Applied Regression Modeling, 3rd Edition

Chapter 1Foundations

This chapter provides a brief refresher of the main statistical ideas that are a useful foundation for the main focus of this book, regression analysis, covered in subsequent chapters. For more detailed discussion of this material, consult a good introductory statistics textbook such as Freedman et al. (2007) or Moore et al. (2018). To simplify matters at this stage, we consider univariate data, that is, datasets consisting of measurements of a single variable from a sample of observations. By contrast, regression analysis concerns multivariate data where there are two or more variables measured from a sample of observations. Nevertheless, the statistical ideas for univariate data carry over readily to this more complex situation, so it helps to start out as simply as possible and make things more complicated only as needed.

After reading this chapter you should be able to:

• Summarize univariate data graphically and numerically.
• Calculate and interpret a confidence interval for a univariate population mean.
• Conduct and draw conclusions from a hypothesis test for a univariate population mean using both the rejection region and p‐value methods.
• Calculate and interpret a prediction interval for an individual univariate value.

1.1 Identifying and Summarizing Data

One way to think about statistics is as a collection of methods for using data to understand a problem quantitatively—we saw many examples of this in the introduction. This book is concerned primarily ...