math notation

doc/src/Regression/Regression.do.txt

@@ -1901,13 +1901,13 @@ $X_j$, ($i\neq j$):
 !split
 ===== Covariance example =====
 
-Suppose we have defined three vectors $\hat{x}, \hat{y}, \hat{z}$ with
+Suppose we have defined three vectors $\bm{x}, \bm{y}, \bm{z}$ with
 $n$ elements each. The covariance matrix is defined as
 
 
 !bt
 \[
-\hat{\Sigma} = \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{xz} \\
+\bm{\Sigma} = \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{xz} \\
                               \sigma_{yx} & \sigma_{yy} & \sigma_{yz} \\
                               \sigma_{zx} & \sigma_{zy} & \sigma_{zz}
              \end{bmatrix},
@@ -1926,11 +1926,11 @@ the exact mean valu\ es.
 
 The following simple function uses the _np.vstack_ function which
 takes each vector of dimension $1\times n$ and produces a $3\times n$
-matrix $\hat{W}$
+matrix $\bm{W}$
 
 !bt
 \[
-\hat{W} = \begin{bmatrix} x_0 & y_0 & z_0 \\
+\bm{W} = \begin{bmatrix} x_0 & y_0 & z_0 \\
                           x_1 & y_1 & z_1 \\
                           x_2 & y_2 & z_2 \\
                           \dots & \dots & \dots \\
@@ -1941,8 +1941,8 @@ matrix $\hat{W}$
 !et
 
 which in turn is converted into into the $3\times 3$ covariance matrix
-$\hat{\Sigma}$ via the Numpy function _np.cov()_. We note that we can
-also calculate the mean value of each set of samples $\hat{x}$ etc
+$\bm{\Sigma}$ via the Numpy function _np.cov()_. We note that we can
+also calculate the mean value of each set of samples $\bm{x}$ etc
 using the Numpy function _np.mean(x)_. We can also extract the
 eigenvalues of the covariance matrix through the _np.linalg.eig()_
 function.
@@ -2550,7 +2550,7 @@ where we have used  that $\mathbb{E} (\mathbf{Y} \mathbf{Y}^{T}) =
 \sigma^2 \, \mathbf{I}_{nn}$. From $\mbox{Var}(\bm{\beta}) = \sigma^2
 \, (\mathbf{X}^{T} \mathbf{X})^{-1}$, one obtains an estimate of the
 variance of the estimate of the $j$-th regression coefficient:
-$\hat{\sigma}^2 (\hat{\beta}_j ) = \hat{\sigma}^2 \sqrt{
+$\bm{\sigma}^2 (\bm{\beta}_j ) = \bm{\sigma}^2 \sqrt{
 [(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} }$. This may be used to
 construct a confidence interval for the estimates.