送交者: zzzzz 于 November 04, 2003 12:08:57:
回答: 请教个统计问题 由 悠云 于 November 04, 2003 03:12:09:
Let X be a random variable having uniform distribution in the interval (-1, 1). Consider random variables
Y = X^{3} and Z = YX = X^{4}.
"假如某一因变量与两个自变量相关", for example, Z = YX.
"而这两个自变量又互相相关" since Y = X^{3} and X = Y^{1/3}.
"将这两个自变量分别固定做偏相关，这俩又都与因变量不相关了"
see
Cov(X, Z) = E(XZ) - E(X)E(Z)
= E(X^{5}) - E(X)E(X^{4})
= 0 - 0 = 0
Cov(Y, Z) = E(YZ) - E(Y)E(Z)
= E(X^{7}) - E(X^{3})E(X^{4})
= 0 - 0.