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
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

a. Find the sample regression equation for the model: Salary = β₀ + β₁Education + ε. (Round answers to 3 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 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? (Round answer to the nearest whole number.)

SalaryˆSalary^               $ ________

Answer 1

using excel data analysis tool for regression,steps are: write data>menu>data>data analysis>regression>enter required labels>ok> and following o/p is obtained

Regression Statistics
Multiple R	0.4779
R Square	0.2284
Adjusted R Square	0.1855
Standard Error	26.6647
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3787.9	3787.9	5.33	0.0331
Residual	18	12798.1	711.0
Total	19	16586.0
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	46.8613	10.5678	4.4344	0.0003	24.6593	69.0633
X	4.5255	1.9607	2.3081	0.0331	0.4063	8.6448

a)

salary^ = 46.861   +   4.526* education

b)

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

c)

salary^ = 46.861   +   4.526* education

salary^ = 46.861   +   4.526*8 = 83.066

answer : $83066