.177 34.21255 1.43E-11 Residual 44 2 547.948 57.90791 Total 47 8 491,479 Coefficients Standard Error Star P-value Lower 95% Upper 95% Intercept -20.7201 17.52137 -1.18256 0.243333 -56.0321 14.59186 Graduation Rate 0.748183 .16596 4.508213 4.8E-050.413712 1 .082653 % of Classes Under 20 0.029041 0.139321 0.208444 0.835844 -0.25174 0.309824 Student Faculty Ratio -1.19201 0.386723 -3.08234 0.003538 -1.9714 -0.41262 1. What is the estimated regression line? 2. What percentage of the variation in "alumni giving rate" is explained by the variations in the three independent variables "graduation rate", "% of classes under 20 students and student faculty ratio"? 3. Conduct an overall test for the significance of slopes (He: all slopes are 0; Hi: at least one is different from 0). State the evidence and conclusion. 4. What is the slope of the estimated regression line with respect to the variable "graduation rate"? How do you interpret this? Sraigta Straight 5. State the 95% confidence interval for slope with respect to "graduation rate". 6. For a university with a "graduation rate" being 80, "% of classes under 20 students" being 60, and "student faculty ratio" being 12, find the point estimate for alumni giving rate". 7. If you had to drop one independent variable from the model, which is the best candidate? Why?

Answer 1

Solution - The estimated regression line is Alumni giving Tate -20-7201 +0.743)83 Graduateon yale + 0.029041% of class under 20 - 119201 Student faculty otio. 2) Here R = 0.699941 - ie R² = 69.ggal % → 69.9941 % of the variation in alumni giving rate is explained by the variations in the three Independent variables graduation rate % of class under 20", and "student faculty ratio: - To test Ho i all stops are zero vs Hi: O least one is different from zero. - VS Ho Bi= 82 = 83 = 0 Hih at least one of the Bj to j= 1:3 where. Bi is a coeffierent 82 is a coefficient Ba is a coefficient of graducation ratio. of class under 20. of student facuity ratio. I 4 value of the test is = 1.43 € Disicion sule. . if p-value ka then we reject Ho at dildos Here P-value cx=0.01 . le 1.43 X 10-10 20.01. we reject to at ar. significant level.

conclusion', At least one coefficient is not equal to zero. 47 The slope respect of estimated Tegression line with rep. bo vamable "gratuation rate" is 0.748183 interpitation : at If we increase one thit ga gratucation rate by one unit then Alumni giving rate increase by 0.748483 unit. is 95% CI for a aradution rate (0.413712, 1082653) 6) put - & in aratuation rate = 80 , 7. of class under 20=60 student faculty ratio = 12 estimated regression sine ie in past i Alumni giving role = -20 7201 +0.748183 x 80 +0.029041 X6o -1.19201 x 12 Alumni quing Tale - 26. 57288. 7 check the p-values of the a independent variable. which p-value is keio large o it can be droop in the mode. The p-value of the y. of class ander 20 is 0.835844 is loroge compare to other two variable there fore. the variable to of class under 20 is drop in the model.