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
35	1
67	6
79	2
46	1
69	7
78	5
111	6
62	0
20	4
25	5
100	6
47	5
64	3
66	9
154	7
61	0
87	1
60	3
123	7
32	0

a. Find the sample regression equation for the model: Salary = β₀ + β₁Education + ε. (Round answers 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 $8,590.

• 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 $5,460.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $5,460.

c. What is the predicted salary for an individual who completed 5 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)

SalaryˆSalary^               $

Answer 1

The statistical software output for this problem is:

Hence,

a) Regression equation:

Salary = 48.02 + 5.46 Education

b) As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $5,460.

c) Predicted salary = $ 75303