# mavam/stat-cookbook

Fix conditional variance of LS estimate.

In 18.1, the equation of the conditional variance of beta hat lacked a square
operation in the denominator.

Moreover, at the end of 18.1, the statement about the estimator under the
assumption or Normality now includes a more precise formulation.

Contributed by Travis Walter.
 @@ -1574,7 +1574,7 @@ \subsection{\T{Simple Linear Regression}} = \frac{\sumin X_iY_i-n\Xbar\Ybar}{\sumin X_i^2 - n\Xsqbar} \\ \E{\bhat\giv X^n} &= \begin{pmatrix}\beta_0 \\ \beta_1\end{pmatrix} \\ \V{\bhat\giv X^n} &= - \frac{\sigma^2}{n s_X} + \frac{\sigma^2}{n s^2_X} \begin{pmatrix}n^{-1}\sumin X_i^2 & -\Xnbar \\ -\Xnbar & 1\end{pmatrix} \\ \sehat(\bhat_0) &= \frac{\shat}{s_X\sqrt{n}} \sqrt{\frac{\sumin X_i^2}{n}} \\ \sehat(\bhat_1) &= \frac{\shat}{s_X\sqrt{n}} @@ -1614,7 +1614,8 @@ \subsection{\T{Simple Linear Regression}} \end{align*} \T{Under the assumption of Normality, - the least squares estimator is also the MLE} + the least squares parameter estimators are also the MLEs, + but the least squares variance estimator is not the MLE} $\shat^2 = \frac{1}{n}\sumin \ehat_i^2$ \subsection{\T{Prediction}}