| Abstract: | This paper considers the effects of multicollinearity on the multiple coefficient of determination and on the standard errors of the estimated regression coefficients. Limiting results are well known for these problems, and some particular cases have been investigated. However, the limiting cases do not explain the nonmonotonic relationships that have been observed in practice. This paper explores these relationships and attempts to provide a unifying graphical explanation that includes the previous results as special cases. Implications for stepwise regression and for the interpretation of any multiple regression involving multicollinear independent variables are discussed. |
