cleaning up
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@@ -600,7 +600,7 @@ $$
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and minimizing we have that
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<p> <br>
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$$
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\hat{\boldsymbol{\beta}}_{\mathrm{OLS}} = \boldsymbol{y}.
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\hat{\beta}_i^{\mathrm{OLS}} = y_i.
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$$
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<p> <br>
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</section>
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@@ -620,7 +620,7 @@ $$
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and minimizing we have that
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<p> <br>
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$$
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\hat{\boldsymbol{\beta}}_{\mathrm{Ridge}} = \frac{\boldsymbol{y}}{1+\lambda}.
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\hat{\beta}_i^{\mathrm{Ridge}} = \frac{y_i}{1+\lambda}.
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$$
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<p> <br>
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</section>
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@@ -627,7 +627,7 @@ $$
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and minimizing we have that
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$$
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\hat{\boldsymbol{\beta}}_{\mathrm{OLS}} = \boldsymbol{y}.
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\hat{\beta}_i^{\mathrm{OLS}} = y_i.
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$$
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<p>
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@@ -643,7 +643,7 @@ $$
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and minimizing we have that
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$$
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\hat{\boldsymbol{\beta}}_{\mathrm{Ridge}} = \frac{\boldsymbol{y}}{1+\lambda}.
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\hat{\beta}_i^{\mathrm{Ridge}} = \frac{y_i}{1+\lambda}.
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$$
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<p>
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@@ -632,7 +632,7 @@ $$
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and minimizing we have that
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$$
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\hat{\boldsymbol{\beta}}_{\mathrm{OLS}} = \boldsymbol{y}.
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\hat{\beta}_i^{\mathrm{OLS}} = y_i.
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$$
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<p>
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@@ -648,7 +648,7 @@ $$
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and minimizing we have that
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$$
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\hat{\boldsymbol{\beta}}_{\mathrm{Ridge}} = \frac{\boldsymbol{y}}{1+\lambda}.
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\hat{\beta}_i^{\mathrm{Ridge}} = \frac{y_i}{1+\lambda}.
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$$
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<p>
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Binary file not shown.
@@ -678,7 +678,7 @@
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"metadata": {},
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"source": [
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"$$\n",
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"\\hat{\\boldsymbol{\\beta}}_{\\mathrm{OLS}} = \\boldsymbol{y}.\n",
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"\\hat{\\beta}_i^{\\mathrm{OLS}} = y_i.\n",
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"$$"
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]
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},
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@@ -712,7 +712,7 @@
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"metadata": {},
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"source": [
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"$$\n",
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"\\hat{\\boldsymbol{\\beta}}_{\\mathrm{Ridge}} = \\frac{\\boldsymbol{y}}{1+\\lambda}.\n",
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"\\hat{\\beta}_i^{\\mathrm{Ridge}} = \\frac{y_i}{1+\\lambda}.\n",
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"$$"
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]
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},
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@@ -378,7 +378,7 @@ C(\bm{\beta})=\sum_{i=0}^{p-1}(y_i-\beta_i)^2,
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and minimizing we have that
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!bt
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\[
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\hat{\bm{\beta}}_{\mathrm{OLS}} = \bm{y}.
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\hat{\beta}_i^{\mathrm{OLS}} = y_i.
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\]
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!et
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@@ -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,
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and minimizing we have that
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!bt
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\[
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\hat{\bm{\beta}}_{\mathrm{Ridge}} = \frac{\bm{y}}{1+\lambda}.
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\hat{\beta}_i^{\mathrm{Ridge}} = \frac{y_i}{1+\lambda}.
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\]
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!et
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