Matrix Algebra For Linear Models -

y=Xβ+ϵbold y equals bold cap X bold-italic beta plus bold-italic epsilon (Response Vector): An vector of observed dependent variables. Xbold cap X (Design Matrix): An

matrix containing a column of ones for the intercept and columns for each predictor variable. βbold-italic beta (Parameter Vector): A Matrix Algebra for Linear Models

vector of unknown coefficients (slopes and intercept) to be estimated. ϵbold-italic epsilon (Error Vector): An y=Xβ+ϵbold y equals bold cap X bold-italic beta

vector of random errors, often assumed to follow a multivariate normal distribution with mean zero. 2. Core Matrix Operations in Modeling Matrix Algebra for Linear Models