Exponential curve fit matlab

Question

I have the following equation:

I want to do a exponenti

Answer 1

One approach is to use a linear regression of log(y) with respect to u² and a³:

Assuming that u, a, and y are column vectors of the same length:

AB = [u .^ 2, a .^ 3] \ log(y)

After this, AB(1) is the fit value for A and AB(2) is the fit value for B. The computation uses Matlab's mldivide operator; an alternative would be to use the pseudo-inverse.

The fit values found this way are Maximum Likelihood estimates of the parameters under the assumption that deviations from the exact equation are constant-variance normally distributed errors additive to A u² + B a³. If the actual source of deviations differs from this, these estimates may not be optimal.