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Montgomery, D.C., Peck, E.A. and Vining, G.G. (2006) Introduction to linear regression analysis. 4th Edition, Willey, New York.

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  • 标题: 用SAS MACRO程序建立多项式模型与变量筛选Using SAS MACRO Programs to Build a Polynomial Model and Do the Selection of Variables

    作者: 王国征

    关键字: 多项式模型, 泰勒多项式, SAS MACROPolynomial Model, Taylor’s Polynomial, SAS MACRO

    期刊名称: 《Advances in Applied Mathematics》, Vol.4 No.2, 2015-05-20

    摘要: 本篇论文是希望藉助SAS MACRO程序,提出一个能解决建立多项式模型上的困恼。多项式模型在统计分析上一直是被忽略的,这可以很清楚的知道因为在所有的统计分析的出版品中很难找到以多项式回归为主提的例子。这原因无非是无法解决大量变量的模型建立与分析。举例来说要建立一个完整的5个变量的3次多项式总共需要55个变量,而如果变量增加到18个,那建立1个2次多项式就高达189个变量,因此在实用分析上是鲜有这样的例子。本篇论文就是希望能提出1个解决模型建立与初步分析的方法,读者可以藉由在第三章的例子的输出报表中很清楚去比较各个模型的优劣点,这就是为何统计分析需要工具去产生整合型的报表。欠缺这些报表,要去判定模型的好坏(基于预测值的准确度)是很困难的工作。而我之所以强调要用多项式的模型去分析数据有下列几点原因;1) 如果模型为平滑曲面则多项式模型可以提供一个可接受的模型。这可以很容易由泰勒定理得到验证;2) 只要观测值够多,大部分模型的不配合均可以用高阶多项式模型解决;3) 可以避免因为经过模型筛选而删除掉可能是有用的变量。那是因为模型会产生很多的交叉相乘项,既使用模型筛选的程序也很难将一个变量完全去除掉,因此可以保存几乎所有的变量,而因此将不失模型的完整性。本篇论文提供了两支主要的SAS MACRO程序;%Homopoly和%Model_Selection分别会在下个两章节中介绍。程序%Homopoly是用在建立多项式数据文件,而%Model_Selection则是用来提供SAS模型筛选后的总结数据,报表格式是仿照表11.8 Montgomery制作的。读者可以很容易复制到其他的分析。为了要编写程序,我同时提供了20支工具程序,读者可以至以下的网站下载http://tsp.ec.tku.edu.tw/QuickPlace/054569qp/Main.nsf/h_Toc/BADD7D0BFF0 904A1482576D300229684/?OpenDocument。请依循档案README.TXT中的指示去安装即可。The purpose of this paper is trying to provide a useful solution to build a polynomial model. In the past years, there are a few applications on polynomial model; the reason is that it is difficult to create a large number of variables. For example, if you want to build a 3rd order polynomial with 5 variables, then you need 55 variables. If the variables increase to 18, then a 2nd order polynomial model will need 189 variables. It is far away from our ability. That is the reason why I wrote the following programs. There are 3 major reasons that I would like to deal with the polynomial model: 1) if the unknown model was smooth plan curve, then a polynomial model can provide an acceptable approximation. This can be easily seen from the Taylor’s polynomial; 2) as long as we have enough observations, then using a high order polynomial model can solve the unfitted problems; 3) it can avoid deleting important variables from the selection steps, since it is not easy to remove a variable completely from the model because there are too many cross product terms shown in the model. This paper will provide 2 major SAS MACRO programs, %Homopoly and %Model_Selection. The first program is used to generate a polynomial model and the next one will provide summarized result tables similar to the Table 11.8 of Montgomery including the information of the models and necessary statistics. Users can easily apply to do the further analysis. To write those programs, I also wrote another 20 SAS MACRO programs which can be downloaded from the web-site http://tsp.ec.tku.edu.tw/QuickPlace/054569qp/Main. nsf/h_Toc/BADD7D0BFF0904A1482576D300229684/?OpenDocument. Please follow the in-struction given by the readme.txt file.