此篇論文分為兩部份，第一個部份是Cochran-Armitage test for a linear trend中檢定H_0:π_i=π對於所有的i=1,..,I，想利用迴歸模型中的簡單線性迴歸(Simple Linear Regression: Y=β_0+β_1X+ε)取代，進而取代H_0:β_1=0； 另一個部份是在非線性模型下，對y去做轉換，並且提供Box-Cox的方法，可以得到轉換後的結果。 再來看是否有需要去對x做轉換，利用Box-Tidwell的方法去判別。 最後我們在此論文中嘗試去證明出 Pearson Chi-squared 的檢定統計量與迴歸模型中的簡單線性迴歸有相同的結果。並且提供例子與 SAS 相關程式。 The dissertation is divide into two parts. The first part is in Cochran- Armitage test for a linear trend to test H_0:π_i=π for all i=1,..,I, and wants to use simple linear regression of regression model substitutes. Then to test H_0:β_1=0. Another part is under the nonlinear model, makes the transformation on y, and provides Box-Cox method. And obtain the transformation the result. Using the Box-Tidwell method to check whether has the need to transformation on x. Finally in this dissertation, we attempt to prove the Pearson Chi-squared test in a view of a simple linear regression model. Also, we have provided some examples and the associatated SAS programs.
