How to do custom equation (non linear) regression?

I need to find some constant from data that usually is shown in log-log scale, the equation related to the data would be y=(a*x^b)/(26.1-x). How do I find the a and b constants?

Answer 1

[Star Strider]

There are several nonlinear parameter estimation function to choose from.

This uses fitnlm —

yfcn = @(a,b,x) (a*x.^b)./(26.1-x);

T1 = readtable('experiment_data.xlsx');
x = T1.x;
y = T1.y;

B0 = rand(2,1);
mdl = fitnlm(x,y,@(b,x)yfcn(b(1),b(2),x), B0)

mdl = 
Nonlinear regression model:
    y ~ yfcn(b1,b2,x)

Estimated Coefficients:
          Estimate      SE        tStat     pValue 
          ________    _______    _______    _______

    b1    0.059055    0.28207    0.20936    0.83475
    b2     -1.6212     1.5325    -1.0578    0.29362


Number of observations: 75, Error degrees of freedom: 73
Root Mean Squared Error: 0.00156
R-Squared: -0.0655,  Adjusted R-Squared -0.0801
F-statistic vs. zero model: 1.29, p-value = 0.282

xsrt = sort(x);
[ypred,yci] = predict(mdl,xsrt);

figure
plot(x, y, '.', 'DisplayName','Data')
grid
hold on
plot(xsrt, ypred, '-r', 'DisplayName','Function Fit')
plot(xsrt, yci, '--r', 'DisplayName','±95% Confidence Intervals')
hold off
legend('Location','best')

The model is a statistically poor fit to the data and does not describe the data well.

.

[yehuda kristo]

Oh okay I understand it now, Thanks for the explanation Sir.

[Star Strider]

As always, my pleasure!

Answer 2

[Davide Masiello]

Assume these are your experimental data

x = linspace(0,20,30);
y = rand(size(x))/3+(pi*x.^(sqrt(2)/2))./(26.1-x);
figure(1)
plot(x,y,'or')

To find a and b you can do the following.

modelfun = @(p,x) (p(1)*x.^p(2))./(26.1-x);
par = nlinfit(x,y,modelfun,[1 1]);
a = par(1)

a = 6.3320

b = par(2)

b = 0.4825

figure(2)
plot(x,y,'or',x,modelfun(par,x),'k')

Answer 3

[Image Analyst]

I usually use fitnlm (fit non-linear model). You can specify the equation you want to fit to. I'm attaching some examples of fitnlm.

[yehuda kristo]

Hello, thanks for the answer, I've tried the exponential growth example because I think that's the closest one to my data but somehow the calculated regression doesn't come near the data. I don't know what's wrong though.

[Image Analyst]

I think you didn't replace the x and y in the program with your own data properly. Please attach your actual data in a .mat file.

[yehuda kristo]

Here's my .m file and my x and y data

[Image Analyst]

Well, looks like you're going to use Star's solution, so I won't bother, unless you really want me to.