$($True$/$False$)$ Identify whether the following statements are true or false and

present reasons why you believe so$.$ Follow the notation in the lecture.

$($a$)$ If the sample size is large, OLS estimators are BLUE $($Best Linear Unbiased

Estimator$)$ without homoskedasticity.

$($b$)$ The normality assumption of the regression error can be informally tested

by examining the normality of the dependent variable.

$($c$)$ Consider a model with three independent variables:

$Y={}_0+{}_1{x}_1+{}_2{x}_2+{}_3{x}_3+U$

Suppose $x_2$ and $x_3$ are highly correlated, but $x_1$ is completely uncorre$-$

lated with both $x_2$ and $x_3.$ Then

Var$(widehat({)}_1)=\frac{{}^2}{{\displaystyle \underset{?}{\overset{?}{}}}(x_{i1}-{\stackrel{}{x}}_1{)}^2}$

following the notation from the lecture.

$($d$)$ Suppose the true population model is

$Y={}_0+{}_1{x}_1+{}_2{x}_1^2+U$

that is$,$ the second independent variable is the square of the first indepen$-$

dent variable. Suppose we know that ${}_{2}0$ but we inadvertently omit

$x_1^2.$ Then there is an endogeneity problem.