# What is collinearity and how does it differ from multicollinearity?

I was reading this when I came across the term collinearity. I tried looking up what it is but top results are related to multicollinearity.

I could find here about multicollinearity

multicollinearity refers to predictors that are correlated with other predictors in the model

It is my assumption (based on their names) that multicollinearity is a type of collinearity but not sure. Do these 2 terms differ or are they synonyms?

• what from the wikipedia article is not clear? en.wikipedia.org/wiki/Multicollinearity#Definition – TrynnaDoStat Jan 6 '17 at 15:39
• @TrynnaDoStat Well, nothing is unclear, but, one should avoid answering questions in comments. Example here would be that I was taking the information, condensing it, and presenting it as an answer while the comment above was made. – Carl Jan 6 '17 at 15:59

In case of perfect multicollinearity the design matrix $X$ has less than full rank, and therefore the moment matrix $X^{\mathsf{T}}X$ cannot be matrix inverted. Under these circumstances, for a general linear model $y = X \beta + \epsilon$, the ordinary least-squares estimator $\hat{\beta}_{OLS} = (X^{\mathsf{T}}X)^{-1}X^{\mathsf{T}}y$ does not exist.