Consider a simple linear regression model where time is the predictor variable. Assume that the errors are uncorrelated and have constant variance \(\sigma^{2}\). Show that the variances of the model parameter estimates are

\[
V\left(\hat{\beta}_{0}\right)=\sigma^{2} \frac{2(2 T+1)}{T(T-1)}
\]

and

\[
V\left(\hat{\beta}_{1}\right)=\sigma^{2} \frac{12}{T\left(T^{2}-1\right)}
\]