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Question

A researcher suspects gender discrimination in terms of salary at a bank. To test his hypothesis, he has run the

two regressions in the attached spreadsheet. In "Regression 1", salary is the dependent variable, whereas in "Regression 2" he used the natural log of salary as the dependent variable. Which regression model should he choose?


  1. The researcher should choose the model in "Regression 1" because of the higher R2.

2. The researcher should choose the model in "Regression 1" because of the higher adjusted R2.

3. The researcher should choose the model in "Regression 2" because of the lower standard error.

4.We cannot use adjusted R2 or standard errors for model selection in this case, as the models have different dependent variables.



Image for Regression1 and 2 .png

Image for Regression1 and 2 .png

SUMMARY OUTPUT
3 Regression Statistics
Regression Statistics
Multiple F 0.535688
4 Multiple F 0.510894
R Square 0.286961
Regresssion 1
6 R Square 0.261013
Regression 2
Adjusted | 0.280005
6 Adjusted | 0.253803
7
Standard [ 9551.132
Standard | 0.203219
Observati
8
Observati
208
208
9
ANOVA
10 ANOVA
11
df
SS
MS
df
F
gnificance F
SS
MS
F gnificance F
Regressio
2 7.53E+09 3.76E+09 41.25095 8.79E-16
12 Regressio
2 2.990233 1.495117
36.2033 3.43E-14
Residual
205 1.87E+10 91224120
13 Residual
205 8.466049 0.041298
Total
207 2.62E+10
14 Total
207 11.45628
15
16
Coefficient:andard Err t Stat
P-value Lower 95%Upper 95%%ower 95.09pper 95.0%
Coefficient:andard Err t Stat
P-value Lower 95%Upper 95%ower 95.09pper 95.0%
Intercept 27915.44 2791.203 10.00122 1.97E-19
22412.3 33418.59
22412.3 33418.59
17 Intercept 10.32847 0.059388 173.9146 1.4E-224 10.21138 10.44556 10.21138 10.44556
-11757 -6176.95
18 Female
-0.18031 0.030109 -5.98867 9.35E-09 -0.23968 -0.12095 -0.23968 -0.12095
Female
-8966.98 1415.108
-6.33661 1.46E-09
-11757 -6176.95
Age
446.6467 64.48431
6.92644
5.46E-11 319.5092 573.7842 319.5092 573.7842
19 Age
0.008837 0.001372 6.441094 8.29E-10 0.006132 0.011542 0.006132 0.011542
20
21
22
23

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