Power fit with 3 parameters

Hi all,

I have 3 groups of XY data, these data are each pretty well described by a power function. Each group reflects a different treatment type (like drug dosage) and I would like this treatment type to be taken into account in the power function.

The aim would be to get one equation that can be used to predict Y given X and treatment type.

So far I have used the curve fitting toolbox to fit power functions to the curves quite easily like the example below, but I don't know what to do next.

Adding treatment type as a Z value doesn't really give a clear result, it seems that Matlab tries to fit a surface to the data which doesn't work very well - either because the data are too sparse or because the treatment type parameter is scaled differently to the others.

x = 1:100;  % X values
y1 = 2*(x.^2); % example data - power function 1
y2 = 2*(x.^2.1); % example data - power function 2
y3 = 2*(x.^2.2); % example data - power function 3
z1 = ones(size(y1)).*16; % treatment type
z2 = ones(size(y1)).*32; % treatment type
z3 = ones(size(y1)).*128; % treatment type

% plot the different groups
figure 
plot(x,y1,x,y2,x,y3); hold on;
    
% fit a curve to the first data group to extract the original power function parameters
[xData,yData] = prepareCurveData(x,y1);
ft = fittype('power1');
opts = fitoptions('Method','NonlinearLeastSquares');
opts.Display = 'Off';
opts.StartPoint = [2 2];
[fitresult, gof] = fit( xData, yData, ft, opts );
fitresult.a
fitresult.b

Answer 1

[Abhisek Pradhan]

As per the code from a given value of X, we get three values of Y, this can be done by using fit function for all three corresponding datasets of X and Y.

Again, using the fit Function with a suitable fitting algorithm we can form a relation between Y and Z. And for different Z values we can get corresponding Y values. Thus, we can predict Y values for given values of X and Z.

Following link has question related to concerned topic.