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:

Education 3 4 6 2 5 4 8 0

Salary $40 36 56 35 72 47 107 52

a) Find the sample regression equation for the model: Salary = ?0 + ?1Education + ?. (Round intermediate calculations to 4 decimal places. Enter your answers in thousands rounded to 2 decimal places.)

b) Interpret the coefficient for education.

c) What is the predicted salary for an individual who completed 7 years of higher education? (Round intermediate coefficient values to 2 decimal places and final answer, in dollars, to the nearest whole number.)

Question

Mathematics

Seamus Duarte

22 April, 05:18

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:

Education 3 4 6 2 5 4 8 0

Salary $40 36 56 35 72 47 107 52

a) Find the sample regression equation for the model: Salary = ?0 + ?1Education + ?. (Round intermediate calculations to 4 decimal places. Enter your answers in thousands rounded to 2 decimal places.)

b) Interpret the coefficient for education.

c) What is the predicted salary for an individual who completed 7 years of higher education? (Round intermediate coefficient values to 2 decimal places and final answer, in dollars, to the nearest whole number.)

+3

Answers (1)

Know the Answer?

Melody · Answer 1

A.) ŷ = 7X + 27.625

B.) check Explanation

C.) $77,000

Step-by-step explanation:

Given the following:

Education (x) : 3 4 6 2 5 4 8 0

Salary (y) : $40 36 56 35 72 47 107 52

A.) Using the linear regression calculator:

ŷ = 7X + 27.625

Salary = 7 (education) + 27.625

B.) The Coefficient for education refers to the gradient or slope of the linear graph, the Coefficient is the ratio of the change in salary earned to education. The slope, which is the Coefficient of education is 7.

C.) What is the predicted salary for an individual who completed 7 years of higher education?

ŷ = 7X + 27.625

Salary = 7 (education) + 27.625

Salary = 7 (7) + 27.625

Salary = 49 + 27.625

Salary = $76.625

Salary = $77,000 (nearest whole number)