Matrix is singular, RCOND=NAN for a OLS regression

Hello all,

I am attempting to code an OLS regression, using a OLS-function of my own design. The code looks as follows:

Y = lntrentsa;
nobs = size(Y,1);
X = [ones(nobs,1), airbnbsa, airbrnb*oorate10];
knum = size(X,2);

b = inv(X'*X) * X'*Y; 

However, I am unable to get an output for b(eta) as I get the error message:

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN

Would anyone know why this might be? Which Matrix does the error message mean? I have attempted rewriting b but I still only get Nan values:

b = (X'*X)\ X'*Y

My dataset is quite large (nobs = 745776), could this perhaps have an influence?

I'd be grateful for any advice! Thank you

Answer 1

[Bruno Luong]

First make sure your data X and Y contain only finite elements (no NaN, Inf, or such).

Instead of

b = inv(X'*X) * X'*Y;

try (R2018a or later required)

[XN,C,S] = normalize(X);
b = ((XN+C./S)\Y) ./ S.';

[JoV]

Thank you very much for your quick reply! Unfortunately it doesn't seem to have solved my problem. I have cleaned my data-set and should no longer have any NaN values. However, with your described-above fix I get the following error message:

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 3.616900e-18

It seems to not have an issue with two other values in my OLS: my standard error (se) and t-value (t-val):

function res = OLS_estimation(Y,X) 
% define the covariate dimensions
nobs = size(X,1);     
knum = size(X,2);      

% calculate the parameter
%b = (X'*X)\(X'*Y);
[XN,C,S] = normalize(X);
b = ((XN+C./S)\Y) ./ S.';

% calculate the errors and sample variance
e = X*b-Y;
s2 = (e'*e)/(nobs-knum);
se = sqrt(diag(s2 * inv(X'*X)));

%calculate the t-values and p-values
t_Val = b./sqrt(s2*diag(inv(X'*X))); 
p_Val = tdis_prb(t_Val, nobs -knum); 

Would you perhaps have an idea as to why this is happening?

[Bruno Luong]

So may be your matrix is really singular (rank(X) < 3), in this case you migh wanr to do

b = pinv(X'*X) * X'*Y;

or

[XN,C,S] = normalize(X);
XN = (XN+C./S);
b = (pinv(XN'*XN) * XN'*Y) ./ S.';

But MATLAB warning is still valid: the result may be innacurate, simply your data are not allowed to observe whatever the parameters b you want to compute.

[Bruno Luong]

You might also want to experiment with different method of normalizing, e.g.,

[XN,C,S] = normalize(X,'medianiqr')