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Least Squares Fitting--Logarithmic

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

Given a function of the form

y=a+b\ln x,
\end{displaymath} (1)

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

See also Least Squares Fitting, Least Squares Fitting--Exponential, Least Squares Fitting--Power Law

© 1996-9 Eric W. Weisstein