$a.$ Explain thoroughly, with examples, the following:

$i.$ Multicollinearity

$ii.$ Efficiency

$b.$ What are the implications $of$ heteroscedasticity for the OLS estimators $of$ slope

coefficients $in$ Multiple Linear Regression model and their variances? What are the

different ways $of$ checking heteroscedasticity? How will you proceed with OLS

estimation $in$ the presence $of$ heteroscedasticity?

$c.$ State the Gauss$-$Markov assumptions required for OLS estimator $tobe$ BLUE. What $is$ the

addition $inCLRM$ Assumptions? Why $isit$ needed?

$d.$ The following model allows the return $on$ education $to$ depend upon the total amount $of$

both parents' education, called pareduc:

$log($ wage $)=+educ+$ educ ${?}^{(}()()*)$ pareduc $+$ nexper $+tenure+u$

$(i)$ Show that, $in$ decimal form, the return $to$ another year $of$ education $in$ this model $is$

$log\frac{\text{w}\text{a}\text{g}\text{e}}{}$ educ $=+pareduc$

What sign $do$ you expect fore? Why?

$(ii)$ Which level $of$ pareduc will you use $to$ estimate wage