Question

2. A university placement director is interested in the effect GPA and the number of activities listed on the resume might have on the starting salaries of this year's graduation class. He has selected the data shown in cells S3 to U12 on the answers sheet for a sample of 12 graduates. Using these data,
	a. determine the multiple regression equation for starting salaries
	b. compute the estimated starting salary of Dave, a student with a 3.6 GPA and 3 university activities
	c. determine the 95% prediction interval for Dave's starting salary
	d. determine the 95% confidence interval for the mean starting salary of 10 students with the same GPA and number of activities as Dave
	e. determine the 95% confidence intervals for the population partial regression coefficients, β1 and β2
	f. conduct significance tests at the 95% significance levels for the two partial regression coefficients.
	g. show a histogram and a normal probability plot to determine whether or not the error terms are normally distributed
	h. compute the Variance Inflation Factor and state whether or not multicollienarity is a problem in this model
	i. plot the error terms from each of the two independent variables to see whether or not autocorrelation is a problem
Graduate	Salary	GPA	Activities
1	40	3.2	2
2	46	3.6	5
3	38	2.8	3
4	39	2.4	4
5	37	2.5	2
6	38	2.1	3
7	42	2.7	3
8	37	2.6	2
9	44	3.0	4
10	41	2.9	3

Answer 1

a)

The multiple regression equation for starting salaries is
Salary = 24.3092 + 3.8416 GPA + 1.6810 Activities

b)  The estimated starting salary of Dave, a student with a 3.6 GPA and 3 university activities is

Salary = 24.3092 + 3.8416*3.6+ 1.6810*3= 43.1820.

c) The 95% prediction interval for Dave's starting salary is (38.837, 47.527).

d) The 95% confidence interval for the mean starting salary of 10 students with the same GPA and number of activities as Dave is (40.508, 45.857).

e) The 95% confidence intervals for the population partial regression coefficients, β₁ and β₂

	Lower 95%	Upper 95%
β1	0.9233	6.7600
β2	0.4298	2.9322