Maximum likelihood estimation is an essential approach to estimate parameters in statistics. It requires statistical assumptions on error pattern. I will introduce this technique with really simple statistical model - linear regression.
繼續閱讀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
$$
\begin{align}
Var[X] &= \mathbb{E}[(X - \mu)^2] \\
&= \frac{1}{n} \sum_{i=1}^n (x_i - \mu)^2
\end{align}
$$