= Solution
{c}
The <least-squares estimators> depend only on the observed responses and design, so the formulas in <7/b/i> still hold. Their <variances> and <covariance> need only the error <covariance matrix>, now $I_n$. Therefore
$$
\boxed{\operatorname{Var}(\widehat\beta)=\frac1{S_{xx}},\qquad
\operatorname{Cov}(\widehat\alpha,\widehat\beta)=0.}
$$
For example the first formula follows from $\operatorname{Var}(\sum_i x_i\epsilon_i)=\sum_i x_i^2$, and the second from $\sum_i x_i=0$. The formulas remain the same as before with $\sigma^2=1$; this calculation does not establish <independence> or a <normal distribution> for the <estimators>.
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