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How to do custom equation (non linear) regression?

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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?

Accepted Answer

Star Strider
Star Strider on 12 Apr 2023
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.
.

More Answers (2)

Davide Masiello
Davide Masiello on 12 Apr 2023
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')

Image Analyst
Image Analyst on 12 Apr 2023
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.
  4 Comments
Image Analyst
Image Analyst on 12 Apr 2023
Well, looks like you're going to use Star's solution, so I won't bother, unless you really want me to.

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