Search results
Results From The WOW.Com Content Network
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 ...
However, a question arises as to which residuals to resample. Raw residuals are one option; another is studentized residuals (in linear regression). Although there are arguments in favor of using studentized residuals; in practice, it often makes little difference, and it is easy to compare the results of both schemes.
In statistics, Grubbs's test or the Grubbs test (named after Frank E. Grubbs, who published the test in 1950 [1]), also known as the maximum normalized residual test or extreme studentized deviate test, is a test used to detect outliers in a univariate data set assumed to come from a normally distributed population.
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 ...
Consider a set of data points, (,), (,), …, (,), and a curve (model function) ^ = (,), that in addition to the variable also depends on parameters, = (,, …,), with . It is desired to find the vector of parameters such that the curve fits best the given data in the least squares sense, that is, the sum of squares = = is minimized, where the residuals (in-sample prediction errors) r i are ...
Fitting of a noisy curve by an asymmetrical peak model () with parameters by mimimizing the sum of squared residuals () = at grid points , using the Gauss–Newton algorithm. Top: Raw data and model. Bottom: Evolution of the normalised sum of the squares of the errors.