Chapter 8. Regression

 

This chapter covers

  • Fitting and interpreting linear models
  • Evaluating model assumptions
  • Selecting among competing models

In many ways, regression analysis lives at the heart of statistics. It’s a broad term for a set of methodologies used to predict a response variable (also called a dependent, criterion, or outcome variable) from one or more predictor variables (also called independent or explanatory variables). In general, regression analysis can be used to identify the explanatory variables that are related to a response variable, to describe the form of the relationships involved, and to provide an equation for predicting the response variable from the explanatory variables.

For example, an exercise physiologist might use regression analysis to develop an equation for predicting the expected number of calories a person will burn while exercising on a treadmill. The response variable is the number of calories burned (calculated from the amount of oxygen consumed), and the predictor variables might include duration of exercise (minutes), percentage of time spent at their target heart rate, average speed (mph), age (years), gender, and body mass index (BMI).

From a theoretical point of view, the analysis will help answer such questions as these:

8.1. The many faces of regression

8.2. OLS regression

8.3. Regression diagnostics

8.4. Unusual observations

8.5. Corrective measures

8.6. Selecting the “best” regression model

8.7. Taking the analysis further

8.8. Summary

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