Linear models: Estimation

In this unit, we will focus on estimation of coefficients in the linear regression model (eqs. 1.1 and 1.2). We start by discussing the interpretation of linear models (2  Interpreting linear models). Then, we discuss least squares estimates from the algebraic, geometric, and probabilistic perspectives (3  Least squares estimation). We then discuss important properties of least squares estimates, including orthogonality relationships least squares estimation implies (4  Analysis of variance) and the effects of collinearity (5  Collinearity and adjustment). We conclude with an R demo (6  R demo).