I want to find coefficients of a equation that gives the relationship between two data sets.

I have two columns of data. First column is H (solar radiation), second column is T (temperature). And I know the relationship between them. The relationship is H =a*[1-exp{-b*(T)^c}]. a, b and c are emprical coefficients. And these coefficients are constants. I want to find best fitted emprical coefficients in this data set. I have got 3081 {H,T} values in Excel. Thanks.

Answer 1

[John D'Errico]

Use the curve fitting toolbox. Or lacking that, use the optimization toolbox, so lsqnonlin or lsqcurvefit. Or use nlinfit from the stats TB. Or, lacking all of them, use lots of tools you can find on the file exchange.

Expect to have serious numerical problems IF you are not careful. I.e., you will probably want GOOD starting values for those parameters. Exponents are always dangerous to try to estimate. And worse, you have an exponential of an exponentiated parameter.