The Dean of the Business School at a Small Florida $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$$

Multiple Choice

The dean of the Business School at a small Florida college wishes to determine whether the grade -point average (GPA) of a graduating student can be used to predict the graduate's starting salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting salaries. Records for 23 of last year's Business School graduates are selected at random, and data on GPA (x) and starting salary (y, in $thousands) for each graduate were used to fit the model $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$$
The results of the simple linear regression are provided below.
$\begin{array}{ll}\hat{y}=4.25+2.75 x, & S S_{x y}=5.15, S S_{x x}=1.87 \\S S y y=15.17, S S E=1.0075\end{array}$

Calculate the value of $r ^ { 2 }$ , the coefficient of determination.

A) 0.934
B) 0.661
C) 0.872
D) 0.339