Editing Gauss–Markov theorem (section)

===Full rank===
The sample data matrix <math>\mathbf{X}</math> must have full column [[Rank (linear algebra)|rank]].
:<math>\operatorname{rank}(\mathbf{X}) = k</math>
Otherwise <math>\mathbf{X}^\operatorname{T} \mathbf{X}</math> is not invertible and the OLS estimator cannot be computed.

A violation of this assumption is [[Multicollinearity|perfect multicollinearity]], i.e. some explanatory variables are linearly dependent. One scenario in which this will occur is called "dummy variable trap," when a base dummy variable is not omitted resulting in perfect correlation between the dummy variables and the constant term.<ref>{{cite book |first=Jeffrey |last=Wooldridge |author-link=Jeffrey Wooldridge |title=Introductory Econometrics |publisher=South-Western |edition=Fifth international |year=2012 |isbn=978-1-111-53439-4 |page=[https://archive.org/details/introductoryecon00wool_406/page/n247 220] |url=https://archive.org/details/introductoryecon00wool_406|url-access=limited }}</ref>

Multicollinearity (as long as it is not "perfect") can be present resulting in a less efficient, but still unbiased estimate. The estimates will be less precise and highly sensitive to particular sets of data.<ref>{{cite book |first=John |last=Johnston |author-link=John Johnston (econometrician) |title=Econometric Methods |location=New York |publisher=McGraw-Hill |edition=Second |year=1972 |isbn=0-07-032679-7 |pages=[https://archive.org/details/econometricmetho0000john_t7q9/page/159 159–168] |url=https://archive.org/details/econometricmetho0000john_t7q9/page/159 }}</ref> Multicollinearity can be detected from [[condition number]] or the [[variance inflation factor]], among other tests.