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Residuals can be tested for homoscedasticity using the Breusch–Pagan test, [20] which performs an auxiliary regression of the squared residuals on the independent variables. From this auxiliary regression, the explained sum of squares is retained, divided by two, and then becomes the test statistic for a chi-squared distribution with the ...
White test is a statistical test that establishes whether the variance of the errors in a regression model is constant: that is for homoskedasticity. This test, and an estimator for heteroscedasticity-consistent standard errors , were proposed by Halbert White in 1980. [ 1 ]
Homogeneity can be studied to several degrees of complexity. For example, considerations of homoscedasticity examine how much the variability of data-values changes throughout a dataset. However, questions of homogeneity apply to all aspects of the statistical distributions, including the location parameter
Partial regression plot Student's t test for testing inclusion of a single explanatory variable, or the F test for testing inclusion of a group of variables, both under the assumption that model errors are homoscedastic and have a normal distribution .
In statistics, Bartlett's test, named after Maurice Stevenson Bartlett, [1] is used to test homoscedasticity, that is, if multiple samples are from populations with equal variances. [2] Some statistical tests, such as the analysis of variance, assume that variances are equal across groups or samples, which can be checked with Bartlett's test.
It tests the null hypothesis that the population variances are equal (called homogeneity of variance or homoscedasticity). If the resulting p -value of Levene's test is less than some significance level (typically 0.05), the obtained differences in sample variances are unlikely to have occurred based on random sampling from a population with ...
Suppose that we estimate the regression model = + +, and obtain from this fitted model a set of values for ^, the residuals. Ordinary least squares constrains these so that their mean is 0 and so, given the assumption that their variance does not depend on the independent variables, an estimate of this variance can be obtained from the average of the squared values of the residuals.
For this test, a single regression model is fitted to the complete dataset. The squares of the residuals are listed according to the order of the pre-identified explanatory variable. The test statistic used to test for homogeneity is the number of peaks in this list: ie. the count of the number of cases in which a squared residual is larger ...