資料的單位通常是以量測方便而定的,這可能並不適合用在描述資料的簡化模型上. 為能夠達到模型的簡化, 我們通常會需要轉換反應變數或解釋變數或是兩者. 轉換的目的除了建構簡單適合的模式外, 也包括使得所選擇的模式能夠符合各項模型假設. Box and Cox (1964) 所提出的轉換應是在應用上最為成功的一個. 而他們也提出了以對反應變數作轉換以使得模式符合各項假設的選擇標準.
藉著現今電腦與軟體在快速計算, 處理複雜程式, 以及繪製各式圖形的能力, 我們得以對此些方法能夠作得更有效率並得以擴充與延伸.

我們重新檢視幾個 Draper and Hunter (1969) 上的例子為開端, 提出了改進的做法. 接著我們檢視 Snee (1986) 所提出處理多重模型的方法, 以有效率的程式來處理複雜的計算問題. 然後我們就診斷模型假設討論的加法性模式, 誤差變異齊一, 以及誤差為常態分配等的模型假設. 我們提出一個名為 P-值圖的做法, 來整合轉換的選擇以同時能夠滿足各項模型假設. 而一些與轉換和模型建構相關的議題亦包括於後.

Usually, the units in which data are recorded are chosen merely as a matter of convenience in measurement. They need not be those in which the system that generates the data is modeled in its possible simplest form. To achieve simplicity, transformations may be applied to the response, or the explanatory variables, or both. Such purpose of taking transformation includes not only on building simple and proper model, but also on making the proposed model satisfy various model assumptions. The Box and Cox (1964) version of power transformation has been the most accepted one in practice. They also proposed a useful and practical criterion for achieving a model that satisfies various model assumptions
via power transformation on the response variable.
With the capability of modern computer and softwares: faster computing, handling of complicated programming, and generating of sophisticated graphs, we are able to make use of such approach more efficiently, and have the approach further extended and generalized.

We start by having some examples in Draper and Hunter (1969) actually re-revisited, and propose ways to improve their results. Then, we examine the approach proposed by Snee (1986) in handling multiple model structure with an efficient way in programming to deal with complicated computation
issue. Then, we discuss issues about diagnosis on model assumptions regarding additive model, homogeneous error variance, and normally distributed error. A so-called P-value plot approach is proposed to unify the ways of choosing transformation to make the proposed model
satisfy various assumptions simultaneously.
Relevant but miscellaneous issues of transformation and model building are included thereafter.

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