Question about non linear experimental data fitting with one independent and two dependent variables

Hello I have some experimental data and i am trying to find a relation between them.Because the measurement techniques for this field are not so advanced the data are not exactly in the curve.The non linear regression that is going to be used has two independent and one dependent variable(x and R is the independent and c is y the dependent as c(R,x)).where 0<x<12.The table of data is below.

     C                               Log10(R)

4.0452        1.3169      
4.0148        1.3169      
4.0722        1.3400      
4.1397        1.4399      
3.8377        1.1000      
3.9568        1.1323      
2.1806        1.0000      
2.5000        1.0000      
2.2159        1.0000      
4.1859        1.5300      
4.1864        1.3700      
4.1866        1.6700      
4.1847        1.3600

Can anyone provide me with some guidelines to do the regression as i am new in matlab and i am not so fluent on how to use it in statistics? Thank you in advance

Answer 1

[Star Strider]

NOTE — The title of your question is different from your Question. I went with the text of your question, not the title in my Answer.

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It is relatively straightforward to do a nonlinear regression with two independent variables, but not immediately obvious. It’s necessary to create a matrix from the independent variables, and use the columns of the independent variable matrix within the function to use the independent variables where they are needed. I created a function to illustrate this, and then used fminsearch to do the regression. Note that the independent varaibles are in the ‘Xm’ matrix, and that I used each column separately in the objective function:

D = [ 4.0452        1.3169      
      4.0148        1.3169      
      4.0722        1.3400      
      4.1397        1.4399      
      3.8377        1.1000      
      3.9568        1.1323      
      2.1806        1.0000      
      2.5000        1.0000      
      2.2159        1.0000      
      4.1859        1.5300      
      4.1864        1.3700      
      4.1866        1.6700      
      4.1847        1.3600];

D = [[0:12]' D];                                                % Create ‘D’ (Add ‘[0:12]'’ Vector)

Xm = D(:,1:2);                                                  % Independent Variable
R = 10.^D(:,3);                                                 % Dependent Variable

f = @(B,Xm) B(1).*sin(B(2).*Xm(:,1)+B(3)) + B(4).*Xm(:,2);      % Create Model (Objective Function)
B0 = ones(4,1);
SSECF = @(B) sum((R - f(B,Xm)).^2);                             % Sum Squared Error Cost Function
[B_est,SSE] = fminsearch(SSECF, B0);                            % Estimate Parameters

figure(1)
plot3(D(:,1),  D(:,2),  10.^D(:,3), 'bp')
hold on
plot3(D(:,1), D(:,2), f(B_est,Xm), '-r')
hold off
grid on
xlabel('X')
ylabel('Y')

I actually got a decent fit with my little function. I wish you the same with yours!

Make the appropriate changes to ‘B0’ for your function. (Mine has four parameters, so ‘B0’ has to have the same length.) If you call your function ‘f’, that is the only is probably the only change you will need to do to my code. The ‘SSE’ output from the fminsearch call is the sum-squared-error at convergence.