Regression analysis: model the relationship between variables
Y: dependent variable, response variable being measured, regressand
x = (x_1,…, x_p): predictors, independent variable, regressor, covariates

(weighted) Multiple linear regression models
Assume $Y = (Y_1 ,…, Y_n)$ are independent normal random variables with
$E(Y) = \mu = X \beta$, $Var(Y)= \sigma = \sigma^2 W^{-1} $, where matrix $W$ is diagonal, with $w_ii >0$ weights, $\sigma^2$ dispersion parameter (vector), $\beta=(\beta_1,…,\beta_p)$ parameter vector, $X=(x_{i,j}), (x_{ij})_{i=1,..n, j=1,…,p} $, so that $x_i$: data of object $i$ of length $p$, categorical or numerical data,

An observation (a realisation) of $Y_i$ is the mean of a sample of $w_i$ iid observations, $\sigma_i$, individual variance

Maximum likelihood estimator: a random variable, that when $X=x$, maximize the likelihood of {X=x}, given the distribution is parameterized by the estimators, (for normal distribution, the parameters are mean and variance)

exponential dispersion family $f_Y(y;\theta,\psi)= \exp(\frac{y\theta-b(\theta)}{\psi} + c(y;\psi)), y \in D_\psi$, D support of density, the mean does not depend on $\psi$

Kalman filter can be interpreted from the framework of dynamic lienar model. Dynamic generlized linear model can be used to analysis time series.