How do I apply exponential and logarithmic curve fitting

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

[Star Strider]

What do you mean by ‘code not working at all’?

It’s not obvious to me what you mean here: y=log_a(x)+b. (I don’t understand ‘log_a(x)’.)

[Iro]

I mean that I make some kind of mistake in the definition of the function when I use nlinfit so the code does not work.

With log_a(x) I mean the logarithm of x with base a.

[yeungor]

Have you tried fitting an exponential of the inverse? If x = f(y), then y = f^-1(x) and you can use 'fit' and the 'exp' for an exponential fit.

Answer 1

[Star Strider]

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.

Answer 2

[Danilo NASCIMENTO]

You can use cf = fit(x,y,'exp1'); where x and y are your set of points.

[Iro]

Hi, thanks for your answer. I have used this function for the exxponential scatter but it doesn't give me good fitting. Do you know how I can get into account the constant c in the above equation using fit with 'exp1' ?

Thanks