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.

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).
$

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).
$ ( , )

Answer 1

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)