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On the other hand, the internally studentized residuals are in the range , where ν = n − m is the number of residual degrees of freedom. If t i represents the internally studentized residual, and again assuming that the errors are independent identically distributed Gaussian variables, then: [2]
In regression analysis, the distinction between errors and residuals is subtle and important, and leads to the concept of studentized residuals. Given an unobservable function that relates the independent variable to the dependent variable – say, a line – the deviations of the dependent variable observations from this function are the ...
DFFITS also equals the products of the externally Studentized residual (()) and the leverage factor (/ )): [2] = Thus, for low leverage points, DFFITS is expected to ...
where is the index of independent variable, is the index of observation and [] are the residuals from regressing against the remaining independent variables. Note that the partial leverage is the leverage of the i t h {\displaystyle {i}^{th}} point in the partial regression plot for the j t h {\displaystyle {j}^{th}} variable.
Given a sample set, one can compute the studentized residuals and compare these to the expected frequency: points that fall more than 3 standard deviations from the norm are likely outliers (unless the sample size is significantly large, by which point one expects a sample this extreme), and if there are many points more than 3 standard ...
The studentized range distribution function arises from re-scaling the sample range R by the sample standard deviation s, since the studentized range is customarily tabulated in units of standard deviations, with the variable q = R ⁄ s. The derivation begins with a perfectly general form of the distribution function of the sample range, which ...
Residuals have emerged as a key sticking point in the current pair of Hollywood strikes. But what are they, and how do they work?
In statistics, the studentized range, denoted q, is the difference between the largest and smallest data in a sample normalized by the sample standard deviation. It is named after William Sealy Gosset (who wrote under the pseudonym " Student "), and was introduced by him in 1927. [ 1 ]