For a linear regression model with two-predictor variables, the effects of the correlation between the two predictors on estimated standardized regression coefficients and $R^2$ have been well studied. However, the role the correlation plays may sometimes be overstated, such that confusion and misconceptions may arise. In this article, we revisit the issue from the perspective of a semipartial correlation coefficient. We find that by taking this perspective we are not only able to reach the same conclusions while avoiding those misunderstandings, we are also able to gain more insight. In addition, we also take a geometrical approach to illustrate how estimated standardized regression coefficients and $R^2$ behave as the correlation varies. Geometrical displays provide readers with a way to visualize the behavior changes and to understand the reasons behind those changes more easily. Although we focus mainly on two predictors in this article, the conclusions can be easily extended to a general k-predictor case.

对于具有两个预测变量的线性回归模型，两个预测变量之间的相关性对估计的标准回归系数和 ${\mathrm{[R}}^2$已经被充分研究。但是，相关性所扮演的角色有时可能被夸大了，从而可能引起混乱和误解。在本文中，我们从半偏相关系数的角度重新审视了这个问题。我们发现，通过这种观点，我们不仅能够得出相同的结论，同时避免了这些误解，而且还可以获得更多的见解。此外，我们还采用几何方法来说明估计的标准回归系数和${\mathrm{[R}}^2$随相关性的变化而变化。几何显示为读者提供了一种可视化行为变化并更容易理解这些变化背后原因的方法。尽管我们在本文中主要关注两个预测变量，但结论可以轻松地扩展到一般的k预测变量情况。