The first seven exercises refer to the table of estimated regressions below, com

Question

The first seven exercises refer to the table of estimated regressions below, com- puted using data for 1998 from the CPS. The data set consists of information on 4,000 full-time full-year workers. The highest educational achievement for Results of Regressions of Average Hourly Earnings on Gender and Education Binary Variables and other characteristics using 1998 data from the Current Population Survey Dependent variable: Average Hourly Earnings (AHE) Regressor College (X) 5.46 (0.21) -2.64 (0.20) 5.48 (0.21) -2.62 (0.20) 0.29 (0.04) 5.44 (0.21) -2.62 (0.20) 0.29 (0.04) 0.69 (0.30) 0.60 (0.28) -0.27 (0.26) 3.75 Female (%) Age (X) Northeast (X) Midwest (X3) South (X 12.69 (0.14) Intercep 4.40 Summary Statistics and Joint Tests F-Statistic for regional effects0 SER 6.10 6.21 0.194 6.27 6.22 0.176 0,190 4000.0 4000.0 4000.0

Explanation / Answer

Part-a

Degree of freedom of joint test=(3,4000-7)=(3,3993)

A 5% level critical F=2.6071

As calculated F=6.10>2.6071, we conclude that there are important and significant regional effects.

Part-b

Region West is omitted to avoid perfect collinearity as intercept is included in model.

If it was included then no solution exists due to singularity

Part-c

For Junita expected earning=3.75-0.27*1+0.60*0+0.69*0+0.29*28-2.62*1+5.44*1=14.42

For Molly expected earning=3.75-0.27*0+0.60*0+0.69*0+0.29*28-2.62*1+5.44*1=14.69

For Jenifer expected earning=3.75-0.27*0+0.60*1+0.69*0+0.29*28-2.62*1+5.44*1=15.29

Part-ci

95% confidence interval for difference in Juanita and molly=(14.42-14.69)±1.96*sqrt(6.21/(4000-7))

=(-0.347295145                 -0.192704855)

Part-cii

Expected difference in Juanita and Jennifer = 14.42-15.29=-0.87

Part-ciii
This is same as we calculated in Part-ci and there is no difference in calcualtions as West effect is included in intercept.

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