[問題] 由VAR(Y)=EVAR(Y|X)+VARE(Y|X)推導到迴歸分析
http://en.wikipedia.org/wiki/Variance
Decomposition
The general formula for variance decomposition or the law of total variance
is: If X and Y are two random variables and the variance of X exists, then
Here, E(X|Y) is the conditional expectation of X given Y, and Var(X|Y) is the
conditional variance of X given Y. (A more intuitive explanation is that
given a particular value of Y, then X follows a distribution with mean E(X|Y)
and variance Var(X|Y). The above formula tells how to find Var(X) based on
the distributions of these two quantities when Y is allowed to vary.) This
formula is often applied in analysis of variance, where the corresponding
formula is
SSTotal = SSBetween + SSWithin.
It is also used in linear regression analysis, where the corresponding
formula is
SSTotal = SSRegression + SSResidual.
This can also be derived from the additivity of variances, since the total
(observed) score is the sum of the predicted score and the error score, where
the latter two are uncorrelated.
請問該如何下手才能推導到SSTotal = SSRegression + SSResidual.呢?
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11/10 07:18, , 1F
11/10 07:18, 1F