Warning: Rank deficient, rank = 1, tol = 1.324612e-01.

I'm trying to code a linear regression model using the following as a fuction script...

function [R,m,b] = ecregression(x,y)

    x = x';
    y = y';
    
    format long
    X = [ones(length(x),1) x];
    b = X\y;
    
    R = corr(x,y);
    m = b(2);
    b = b(1);
end

When I try and run this in my plot window with the code...

[R2, m2, b2] = ecregression(Y, season_avg2);
plot(Y, (m2.*Y)+b2, 'Color', 'k')

I get the error message...

Warning: Rank deficient, rank = 1, tol =  1.324612e-01. 
> In ecregression (line 8)
  In Extra_Credit (line 207)

(Line 207 is [R2, m2, b2] in the second code and line 8 is b = X\y)

How do I go about eliminating this error?

[the cyclist]

Can you upload a sample of data that gives the error, in a MAT file?

[KALYAN ACHARJYA]

What are the values of input arguments to pass to the function?

Y and season_avg2

[McKenzie Peters]

Y (stands for years) is a 1x68 double array where Y(1) = 1948 and Y(68) = 2015

season_avg is another 1x68 double array of various temperatures

Answer 1

[Ridwan Alam]

x = A\B solves the system of linear equations A*x = B. The matrices A and B must have the same number of rows. MATLAB® displays a warning message if A is badly scaled or nearly singular, but performs the calculation regardless.

In your case, A=X. column 1 of X is all 1's, making the rank of X = 1. That's what this warning is about. But I don't think that should prevent the calculation of b. Is it?