typo in regression
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@@ -422,14 +422,14 @@ $$
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or using the matrix \( \boldsymbol{X} \) and in a more compact matrix-vector notation as
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$$
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C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)\right\}.
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C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)\right\}.
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$$
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This function is one possible way to define the so-called cost function.
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<p>
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It is also common to define
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the function \( Q \) as
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the function \( C \) as
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$$
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C(\boldsymbol{\beta})=\frac{1}{2n}\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2,
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@@ -567,7 +567,7 @@ $$
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or using the matrix \( \boldsymbol{X} \) and in a more compact matrix-vector notation as
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<p> <br>
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$$
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C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)\right\}.
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C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)\right\}.
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$$
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<p> <br>
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@@ -575,7 +575,7 @@ This function is one possible way to define the so-called cost function.
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<p>
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It is also common to define
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the function \( Q \) as
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the function \( C \) as
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<p> <br>
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$$
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@@ -700,14 +700,14 @@ $$
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or using the matrix \( \boldsymbol{X} \) and in a more compact matrix-vector notation as
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$$
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C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)\right\}.
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C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)\right\}.
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$$
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This function is one possible way to define the so-called cost function.
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<p>
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It is also common to define
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the function \( Q \) as
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the function \( C \) as
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$$
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C(\boldsymbol{\beta})=\frac{1}{2n}\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2,
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@@ -705,14 +705,14 @@ $$
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or using the matrix \( \boldsymbol{X} \) and in a more compact matrix-vector notation as
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$$
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C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)\right\}.
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C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)\right\}.
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$$
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This function is one possible way to define the so-called cost function.
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<p>
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It is also common to define
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the function \( Q \) as
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the function \( C \) as
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$$
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C(\boldsymbol{\beta})=\frac{1}{2n}\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2,
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@@ -346,7 +346,7 @@ C(\bm{\beta})=\frac{1}{n}\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2=\frac{1}
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or using the matrix $\bm{X}$ and in a more compact matrix-vector notation as
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!bt
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\[
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C(\bm{\beta})=\frac{1}{n}\left\{\left(\bm{y}-\bm{X}^T\bm{\beta}\right)^T\left(\bm{y}-\bm{X}^T\bm{\beta}\right)\right\}.
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C(\bm{\beta})=\frac{1}{n}\left\{\left(\bm{y}-\bm{X}\bm{\beta}\right)^T\left(\bm{y}-\bm{X}\bm{\beta}\right)\right\}.
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\]
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!et
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This function is one possible way to define the so-called cost function.
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@@ -354,7 +354,7 @@ This function is one possible way to define the so-called cost function.
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It is also common to define
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the function $Q$ as
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the function $C$ as
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!bt
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\[
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