Least Squares Fitting--Power Law

$\begin{figure}\begin{center}\BoxedEPSF{LeastSquaresPower.epsf scaled 800}\end{center}\end{figure}$

Given a function of the form

$\begin{displaymath} y=Ax^B, \end{displaymath}$

(1)

$\displaystyle b$	$\textstyle =$	$\displaystyle {n\sum(\ln x\ln y)-\sum(\ln x)\sum(\ln y)\over n\sum [(\ln x)^2]-\left({\sum \ln x}\right)^2}$	(2)
$\displaystyle a$	$\textstyle =$	$\displaystyle {\sum(\ln y)-b\sum(\ln x)\over n},$	(3)

where $B\equiv b$ and $A\equiv\mathop{\rm exp}\nolimits (a)$ .