An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using 25 data points is shown below. $$\hat { \beta } _ { 0 } = - 92040 \hat { \beta } 1 = 228 s = 3213 r ^ { 2 } = .66 r = .81 \mathrm { df } = 23 \quad t = 6.67$$ A 95% prediction interval for SALARY when GMAT = 600 is approximately ($37,915, $51,984). Interpret this interval.
A) We are 95% confident that the SALARY of a top business school graduate with a GMAT of 600 will fall between $37,915 and $51,984.
B) We are 95% confident that the mean SALARY of all top business school graduates with GMATs of 600 will fall between $37,915 and $51,984.
C) We are 95% confident that the increase in SALARY for a 600-point increase in GMAT will fall between $37,915 and $51,984.
D) We are 95% confident that the SALARY of a top business school graduate will fall between $37,915 and $51,984.

Question

Quizplus · Accepted Answer

A prediction interval provides a range where we expect the salary of an individual graduate with a GMAT score of 600 to fall, with 95% confidence.

An Academic Advisor Wants to Predict the Typical Starting Salary β^0=−92040β^1=228s=3213r2=.66r=.81df=23t=6.67\hat { \beta } _ { 0 } = - 92040 \hat { \beta } 1 = 228 s = 3213 r ^ { 2 } = .66 r = .81 \mathrm { df } = 23 \quad t = 6.67β^​0​=−92040β^​1=228s=3213r2=.66r=.81df=23t=6.67

An Academic Advisor Wants to Predict the Typical Starting Salary $\hat { \beta } _ { 0 } = - 92040 \hat { \beta } 1 = 228 s = 3213 r ^ { 2 } = .66 r = .81 \mathrm { df } = 23 \quad t = 6.67$