Chapter 5 Linear regression models

In this chapter we discuss linear regression models. The basic concept is that we forecast the time series of interest \(y\) assuming that it has a linear relationship with other time series \(x\).

For example, we might wish to forecast monthly sales \(y\) with total advertising spend \(x\) as the predictor. Or we might forecast daily electricity demand \(y\) using temperature \(x_1\) and the day of week \(x_2\) as predictors.

The forecast variable \(y\) is sometimes also called the regressand, dependent or explained variable. The predictor variables \(x\) are sometimes also called the regressors, independent or explanatory variables. In this book we will always refer to them as the “forecast variable” and “predictor variables”.