This chapter is designed to provide some common background. We introduce linear models and ordinary least squares, which are starting points for more recent developments presented in later chapters. Although we do present standard distributional theory and inferential methods under homoscedastic Gaussian errors, we also focus on model misspecification, as well as techniques for assessing goodness-of-fit by looking for signal in the residuals. The chapter concludes with a discussion of some key approaches to multiple testing, a problem that occurs for example when testing for the individual significance of several predictors in regression settings.