標準化迴歸係數的正確解釋

Proper Interpretation of Standardized Regression Coefficients

林新沛(San-Pui Lam)

《中山管理評論》 13卷2期 (2005/06) Pp. 533-548

摘要

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係數的解釋卻仍時有錯誤。本文以假設性的數據為例，配合數學演算証明：當自變項超過兩個時，標準化迴歸係數並不適合作為評斷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係數在統計上不顯著也不表示該變項不重要。根據這些迴歸係數的特性，本文針對過去管理學文獻對標準化迴歸係數的應用與解釋，和統計及研究方法教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裡自變項的重要性。

關鍵字

標準化迴歸係數 ； 零階相關 ； 壓抑變項

並列摘要

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 a β does not give sufficient evidence on the triviality of the corresponding IV. According to these limitations on βs, this paper discuss expression problems in textbooks on research methods and statistics, as well as problems in the management science literature. How βs should be properly interpreted with other information-such as zero-order correlations-is also discussed.

並列關鍵字

Standardized Regression Coefficient ； Zero-order Correlation ； Suppressor Variable

參考文獻

Tabachnick, B. G.,Fidell, L. S.(2001).Using multivariate statistics.Needham Heights, MA:Allyn & Bacon.