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. $$\begin{aligned}
\hat { y } = 4.25 + 2.75 x , & S S _ { x y } = 5.15 , S S _ { X x } = 1.87 \
S S _ { y y } & = 15.17 , S S E = 1.0075
\end{aligned}$$ Compute an estimate of ?, the standard deviation of the random error term.
A) .048
B) 0.219
C) .689
D) 1.0075

Question

Quizplus · Accepted Answer

The standard deviation of the random error term, often denoted as the standard error of the estimate, is calculated as the square root of the mean square error (MSE). MSE is the SSE divided by the degrees of freedom (n-2). Here, SSE = 1.0075 and n = 23, so MSE = 1.0075 / (23-2) = 0.048. The standard deviation is the square root of 0.048, which is approximately 0.219.

The Dean of the Business School at a Small Florida E(y)=β0+β1xE ( y ) = \beta _ { 0 } + \beta 1 xE(y)=β0​+β1x

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