MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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The following results were obtained by regressing mean hourly wage in dollars (Y) on years of schooling (X).

 

Dependent Variable: MEAN_WAGE

 

 

Method: Least Squares

 

 

Date: 02/15/15   Time: 11:11

 

 

Sample: 1 13

 

 

 

Included observations: 13

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

 

 

 

 

 

 

 

 

 

 

 

 

 

C

-0.014453

0.874624

-0.016525

0.9871

 

YEARS_SCHOOLING

0.724097

0.069581

10.40648

0.0000

 

 

 

 

 

 

 

 

 

 

 

 

 

R-squared

0.907791

    Mean dependent var

8.674708

 

Adjusted R-squared

0.899409

    S.D. dependent var

2.959706

 

S.E. of regression

0.938704

    Akaike info criterion

2.852004

 

Sum squared resid

9.692810

    Schwarz criterion

2.938920

 

Log likelihood

-16.53803

    Hannan-Quinn criter.

2.834139

 

F-statistic

108.2948

    Durbin-Watson stat

1.737984

 

Prob(F-statistic)

0.000000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                 
  1. Interpret the regression coefficients. Do they make economic sense?
  2. Would you conclude that there is a statistically significant relationship at the 5% level between mean hourly wage (Y) and years of schooling (X)? (Hint: Test H0: β2=0)
  3. Comment about the goodness of fit of the above regression model?
  4. Test the null hypothesis, H02=1, (vs. H1: β2≠1) at the 1% level of significance.

 

1. The following results were obtained by regressing hourly wage on years of schooling. (6
marks)
Dependent Variable: Hourly wage
Method: Least Squares
Included observations: 13
Variable
Coefficient Std. Error t-Statistic
Prob.
Intercept
Years of Schooling 0.724097
-0.014453
0.874624 -0.016525
0.9871
0.069581
10.40648
0.0000
R-squared
Adjusted R-squared 0.899409 S.D. dependent var
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
0.907791 Mean dependent var 8.674708
2.959706
0.938704 Akaike info criterion 2.852004
9.692810 Schwarz criterion
2.938920
-16.53803 Hannan-Quinn criter. 2.834139
108.2948 Durbin-Watson stat
1.737984
Prob(F-statistic) 0.000000
a. Interpret the regression coefficients. Do they make economic sense?
b. Analyze whether the intercept and slope coefficient are statistically significant at the 5%
level.
c. Comment about the goodness of fit of the above regression model using r-squared and
adjusted r-squared? Also differentiate between r-squared and adjusted r-squared.
d. Test the null hypothesis, Ho:B2=0.75, (vs. H1: B2#0.75) at the 5% level of significance.
e. Explain whether the overall model is statistically significant at the 5% level.
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Transcribed Image Text:1. The following results were obtained by regressing hourly wage on years of schooling. (6 marks) Dependent Variable: Hourly wage Method: Least Squares Included observations: 13 Variable Coefficient Std. Error t-Statistic Prob. Intercept Years of Schooling 0.724097 -0.014453 0.874624 -0.016525 0.9871 0.069581 10.40648 0.0000 R-squared Adjusted R-squared 0.899409 S.D. dependent var S.E. of regression Sum squared resid Log likelihood F-statistic 0.907791 Mean dependent var 8.674708 2.959706 0.938704 Akaike info criterion 2.852004 9.692810 Schwarz criterion 2.938920 -16.53803 Hannan-Quinn criter. 2.834139 108.2948 Durbin-Watson stat 1.737984 Prob(F-statistic) 0.000000 a. Interpret the regression coefficients. Do they make economic sense? b. Analyze whether the intercept and slope coefficient are statistically significant at the 5% level. c. Comment about the goodness of fit of the above regression model using r-squared and adjusted r-squared? Also differentiate between r-squared and adjusted r-squared. d. Test the null hypothesis, Ho:B2=0.75, (vs. H1: B2#0.75) at the 5% level of significance. e. Explain whether the overall model is statistically significant at the 5% level.
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