Regression design matrix is rank deficient to within machine precision. How do I interpret this error?

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Rucha Apte
Rucha Apte 2020-3-6
评论： Star Strider 2022-5-19
I tried using Linear Regresssion commant regress on my train and test data and I am getting a warning saing 'X is rank deficient to within machine precision'. I am not able to interpret the error.

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Star Strider
Star Strider 2020-3-6
It means that at least one of the columns in the design matrix is close to being all zeros.
Without knowing more, one way to avoid that could be to re-scale all the variables (independent and dependent) to some larger values. Re-scaling them could mean adding a constant value to all of them. This would need to be done with caution, since it would be possible to end up with useless results.
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Sascha Frölich
Sascha Frölich 2022-5-19
编辑：Sascha Frölich 2022-5-19
Hey, I get the same error, and no matter what large values I add to my design matrix (to the point that every value is way beyond zero), the error persists. Why could that be?
Nevermind I just figured it out; I had included a constant regressor, while MATLAB includes an intercept term by itself, so my design matrix was redundant. Cheers!
Star Strider
Star Strider 2022-5-19
Ran in:
@Sascha Frölich —
One possibility is that one or more columns of the design matrix are linearly dependent.
x = randn(5,1);
DM = [x x+eps ones(size(x))];
y = randn(5,1);
B = DM \ y
Warning: Rank deficient, rank = 2, tol = 2.557037e-15.
B = 3×1
-0.8939 0 0.3358
Here, the first and second columns of ‘DM’ are liniearly dependent withiin machine tolerance.
.

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