Linear regression returns NaN for one of five regressors

Hi,

I am trying to perform a linear regression model in MATLAB R2019a on the data as attached using the following command:

lm = fitlm(x,y)

The regression works fine for all but one regressor (see below). There is no linear dependence in the design matrix, although I do get the warning "Regression design matrix is rank deficient to within machine precision." I don't understand where this warning comes from. What's wrong? Any help is greatly appreciated!

Linear regression model:
y ~ 1 + x1 + x2 + x3 + x4 + x5

Estimated Coefficients:
Estimate      SE       tStat       pValue   
________    ______    _______    ___________

(Intercept)     414.36      3.703      111.9    1.0822e-300
x1              2.2506      4.244     0.5303         0.5962
x2             -48.916     5.0516    -9.6833     4.9268e-20
x3             -43.883     5.0516     -8.687     1.0056e-16
x4                   0          0        NaN            NaN
x5              -46.96     5.0516    -9.2961     1.0126e-18

[Star Strider]

The file refuses to load and crashes MATLAB (R2022a).

Answer 1

[Torsten]

Adding columns 2,3,4 and 5 shows that the rank of the matrix

[ones(size(x,1),1),x];

will be the same as the rank of x, namely 5, not 6.

Thus you can work with intercept, but you must drop one of the independent variables x2, x3, x4 or x5.

[Sascha Frölich]

Yes that makes total sense, thank you!