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 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.
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr or 3 σ, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean ...
In statistics, DFFIT and DFFITS ("difference in fit(s)") are diagnostics meant to show how influential a point is in a linear regression, first proposed in 1980. [ 1 ] DFFIT is the change in the predicted value for a point, obtained when that point is left out of the regression:
In another usage in statistics, normalization refers to the creation of shifted and scaled versions of statistics, where the intention is that these normalized values allow the comparison of corresponding normalized values for different datasets in a way that eliminates the effects of certain gross influences, as in an anomaly time series. Some ...
In statistics, Studentization, named after William Sealy Gosset, who wrote under the pseudonym Student, is the adjustment consisting of division of a first-degree statistic derived from a sample, by a sample-based estimate of a population standard deviation.
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 ...
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.