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Least Squares Fitting--Power Law

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

Given a function of the form

\end{displaymath} (1)

Least Squares Fitting gives the Coefficients as
$\displaystyle b$ $\textstyle =$ $\displaystyle {n\sum(\ln x\ln y)-\sum(\ln x)\sum(\ln y)\over n\sum [(\ln x)^2]-\left({\sum \ln x}\right)^2}$ (2)
$\displaystyle a$ $\textstyle =$ $\displaystyle {\sum(\ln y)-b\sum(\ln x)\over n},$ (3)

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

See also Least Squares Fitting, Least Squares Fitting--Exponential, Least Squares Fitting--Logarithmic

© 1996-9 Eric W. Weisstein