correcting typos
This commit is contained in:
@@ -389,7 +389,7 @@ MathJax.Hub.Config({
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<p>
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<center><h4>Sep 9, 2021</h4></center> <!-- date -->
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<center><h4>Sep 10, 2021</h4></center> <!-- date -->
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<br>
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<p>
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@@ -148,7 +148,7 @@ MathJax.Hub.Config({
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<p> <br>
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<center><h4>Sep 9, 2021</h4></center> <!-- date -->
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<center><h4>Sep 10, 2021</h4></center> <!-- date -->
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<br>
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<p>
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@@ -1353,8 +1353,7 @@ where we have used that \( \mathbb{E} (\mathbf{Y} \mathbf{Y}^{T}) =
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\sigma^2 \, \mathbf{I}_{nn} \). From \( \mbox{Var}(\boldsymbol{\beta}) = \sigma^2
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\, (\mathbf{X}^{T} \mathbf{X})^{-1} \), one obtains an estimate of the
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variance of the estimate of the \( j \)-th regression coefficient:
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\( \boldsymbol{\sigma}^2 (\boldsymbol{\beta}_j ) = \boldsymbol{\sigma}^2 \sqrt{
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[(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} } \). This may be used to
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\( \boldsymbol{\sigma}^2 (\boldsymbol{\beta}_j ) = \boldsymbol{\sigma}^2 [(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} \). This may be used to
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construct a confidence interval for the estimates.
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<p>
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@@ -308,7 +308,7 @@ MathJax.Hub.Config({
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<p>
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<center><h4>Sep 9, 2021</h4></center> <!-- date -->
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<center><h4>Sep 10, 2021</h4></center> <!-- date -->
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<br>
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<p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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@@ -1373,8 +1373,7 @@ where we have used that \( \mathbb{E} (\mathbf{Y} \mathbf{Y}^{T}) =
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\sigma^2 \, \mathbf{I}_{nn} \). From \( \mbox{Var}(\boldsymbol{\beta}) = \sigma^2
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\, (\mathbf{X}^{T} \mathbf{X})^{-1} \), one obtains an estimate of the
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variance of the estimate of the \( j \)-th regression coefficient:
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\( \boldsymbol{\sigma}^2 (\boldsymbol{\beta}_j ) = \boldsymbol{\sigma}^2 \sqrt{
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[(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} } \). This may be used to
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\( \boldsymbol{\sigma}^2 (\boldsymbol{\beta}_j ) = \boldsymbol{\sigma}^2 [(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} \). This may be used to
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construct a confidence interval for the estimates.
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<p>
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@@ -313,7 +313,7 @@ MathJax.Hub.Config({
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<p>
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<center><h4>Sep 9, 2021</h4></center> <!-- date -->
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<center><h4>Sep 10, 2021</h4></center> <!-- date -->
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<br>
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<p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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@@ -1378,8 +1378,7 @@ where we have used that \( \mathbb{E} (\mathbf{Y} \mathbf{Y}^{T}) =
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\sigma^2 \, \mathbf{I}_{nn} \). From \( \mbox{Var}(\boldsymbol{\beta}) = \sigma^2
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\, (\mathbf{X}^{T} \mathbf{X})^{-1} \), one obtains an estimate of the
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variance of the estimate of the \( j \)-th regression coefficient:
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\( \boldsymbol{\sigma}^2 (\boldsymbol{\beta}_j ) = \boldsymbol{\sigma}^2 \sqrt{
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[(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} } \). This may be used to
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\( \boldsymbol{\sigma}^2 (\boldsymbol{\beta}_j ) = \boldsymbol{\sigma}^2 [(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} \). This may be used to
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construct a confidence interval for the estimates.
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<p>
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