t*****3
发帖数: 878 | 1 【 以下文字转载自 Statistics 讨论区 】
发信人: temp123 (ttt), 信区: Statistics
标 题: 一个概念性的问题 ，请求帮助~~~~~
发信站: BBS 未名空间站 (Sun Aug 26 21:10:35 2007)
A，B，C三个RANDOM VARIABLES。
1) A 和B 正相关，significant的。
2) C = beta * A + error 这个regression中，发现 beta是significantly
positive的
问题： 那么在 C = beta’ * B + error’ 这个regression中，是不是beta'也一定
是significantly positive的？至少POSITIVE？--- 可能不可能是negative的？
并请稍微解释或者举例一下！！多谢各位大侠了！！ | g*****y
发帖数: 6325 | 2 let A=alpha*B+error1 (alpha is positive)
Then C= beta'*(alpha*B+error1)+error'=beta'*alpha*B+ beta'*error1+error';
beta' is positive, alpha is positive, the beta'*alpha is positive. | l**********t
发帖数: 5754 | 3 my 2 cents.
assuming the regression C = beta * A + error is liner,
beta =COV(A, C)/VAR(A) > 0 so COV(A,C) >0,
also, COV(A, B) > 0 as given,
question: is it possible to have COV(B, C)/VAR(B) < 0, or COV(B, C) <0
I think it is possible to have a negative COV(B,C),given COV(A,C) and COV(A,
B) are positive, as long as the covariance/correlation matrix of A, B, C is
still positive definite. For example, I can have
COR(A,B) = 0.5
COR(A,C) = 0.5
COR(B,C) = -0.1 |
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