The following results were obtained from a regression of n = 39 records of millions of dollars of grants received by academics based on their number of publications, years of experience, and the size of the department in which they work.
a. Fill in the blanks in the ANOVA table.
b. What is the value of r2?
c. Test the null hypothesis that r2= 0 by comparing the F-statistic from the table with its critical value.
d. What do you conclude from the variance inflation factors (VIFs)? What, if any, modification would you suggest in light of these values?
e. What is the predicted grant-based income of an academic with 8 publications and 10 years of experience, working in a department with 9 staff members? We can calculate
y = 0.004 * 8 + 0.119 * 10 - 0.006 * 9 - 0.127
= 1.041
A. 
B. Utilising statistical software, the r2 value is .947.
C. The F-statistic calculated in the table is 210.6, which vastly exceeds the critical value of
F0.05,3,35 approximately 2.88. Thus, we reject the null hypothesis that r2 = 0.
D. The VIF values are less than 5, but the relatively high values associated with both publications
and experience suggest that one could possibly be excluded in favor of the other.
E. The lucky researcher might be estimated to be able to bring in 1.041 million dollars in grant
money.
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