Alumni donations are an important source of revenue for universities. One fundraiser is trying create a model to predict alumni giving rate as a function of 1) graduation rate, 2) percenas smaller class sizes and 3) student faculty ratio. The hypothesized model is y-Bo+B, x, + B₂x₂ + Bx + 6 In this equation, y is alumni giving percentage lie 201 is graduation percentage (1.80) percentage of classes with less than 20 students (ie. 50), and xs is student/faculty ratio A regression analysis of 48 national universities resulted in the following output: age (i. e. 202 less than 20 on analysis of Regression Statistics Multiple R 0.836624531 R Square 0.699940606 Adjusted R Square 0.679482011 Standard Error 7.609724781 Observations 48 ANOVA dr Significance F 1.43233E-11 Regression Residual Total 3 44 47 SS MS F 5943.531072 1981.177 34.21255 2547.948094 57.90791 8491.479167 Coefficients Standard Error Star P-value Lower 95% Upper 95% Intercept -20.7201343 17.52136501 -1.18256 0.243333 -56.03212475 14.5918561 0.748182799 0.165959959 4.508213 4.8E-05 0.413712483 1.08265312 % of Classes Under 20 0.029040648 0.139321322 0.208444 0.835844 -0.251743023 0.30982432 Student Faculty Ratio - 1.19201069 0.386723104 -3.08234 0.003538 -1.971399888 -0.4126215 1) The quality measure we use to check the validity of the model is
a. Significance F b. Coefficient of determination >
c. SSE d. Standard error >
e. none of the above.
2) Which of the following is the correct interpretation of the graduation rate" coefficient?
a. For each point increase in alumni giving percentage, graduation rate increases by .75%
b. For each point increase in graduation percentage, alumni giving rate increases by 41%
c. For each point increase in alumni giving percentage, graduation rate increases by 41%
d. For each point increase in graduation percentage, alumni giving rate increases by .75%
e. none of the above.
3) How do you interpret the value of the intercept term bo?
a. It is the loss a university must absorb if alumni funds dry up
b. It is the historical minimum alumni giving percentage
c. It is the average amount of funds these 48 universities raise yearly
d. It cannot be interpreted because zero graduation rate, zero small class size and zero student faculty ratio are outside the ranges used to develop the regression model.
e. none of the above.
4) As student/faculty ratio increases, how does this affect giving rate and why
a. Cannot tell without a specific student/faculty percentage
b. Alumni giving rate improves since the sign of the coefficient is negative
c. Alumni giving rate drops since the sign of the coefficient is negative
d. Must perform a correlation analysis to determine the relation between the two variables
e. none of the above.
5) Based on a t-test and at 5% level of significance, we can conclude that the coefficient of the following independent variable(s) is
0: a. Graduation rate
b. % of classes under 20
c. Student/faculty ratio
d. Graduation rate & student/faculty ratio
e. none of the above.
6) The coefficient of determination for this regression implies
a. that the independent variables are positively correlated
b. the value is too high and therefore the model is not valid
c. approximately 70% of the change in alumni giving rate is explained by the change in the independent variables
d. we can reject that the coefficients are all zero since the value is greater than a
e. none of the above.
7) UTILIZING THE CONCLUSION IN QUESTION ) ABOVE, we predict that a university with an 85% graduation rate, 52% small classes and a student/faculty ratio of 12 will have an alumni giving rate of
a. 30.08
b. 28.57
c. 44.39
d. 35.16
e. none of the above.