Error and residual
Definition taught in Bayesian linear regression, part of Bayesian statistics
Error and residual
| Type | Definition |
| Taught in | Bayesian linear regression |
| Part | Bayesian statistics |
The true error is
\varepsilon_i=Y_i-{\boldsymbol{x}}_i^\top{\boldsymbol{\beta}},
which contains the unknown true coefficient vector. After fitting the model, the residual is
e_i=y_i-{\boldsymbol{x}}_i^\top\widehat{\boldsymbol{\beta}}.
Errors are independent model variables under Equation (1) in Bayesian linear regression; residuals are observable functions of the entire fitted dataset and are not iid. The conventional name “sum of squared errors” is therefore slightly loose: the fitted quantity is a sum of squared residuals.
Used in
- Taught in Bayesian linear regression, where the derivation and examples are.
- All 8 questions on Bayesian linear regression
See also
Gaussian linear model · Ordinary least squares · Sampling distribution of the OLS estimator · Studentised coefficient pivot · Least-squares decomposition · Conditional coefficient posterior · Marginal variance posterior · Marginal Student posterior