## Transcribed Text

Question 3
The following table shows estimation results using the ordinary least squares method:
Dependent Variable: LWAGE
Method: Least Squares (Gauss-Newton / Marquardt steps)
Date: 10/10/17 Time: 14:01
Sample: 1 50
Included observations: 50
LWAGE = c(1) + C(2)*EDUC + C(3)*MARRIED + C(4)'URBAN
Coefficient
Std. Error
t-Statistic
Prob.
C(1)
5.804356
0.393738
14.74166
0.0000
C(2)
0.047844
0.021277
2.248627
0.0294
C(3)
0.297224
0.179578
1.655130
0.1047
C(4)
0.198999
0.156047
1.275245
0.2086
R-squared
0.165986
Mean dependent var
6.948572
Adjusted R-squared
0.111594
S.D. dependent var
0.361979
S.E. of regression
0.341185
Akaike info criterion
0.763833
Sum squared resid
5.354721
Schwarz criterion
0.916795
Log likelihood
-15.09582
Hannan-Quinn criter.
0.822081
F-statistic
3.051644
Durbin-Watson stat
2.107641
Prob(F-statistic)
0.037780
where Iwage is monthly income measured in pounds (in logarithmic form), educ is years of
formal education, married is 1 if the person is married, urban is 1 if the person lives in urban
area.
a) Report the results and interpret the estimates.
[20 marks]
b) Explain the difference between R2 and R².
[10 marks]
Dependent Variable: LWAGE
Method: Least Squares (Gauss-Newton /Marquardt steps)
Date: 10/10/17 Time: 14:02
Sample: 1 50
Included observations: 50
LWAGE = C(1) + C(2) *EDUC
Coefficient
Std. Error
t-Statistic
Prob.
C(1)
6.346068
0.309441
20.50815
0.0000
C(2)
0.041438
0.021005
1.972725
0.0543
R-squared
0.074996
Mean dependent var
6.948572
Adjusted R-squared
0.055725
S.D. dependent var
0.361979
S.E. of regression
0.351749
Akaike info criterion
0.787381
Sum squared resid
5.938916
Schwarz criterion
0.863862
Log likelihood
-17.68452
Hannan-Quinn criter.
0.816505
F-statistic
3.891645
Durbin-Watson stat
2.167601
Prob(F-statistic)
0.054302
c) Together with estimation results from part (a), evaluate the statement that 'both gender
and location should be excluded from the model'.
[20 marks]
[50 marks total]
Question 4
The following table shows estimation results using the ordinary least squares method:
Dependent Variable: LWAGE
Method: Least Squares (Gauss-Newton / Marquardt steps)
Date: 10/10/17 Time: 14:10
Sample: 1 50
Included observations: 50
LWAGE = C(1) + C(2)*EDUC + C(3)*EDUC^2 + C(4) *EXPER + C(5)
*MARRIED
Coefficient
Std. Error
t-Statistic
Prob.
C(1)
-0.240916
2.093658
-0.115070
0.9089
C(2)
0.897313
0.281610
3.186364
0.0026
C(3)
-0.028876
0.009495
-3.041280
0.0039
C(4)
0.022303
0.016498
1.351835
0.1832
C(5)
0.168860
0.181068
0.932576
0.3560
R-squared
0.284714
Mean dependent var
6.948572
Adjusted R-squared
0.221133
S.D. dependent var
0.361979
S.E. of regression
0.319459
Akaike info criterion
0.650265
Sum squared resid
4.592439
Schwarz criterion
0.841468
Log likelihood
-11.25663
Hannan-Quinn criter.
0.723076
F-statistic
4.477966
Durbin-Watson stat
2.114982
Prob(F-statistic)
0.003939
where Iwage is monthly income measured in pounds (in logarithmic form), educ is years of
formal education, exper is years of workforce experience.
a) Report the results and interpret the estimates.
[20 marks]
b) Calculate the precise impact of married on wage.
[10 marks]
c) Evaluate the statement that 'one more year of education always has a positive impact
on wage.
[20 marks]
[50 marks total]
Question 5
a) Explain the five assumptions for the simple linear model, and show the theorem
associated with the mean and variance of estimate B1.
[30 marks]
b) Use the expression for the variance of B1 from (a), derive the standard error of B1.
[20 marks]
[50 marks total]

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