The Art of Statistics: How to Learn from Data

by David Spiegelhalter

Summary • Regression models provide a mathematical representation between a set of explanatory variables and a response variable. • The coefficients in a regression model indicate how much we expect the response to change when the explanatory variable is observed to change. • Regression-to-the-mean occurs when more extreme responses revert to nearer the long-term average, since a contribution to their previous extremeness was pure chance. • Regression models can incorporate different types of response variable, explanatory variables and non-linear relationships. • Caution is required in interpreting models, which should not be taken too literally: ‘All models are wrong, but some are useful.’