They have the same distribution, but are not independent due to constraints on the residuals having to sum to 0 and to have them be orthogonal to the design matrix. The issue is the difference between errors and residuals in statistics, particularly the behavior of residuals in regressions.Ĭonsider the simple linear regression model The key reason for studentizing is that, in regression analysis of a multivariate distribution, the variances of the residuals at different input variable values may differ, even if the variances of the errors at these different input variable values are equal. See also: Errors and residuals in statistics ( Learn how and when to remove this template message) ( February 2014) ( Learn how and when to remove this template message) Please help to ensure that disputed statements are reliably sourced. Relevant discussion may be found on the talk page. This article's factual accuracy is disputed.
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