Clear Filters
Clear Filters

How to do custom equation (non linear) regression?

22 views (last 30 days)
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);
plot(x, y, '.', 'DisplayName','Data')
hold on
plot(xsrt, ypred, '-r', 'DisplayName','Function Fit')
plot(xsrt, yci, '--r', 'DisplayName','±95% Confidence Intervals')
hold off
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);
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

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.
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.

Sign in to comment.


Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!