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?
Best Answer
In statistics, the terms collinearity and multicollinearity are overlapping. Collinearity is a linear association between two explanatory variables. Multicollinearity in a multiple regression model are highly linearly related associations between two or more explanatory variables.
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.