Regression analysis/Data fitting

I have an emperical formula RR = P^x Z^y (a + b *V + c *V^2 ). x,y are regression exponents a,b,c are regression constants P,Z,V are variables such that RR=f(P,Z,V)

I have data that relates RR and P,Z,V. Is it possible to fit this data to this particular formulae using matlab 2011? if so are there any similar tuitorial or helpful videos?

Thank you in advance.

Answer 1

[Matt J]

FMINSPLEAS from the File Exchange would be worth a try

http://www.mathworks.com/matlabcentral/fileexchange/10093-fminspleas

It will let you take advantage of the fact that the equation has a linear dependence on some of your parameters (a,b,c) and nonlinear dependence on other parameters (x,y) to do a more efficient fit.

[Alexander]

As you advised, I've downloaded the fminpleas function.

%Example 2 from the fminpleas file%

x = rand(500,1);

y = 4 - 3*sin(2*x) + 2*cos(3*x) + randn(size(x))/10;

funlist = {1, @(c,xdata) sin(c(1)*xdata), @(c,xdata) cos(c(2)*xdata)};

[INLP,ILP] = fminspleas(funlist,[3 4],x,y)

What is the purpose of the function handle 'funlist' in the above program;How does it relate to 'y'? What must I do with the INLP and INL values?

[Matt J]

funlist specifies the nonlinear parts of the terms in the model equation, or if there is a purely linear term, you put funlist{i}=1. So, the above example corresponds to a model equation,

 y=A+ B*sin(c(1)*x) + C*cos(c(2)*x)

where the unknowns are A,B,C, c(1) and c(2). The coefficients A,B,C are what the fminspleas documentation calls Intrinsically Linear Parameters (ILP) because the model equation depends on those linearly. Conversely, lower case c is an Intrinsically Non-Linear Parameter (INLP) vector. fminspleas returns these as 2 separate output argument vectors. So, if the fit succeeds, then this

   [INLP,ILP] = fminspleas(funlist,[3 4],x,y)

will give you INLP=[2,3] and ILP=[4,-3,2].

[Alexander]

Thanks a lot Matt. That was extremly helpful.

Answer 2

[Matt J]

Your equations are linear in the unknowns a,b,c. Use any MATLAB linear equation solver to find them, e.g.,

http://www.mathworks.com/help/matlab/ref/mldivide.html

[Alexander]

Hi Matt! The equation I've written in a non-linear equation. Thanks for trying :)

[Matt J]

The non-linearity is not apparent. You should clarify the equation if you want further responses from people.

Remember, it is the dependence on the unknowns, a,b,c that matters. That dependence looks linear from what you have written.

[Tom Lane]

I think Matt is saying that if you change

RR = P^x Z^y (a + b *V + c *V^2 )

to

RR ./ (P^x Z^y ) = a + b *V + c *V^2

then it looks linear in a,b,c. You might try polyfit if you write it this way.

[Alexander]

@ Matt J: I am sorry but I still don't follow you when you say that the equation I specified with three variables, all raised to the unknown power >1, is a Linear equation. Maybe I need to rephrase the question as you suggested but I found the answer I was looking for from Tony lane. Anyhow, a genuine thank you for your prompt response.

@Tom Lane: Thanks for clarifying that. I guess polyfit should work well because I was able to find approximate estimations of the powers x and y.

[Matt J]

I am sorry but I still don't follow you when you say that the equation I specified with three variables, all raised to the unknown power >1, is a Linear equation

I was under the impression that a,b,c were the only unknowns. I did not see that x,y were also unknowns. If a,b,c were the only unknowns and all the rest were knowns or constants, I think you can see that the equation is linear w.r.t. the unknowns a,b,c

Since x,y are also unknowns, neither my suggestion, nor Tom's suggestion of POLYFIT will work. See my new Answer, suggesting fminspleas, however.

[Tom Lane]

Actually I didn't realize x and y were to be estimated either, but I'm glad you found some approximation that would allow you to proceed.

[Alexander]

Thank you Tom for your support. I'm relatively new to matlab and I got to learn a little more about polyfit in the process thanks to you. Fminspleas would be the best choice in my case.