在探討一個連續型反應變數與一個以上的解釋變數之間的關係時，線性迴歸是一種經常被使用的統計方法。當額外的解釋變數加入模型時，研究者通常著重於迴歸係數估計值與其t統計量的行為表現以及判定係數（R-square）的增加程度等迴歸結果，然而這些結果與新加入的解釋變數及原先已存在於模型裡的解釋變數之間的共線性（collinearity）不無關係。本文主要在探討共線性的效果對於迴歸係數估計值與其t統計量以及判定係數的行為表現之影響。本文研究中發現，當額外的解釋變數加入模型時，新模型的迴歸分析結果可以完全透過三個相關係數以及原模型的判定係數來詮釋，因此可以進一步透過這些訊息來預期新的模型之下的迴歸結果。另一方面，藉由將額外加入的解釋變數視為研究所感興趣的解釋變數，而將原先存在於模型裡的解釋變數視為共變量（covariate），本文亦透過類似的方式來探討共線性的效果對於模型裡collapsibility之影響。所謂的collapsibility是指無論共變量是否存在於模型裡，皆不會影響到研究中所感興趣的解釋變數與反應變數之間的關係。整體而言，本文研究發現當共線性存在於線性迴歸模型中，並不一定會對於迴歸結果造成不好的影響。因此，當模型裡解釋變數間存在共線性時，變數是否從模型中移除必須謹慎思量。

Linear regression is a statistical method that allows researchers to summarize and study the relationship between a response and one or more predictor variables. When adding a predictor into a model, we are most interested in knowing its estimated regression coefficient, the corresponding t-statistic, and the value of R-square that increases. One apparent issue that might impact the results is the collinearity between the added-predictor and those already in the model. In this study, we investigate behavior patterns of the estimated regression coefficient, the corresponding t-statistic and R-square as the collinearity varies. We argue that all the above mentioned statistics are functions of three correlation coefficients and an R-square, and provide summary tables that can be used to anticipate the behavior of the statistics. On the other hand, by treating the added-predictor as the predictor of interest, and those predictors already in the model as covariates, we are able the apply similar techniques to deal with the impact of collinearity on collapsibility, that is, whether the relationship between the response and the predictor of interest remains the same if the covariates are dropped from the model. Overall, we found that collinearity in a linear regression model may not necessarily yield ill effects as we normally think. We urge researchers to think twice before dropping a collinear predictor from further model consideration.

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