Analysis of variance (ANOVA) starts from the analysis of variance which is caught by the model or not. If the variance is modeled, then the variance must be explained by the model, I mean of which is “caught” by the model. If it is not, variance is left unexplained as noises. These two concepts forms explained variance (or between-group variance in categorical factor) and unexplained variance (or within-group variance in categorical factor).
繼續閱讀Random variable $X$, we have the variance
$$
\begin{align}
Var[X] &= \mathbb{E}[(X - \mu)^2] \\
&= \frac{1}{n} \sum_{i=1}^n (x_i - \mu)^2
\end{align}
$$