Regression and correlation

Written by Ronny Gunnarsson and first published on June 22, 2014.
Last revised on September 8, 2019.

There is an updated version of the EPV-calculator found here: https://infovoice.se/epv-calculator/

Suggested pre-reading	What this web page adds
Introduction to statistics Observations and variables Inferential statistics Choosing statistical analysis Associations and predictions	This web-page provides an introduction to regression and correlation. Reading this will give you an introduction and overview of these concepts necessary to understand more (on following pages going into more details).

Table of Contents (with links)

Introduction to correlation

(This section is still under construction. Sorry for the inconvenience.)

Introduction to regression

Regression and correlation focuses on how variables correlate. Often one or several variables are defined as dependent meaning that they are believed to alter when the value of other independent variables change. There are different types of regression :

Simple regression: One dependent and one independent variable
Multivariable regression = multiple regression: More than one independent variable
Multivariate regression: More than one dependent variable
Multivariate multivariable regression: More than one dependent variable as well as more than one independent variable.

Linear regression

The dependent variable and different types of linear regression

Standard linear regression: The dependent variable is measured with an interval or ratio scale.
Logistic regression: The dependent variable is almost always binary (there is an exception with ordinal logistic regression where the dependent variable can be measured by an ordinal scale).
Cox regression: The dependent variable consists of two variables. One is stating if the event of interest has happened (usually coded as “1”) or not (usually coded as “0”). The other variable states the time an individual has been followed so far irrespective if the event has happened.

Overview of different types of linear regression

	Simple regression	Multivariable regression = multiple regression	Multivariate regression	Multivariate multivariable regression
Standard linear regression	Simple standard linear regression = Unadjusted standard linear regression	Multivariable standard linear regression = multiple standard linear regression = adjusted standard linear regression	Factor analysis	Factor analysis
Logistic regression	Simple logistic regression = unadjusted logistic regression	Multivariable logistic regression = multiple logistic regression = adjusted logistic regression	Multivariate probit regression (bivariate probit regression is a special case with two dependent variables)	Multivariate multivariable probit regression
Proportional hazards regression = Cox regression	Simple proportional Hazards regression	Multivariable proportional Hazards regression / multiple proportional hazards regression	?	?

Non-linear regression