Consider the following simple linear regression model designed $to$ examine the relationship between

earnings and educational attainment:

Wage ${?}_{(}()()i)={}_0+{}_1$ Educ ${?}_{(}()()i)+{}_i$

Where i indexes individuals, Wage ${?}_{(}()i)isan$ individual's wage measured $in$ dollars, $Edu{c}_{i}is$ the number $of$

years $of$ schooling, and ${}_{i}is$ a random error term. $We$ would expect, $on$ average, higher levels $of$

education $tobe$ associated with higher incomes. However, the simple regression model ignores the fact

that earnings tend $to$ increase with age, regardless $of$ educational attainment. Thus, a more appropriate

model might $be$:

Wage ${?}_{(}()()i)={}_0+{}_1$ Educ ${?}_{(}()()i)+{}_2$ Age ${?}_{(}()()i)+{}_i$

Where $Ag{e}_{i}isan$ individual's age measured $in$ years.

$a.If$ Corr$(Edu{c}_i,Ag{e}_i)>0$ and you estimate model $(1)$ when the true model $is$ model $(2),$ will your

estimate $of{}_{1}be$ unbiased? Will $itbe$ consistent? Provide a detailed explanation.

$b.If$ Corr$(Edu{c}_i,Ag{e}_i)>0$ and you estimate model $(1)$ when the true model $is$ model $(2),$ will your

estimate $of{}_1$ overstate, understate, $or$ correctly state the impact $of$ education $on$ earnings $in$ the

regression? Why?

$c.If$ Corr$(Edu{c}_i,Ag{e}_i)=0$ and you estimate model $(1)$ when the true model $is$ model $(2),$ will your

estimate $of{}_{1}be$ unbiased? Will $itbe$ consistent? Provide a detailed explanation.

$d.$ Finally, suppose Corr$(Edu{c}_i,Ag{e}_i)=0$ and you estimate model $(1)$ when the true model $is$ model $(2).$

How would the results you obtain from model $(1)$ differ from the results you would obtain from model

$(2)?$ Specifically, what differences would you expect between the $R^{21}s,$ the estimates $of{}_1$ and the

standard errors $of$ hat$({)}_1$ between the two models?