Question

BUS 3700, Quiz 9. 11/7/2019 Name: For a random list of universities, the following variables were noted graduation rate", of classes under 20 students faculty ratio", and "alumni giving rate A partial set of data is shown below: University Graduation Rate % of Classes Under 20 Student Faculty Ratio Alumni Giving Rate 3913 A linear regression model was created to explain the alumni sing 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 48 L ANOVA SS MS Significance F Regression 5943.331 1981.177 34.21255 1.43E-11 Residual 2547.948 57.90791 Total 8491479 Coefficients Standard Error Stor P e Lower 95% Upper 95% -20.7201 Intercept 17.32137 -1.18256 0.243333 -56,0321 1 4.59186 Graduation Rate 0,748183 0.165964 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? 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 Tegression line is Aumoi aiving Tate-20.720) +0748)83 GToduateon Yale + 0.029o41 % af class under 20 -1:19261 stu dent faculty otio R=669994 ie p- 69 9941 % 2) Hene 6.9941 of the vaniation in alumni giuing Tade is explained by the variations in the thee independent vamiablesgaduation Tede % od class undes 20", andstu dent Paculty cdio To test He a1l slops are 7em0 Hiat least ane is dilesent fom zero e at least one of the Bi+o HI NS is a coeffieint f graduatioan utio B2 is a coefficient d clasS unders 20 coefficient of student Racuty uho wheRR Ba is a J43E Pvalue the test is Disicion ule- if p.value a hen we Teiect Ho at dIOS dere P-value cK2o.01 143 X10 o.0 (-e we reject Ho out 1 significant level

Conclusion At least one coefficient s not equal to zerso eqdession line oith o vamable asatuation Tcute is a148123 4 The slope ot estimated Tes pect ep interpitation Px thpit go gatuction rate rf we increase Dy one unit then Alumni qivin q mate increase by 0.743483 unit 95 c axadutian tade (0.413712 108265a) 6 put aratuation ale 80 . ct class undes 20 60 Shident faculty octio- 12 in estimaled negaession ine ie in pant Alumni giving rale-207201 + 0.748183 x80 +0-023041 X60 .19201 12 Aumoi gvng ate 26.S7288 check the pNalues cf the 3 independent vamable which pvalue. is heio larae eo it can be drop in the made The p.value o the y c class anders 20 is o 835844 is laroge compase to other tuoo vaniah le thenefove the vaniable o of class unders 20 model is dhop in the

coeffient ot ao lass unders 20. B2 is To test Ho B2 0 0835844 Pvalue for a B2 is IP p.value yo J.0.s we neiect H at Here Pvalue x 0.05 we failed to reject Ho at sodos 82 is not conbutly signiticany is varicable to the model ot ciass undex drop 20