You are now interested in analyzing the relationship between income and educatio

Question

You are now interested in analyzing the relationship between income and education. Considering the following STATA output answer the questions below. The variable "lwage is ln(wage); "edu" and "age" stand for education and age (in years), respectively; "age_sq" is age^2; and "married" is a dummy variable that equals one if the individual is married. It is assumed that errors are homoskedastic. For items (c), (d) and (e), you do not need to calculate the exact value, just report a formula based on the information given above. (a) Interpret the coefficients of "edu" and "married." (b) Does "age" have any effect on wage? How would you test this statement? Do you have enough information to state that "age" have no effect on wage? (c) Compute "Std. Error, " "t, " and the 95% lower bound for married. (d) Compute the TSS and the missing value for "F(4, 930)". (e) What is the Adjusted-R^2? What is the Root MSE?

Explanation / Answer

Part-a

Coefficient of edu is 0.061802 which means that corresponding to on year increase in age there is 6.1802% increase in wage, holding other predictors fixed.

Coefficient of married is 0.2083059 which means that married have 20.83% higher wage as compared to non married , holding other predictors fixed.

Part-b

Age has no effect on wage as both the coefficients of age and age_sq are insignificant with p-values>0.10.

Part-c

For married 95% confidence interval upper bound=slope+t(0.05,930)*SE

So, 0.2898153=0.2083059+1.96*SE

Hence SE of married= (0.2898153-0.2083059)/1.96=0.041586429

So test statistic t=slope/SE=0.2083059/0.041586429=5.008987427

p-value=P(|t(930)||> 5.008987427)= 6.54655E-07

Lower limit of 95% CI=0.2083059-1.96*0.041586429=0.126796499

Part-d

R-square=SSR/TSS

So, TSS=SSR/(R-sqaure)=24.505861/0.1479=165.692096

So SSE=165.692096-24.505861=141.186235

So, F(4,930)= (SSR/4)/(SSE/930) =(24.505861/4)/( 141.186235/930)= 40.35529868

Part-e

Adjsted R2=1-( SSE/930)/(TSS/(N-1))

=1-(141.186235/930)/( 165.692096/934)

=0.144235054

Root MSE=sqrt(SSE/930)=sqrt(141.186235/930)= 0.389632078

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