# 14: Multiple and Logistic Regression

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The principles of simple linear regression lay the foundation for more sophisticated regression methods used in a wide range of challenging settings. In Chapter 8, we explore multiple regression, which introduces the possibility of more than one predictor, and logistic regression, a technique for predicting categorical outcomes with two possible categories.

• 14.1: Introduction to Multiple Regression
Multiple regression extends simple two-variable regression to the case that still has one response but many predictors. The method is motivated by scenarios where many variables may be simultaneously connected to an output.
• 14.2: Model Selection
The best model is not always the most complicated. Sometimes including variables that are not evidently important can actually reduce the accuracy of predictions. In this section we discuss model selection strategies, which will help us eliminate from the model variables that are less important. In this section, and in practice, the model that includes all available explanatory variables is often referred to as the full model. Our goal is to assess whether the full model is the best model.
• 14.3: Checking Model Assumptions using Graphs
Multiple regression methods generally depend on the following four assumptions: the residuals of the model are nearly normal, the variability of the residuals is nearly constant, the residuals are independent, and each variable is linearly related to the outcome.
• 14.4: Introduction to Logistic Regression
In this section we introduce logistic regression as a tool for building models when there is a categorical response variable with two levels. Logistic regression is a type of generalized linear model (GLM) for response variables where regular multiple regression does not work very well. In particular, the response variable in these settings often takes a form where residuals look completely different from the normal distribution.
• 14.5: Exercises
Exercises for Chapter 8 of the "OpenIntro Statistics" textmap by Diez, Barr and Çetinkaya-Rundel.
• 14.6: Statistical Literacy
• 14.E: Regression (Exercises)

Thumbnail: The logistic sigmoid function. (Public Domain; Qef).

This page titled 14: Multiple and Logistic Regression is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by David Diez, Christopher Barr, & Mine Çetinkaya-Rundel via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.