# User Contributed Dictionary

### Noun

homoscedasticity (or homoskedasticity)### Antonyms

### Related terms

# Extensive Definition

In statistics, a sequence or a vector of
random
variables is homoscedastic if all random variables in the
sequence or vector have the same finite
variance. This is also
known as homogeneity of variance. The complementary notion is
called heteroscedasticity.
The alternative spelling homo- or heteroskedasticity is equally
correct and is also used frequently.

As described by Joshua
Isaac Walters, "the assumption of homoscedasticity simplifies
mathematical and computational treatment and usually leads to
adequate estimation results (e.g. in data mining)
even if the assumption is not true." Serious violations in
homoscedasticity (assuming a distribution of data is homoscedastic
when in actuality it is heteroscedastic) result in underemphasizing
the
Pearson coefficient.

In a scatterplot of data,
homoscedasticity looks like an oval (most x values are concentrated
around the mean of y, with fewer and fewer x values as y becomes
more extreme in either direction). If a scatterplot looks like any
geometric shape other than an oval, the rules of homoscedasticity
may have been violated.

## Assumptions of a regression model

In simple linear regression analysis, one assumption of the fitted model is that the standard deviation of the error terms are constant and does not depend on the x-value. Consequently, each probability distributions for each y (response variable) has the same standard deviation regardless of the x-value (predictor). In short, this assumption is homoskedasticity.## Testing

Residuals can be tested for homoscedasticity
using the Breusch-Pagan
test, which regresses square residuals to independent
variables. The BP test is sensitive to normality so for general
purpose the Koenkar-Basset or generalized Breusch-Pagan test
statistic is used. For testing for groupwise heteroscedasticity,
the Goldfeld-Quandt test is needed.

## Homoscedastic distributions

Two or more normal
distributions, N(\mu_i,\Sigma_i), are homoscedastic if they
share a common covariance
(or correlation)
matrix, \Sigma_i = \Sigma_j,\ \forall i,j. Homoscedastic
distributions are especially useful to derive statistical pattern
recognition and machine
learning algorithms. One popular example is Fisher's
linear discriminant analysis.

homoscedasticity in German: Homoskedastizität
und Heteroskedastizität

homoscedasticity in Spanish:
Homocedasticidad

homoscedasticity in Hebrew: הומוסקדסטיות

homoscedasticity in Hungarian:
Homoszkedaszticitás

homoscedasticity in Italian:
Omoschedasticità

homoscedasticity in Dutch:
Homoscedasticiteit

homoscedasticity in Polish:
Homoskedastyczność

homoscedasticity in Sundanese:
Homoscedasticity