Rank deficiency when trying to use fitlm

I am trying to fit a simple regression model to some data (y ~ 1 + x1). However, I am not getting an estimate for the y-intercept because my design matrix is rank-deficient (Note: Xs and Ys are large column vectors, 4502342x1):

>> fitlm(Xs,Ys)
Warning: Regression design matrix is rank deficient to within machine precision. 
> In classreg.regr.CompactTermsRegression/checkDesignRank (line 35)
  In LinearModel.fit (line 1236)
  In fitlm (line 121) 
ans = 
Linear regression model:
    y ~ 1 + x1

Estimated Coefficients:
                   Estimate       SE         tStat     pValue
                   ________    _________    _______    ______
    (Intercept)           0            0        NaN     NaN  
    x1             -0.64712    0.0041947    -154.27       0  

Number of observations: 3129429, Error degrees of freedom: 3129428
Root Mean Squared Error: 39.3
R-squared: 0.0852,  Adjusted R-Squared 0.0852
F-statistic vs. constant model: Inf, p-value = NaN

I tried researching what rank deficiency means in this context, but didn't have much luck. When I take a subset of the data, e.g.:

rsam = randsample(length(Xs),round( length(Xs) / 100 ));
fitlm(Xs(rsam),Ys(rsam))

I have absolutely no trouble at all; output is great. Can anyone shed some light on this?

[dpb]

Need to see the actual case that created the problem...you say you have a 1D vector of a given size which doesn't match what the output says number of observations is and the model is

 y ~ 1 + x1 + x2

which should only occur w/ a two-column X input unless the model was defined externally but your call doesn't show that...I can't reproduce the symptom here w/o some other machinations.

[ohmstead]

Apologies, the two predictor variables were from trying to test a matrix of inputs (4502342x2) that has a column of ones, as the regress.m function requires (I've tried the fitlm function with both a single 4502342x1 matrix as well; same rank deficiency warning). Ignore the second variable. I've updated my post to reflect what it should say.

I would upload the vectors for you to mess around with, but the two vectors saved are over the size limit (they're 17.2 MB), and when I reduce them down enough to meet the upload limit of 5 MB, then the rank deficiency error goes away.

[dpb]

OK, if it isn't related to not showing what actually generated the error, then the full vector contains data that are linear combinations of others. What does

rank(Xs)

return?

[ohmstead]

>> rank(Xs)
ans =
     1

Answer 1

[Todd Harris]

I was having this problem but managed to solve it by converting the input for the fitlm function to double (they were single originally). Hope this helps.