ABSTRACT
Linear regression analysis is a statistical tool for evaluating the relationship between a continuous random variable Y and several independent variables x1, · · · ,xp according to the model
Y = β0 +β1x1 + · · ·+βpxp + e. (1.1)
Here β0, · · · ,βp are unknown constants, and e is an unobservable random error which is assumed to have a normal distribution with mean zero and unknown variance σ2 > 0 throughout this book. The parameters βi and σ2 characterize the model and are estimated from the observed data. The quantity Y is often referred to as the response or dependent variable, as it depends on the xi’s through the linear relationship β0 + β1x1 + · · ·+ βpxp. As the value of Y may be predicted from the xi’s by using the relationship (1.1), the xi’s are often called the predictors or predictor variables or covariates. Throughout this book it is assumed that the predictors are not random variables.
