[regression] all equations are numbered

regression/lecture/regression-chapter.tex

@@ -16,6 +16,11 @@
 
 \include{regression}
 
+\subsection{Notes}
+\begin{itemize}
+\item Fig 8.2 right: this should be a chi-squared distribution with one degree of freedom!
+\end{itemize}
+
 \subsection{Start with one-dimensional problem!}
 \begin{itemize}
 \item Just the root mean square as a function of the slope

regression/lecture/regression.tex

@@ -283,10 +283,11 @@ the partial derivatives using the difference quotient
 (Box~\ref{differentialquotientbox}) for small steps $\Delta m$ and
 $\Delta b$. For example, the partial derivative with respect to $m$
 can be computed as
-\[\frac{\partial f_{cost}(m,b)}{\partial m} = \lim\limits_{\Delta m \to
+\begin{equation}
+  \frac{\partial f_{cost}(m,b)}{\partial m} = \lim\limits_{\Delta m \to
   0} \frac{f_{cost}(m + \Delta m, b) - f_{cost}(m,b)}{\Delta m}
-\approx \frac{f_{cost}(m + \Delta m, b) - f_{cost}(m,b)}{\Delta m} \;
-. \]
+\approx \frac{f_{cost}(m + \Delta m, b) - f_{cost}(m,b)}{\Delta m} \; . 
+\end{equation}
 The length of the gradient indicates the steepness of the slope
 (\figref{gradientquiverfig}). Since want to go down the hill, we
 choose the opposite direction.
@@ -341,7 +342,9 @@ descent works as follows:
   sufficiently close to zero (e.g. \varcode{norm(gradient) < 0.1}).
 \item \label{gradientstep} If the length of the gradient exceeds the
   threshold we take a small step into the opposite direction:
-  \[p_{i+1} = p_i - \epsilon \cdot \nabla f_{cost}(m_i, b_i)\]
+  \begin{equation}
+    p_{i+1} = p_i - \epsilon \cdot \nabla f_{cost}(m_i, b_i)
+  \end{equation}
   where $\epsilon = 0.01$ is a factor linking the gradient to
   appropriate steps in the parameter space.
 \item Repeat steps \ref{computegradient} -- \ref{gradientstep}.