Consider the relationship between hourly wage rate and educationattainment. A random sample of 21 male workers was collected toestimate the following model
Yi =β0+β1Xi+ui,fori=1,...,21.
Here,Yiisthelogarithmofhourlywagerate,log(wage),forthei-thworker.Xiistheeducation level, husedu, of the i-th worker, which is measuredas the years of schooling, and ui is the error term for the i-thworker. The ordinary least squares (OLS) estimation of the model isreported in the table below. The variable ones
18. (3points)Accordingtotheestimates,whatisthepredictedvalueofthelogarithmofhourlywage for a male worker with 12 years of schooling?
19. (3 points) The standard error of β1 is se(β1) = 0.016 asshown in the OLS results. Test the hypothesis
H0 :β1 =0.03 H1 : β1 ̸= 0.03.
Use the 0.01 significance level.
20. (3 points) Construct the 95% confidence interval for thepopulation parameter β1.
21. (3 points) The standard error of the regression is 0.1853(not shown in the results table), and the R -squared is 0.525. Usethese values to obtain the total sum of squares of the dependentvariable.
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