Question

# A number of different multiple regression equations could be developed to estimate the percentage of alumni...

A number of different multiple regression equations could be developed to estimate the percentage of alumni that make a donation. The following estimated regression equation using just two independent variables, Graduation Rate and Student/Faculty Ratio, is shown below.

From this model, if universities want to increase the percentage of alumni who make a donation, what is your recommendation?

 Regression Statistics Multiple R 0.8364 R Square 0.6996 Adjusted R Square 0.6863 Standard Error 7.5284 Observations 48 ANOVA df SS MS F Significance F Regression 2 5941.0150 2970.5075 52.4112 1.76525E-12 Residual 45 2550.4641 56.6770 Total 47 8491.4792 Coefficients Standard Error t Stat P-value Intercept -19.1063 15.5501 -1.2287 0.2256 Graduation Rate 0.7557 0.1602 4.7167 2.34782E-05 Student/Faculty Ratio -1.2460 0.2843 -4.3825 6.95424E-05

Slope coefficient corresponding to graduation rate and student/faculty ratio are significant because the p values are smaller than the significance level of 0.05

So, it is important for us to include both independent variable while taking any decision

Regression equation is given as

Percentage of alumni = -19.1063 + 0.7557(graduation rate) - 1.2460(student/faculty ratio)

Slope of student/faculty ratio is negative, this means that if we increase the student/faculty ratio, then it will decrease the percentage of alumni. Slope of graduation rate is positive, this means that if we increase the graduation rate then it will increase the percentage of alumni

So, it is appropriate that we increase the graduation rate and at the same, we must reduce the student/faculty ratio.

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