What are Error terms in Regression?

An error term is a residual variable produced by a statistical or mathematical model, which is created when the model does not fully represent the actual relationship between the independent variables and the dependent variables. As a result of this incomplete relationship, the error term is the amount at which the equation may differ during empirical analysis. The error term is also known as the residual, disturbance, or remainder term, and is variously represented in models by the letters e, ε, or u.

  • An error term appears in a statistical model, like a regression model, to indicate the uncertainty in the model.
  • The error term is a residual variable that accounts for a lack of perfect goodness of fit.
  • Heteroskedastic refers to a condition in which the variance of the residual term, or error term, in a regression model varies widely.

The standard error of the regression (S), also known as the standard error of the estimate, represents the average distance that the observed values fall from the regression line. Conveniently, it tells you how wrong the regression model is on average using the units of the response variable.

The wrong type of errors-in-variables regression is often used when dealing with an asymmetric relationship - in other words where there is a clear independent and dependent variable. In this situation, orthogonal regression (including major axis and reduced major axis) is inappropriate.