Re: [問題]推論統計(完全不懂)
※ 引述《imgodya (許我一個PhD)》之銘言：
: Find E{R^2/(1-R^2)} under the null hypothesis, where R^2 is the sample squared
: multiple correlation coefficient. Hint: E{[χ^2]^k} = 2^kΓ(v/2 + k)/Γ(v/2),
: whereχ^2 is aχ^2-distributed random variable with v degrees of freedom.
: 翻了很多書 不太懂這個問題的定理
: 想請問要如何推導??
Under the null hypothesis,
R^2 R^2 *SST SSR SSR/ σ^2
------- = -------------- = ------- = ------------
1-R^2 (1-R^2) *SST SSE SSE/ σ^2
(k-1 is the number of explanatory variables)
Since SSR/ σ^2 and SSE/ σ^2 are inpependent χ^2-distributed
random variable with degrees of freedom k-1 and n-k respectively
under null hypothesis.
R^2 SSR/ σ^2 1
E(-------) = E(-----------) = E( SSR/ σ^2 * ------------)
1-R^2 SSE/ σ^2 SSE/ σ^2
1
=E( SSR/ σ^2 )* E ( ------------)
SSE/ σ^2
Compute these expectations with the hint
E{[χ^2]^k} = 2^kΓ(v/2 + k)/Γ(v/2)
SSR/ σ^2 ~ χ^2(k-1) E(SSR/ σ^2)= k-1
SSE/ σ^2 ~ χ^2(n-k) 1
E ( --------- ) = 2^(-1)Γ( (n-k)/2 -1 )/Γ( (n-k)/2 )
SSE/ σ^2
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 203.73.183.95
※ 編輯: jangwei 來自: 203.73.183.95 (02/23 01:04)
推
02/23 03:01, , 1F
02/23 03:01, 1F
推
02/23 11:10, , 2F
02/23 11:10, 2F
討論串 (同標題文章)
本文引述了以下文章的的內容：
完整討論串 (本文為第 2 之 2 篇)：