標準化迴歸係數的正確解釋

Proper Interpretation of Standardized Regression Coefficients

多元迴歸裡的標準化迴歸係數常被用來表達一個自變項的作用、預測力或解釋力。但是，學界和管理者對標準化迴歸系的解釋卻仍時有錯誤。本文以假設時生的數據為例，配合數學演算証明：當自變項超過兩個時，標準化迴歸系數並不適合作為評自變項相對重要性的唯一依據。同時，本文也透過例子指出：即使自變項只有兩個，一個自變項的標準化迴歸系數在統計上不顯著也不表示該變項不重要。根據這些迴歸系數的特性，本文針對過去管理學文獻對標準化迴歸係數的應用解釋，和統計及研究方法科書容易讓人誤解的部分，提出了討論和建議。本文並舉出正確解讀迴歸係數的注意事項。並指出如何結合其他資訊探討多元迴歸自變項的重要性。

The standardized regression coefficient has been a common tool for assessing the effect, predictive power or explanative power of an independent variable (Ⅳ). However, researchers and managers often failed to interpret regression coefficients properly. With mathematical proofs and hypothetical data, this paper demonstrated that when there are more than 2 Ⅳs, inference on the relative importance of these Ⅳs should not be made from standardized regression coefficients (βs) alone. The hypothetical data also show that even when there are only 2 Ⅳs, the nonsignificance of aβdoes not give sufficient evidence on the triviality of the corresponding Ⅳ. According to these limitations onβs, this paper discuss expression problems in textbooks on research methods and statistics, as well as problems in the management science literature. Howβs should be properly interpreted with other information—such as zero-order correlations—is also discussed.