Question

A social scientist would like to analyze the relationship between educational attainments (years in higher ed) and annual salary (in $1,000s). He collects the data above.

Salary	Education
40	3
53	4
80	6
41	2
70	5
54	4
110	8
38	0
42	3
55	4
85	6
42	2
70	5
60	4
140	8
40	0
76	5
65	4
125	8
38	0

a. What is the equation for predicting salary based on educational attainment?

b. What is the coefficient for education?

c. what is the predicted salary for someone with 4 years of higher ed?

Answer 1

a.

X - Mx	Y - My	(X - Mx)2	(X - Mx)(Y - My)
-1.05	-26.2	1.1025	27.51
-0.05	-13.2	0.0025	0.66
1.95	13.8	3.8025	26.91
-2.05	-25.2	4.2025	51.66
0.95	3.8	0.9025	3.61
-0.05	-12.2	0.0025	0.61
3.95	43.8	15.6025	173.01
-4.05	-28.2	16.4025	114.21
-1.05	-24.2	1.1025	25.41
-0.05	-11.2	0.0025	0.56
1.95	18.8	3.8025	36.66
-2.05	-24.2	4.2025	49.61
0.95	3.8	0.9025	3.61
-0.05	-6.2	0.0025	0.31
3.95	73.8	15.6025	291.51
-4.05	-26.2	16.4025	106.11
0.95	9.8	0.9025	9.31
-0.05	-1.2	0.0025	0.06
3.95	58.8	15.6025	232.26
-4.05	-28.2	16.4025	114.21
		SS: 116.95	SP: 1267.8

Sum of X = 81
Sum of Y = 1324
Mean X = 4.05
Mean Y = 66.2
Sum of squares (SSX) = 116.95
Sum of products (SP) = 1267.8

Regression Equation = ŷ = bX + a

b = SP/SSX = 1267.8/116.95 = 10.8405

a = MY - bMX = 66.2 - (10.84*4.05) = 22.2959

ŷ = 10.8405X + 22.2959

b. Here slope value is coefficient of education, which means for every increase in year there is 10.840 increase in y.

c. For x=4, ŷ = (10.8405*4) + 22.2959=65.6579