應用迴歸分析於效率評估之研究

資料包絡分析法非常敏感，所需使用之評估數據資料需要非常精確，為了改善由於數據難以精確，所造成效率評估誤差之缺失，此即為本研究之目的。本研究運用資料包絡分析法之CCR模式，求得各受評單位之效率值，以這些效率值作為迴歸分析之依變項，以各受評單位之投入、產出作為自變項，實施迴歸分析。迴歸分析模式中，各投入變項之迴歸係數皆需為負值；各產出變項之迴歸係數皆需為正值，以符合DEA「同向性」之要求；再考慮各自變項之迴歸係數顯著性p值，宜小於0.05，以符合DEA「線性規劃」之要求。經各自變項之迴歸係數之上、下限，分別計算各受評單位「效率區間」之上、下限。以各受評單位之「效率區間」之平均數除以標準差，作為各受評單位之效率評估。經本文之三個案例說明，對於各受評單位之效率評估，不僅可以得出明確合理的實施，而且能夠對於不適實施資料包絡分析法效率評估給予判定。

關鍵字

資料包絡分析法；迴歸分析模式；效率區間

並列摘要

Given that Data Envelopment Analysis (DEA) tends to be influenced by data accuracy, it is necessary to utilize precise data to obtain valid evaluation. The current research aims at reducing the efficiency evaluation errors caused by imprecise data. The DEA CCR model is adopted to calculate the efficiency values of Decision Making Units (DMUs); these efficiency values were considered as the dependent variables, and the input and output values of DMUs were considered as the independent variables for regression analysis. In this regression analysis model, the input variables of regression coefficients should be negative values, and the output values of regression coefficients should be positive values to comply with DEA's requirements for "isotonicity". Additionally, it would be better if the p value in the test of significance is < 0.05 to satisfy DEA's requirements for "linear programming". The research used the upper limit and lower limit of each variable's regression coefficient to separately calculate the upper limit and lower limit of each DMU's interval efficiency. Afterwards, the DMUs' efficiency was assessed via dividing the mean of DMU's interval efficiency by standard deviation. As demonstrated by the three research cases, the efficiency evaluation for each DMU can not only provide concise and reasonable results but also identify whether the DEA efficiency evaluation method is applicable for DMUs.