Question

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

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.

 GPA Monthly Salary (\$) 2.6 3600 3.4 3900 3.6 4300 3.2 3800 3.5 4200 2.9 3900

The estimated regression equation for these data is  = 2090.5 + 581.1x and MSE = 21,284.

a. Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal).
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b. Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA (to 2 decimals).
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c. Develop a 95% prediction interval for Ryan Dailey, a student with a GPA of 3.0 (to 2 decimals).
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a. Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal).

= 2090.5 + 581.1*3 = 3833.8
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b. Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA (to 2 decimals).

predict(model, data.frame(x=3) ,interval = "confidence")
fit      lwr      upr
1 3833.784 3643.485 4024.082

(3643.49,4024,08)

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

predict(model, data.frame(x=3) ,interval = "prediction")
fit      lwr      upr
1 3833.784 3386.254 4281.313

=(3386.25,4281.31)