Consider Y = b_0 X_0 + ... + b_(p-1) X_(p-1) + e
Let Y~ be the fitted values.
Let r < p. Consider a reduced model with only r parameters.
Say Y = b_0 X_0 + ... + b_(r-1) X_(r-1) + e
Let YR~ be the fitted values in this reduced model.
Prove: ||Y - YR~||^2 = ||Y - Y~||^2 + ||Y~ - YR~||^2
Also, give the corresponding decomposition of degrees of freedom.
也就是說要證明 (Y - Y~) 和 (Y~ - YR~) 垂直 (或說正交)
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現在很麻煩 因為我只知道 basic ANOVA 有 (Y- Y~) 和 (Y~ - Y) 垂直
自由度我也不太確定 ...
任何意見感激不盡 ((_ _))
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