For broader coverage of this topic, see Studentization.
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In statistics, a studentized residual is the dimensionless ratio resulting from the division of a residual by an estimate of its standard deviation, both expressed in the same units. It is a form of a Student's t-statistic, with the estimate of error varying between points.
This is an important technique in the detection of outliers. It is among several named in honor of William Sealey Gosset, who wrote under the pseudonym "Student" (e.g., Student's distribution). Dividing a statistic by a sample standard deviation is called studentizing, in analogy with standardizing and normalizing.
and 23 Related for: Studentized residual information
In statistics, a studentizedresidual is the dimensionless ratio resulting from the division of a residual by an estimate of its standard deviation, both...
mortgage Residual (statistics) StudentizedresidualResidual time, in the theory of renewal processes Residual (numerical analysis) Minimal residual method...
called the regression errors and regression residuals and where they lead to the concept of studentizedresiduals. In econometrics, "errors" are also called...
the goodness of fit of the regression, analyzing whether the regression residuals are random, and checking whether the model's predictive performance deteriorates...
population of all possible observations, the residuals should belong to a Student's t-distribution. Studentizedresiduals are useful in making a statistical test...
Regression validation Mean and predicted response Errors and residuals Goodness of fit Studentizedresidual Gauss–Markov theorem Mathematics portal v t e...
for the point. DFFITS also equals the products of the externally Studentizedresidual ( t i ( i ) {\displaystyle t_{i(i)}} ) and the leverage factor (...
used in statistical hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions (see...
studentized means that the variable's scale was adjusted by dividing by an estimate of a population standard deviation (see also studentizedresidual)...
context of resampling and, in particular, bootstrapping. Studentized range Studentizedresidual Pivotal quantity Dodge, Y. (2003) The Oxford Dictionary...
mixed models may not, however, be the only solution. LMM's have a constant-residual variance assumption that is sometimes violated when accounting or deeply...
Regression validation Mean and predicted response Errors and residuals Goodness of fit Studentizedresidual Gauss–Markov theorem Mathematics portal v t e...
Regression validation Mean and predicted response Errors and residuals Goodness of fit Studentizedresidual Gauss–Markov theorem Mathematics portal v t e...
Regression validation Mean and predicted response Errors and residuals Goodness of fit Studentizedresidual Gauss–Markov theorem Mathematics portal v t e...
\mathbf {x} } . Ordinary least squares seeks to minimize the sum of squared residuals, which can be compactly written as ‖ A x − b ‖ 2 2 , {\displaystyle \left\|A\mathbf...
Regression validation Mean and predicted response Errors and residuals Goodness of fit Studentizedresidual Gauss–Markov theorem Mathematics portal v t e...
Gentle, James (2007). "6.8.1 Solutions that Minimize Other Norms of the Residuals". Matrix algebra. Springer Texts in Statistics. New York: Springer. doi:10...
Regression validation Mean and predicted response Errors and residuals Goodness of fit Studentizedresidual Gauss–Markov theorem Mathematics portal v t e...
Influential observation Random sample consensus Robust regression Studentizedresidual Winsorizing Grubbs, F. E. (February 1969). "Procedures for detecting...
the standard error (SE) of BP, and applying Student's t-test significance of A1 and A2 applying Student's t-distribution and the standard error SE of...
E(e_{i}|X_{i})=0} The variance of the residuals e i {\displaystyle e_{i}} is constant across observations (homoscedasticity). The residuals e i {\displaystyle e_{i}}...
also many examples of its application. Projection (linear algebra) Studentizedresiduals Effective degrees of freedom Mean and predicted response Basilevsky...
than two categories. Some examples would be: Which major will a college student choose, given their grades, stated likes and dislikes, etc.? Which blood...
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