Answered: The following sample data contains the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The following sample data contains the number of years of college and the current annual salary for a random sample of heavy equipment salespeople. A researcher believes that spending more years in college leads to higher annual income.

Annual Income (in thousands)	Years in College
20.	2.
23.	2.
25.	4.
55.	5.
28.	3.
28.	2.
37.	4.
35.	3.
40.	4.
39.	4.

The researcher thought that another variable, gender, might also affect the income level. Thus, he created a dummy variable for gender (1 for male and 0 for female) and estimated the regression model with two independent variables.

Write down the estimated regression equation.

What is the value of R square in this regression model? Compared with y = 6.5 + 8.0x?

Interpret the meaning of the regression coefficient of Year in College (how does year in college affect salary?). Does this variable have a significant impact on income level at α= .05? How does one more year in college affect salary if the gender is the same? How do you get this conclusion?

SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R S
Standard Er
0.920
0.847
0.803
4.610
Observations
10.000
ANOVA
df
SS
MS
F
Significance F
Regression
2.000
823.223
411.612
19.366
0.001
Residual
7.000
148.777
21.254
Total
9.000
972.000
Upper 95% Lower 95.0% Upper 95.0%
(10.434)
Coefficients Standard Erroi
t Stat
P-value
Lower 95%
Intercept
1.983
5.251
0.378
0.717
(10.434)
14.401
14.401
Years in Coll
7.851
1.452
5.408
0.001
4.418
11.284
4.418
11.284
gender
8.512
2.978
2.858
0.024
1.470
15.555
1.470
15.555

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