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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 ...
Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolute values (LAV), is a statistical optimality criterion and a statistical optimization technique based on minimizing the sum of absolute deviations (also sum of absolute residuals or sum of absolute errors) or the L 1 norm of such values.
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Average absolute deviation is a measure of the dispersion in a dataset that is less influenced by extreme values. It is calculated by finding the absolute difference between each data point and the mean, summing these absolute differences, and then dividing by the number of observations.
IRLS is used to find the maximum likelihood estimates of a generalized linear model, and in robust regression to find an M-estimator, as a way of mitigating the influence of outliers in an otherwise normally-distributed data set, for example, by minimizing the least absolute errors rather than the least square errors.
For absolute errors, the opposite is true: are sensitive to multiplication by constants, ... Errors and residuals in statistics; Experimental uncertainty analysis;
These deviations are called residuals when the calculations are performed over the data sample that was used for estimation (and are therefore always in reference to an estimate) and are called errors (or prediction errors) when computed out-of-sample (aka on the full set, referencing a true value rather than an estimate). The RMSD serves to ...