A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below:
$$\begin{array}{l}
\text { Least Squares Linear Regression of Salary }\
\begin{array} { l c c c c c c c c }
\text { Predictor } & & & & & & & \
\text { Variables } & \text { Coefficient } &{ \text { Std Error } } & \text { T } & & \text { P } & \multicolumn{2}{c} { \text { VIF } } \
\text { Constant } & - 203.402 & 51.6573 & - 3.94 & & 0.0002 & 0.0 \
\text { Gmat } & 0.39412 & 0.09039 & 4.36 & & 0.0000 & 2.0 & \
\text { Tuition } & 0.92012 & 0.17875 & 5.15 & & 0.0000 & 2.0 &
\end{array}
\end{array}$$ The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000 and the GMAT score was 675. The results are shown here:

95% confidence interval for E(Y): ($126,610, $136,640)
95% prediction interval for Y: ($90,113, $173,160)

Which of the following interpretations is correct if you want to use the model to estimate Y for a single MBA program?
A) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall
Between $126,610 and $136,640.
B) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between
$126,610 and $136,640.
C) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between
$90,113 and $173,16,30.
D) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall
Between $90,113 and $173,16,30.

Question

A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: 
$$\begin{array}{l}
\text { Least Squares Linear Regression of Salary }\
\begin{array} { l c c c c c c c c } 
\text { Predictor } & & & & & & & \
\text { Variables } & \text { Coefficient } &{ \text { Std Error } } & \text { T } & & \text { P } & \multicolumn{2}{c} { \text { VIF } } \
\text { Constant } & - 203.402 & 51.6573 & - 3.94 & & 0.0002 & 0.0 \
\text { Gmat } & 0.39412 & 0.09039 & 4.36 & & 0.0000 & 2.0 & \
\text { Tuition } & 0.92012 & 0.17875 & 5.15 & & 0.0000 & 2.0 &
\end{array}
\end{array}$$ The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000 and the GMAT score was 675. The results are shown here:

95% confidence interval for E(Y): ($126,610, $136,640)
95% prediction interval for Y: ($90,113, $173,160)

Which of the following interpretations is correct if you want to use the model to estimate Y for a single MBA program?
A) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall
Between $126,610 and $136,640.
B) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between
$126,610 and $136,640.
C) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between
$90,113 and $173,16,30.
D) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall
Between $90,113 and $173,16,30.

Quizplus · Accepted Answer

The prediction interval is used to estimate the range in which the starting salary for a single MBA program will fall, which is between $90,113 and $173,160.

A Study of the Top MBA Programs Attempted to Predict