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 (\$) 2.7 3,600 3.5 3,800 3.7 4,200 3.2 3,700 3.4 4,200 2.7 2,400

The estimated regression equation for these data is = -277.3 + 1,227.3x and MSE =217,386.

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)

The point estimate of the starting salary for a student with a GPA of 3.0 is

Monthly Salary = -277.3 + 1227.3 * 3.0 = 3404.6

b)

Independent variable (x): GPA

Following table shows the calculations:

 GPA, X X^2 2.7 7.29 3.5 12.25 3.7 13.69 3.2 10.24 3.4 11.56 2.7 7.29 Total 19.2 62.32

Sample size: n=6

Now,

Since MSE = 217386 so

The critical value of t for 95% confidence interval with df = 4 is 2.776.

The 95% confidence interval for the mean starting salary for all students with a 3.0 GPA is

The required 95% confidence interval is (2808.49, 4000.71).

(c)

The 95% prediction interval for the mean starting salary for all students with a 3.0 GPA is

The required 95% prediction interval is (1979.62, 4829.58)