A Study of the Top MBA Programs Attempted to Predict $\text { Predictor }$

question 125

Multiple Choice

A study of the top MBA programs attempted to predict the average starting salary (in $1000ʹs) of graduates of the program based on the amount of tuition (in $1000ʹs) charged by the program and
The average GMAT score of the programʹs students. The results of a regression analysis based on a
Sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary

$\text { Predictor }$


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 $\mathrm { E } ( \mathrm { Y } ) : ( \$ 126,610 , \$ 136,640 )$
$95 \%$ prediction interval for $\mathrm { Y } : ( \$ 90,113 , \$ 173,160 )$
Which of the following interpretations is correct if you want to use the model to estimate $E ( Y )$ for all MBA programs?

• 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 \(\$ 173,16,30\).

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Definitions:

Yearly Income

The total amount of money earned or received over one year.

SST

SST stands for Sum of Squares Total, a term used in statistics to describe the total variation within a dataset.

Determination

In the context of statistical analysis, often refers to the degree of variance in observations explained by the model, usually in the form of the coefficient of determination (R-squared).

Estimated Regression Equation

An equation that estimates the relationship between dependent and independent variables in a regression model.