homoscedasticity

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.

• Regression Analysis for Forecast Improvement

  • The variance of the error is constant across observations (homoscedasticity).

• Further Discussion of ANOVA

  • Residuals are examined or analyzed to confirm homoscedasticity and gross normality.