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

Y-salary

X-education

use R studio.

use lm function to fit linear model of salary on experience

summary function to get the summary of thr model output.

Rcode:

df1 =read.table(header = TRUE, text ="
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

"
)
df1
linmod = lm(Salary~Education,data=df1)
summary(linmod)

Output:

Call:
lm(formula = Salary ~ Education, data = df1)

Residuals:
Min 1Q Median 3Q Max
-14.817 -8.169 -2.658 4.661 30.980

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 22.296 5.636 3.956 0.000927 ***
Education 10.841 1.195 9.072 3.91e-08 ***
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 12.92 on 18 degrees of freedom
Multiple R-squared: 0.8206,   Adjusted R-squared: 0.8106
F-statistic: 82.31 on 1 and 18 DF, p-value: 3.908e-08

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

salary= 22.29585 +10.84053 *Education

b	What is the coefficient for education?

coeffcient of education =slope= 10.84053

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

we have

salary= 22.29585 +10.84053 *Education

For education=4 we get

salary= 22.29585 +10.84053 *4

=65.65797

Predicted salary for someone with 4 years of higher ed=65.65797