linear/nonlinear regression and statistical parameters

Hello,

I am trying to use linear and nonlinear regression to predict a response. I am wondering how I can get the most possible statistical results from regress or nlinfit (like durbin watson, probabilities, R2, adjusted R2, etc.). (as far as I understood regstat is not a good option since it restricted to a few models.) Here is the piece of code that I am using as a sample and the results. I also couldn't interpret the results of stats that I am getting now. Any help is appreciated. (I post the linear regression code as a separate post to avoid confusing.)

y=(c.^4+2*c.*p+3*p.^3-c+2*d.^0.5)'; % a sample response

X = [c;p;d]';

modelfun = @(b,x) b(1)*x(:,1).^4 + b(2)*x(:,1).*x(:,2)+ ... b(3)*x(:,2).^3 + b(4)*x(:,1)+b(5)+b(6)*x(:,3).^b(7);

beta0 = [1 -2 0 -1 0 1 1];

opts = statset('nlinfit');

opts.RobustWgtFun = 'bisquare';

[beta,stats] = nlinfit(X,y,modelfun,beta0,opts)

Results: beta =

    1.0057   -1.4588    2.8133  -15.5212  -18.0241    3.1540    2.7378

stats = (I dont know what the followings are)

1.0e-012 *

    0.0071
    0.1172
    0.1279
    0.3979
    0.7958

Answer 1

[Star Strider]

I do not know what version of MATLAB (and the Statistics Toolbox) you are using, but in R2015a, the second output (here ‘stats’) are the residuals (differences between the data and model fit to each element in the dependent variable). Your model is nonlinear in the parameters, so nlinfit is appropriate. Consider using fitnlm to get more statistics. (Consider nlinfit and nlparci if you want to get confidence intervals on the parameters.)

[Star Strider]

Reza S’s ‘Answer’ moved here ...

Thanks for the answer. I am using 2011 and hence those functions don't work. I will try to see if I can upgrade it to the newer versions for more statisticals.

[Star Strider]

My pleasure.

What does the documentation for R2011a/b say is the second output of nlinfit?

I don’t remember when fitnlm was introduced.

[Reza S]

I have updated my MATLAB to 2014Ra. Now I am good. Thanks

[Star Strider]

My pleasure.

You should also be able to update to R2014b as well with the same license. I suggest that you not uninstall R2014a after you install R2104b because the ‘old’ graphics (and all the File Exchange contributions that use them) will still work with it.