Question

20. 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
	⋮			⋮
	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 increase by $8,590.

• 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 decrease by $5,460.

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

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

Answer 1

A) The sample regression equation for the model is

Salary^{^}=48.016 +5.457 * Education

B) Since the value of β1=5.457~5.46. So,

Interpretation of coefficients is Education increases by 1 unit, an individual’s annual salary are predicted to increase by $5,460.

C) The predicted salary for an individual who completed 5 years of higher education is 75$ (approx)

Note: I have done this problem in R. So, I am attaching my R-code for your reference.

> Salary<-c(35,67,79,46,69,78,111,62,20,25,100,47,64,66,154,61,87,60,123,32)
> Education<-c(1,6,2,1,7,5,6,0,4,5,6,5,3,9,7,0,1,3,7,0)
> length(Education
+ )
[1] 20
> length(Salary)
[1] 20
> model<-lm(Salary~Education)
> model

Call:
lm(formula = Salary ~ Education)

Coefficients:
(Intercept) Education
48.016 5.457

> pred<-predict(model,data.frame(Education=5))
> pred
1
75.30311