Standardized coefficients of multiple regression, also known as beta coefficients, by absolute value are usually smaller than one, but sometimes they can exceed one. This effect had been studied mostly for models with two predictors, where it was explained by the high collinearity between them. The current paper considers multiple linear regression and defines the necessary and sufficient conditions for beta coefficients to exceed one. These conditions determine a measure of each predictor’s connection to the dependent variable in the model relative to the connection with other predictors. This criterion presents a new measure for diagnostics of the multicollinearity, which can be employed additionally to the commonly used variance inflation factor. A new interpretation is given to the meaning of the squared beta coefficients themselves. Numerical examples demonstrate these novel features. The obtained results are useful in applied regression analysis, helping practitioners and educators to understand and to explain the outcomes of regression modeling.
Stan Lipovetsky (Wed,) studied this question.