A Two Model Approach for Regression Diagnostics Applied to Furniture Design

雙模型分析法於迴歸診斷之應用—以家具設計為例

10.6220/joq.2016.23(1).01

曾世賢(Shih-Hsien Tseng)；徐堯(Yao Hsu)

線性模式 ； 一般最小平方法 ； 模型選擇 ； 調整判定係數 ； 期望平均方誤根 ； linear models ； ordinary least squares ； model selection ； adjusted R^2 ； root expected mean squared error

品質學報

23卷1期（2016 / 02 / 28）

1 - 24

英文

為能提供迴歸分析中有關偏差(bias)等診斷資訊，本文提出一雙模形分析方法(twomodel approach)來加以處理，並以家具設計為例來展示此方法的有效性。本研究所提出之方法具備迴歸分析中常使用之調整的判定係數(adjusted R^2)之優點並同時提供模型預測偏誤誤差之資訊。此外，本方法修正一般在使用C_p時因自由度問題而無法使用一般最小平方法估計模型偏誤之缺點。本研究所提出之模型診斷方式具有簡單表達模型預測誤差值的特性，其主要表達方式為模型預測值增或減一期望預測誤差值，並透過所設計之測試平臺可同時針對偏誤、多重共線性與實驗設計中資料點分布不對稱性進行探討與測試，最後並透過一家具設計案例說明此方法之應用。

This paper proposes a two model approach for regression in order to provide diagnostic information about the bias and other summative information related to furniture design. In the context of regression, the resulting quantity, like the commonly used adjusted R^2 statistic, provides a measure of explanatory power, but which also explicitly accounts for bias errors. Unlike the familiar C_p statistic, the proposed diagnostic can be estimated even if the bias sources are inestimable using ordinary least squares. Interpreted in simple terms, the proposed diagnostic is the expected plus or minus prediction errors in the units of the response. The proposed diagnostic is studied using a test-bed, also proposed here, which accounts for bias, multicollinearity, and mismatches between region of interest moments and the input pattern or experimental design moments. An application to furniture design is used to illustrate the methods.

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