Question

The following data provide the starting salary for students who recently graduated from a local university and accepted jobs soon after graduation. The starting salary, grade-point average (GPA), and major (business or other) are provided.

SALARY	$29,500	$46,000	$39,800	$36,500
GPA	3.1	3.5	3.8	2.9
Major	Other	Business	Business	Other
SALARY	$42,000	$31,500	$36,200
GPA	3.4	2.1	2.5
Major	Business	Other	Business

1. Using a computer, develop a regression model that could be used to predict starting salary based on GPA and major.
2. Use this model to predict the starting salary for a business major with a GPA of 3.0.
3. What does the model say about the starting salary for a business major compared to a non-business major?
4. Do you believe this model is useful in predicting the starting salary? Justify your answer using information provided in the computer output.

Answer 1

	Coefficients	SE	T-stat	P-value
Intercept	24328	9025	2.696	0.0543
GPA(X1)	3027	3234	0.936	0.4023
Major(X2)	6684	3594	1.86	0.1364

Linear model can be written as

Y' = 24328 + 3027*X1 + 6684*X2

b,

For a student with GPA= 3

with business major X1 = 3 and X2 = 1

Y' = 24328 + 3027*X1 + 6684 * X2

by substituiting X1 and X2.

Y' = 24328 + 3027 * 3 + 6684*1

=40093

c.

Salary of the business major is high when compared to no business major as the predicted value shows $40093.

d.

	df	SS	MS	F value	P(>f)
Regression	2	137598209	68799105	4.386	0.098
Residuals	4	62738933	15684733
Total	6	200337142

P-value of regression is 0.098(>0.05)

We can conclude that there does not exist any significant relationship between the variables.

R^2 = SSR/SST = 0.6868(68.68%)

Regression model is somehow only partially useful to predict starting salary.