The following data are the monthly salaries y and the grade point averages x for

Question

The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration.

The estimated regression equation for these data is = -807.1 + 1,392.9x and MSE =161,339.

a. Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal).
$

b. Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA (to 2 decimals).
$ (  ,  )

c. Develop a 95% prediction interval for Ryan Dailey, a student with a GPA of 3.0 (to 2 decimals).
$ (  ,  )

GPA Monthly Salary ($) 2.7 3,500 3.5 3,900 3.6 4,300 3.2 3,700 3.5 4,100 2.7 2,400

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Monthly Salary ($)
Independent Variable: GPA
Monthly Salary ($) = -807.14286 + 1392.8571 GPA
Sample size: 6
R (correlation coefficient) = 0.84636076
R-sq = 0.71632653
Estimate of error standard deviation: 401.67062

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

a) Point estimate = $ 3371.4

b) 95% confidence interval: $ (2855.18, 3887.67)

c) 95% prediction interval: $ (2142.52, 4600.34)

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -807.14286 1411.9818 0 4 -0.57163829 0.5982 Slope 1392.8571 438.25857 0 4 3.1781629 0.0336

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