Question

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

Answer 1

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.