How to fit data to a function form

Apologies if my use of terminology is wrong.

I essentially have four equal sized data sets (eg. x y z w) and I want find an equation that describes one of those data sets as a funtion of the other three. To begin with I'm assuming this is a linear relationship i.e. x = a*y + b*z + c*w.

Is there a way to fit these data sets to find the values of the coefficients a b c?

Thanks for your help!

Answer 1

[Star Strider]

Yes! The mldivide,\ funciton will do this.

x = randn(10,1);
y = randn(10,1);
z = randn(10,1);
w = randn(10,1);

DM = [y(:) z(:) w(:)];                              % Design Matrix
abc = DM \ x(:)

abc = 3×1

-0.0250 -0.2847 -0.4305

Results = table(x(:),DM*abc,x(:)-DM*abc, 'VariableNames',{'Original x','Regressed x','Difference'})

Results = 10×3 table
    Original x    Regressed x    Difference
    __________    ___________    __________

      0.13267        0.10844      0.024228 
      -2.5397        -1.2413       -1.2984 
      0.05946        0.71663      -0.65717 
      0.82979         1.1043       -0.2745 
     -0.11678       -0.37399       0.25721 
      0.42652       -0.55752       0.98404 
      0.26181        0.62586      -0.36404 
       1.0023      -0.039926        1.0422 
      0.57563       -0.16844       0.74407 
     -0.92174       -0.34643      -0.57531 

meanDifference = mean(Results.Difference)

meanDifference = -0.0118

To get statistics on the fit, use regress, fitlm, or similar functions.

.

[Fynn Oppermann]

Thank you!

Would this method still work if my function changes to be nonlinear?

[Star Strider]

My pleasure!

It will only work for linear relations, however coding it for nonlilnear relations would be straightforward and may not involve anythng other than core MATLAB. For a nonlinear regression, one approach would be to use fminsearch if other Toolboxes are not available.

Example —

x = randn(10,1);
y = randn(10,1);
z = randn(10,1);
w = randn(10,1);

yzw = [y(:) z(:) w(:)];                                 % Contatenate Column Vectors

% % % FUNCTION: exp(a*y) * sin(2*pi*b*z) + c*w
objfcn = @(b,iv) exp(b(1)*iv(:,1)) .* sin(2*pi*b(2).*iv(:,2)) + b(3)*iv(:,3)

objfcn = function_handle with value:
    @(b,iv)exp(b(1)*iv(:,1)).*sin(2*pi*b(2).*iv(:,2))+b(3)*iv(:,3)

B = fminsearch(@(b) norm(x(:) - objfcn(b,yzw)), rand(3,1))

B = 3×1

0.3240 1.2573 0.0702

fprintf(1, '\n\ta = %9.4f\n\tb = %9.4f\n\tc = %9.4f\n',B)

	a =    0.3240
	b =    1.2573
	c =    0.0702

Results = table(x(:), objfcn(B,yzw), x(:)-objfcn(B,yzw), 'VariableNames',{'Original x','Regressed x','Difference'})

Results = 10×3 table
    Original x    Regressed x    Difference
    __________    ___________    __________

       1.1085       0.83031        0.27821 
      0.90088       0.47772        0.42316 
     -0.67653       0.63336        -1.3099 
    0.0039623      -0.88416        0.88813 
       1.1665       0.61915        0.54735 
      0.80068       0.90119       -0.10051 
      0.12086      -0.39058        0.51144 
     -0.59784       0.17719       -0.77503 
      0.88238       0.58316        0.29923 
     0.033881      -0.74814        0.78202 

Here, ‘iv’ is the independent variable matrix, composed of the independent variable vectors. This allows a single variable to be passed to any of the curve-fitting (parameter estimation) functions, as their syntax requires, while fitting every independent variable.

Since there are only three parameters, the fminsearch function can likely do a decent approximaton to the desired parameter estimates.

.