Question

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:

Salary			Education
	42			6
	48			7
	⋮			⋮
	42			0

a. Find the sample regression equation for the model: Salary = β₀ + β₁Education + ε. (Round answers to 3 decimal places.)

Salaryˆ= _(answer)__ + __(answer)__ Education

b. Interpret the coefficient for Education.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $4,526.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $4,526.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.

c. What is the predicted salary for an individual who completed 8 years of higher education?

$___(answer)___

Data:

Salary	Education
42	6
48	7
82	1
46	3
67	1
54	5
105	6
42	0
38	4
56	6
90	2
44	7
67	5
64	7
143	12
43	0
76	7
64	4
127	6
42	0

Answer 1

enter the data set into excel sheet in column A for salary and column B for education from cell 1 to 21

use SLOPE and INTERCEPT function to find the regression equation

=SLOPE(A2:A21,B2:B21)

= 4.526

and

=INTERCEPT(A2:A21,B2:B21)

= 46.861

(A) Regression equation Salary = 46.861 + 4.526(education)

(B) Slope of education is 4.526, which is positive. So, for every one year increase in education, there will be an increase of 4526 in salary

option B

(C) setting education = 8 in the regression equation, we get

= 46.861 + 4.526(education)

= 46.861 + 4.526(8)

= 83.069 (rounded to 3 decimals and in thousand dollars)

or 83000 (rounded to nearest whole number and in dollars)