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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.
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mavam committed Jan 31, 2013
1 parent 3ea807b commit 758a5bae6d25eb3f67a28537dd5c9c3db2648368
Showing with 3 additions and 2 deletions.
  1. +3 −2 cookbook.tex
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@@ -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}}

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