Points are collinear when they lie on a single line. Two vectors are collinear when their linear span has dimension at most one. For a nonzero vector , this means that the other vector is for some scalar . This algebraic convention includes the zero vector; the directional use of “parallel” sometimes assumes both vectors are nonzero.
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Collinearity refers to a geometric condition where three or more points lie on the same straight line. In the context of statistics and data analysis, collinearity often describes a situation in regression analysis where two or more predictor variables are highly correlated, meaning that they have a linear relationship with each other. This can lead to difficulties in estimating the relationships between the predictor variables and the dependent variable, as it becomes challenging to determine the individual effect of each predictor.