Question

. A social scientist would like to analyze the relationship between educational attainment and salary. He collects the following sample data, where Education refers to years of higher education and Salary is the individuals annual salary in thousands of dollars:

education salary

3	41
4	46
6	59
2	49
5	68
4	43
8	91
0	40

A. Find the sample regression equation for the model: Salary = ?0 + ?1Education + ?. (Round intermediate calculations to 4 decimal places. Enter your answers in thousands rounded to 2 decimal places.) b)Interpret the coefficient for education. c. What is the predicted salary for an individual who completed 7 years of higher education? (Round intermediate coefficient values to 2 decimal places and final answer, in dollars, to the nearest whole number.)

Answer 1

The statistical software output for this problem is:

Parameter estimates: Std. Err. Alternative DF P-value Parameter Estimate T-Stat Intercept 6 4.1121145 0.0063 30.720238 7.4706669 +0 6 3.6876061 Slope 5.9761905 1.6206152 0.0102 Analysis of variance table for regression model: P-value Source DF MS F-stat 1 1500.0238 1500.0238 13.598439 Model 0.0102 6 661.85119 110.30853 Error Total 2161.875 Predicted values: X value s.e.(Pred. y) Pred. Y 95% C.I. for mean 95% P.I. for new 72.553571 6.1176882 (57.584128, 87.523015) (42.812304, 102.29484)

Hence,

a) Regression equation:

Salary = 30.72 + 5.98 Education

b) For every one year increase in education, salary increases by $5980

c) Predicted salary = 72554