在迴歸分析的使用上，我們必須要檢測所設定迴歸模型符合迴歸的三個基本假設，分別為(1)獨立假設、(2)常態假設、(3)常數變異數。而針對每個假設，很多學者也分別提出了一些檢定的方法。

在1983年，R. Dennis Cook & Sanford Weisberg 對於常數變異數這個假設提出了一個檢定方法。他們利用分數檢定來檢定模型是否符合此假設，並用圖形來加以輔助，不過並未加以證明。

在此篇論文中，我們嘗試證明他們在當時所做出來的結果，並提供SAS的程式。

In using Regression model, we have to support these three basic assumptions which in Regression. They are (1) Independence, (2) Normality, and (3) Constant Variance. And many scholars provide several diagnostic techniques for each assumption.

In 1983, R. Dennis Cook & Sanford Weisberg were given a diagnostic method for checking the assumption of constant variance. They try to use the score test to test if the model satisfies the assumption or not. And use the graphic to complement the score test.But without prove all of the result.

In this dissertation, we try to prove the result that they did in 1983.

1. Introduction.......................................1
2. Tests concerning nonconstant variance..............1
 2.1. Models..........................................1
 2.2 Score tests......................................3
  2.2..1 Notations....................................3
  2.2..2 Find MLE of β and σ.........................4
  2.2..3 Information matrix...........................4
  2.2..4 The score test statistic.....................7
  2.2..5 The distribution of score test statistic.....9
3. Graphical Methods.................................14
4. Illustrations.....................................17
 4.1 Cherry trees....................................17
 4.2 Gas vapours.....................................18
5. Comments..........................................21
6. References........................................23
7. Appendix..........................................25
 7.1 SAS program for test statistics.................25
 7.2 SAS program for graphical methods...............29
List of Tables
1 Simulated percentage points from the small-sample null distribution of the score statistic..................13
2 Score tests (a) tree data; (b) gas vapour data.....20
List of Figures
1 ei versus fitted values; tree data..................20
2 ri^2 versus (1-vii)H; tree data.......................20
3 ri versus fitted values; gas vapour data............20
4 ri^2 versus (1-vii)yi; gas vapour data.................20
5 ri^2 versus (1-vii)X1; gas vapour data................21
6 ri^2 versus (1-vii)gi, where the gi are the fitted values from the regression of ei^2/σ^2 on X1 and X4; gas vapour data.....21

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