Residuals

Residuals (Regression) (Regression Analysis) (GWU EMSE-271)
Index | Topics (Logical Lectures) | Lectures | Problems | Readings | Nomenclature | Concepts

"In statistics and optimization, ** statistical errors ** and ** residuals ** are two closely related and easily confused measures of "deviation of a sample from the mean": the **error** of a sample is the deviation of the sample from the (unobservable) //population// mean or actual function, while the //residual// of a sample is the difference between the sample and either (1) the (observed) //sample// mean or (2) the regressed (fitted) function value. The fitted function value is the value that your statistical model says the sample "should" have.

"The distinction is most important in regression analysis, where the subtle behavior of residuals leads to the concept of studentized residuals." - [|Wikipedia]

"For a univariate distribution, the distinction between errors and residuals is just the difference between deviations from the //population// mean versus the //sample// mean."

Differences between the sample values and the unobservable population are statistcal error; between the sample and the observed sample mean, residuals. Statistical errors are independent random variables (if...); while residuals sum to zero, they are not necessarily independent. - [|Wikipedia]


 * See Also:**
 * Analysis of Residuals
 * Heteroscedasticity checked by observing residuals for non-randomness
 * Studentized Residuals in checking for outliers
 * Statistical Model Validation


 * Sources:**
 * Errors and residuals in statistics. (2009, September 24). In //Wikipedia, The Free Encyclopedia//. Retrieved 19:00, December 5, 2009, from []
 * EMSE 271, Fall 2009