In matrix form, the vector of coefficient estimates is derived using the formula: **(X’X) ^{-1}X’Y**, where

**X**is the design matrix where the rows correspond to the observations and columns to the features, and

**Y**is the vector of target values.

Being that the **X’X** matrix has to be inverted, the computation fails if it is completely singular, which occurs in the case of perfect multicollinearity, such as if one feature is a direct function of others. Even if the multicollinearity is not explicit and estimates are able to be derived, the resulting coefficient estimates exhibit a larger standard error, meaning there is less of a chance of finding the feature to be significant based on its p-value. Further, the estimates can be overly sensitive to small changes in the model, meaning that for a given predictor, its effect size could differ drastically if one other variable was added or removed from the composite equation.