在進行迴歸分析時，有時會部到自變數間存在著多元共線性的現象，此共線性常 會產生不可靠的迴歸估計值，而造成分析上的困擾。對此情形，一般實務者常以去除某些自 變數來消除此種困擾；唯如此作法可能導致原先顯著的自變數變成不顯著。此結果使我們注 意到自變數間一定程度的相關可能帶來的正面價值。在兩個自變數的情形下，我們發現即使 反應變數與各個自變數聞均無顯著的線性關係，但只要兩個自變數間有一定程度的相關，且 反應變數和此二自變數相關係數的乘積與此二變數本身的相關係數成相反符號時，則此二自 變數聯合起來可能造成顯著性，且在偏F檢定上，亦具有顯著性，因而對反應變數的解釋能 力大為增加。在k個自變數的情況下，我們亦得到類似的結論。因此資料間的相關性不一定 會造成不可靠的估計值；相反的，它可能有助於我們的分析工作。我們所提的方法，在前進 逐次選取法找不到任何一個自變數，或在樣本小但變數多而後退選取法不適用時有其一定的 存在價值。我們以兩個例子來說明所提方法的應用。

　　　　　When independent variables in multiple regression analysis are highly correlated among themselves, multicollinearity among them is said to exist. Multi-collinearity often results in imprecise estimated regression coefficients. To lessen the problems caused by multicollinearity and thereby reduce the standard errors of the estimated regression coefficients, one or several independent variables may be dropped from the model. This remedial measure may cause originally significant independent variables to be nonsignificant and this phenomena reveals the possibility that intercorrelation among independent variables may have a positive effect on regression analysis. In this paper, we find that, in the situation of two independent variables, if the two independent variables have middle to high correlation, and the product of the correlation coefficients between the response variable and each of the two independent variables has different sign from the coefficient of correlation between these two independent variables, then these two independent variables will jointly have significant contribution in explaining the response variable. We get similar results for the case of k independent variables. The method we suggest has the advantage in choosing variables for regression model when we cannot find any variable by forward stepwise regression procedure or backward elimination approach is unsuitable for small sample size. We give two examples to illustrate the concepts.