(5) Prove that $$ \operatorname(Var}\left(\hat{\beta}_{1} ight)=\frac{\sigma {2}}{\sum\left(x_{i}-\bar{x} ight)^{2}} \text { where } \sigma^{2}=\operatorname (Var}\left(u_{i} ight) $$ HINT: in order to do that, you should use $\hat{\beta}_{1}=\frac{\sum\left(x_{i}-\bar{x} ight) y_{i}} {\sum\left(x_{i}-\bar(x} ight)^{2}}$. First substitute for $y_{i}$ from the population regression line and then calculate $\operatorname (Var}\left(\hat{\beta}_{1} ight)$. S.P.PB. 273