臺灣博碩士論文加值系統

線性迴歸模型以常態分配為根基求得假設檢定的統計量,進而計算信賴區間,因此檢定資料是否吻合常態分配其重要性可見一斑。一般而言檢定常態分配的方法不外乎:(1)Normal Probability Plot (2)Shapiro-Wilks Test。然而同一張圖不同人的解讀或許有不同的結論。因此,以檢定為基礎的Shapiro-Wilks test更顯現出其重要性。一旦拒絕虛無假設,則表示該資料不符合常態分配
,但是沒有拒絕虛無假設並不代表該筆資料來自於常態分配。此項研究為探討現行資料與常態分配的相似性,進而提供給線性迴歸模型的使用者一個更可靠的依據。
此篇論文所提供之方法亦可適用於判斷現行資料與其他分配之相似程度,從中使用者更可以了解此資料最為可能來自於哪個分配。

Linear Regression Model is a model that is meant to find out the statistic of testing hypothesis on the basis oformal distribution and then to calculate the confidence interval. Therefore, the importance of testing if the data match
normal distribution cannot be overemphasized.
Generally speaking, there are two methods of testing normal distribution: one is normal probability plot and the other is Shapiro-Wilks test. However, different people may make different conclusions when they are explaining the same draw due to he different methods they use. As a result, Shapiro-Wilks test, which is based on testing, reveals its importance.Once rejection null hypothesis happens, it means that the data do not match normal distribution. On the other hand,if rejection null hypothesis does not happen, it does not mean that the data come from normal distribution.
This research is meant to investigate the similarity between the present data and normal distribution, and provide the users of linear regression model with a more reliable method.The proposed method provided in this thesis can also apply to judging the degree of similarity between the present data and other distributions, from which the users can clearly know what distribution the data probably come from.

Contents ii
表目錄 iii
Abstract iv
摘要 v
1 緒論 1
1.1 背景 1
1.2 研究目的 2
1.3 本文架構 2

2 文獻探討 3
2.1 Normal probability plot 3
2.2 Kolmogorov-Smirnov Test 4

3 研究方法 5
3.1 模擬 12
3.1.1 同一分配相似係數的檢定 12
3.1.2 不同分配相似係數的檢定 14

4 結論 16

表目錄

表3.1 顯著水準為5%下Shapiro-Wilks 和相似係數
在同一分配改變平均數與變異數的比 13

表3.2 Shapiro-Wilks test和相似係數對於不同分配下在顯著水準5%下檢定的比較 15

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