cleaning up

This commit is contained in:
Morten Hjorth-Jensen
2021-09-08 06:36:44 +02:00
parent 5fcdfec57b
commit 9ae38140a8
6 changed files with 10 additions and 10 deletions
+2 -2
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@@ -600,7 +600,7 @@ $$
and minimizing we have that
<p>&nbsp;<br>
$$
\hat{\boldsymbol{\beta}}_{\mathrm{OLS}} = \boldsymbol{y}.
\hat{\beta}_i^{\mathrm{OLS}} = y_i.
$$
<p>&nbsp;<br>
</section>
@@ -620,7 +620,7 @@ $$
and minimizing we have that
<p>&nbsp;<br>
$$
\hat{\boldsymbol{\beta}}_{\mathrm{Ridge}} = \frac{\boldsymbol{y}}{1+\lambda}.
\hat{\beta}_i^{\mathrm{Ridge}} = \frac{y_i}{1+\lambda}.
$$
<p>&nbsp;<br>
</section>
+2 -2
View File
@@ -627,7 +627,7 @@ $$
and minimizing we have that
$$
\hat{\boldsymbol{\beta}}_{\mathrm{OLS}} = \boldsymbol{y}.
\hat{\beta}_i^{\mathrm{OLS}} = y_i.
$$
<p>
@@ -643,7 +643,7 @@ $$
and minimizing we have that
$$
\hat{\boldsymbol{\beta}}_{\mathrm{Ridge}} = \frac{\boldsymbol{y}}{1+\lambda}.
\hat{\beta}_i^{\mathrm{Ridge}} = \frac{y_i}{1+\lambda}.
$$
<p>
+2 -2
View File
@@ -632,7 +632,7 @@ $$
and minimizing we have that
$$
\hat{\boldsymbol{\beta}}_{\mathrm{OLS}} = \boldsymbol{y}.
\hat{\beta}_i^{\mathrm{OLS}} = y_i.
$$
<p>
@@ -648,7 +648,7 @@ $$
and minimizing we have that
$$
\hat{\boldsymbol{\beta}}_{\mathrm{Ridge}} = \frac{\boldsymbol{y}}{1+\lambda}.
\hat{\beta}_i^{\mathrm{Ridge}} = \frac{y_i}{1+\lambda}.
$$
<p>
Binary file not shown.
+2 -2
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@@ -678,7 +678,7 @@
"metadata": {},
"source": [
"$$\n",
"\\hat{\\boldsymbol{\\beta}}_{\\mathrm{OLS}} = \\boldsymbol{y}.\n",
"\\hat{\\beta}_i^{\\mathrm{OLS}} = y_i.\n",
"$$"
]
},
@@ -712,7 +712,7 @@
"metadata": {},
"source": [
"$$\n",
"\\hat{\\boldsymbol{\\beta}}_{\\mathrm{Ridge}} = \\frac{\\boldsymbol{y}}{1+\\lambda}.\n",
"\\hat{\\beta}_i^{\\mathrm{Ridge}} = \\frac{y_i}{1+\\lambda}.\n",
"$$"
]
},
+2 -2
View File
@@ -378,7 +378,7 @@ C(\bm{\beta})=\sum_{i=0}^{p-1}(y_i-\beta_i)^2,
and minimizing we have that
!bt
\[
\hat{\bm{\beta}}_{\mathrm{OLS}} = \bm{y}.
\hat{\beta}_i^{\mathrm{OLS}} = y_i.
\]
!et
@@ -394,7 +394,7 @@ C(\bm{\beta})=\sum_{i=0}^{p-1}(y_i-\beta_i)^2+\lambda\sum_{i=0}^{p-1}\beta_i^2,
and minimizing we have that
!bt
\[
\hat{\bm{\beta}}_{\mathrm{Ridge}} = \frac{\bm{y}}{1+\lambda}.
\hat{\beta}_i^{\mathrm{Ridge}} = \frac{y_i}{1+\lambda}.
\]
!et