Homoscedasticity

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 complement is called heteroscedasticity. The assumption of homoscedasticity simplifies mathematical and computational treatment and may lead to good 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. Assuming homoscedasticity assumes that variance is fixed throughout a distribution.

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.

(Note: There seems to be no standard agreed-upon spelling for these words; they are sometimes spelled homo- or heteroskedastic or (incorrectly) -schedastic, depending on location and personal taste. In Britain, for example, it is sometimes spelled (spelt) homoskedastic, which is an exception to the rule that American spellings are usually more faithful to the etymologies than British spellings.)

Testing
You can test if the residuals are homoscedastic using the Breusch-Pagan test, which regresses square residuals to Independent variables. The BP test is sensitive to normality so for general purpose use the Koenkar-Basset or generalized Breusch-Pagan test statistic. For testing for groupwise heteroscedasticity, you need to use the Goldfeld-Quandt Test.