MATLAB: How to apply exponential and logarithmic curve fitting

Question

Hi,

I have some scatterplots and I want to check the relationships between the variables which resemble exponential and logarithmic functions. I have tried to use the functions

nlinfit
fittype
fit

but so far not successfully (poor fitting or code not working at all).

How can I check the curves for the above scatters which seem to have the following functions:

y= a*exp(b*x)+c     and      y=log_a(x)+b

in matlab?

Thanks

Iro

Answer 1

The nlinfit function requires that the first argument of the objective function is the parameter vector and the second the vector of independent variables. Using anonymous functions,

y = a*exp(b*x)+c

becomes

y = @(B,x)  B(1).*exp(B(2).*x) + B(3);     % B(1) = a,  B(2) = b,  B(3) = c

For the logarithmic fit, all logs to various bases are simply scaled by a constant. Consider:

a^y = b^x

Taking the log to base a (denoted by loga()) of both sides gives:

y = x*loga(b)

so the log to any base will work.

The anonymous function for your logarithmic regression is then:

y = @(B,x) log(x) + B;     % B = b

or alternatively,

y = @(B,x) B(1).*log(x) + B(2);

Those should work with nlinfit.