how to code to solve for coefficient using linear regression?

I have a equation y=ax^b*e^(cx). I linearized this as lny= lna+ blnx+cx. Now i need to find the coefficients a, b and c. which method should i use. please let me know as soon as possible.

Thank You in advance for ur help..

[Sean de Wolski]

+1, Good question effort, and prodding for interesting answers!

Answer 1

[Tom Lane]

It is hard to know what method you should use without understanding the problem more. One method is this. Suppose x and y are column vectors:

d = [ones(size(x)), log(x), x] \ log(y)
a = exp(d(1)), b = d(2), c = d(3)

Answer 2

[Star Strider]

I suggest that you not linearize it. That distorts the errors, and the estimated parameters will not be accurate. Instead, use an anonymous function such as:

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

then:

Beta0 = rand(3,1);
[Beta,R,J,CovB,MSE] = nlinfit(x, y, yfcn, Beta0);    % Statistics Toolbox

or:

[Beta,resnorm,residual,exitflag,output,lambda,jacobian] = lsqcurvefit(yfcn, Beta0, x, y);    % Optimization Toolbox (allows parameter constraints)

The values of Beta correspond to a, b, and c, in order.

If you do not have access to the Statistics or Optimization Toolboxes, I suggest you use fminsearch and the examples in Curve Fitting via Optimization. (The documentation explains it better than I could.) In that example, replace the FittedCurve line with:

FittedCurve = params(1) .* xdata.^params(2) .* exp(params(3).*xdata);

which is the code for your function.