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

$i.$ Heteroscedasticity

$ii.$ Unbiasedness

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

coefficients $in$ Multiple Linear Regression model and their variances?

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

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

$d.$ Consider the estimated OLS regression $(next$ page$)$ capturing relationship between

weightloss and distance walked $(valuesin$ brackets are the estimated $t-$statistics$)$:

hat$(wght)=-0\mathrm{.}65-8\mathrm{.}2ln($ walk $)+0\mathrm{.}35$ calorie

hat$(R)=0\mathrm{.}53$

where weight $is$ person's weight $in$ kilograms, walk $is$ distance walked $inkm$ per day,

calorie $is$ number $of$ calories consumed $in$ thousands per day

$i.$ Interpret the coefficient $onln(walk).$ Explain what $we$ can capture $by$ walk