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

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 graduateʹs starting
Salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting
Salaries. Records for 23 of last yearʹs 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.
$$\begin{aligned}\hat { y } = 4.25 + 2.75 x , & S S _ { x y } = 5.15 , S S _ { x x } = 1.87 \\S S _ { y y } = 15.17 , S S E = 1.0075\end{aligned}$$
Compute an estimate of $\sigma$ , the standard deviation of the random error term.

A) $1.0075$
B) $.048$
C) $0.219$
D) $.689$