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 
1.76525E12 
Residual 
45 
2550.4641 
56.6770 

Total 
47 
8491.4792 

Coefficients 
Standard Error 
t Stat 
Pvalue 

Intercept 
19.1063 
15.5501 
1.2287 
0.2256 

Graduation Rate 
0.7557 
0.1602 
4.7167 
2.34782E05 

Student/Faculty Ratio 
1.2460 
0.2843 
4.3825 
6.95424E05 
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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