The Vector Geometric Approach to Multicollinearity Diagnostics

Abstract

The problems of multicollinearity among the independent variables in least-squares regression are by now well-known and published. In the presence of multi-collinearity problem, the parameter estimation method based on the ordinary least squares’ procedure is unsatisfactory. Most of the available multicollineraity diagnostic methods may lead to dramatically different conclusions based on their cutoff points and what might be gained from the different alternatives in any specific empirical situation is often unclear due to inadequate knowledge about what degree of collinearity is "harmful". In this paper, we considered the vector geometry approach which is a very useful but are scarcely used tool for illustrating regression analysis to multicollinearity diagnostics. Our result reveals that angles in the range of 19 to 45 degrees are closer to the orthogonality than collinearity Also, the variables are dependent when the vectors are almost parallel while variables are independent, when the vectors are nearly orthogonal. Thus, independent random variables are orthogonal. The paper therefore proposes practical angles and the corresponding correlation coefficients that determine the presence of collinearity in a regression model.

KEY WORDS: Multicollinearity; Vectors; Dimensional Space; Euclidean norm; cosine of angles; correlation coefficient