Core concepts in statistics and research methods. Part 7: regression

Identify the response and the explanatory variables in a regression model. Interpret the regression coefficients (model parameters). Identify an appropriate regression model for the clinical question and the data. Explain the assumptions of simple linear regression. Recognise the differences between linear models and generalised linear models.The term regression dates back to experiments conducted by British biologist Sir Francis Galton in the 19th century. 1 Galton was interested in how strongly traits in one generation were inherited in the next.Working with peas, he measured the sizes of mother and daughter peas and plotted the results on a scatterplot.Galton noticed that the line of best fit was approximately straight with a positive slope that was always < 1. Galton interpreted the slope as demonstrating regression to the mean, whereby very large or very small mother peas tended to produce daughter peas of less extreme size.Although regression to the mean is unrelated to Galton's methodology, the name stuck.Nowadays, we refer to the technique of drawing a straight line of best fit through data points on a scatterplot as simple linear regression.Since Galton's work, regression has developed into one of the most important techniques in all of statistics.Regression provides a unified framework for analysing virtually all data.Most standard statistical tests have a regression equivalent (Table 1).Regression can be used with both traditional (frequentist) and Bayesian frameworks.Although Bayesian inference offers distinct advantages, our focus is frequentist statistics, as this is the most widely used approach to statistical inference.This article is part of a series in BJA Education on statistics and study design. 233]45 Concepts from earlier articles that will assist in understanding the material presented here include the difference between variables and parameters, variance, standard error, test statistics, null distributions, hypothesis tests, p-values and confidence intervals (CIs).