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?
