Question

A college professor would like to analyze the relationship between educational attainment and salary. She collects the following sample data, where Education refers to years of higher education and Salary is the individual’s annual salary (in $1,000s):

Education	3	4	6	2	5	4	8	0
Salary	41	46	59	49	68	43	95	49

a.	Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round intermediate calculations to 4 decimal places. Enter your answers in thousands rounded to 2 decimal places.)

  Salaryˆ=Salary^⁢ =  +   Education   

b.

Interpret the coefficient for Education.

	As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $5,500.
	As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $5,500.
	As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,500.
	As Education inceases by 1 unit, an individual’s annual salary is predicted to decrease by $6,500.

c.	What is the predicted salary for an individual who completed 9 years of higher education? (Round intermediate coefficient values to 2 decimal places and final answer, in dollars, to the nearest whole number.)

SalaryˆSalary^⁢

$

Answer 1

The statistical software output for this problem is:

Simple linear regression results:

Dependent Variable: Salary
Independent Variable: Education
Salary = 34.25 + 5.5 Education
Sample size: 8
R (correlation coefficient) = 0.74886805
R-sq = 0.56080335
Estimate of error standard deviation: 12.877629

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	34.25	9.1599001	≠ 0	6	3.7391237	0.0096
Slope	5.5	1.9870613	≠ 0	6	2.7679065	0.0325

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	95% C.I. for mean	95% P.I. for new
9	83.75	10.928837	(57.0081, 110.4919)	(42.421608, 125.07839)

Hence,

a) Regression equation:

= 34.25 + 5.5 Education

b) As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $5,500. Option B is correct.

c) Predicted salary = $83750