homoscedasticity

(noun)

A property of a set of random variables where each variable has the same finite variance.

Related Terms

  • Multicollinearity
  • covariance
  • nested model
  • iterative

Examples of homoscedasticity in the following topics:

  • Homogeneity and Heterogeneity

    • By drawing vertical strips on a scatter plot and analyzing the spread of the resulting new data sets, we are able to judge degree of homoscedasticity.
    • When various vertical strips drawn on a scatter plot, and their corresponding data sets, show a similar pattern of spread, the plot can be said to be homoscedastic.
    • In technical terms, a data set is homoscedastic if all random variables in the sequence have the same finite variance.
    • A residual plot displaying homoscedasticity should appear to resemble a horizontal football.
    • The assumption of homoscedasticity simplifies mathematical and computational treatment; however, serious violations in homoscedasticity may result in overestimating the goodness of fit.
  • Checking the Model and Assumptions

    • Constant variance (aka homoscedasticity).
    • In order to determine for heterogeneous error variance, or when a pattern of residuals violates model assumptions of homoscedasticity (error is equally variable around the 'best-fitting line' for all points of x), it is prudent to look for a "fanning effect" between residual error and predicted values.
    • Paraphrase the assumptions made by multiple regression models of linearity, homoscedasticity, normality, multicollinearity and sample size.
  • Model Assumptions

    • Constant variance (aka homoscedasticity).
    • In order to determine for heterogeneous error variance, or when a pattern of residuals violates model assumptions of homoscedasticity (error is equally variable around the 'best-fitting line' for all points of $x$), it is prudent to look for a "fanning effect" between residual error and predicted values.
  • Comparing Nested Models

    • Homoscedasticity.
    • The assumption of homoscedasticity, also known as homogeneity of variance, assumes equality of population variances.
  • Least-Squares Regression

    • It is considered optimal in the class of linear unbiased estimators when the errors are homoscedastic and serially uncorrelated.
  • ANOVA Assumptions

    • Both these analyses require homoscedasticity, as an assumption for the normal model analysis and as a consequence of randomization and additivity for the randomization-based analysis.
  • Two-Way ANOVA

  • The F-Test

    • However, when any of these tests are conducted to test the underlying assumption of homoscedasticity (i.e., homogeneity of variance), as a preliminary step to testing for mean effects, there is an increase in the experiment-wise type I error rate.
  • Further Discussion of ANOVA

    • Residuals are examined or analyzed to confirm homoscedasticity and gross normality.
  • Inferential Statistics for b and r

    • Homoscedasticity: The variance around the regression line is the same for all values of X.
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