Terms and Naming Conventions

There can be many different notations and naming convention for the same measurement commonly used in the subject of Linear Model. This page describes names we will use, and their common alternatives.

Used	Common Alternatives	Comment
$SSE$ (Sum of Squares Error)	$RSS$ (Residual Sum of Squares)
$SSR$ (Sum of Squares Regression)	$ESS$ (Explained Sum of Squares)
$SST$ (Sum of Squares Total)	$TSS$ (Total Sum of Squares), $S{S}_{yy}$
$MSE$ (Mean Square Error)	$MSD$ (Mean Square Deviation)
$RMSE$ (Root Mean Square Error)	$RMSD$ (Root Mean Square Deviation)
$p$ : Number of predictors	$k$
$\beta$ : Coefficients	Parameters, $b$, $\mathbf{\beta }$	Parameter might be confused with distribution parameters
$x$ : Predictor $X$	Independent variable, regressor, $\mathbf{X}$	Shorter. Easier to see the difference between “Predictor” vs “Response” than “Dependent” vs “Independent”
$y$ : Response $Y$	Dependent variable, $\mathbf{Y}$	To match with predictor
$ϵ$ : Error	$\epsilon$	Easier to type in LaTeX
Decision rule	Rejection rule, critical region, rejection region	More direct
$N$ : Total sample	$n$	$N$ not confused with $n_i$; more distinguishable