How to solve betainc error in Polyfitn extension (by John D'Errico)?

When using 'just' four point for linear regression in polyfitn, I am often getting this error:

Error using betainc X must be in the interval [0,1].

Error in polyfitn (line 270) polymodel.p = betainc(polymodel.DoF./(t.^2 + polymodel.DoF),polymodel.DoF/2,1/2);

But four points should be enough to fit the plane in 3D space. And I am getting this error also when using more points.

What does this error message means? How to deal with it? Because I have never experienced this error using official polyfit in 2D space.

Thank you!

[Sam Chak]

@John D'Errico probably overlooked this question years ago.

[John D'Errico]

Yes. I never saw the question. Too easy to blink some days, and miss something.

Answer 1

[Raag]

Hi ZuzkaT,

The error you are encountering occurs because the ‘polyfitn’ function attempts to calculate error estimates for your fitted model. When you use exactly the minimum number of data points required for the fit, there is no extra data to estimate variability. This situation leads to an internal division by zero (0/0), which causes the ‘betainc’ function to receive an invalid value.

To address this, instead of using just the minimum number of points, supply additional data so the function can properly compute the error estimates.

Below is a simple example to illustrate the difference between using the minimal data which will trigger the error and using extra data which should work fine:

% Example 1: Minimal data (expected to trigger the error) 
x_min = [1; 2]; 
y_min = [3; 4]; 
try 
   P_min = polyfitn(x_min, y_min, 1); 
catch ME 
   fprintf('Expected error with minimal data:\n%s\n\n', ME.message); 
end 
 
% Example 2: Extra data points (should work without error) 
x_extra = [1; 1; 2; 2]; 
y_extra = [3; 3; 4; 4]; 
P_extra = polyfitn(x_extra, y_extra, 1); 
disp('Fitted model with extra data:'); 
disp(P_extra);

Output:

For a better understanding of the above solution, refer to the following MATLAB documentations:

1. polyfit: https://www.mathworks.com/help/matlab/ref/polyfit.html

2. betainc: https://www.mathworks.com/help/matlab/ref/betainc.html

3. ployfitn: https://www.mathworks.com/matlabcentral/fileexchange/34765-polyfitn

[John D'Errico]

Yes. It appears to be a 0/0 issue, caused when the code is called with insufficient data to estimate a variance.