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Perfect multicollinearity refers to a situation where the predictive variables have an exact linear relationship. When there is perfect collinearity, the design matrix X {\displaystyle X} has less than full rank , and therefore the moment matrix X T X {\displaystyle X^{\mathsf {T}}X} cannot be inverted .
In practice, we rarely face perfect multicollinearity in a data set. More commonly, the issue of multicollinearity arises when there is a "strong linear relationship" among two or more independent variables, meaning that
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