A study of the top 75 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. The results of a simple linear regression analysis are shown below:
Least Squares Linear Regression of Salary
Predictor
Variables Coefficient Std Error T P
Constant 18.1849 10.3336 1.76 0.0826
Size 1.47494 0.14017 10.52 0.0000
R-Squared 0.6027 Resid. Mean Square (MSE) 532.986
Adjusted R-Squared 0.5972 Standard Deviation 23.0865
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. The results are shown here:
95% confidence interval for E(Y): ($123,390, $134,220)
95% prediction interval for Y: ($82,476, $175,130)
Which of the following interpretations is correct if you want to use the model to estimate E(Y) for all MBA programs?
◦ We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition will fall between $82,476 and $175,130.
◦ We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition will fall between $82,476 and $175,130.
◦ We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition will fall between $123,390 and $134,220.
◦ We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition will fall between $123,390 and $134,220.
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