$=1-$ female widehat$(ln(w))=$widehat$(b{)}_0+$widehat$(b{)}_1$educ$+$widehat$(b{)}_2$ male $+$widehat$(b{)}_3($ male $$educ $)+$widehat$(b{)}_4$ age $+$widehat$(b{)}_{5}ag{e}^2+$widehat$(b{)}_{6}ag{e}^3+$widehat$(b{)}_7$ northeast $+$widehat$(b{)}_8$ south $+$widehat$(b{)}_9$ west $,$

where $ln(w)$ denotes the natural logarithm $of$ the wage $w,$ educ denotes years $of$ education, male $is$ a male dummy variable, age denotes

age, and northeast, south, and west are regional dummy variables.

$(a)$ How much $is$ the OLS estimate $of$ the coefficient $on$ male $$educ $?$

$(b)$ How much $is$ its heteroskedasticity$-$robust standard error $(basedonHC3)?$

$(c)$ How much $is$ the OLS estimate $of$ the coefficient $on$ northeast?

$(d)$ How much $is$ its heteroskedasticity$-$robust standard error $(basedonHC3)?$

$(e)$ Consider two males, David and Michael, who differ $in$ their years $of$ education but are otherwise identical. $In$ particular, David has $4$

year $of$ education more than Michael. According $to$ the regression, what $is$ the estimated percentage difference $in$ their wages?

$(f)$ Test $if$ person's age matters for $hi\frac{s}{h}er$ logged wage.

$(i)$ What $is$ the corresponding $F-$statistic?

$(ii)$ Use the table $on$ page $25of$ slide set $6to$ find the critical value $of$ the test statistic $ata5\%$ significance level.

$(iii)So,$ does person's age matter for $hi\frac{s}{h}er$ logged wage?

$(g)$ Test $if$ the coefficient $on$ northeast equals the coefficient $on$ west.

$(i)$ Modify the regression $so$ that you can test the null hypothesis that the aforementioned coefficients are equal $vs$ the two$-$sided

alternative. Which regressor did you change and how?

$(ii)$ What $is$ the relevant $p-$value?

$(iii)So,$ does the coefficient $on$ northeast equal the coefficient $on$ west?