臺灣博碩士論文加值系統

在複迴歸分析（Multiple Regression Analysis）的應用中，非常重要的一個課題是如何去選取最佳之迴歸模式（the Best Subset Regression Model）。本研究結合後退刪除法（Backward Elimination）與根據t檢定搜尋法（Direct Search on t）而建立了一個最佳迴歸模式搜尋法則稱為：修正t檢定搜尋法（Adjust Search on t， ）。
本研究利用電腦模擬的方式產生具三種不同特性的變數結構之資料，分別是獨立性、相關性與共線性。並利用這些資料進行各種搜尋法則的綜合比較，分析比較 在不同特性與不同變數數目的搜尋結果。
本研究發現 有以下幾個特性：
1. 在處理三種不同特性下的資料時，其搜尋結果在 、P值與 等評判準則上比向前選取法(Forward Selection)、後退刪除法、逐步迴歸法(Stepwise Regression)及根據t檢定搜尋法之搜尋結果好，且此結果分別在六個和十個變數之模擬當中，皆得到相同的結果。
2. 比根據t檢定搜尋法可以獲得較佳的搜尋結果，此結果明顯表現在變數之間具共線性的情況之下。
關鍵字：複迴歸分析 , 最佳迴歸模式 , 變數選取 , 相關性 , 多重共線性

Selecting the best regression model is an important issue in the application of multiple regression analysis. This research combined Backward Elimination with Direct Search on t and established a new searching algorithm for finding the best subset regression model which called Adjusted Search on t, .
This reseach used computer program to create three kinds of variable structure datasets, The three kinds of variable structure are: (1) variables that are independent to each; (2) partial variables that are correlated to each; (3) partial variables that appear the chacteristic of multicolinearity. This research compared the results of different
searching methods in different variable structures and different numbers of variable.
The result of this reseach also shows that:
1. is better than the searching methods of Forward Selection , Backward Elimination , Stepwise Regression and Direct Search on t in different data structures based on the indicators of , P-value and . The characteristics do not change both at six and ten variables .
2. One can obtain better result by applying than applying Direct Search on t in the variable structure with multicollinearity.
Keywords: Multiple Regression Analysis ; The Best Subset Regression Model; Variable
Selection; Correlation; Multicollinearity.

目錄
中文摘要 -------------- i
英文摘要 -------------- ii
誌謝 -------------- iii
目錄 -------------- iv
表目錄 -------------- vi
圖目錄 -------------- vii
一、 緒論-------------------- 1
1.1 前言-------------------- 1
1.2 研究動機與目的----- 2
1.3 研究方法-------------- 2
二、 文獻回顧-------------- 4
2.1 迴歸模式之評估準則----- 5
2.1.1 複判定係數----------- 5
2.1.2 調整複判定係數----- 7
2.1.3 值------------------- 8
2.1.4 均方誤差值----------- 9
2.1.5 預估平方差----------- 10
2.2 窮舉迴歸搜尋法----- 10
2.2.1 模式產生順序-------- 11
2.2.2 掃掠運算-------------- 11
2.2.3 迴歸樹----------------- 13
2.3 最佳迴歸模式搜尋---- 14
2.3.1 根據較佳路徑搜尋------ 14
2.3.2 根據t檢定搜尋法------------ 15
2.3.3 逐步迴歸搜尋法--------- 15
2.3.4 最佳子集搜尋法--------- 17
三、 搜尋法則的建立--------- 18
3.1 新搜尋法則的建立------ 18
3.2 實例說明------------------- 21
3.2.1 實例應用--------------- 21
3.2.2 搜尋結果比較-------- 23
3.3 修正t檢定搜尋法結果析---------- 23
3.3.1 關於優劣性的探討------ 24
3.3.2 關於效率的探討----------------- 24
四、 模擬資料建立與搜尋結果分析----- 26
4.1 模擬資料之產生與變數結構之定義-- 26
4.2 修正t檢定搜尋法與其他搜尋法之搜尋結果與分析---- 35
4.2.1 六個變數之搜尋結果分析-- 35
4.2.2 十個變數之搜尋結果分析-------- 39
4.2.3 綜合結果分析------------- 43
4.3 各特性之實例驗證---- 45
五、 結論與未來研究方向---- 47
5.1 結論------------------------------ 47
5.2 未來研究方向----------------- 48
參考文獻 ------------------------ 49
附錄一 ------------------------ 51
附錄二 ------------------------ 52
附錄三 ------------------------ 59
附錄四 ------------------------ 65
附錄五 ------------------------ 72
附錄六 ------------------------ 78
附錄七 ------------------------ 80
附錄八 ------------------------ 82
作者簡歷 ------------------------ 84

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