typo in regression

This commit is contained in:
mhjensen
2020-08-23 22:35:43 +02:00
parent 27914a5a7e
commit a4bb17af29
7 changed files with 10 additions and 10 deletions
@@ -422,14 +422,14 @@ $$
or using the matrix \( \boldsymbol{X} \) and in a more compact matrix-vector notation as
$$
C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)\right\}.
C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)\right\}.
$$
This function is one possible way to define the so-called cost function.
<p>
It is also common to define
the function \( Q \) as
the function \( C \) as
$$
C(\boldsymbol{\beta})=\frac{1}{2n}\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2,
@@ -567,7 +567,7 @@ $$
or using the matrix \( \boldsymbol{X} \) and in a more compact matrix-vector notation as
<p>&nbsp;<br>
$$
C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)\right\}.
C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)\right\}.
$$
<p>&nbsp;<br>
@@ -575,7 +575,7 @@ This function is one possible way to define the so-called cost function.
<p>
It is also common to define
the function \( Q \) as
the function \( C \) as
<p>&nbsp;<br>
$$
@@ -700,14 +700,14 @@ $$
or using the matrix \( \boldsymbol{X} \) and in a more compact matrix-vector notation as
$$
C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)\right\}.
C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)\right\}.
$$
This function is one possible way to define the so-called cost function.
<p>
It is also common to define
the function \( Q \) as
the function \( C \) as
$$
C(\boldsymbol{\beta})=\frac{1}{2n}\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2,
+2 -2
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@@ -705,14 +705,14 @@ $$
or using the matrix \( \boldsymbol{X} \) and in a more compact matrix-vector notation as
$$
C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}^T\boldsymbol{\beta}\right)\right\}.
C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)\right\}.
$$
This function is one possible way to define the so-called cost function.
<p>
It is also common to define
the function \( Q \) as
the function \( C \) as
$$
C(\boldsymbol{\beta})=\frac{1}{2n}\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2,
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+2 -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}
or using the matrix $\bm{X}$ and in a more compact matrix-vector notation as
!bt
\[
C(\bm{\beta})=\frac{1}{n}\left\{\left(\bm{y}-\bm{X}^T\bm{\beta}\right)^T\left(\bm{y}-\bm{X}^T\bm{\beta}\right)\right\}.
C(\bm{\beta})=\frac{1}{n}\left\{\left(\bm{y}-\bm{X}\bm{\beta}\right)^T\left(\bm{y}-\bm{X}\bm{\beta}\right)\right\}.
\]
!et
This function is one possible way to define the so-called cost function.
@@ -354,7 +354,7 @@ This function is one possible way to define the so-called cost function.
It is also common to define
the function $Q$ as
the function $C$ as
!bt
\[