Thinking about linear regression

notes/mml.tex

@@ -104,16 +104,16 @@ \section*{Introduction}
 function taken from \emph{this} set (and matching the data).
 
 There is another snag. It turns out to be quite difficult to get the
-“size” of $\mathcal{F}$ right. If there are too few functions to draw from we
-run the risk of not being able to find \emph{any} function that
-matches the data. In the classical subject of “simple linear
-regression,” for example, one is interested in functions $\setR \to
-\setR$ and one chooses, for $\mathcal{F}$, all first-order polynomials (that is,
-straight-line functions). But hardly any sets of data can be matched
-by a first-order polynomial. (Most sets of three points do not lie on
-a straight line.)
-
-
+“size” of $\mathcal{F}$ right. If there are too few functions to draw from, we
+run the risk of not finding \emph{any} function that matches the
+data.\footnote{In the classical subject of “simple linear regression,” for
+example, one is interested in functions $\setR \to \setR$ and one
+chooses, for $\mathcal{F}$, all first-order polynomials (that is, straight-line
+functions). But hardly any sets of data can be matched by a
+first-order polynomial. (Most sets of three points do not lie on a
+straight line.)}
+
+However, perhaps serendipitously,