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互いに相関する3変量間の回帰分析について
http://hdl.handle.net/10271/2634
http://hdl.handle.net/10271/26347c5adabc-a80d-4e37-9bce-bbc41a38cc3e
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
kiyo27_01.pdf (529.4 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||||
|---|---|---|---|---|---|---|---|---|
| 公開日 | 2013-08-27 | |||||||
| タイトル | ||||||||
| タイトル | 互いに相関する3変量間の回帰分析について | |||||||
| 言語 | ||||||||
| 言語 | jpn | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | partial correlation coefficient | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | regression analysis | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | logarithm of cancer incidence | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | Weibull distribution | |||||||
| 資源タイプ | ||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||
| 資源タイプ | departmental bulletin paper | |||||||
| その他のタイトル | ||||||||
| その他のタイトル | On the Regression Analysis for Mutually Correlated Three Variables | |||||||
| 著者 |
野田, 明男
× 野田, 明男
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| 書誌情報 |
浜松医科大学紀要. 一般教育 巻 27, p. 1-8, 発行日 2013-03-14 |
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| 出版者 | ||||||||
| 出版者 | 浜松医科大学 | |||||||
| 抄録 | ||||||||
| 内容記述タイプ | Abstract | |||||||
| 内容記述 | Let us consider three random variables Xi (i = 1,2,3) with mean μ i and variance σ i 2 . We denote by ρij the correlation coefficient of Xi and Xj , and set {i, j, k} = {1,2,3}. Then the partial correlation coefficient ρij•k is defined to be (ρ ρ ρ )/ ρ ρ ij ik jk ik jk − 1− 2 1− 2 (see [4]), which is equal to the correlation coefficient of residuals Ri•k and Rj•k . Here, we put R X X X X i•k i i i i i ik k k k = −ˆ , ˆ =μ +σρ( −μ)/σ being the least squares regression line of Xi given the value Xk . In §1 we study some properties of these partial correlation coefficients to see their importance in the regression analysis and also in the theory of normal distributions. The purpose of this paper is to investigate the logarithm vk of cancer incidence in Japan (due to [2]), which corresponds to the value xk = 2.5 + 5(k - 1) (1 ≤ k ≤ 18) of age. The fact that the correlation coefficients between three data {xk , uk = log xk , vk} are all near to 1 was observed in [1], which surprised the author and led him to the present study of these data. Indeed, we find outliers in the residuals R R R u•x v•x v•u , , and compute the partial correlation coefficients ruv•x and rxv•u to note two remarkable low values: one is ruv•x = 0.0543 in the range 1 ≤ k ≤ 18 of age and the other is rxv•u= 0.2614 in the range 4 ≤ k ≤ 18 of age, which tells us that our real data vk can be fitted by the regression line on xk (resp. uk) in the former (resp. latter) range of age. The final section is devoted to a study of the simulated data wk that we generate by using the Weibull distribution ([3]). Our method of simulation comes from an approximation of the simulation model proposed in [1]. We obtain results on various kinds of partial correlation coefficients such as r r uw•x vw•x , and r r xw•u vw•u , defined by (1–1), and also rvw•xu defined by (1–4). | |||||||
| ISSN | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 09140174 | |||||||
| NII書誌ID | ||||||||
| 収録物識別子タイプ | NCID | |||||||
| 収録物識別子 | AN10032827 | |||||||
| フォーマット | ||||||||
| 内容記述タイプ | Other | |||||||
| 内容記述 | application/pdf | |||||||
| 著者版フラグ | ||||||||
| 出版タイプ | VoR | |||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||
