heteroscedasticity

Examples of heteroscedasticity in the following topics:

• Homogeneity and Heterogeneity

  • A classic example of heteroscedasticity is that of income versus expenditure on meals.
  • When a scatter plot is heteroscedastic, the prediction errors differ as we go along the regression line.
  • In technical terms, a data set is heteroscedastic if there are sub-populations that have different variabilities from others.
  • The possible existence of heteroscedasticity is a major concern in the application of regression analysis, including the analysis of variance, because the presence of heteroscedasticity can invalidate statistical tests of significance that assume that the modelling errors are uncorrelated and normally distributed and that their variances do not vary with the effects being modelled.

• Checking the Model and Assumptions

  • ., the errors are heteroscedastic) if the response variables can vary over a wide scale.
  • Heteroscedasticity will result in the averaging over of distinguishable variances around the points to yield a single variance (inaccurately representing all the variances of the line).

• Model Assumptions

  • In practice, this assumption is invalid (i.e. the errors are heteroscedastic) if the response variables can vary over a wide scale.
  • Heteroscedasticity will result in the averaging over of distinguishable variances around the points to get a single variance that is inaccurately representing all the variances of the line.

• Plotting the Residuals

  • We see heteroscedasticity in a resitual plot as the difference in the scatter of the residuals for different ranges of values of the independent variable.
  • The existence of heteroscedasticity is a major concern in regression analysis because it can invalidate statistical tests of significance that assume that the modelling errors are uncorrelated and normally distributed and that their variances do not vary with the effects being modelled.

• Inferential Statistics for b and r