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

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.)

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.)

Salary= $ ______

Answer 1

	Education X	Salary Y	X * Y
	6	42	252	36	1764
	7	48	336	49	2304
	1	82	82	1	6724
	3	46	138	9	2116
	1	67	67	1	4489
	5	54	270	25	2916
	6	105	630	36	11025
	0	42	0	0	1764
	4	38	152	16	1444
	6	56	336	36	3136
	2	90	180	4	8100
	7	44	308	49	1936
	5	67	335	25	4489
	7	64	448	49	4096
	12	143	1716	144	20449
	0	43	0	0	1849
	7	76	532	49	5776
	4	64	256	16	4096
	6	127	762	36	16129
	0	42	0	0	1764
Total	89	1340	6800	581	106366

Equation of regression line is


b = 4.526

a =( 1340 - ( 4.5255 * 89 ) ) / 20
a = 46.861
Equation of regression line becomes

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

When X = 8
= 46.861 + 4.526 X
= 46.861 + 4.526 * 8
= 83.07
= 83