An Academic Advisor Wants to Predict the Typical Starting Salary

Short Answer

An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using 25 data points is shown below. $$\hat { \beta } _ { 0 } = - 92040 \hat { \beta } 1 = 228 \mathrm {~s} = 3213 \mathrm { r } ^ { 2 } = .66 \quad r = .81 \mathrm { df } = 23 \quad t = 6.67$$
Give a practical interpretation of $r ^ { 2 } = .66$ .
A) $66 \%$ of the sample variation in SALARY can be explained by using GMAT in a straight -line model.
B) We expect to predict SALARY to within $2 [ \sqrt { .66 } ]$ of its true value using GMAT in a straight-line model.
C) We estimate SALARY to increase $\$ .66$ for every 1 -point increase in GMAT.
D) We can predict SALARY correctly $66 \%$ of the time using GMAT in a straight-line model.