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The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
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Standard method like Gauss elimination can be used to solve the matrix equation for .A more numerically stable method is provided by QR decomposition method. Since the matrix is a symmetric positive definite matrix, can be solved twice as fast with the Cholesky decomposition, while for large sparse systems conjugate gradient method is more effective.
It is remarkable that the sum of squares of the residuals and the sample mean can be shown to be independent of each other, using, e.g. Basu's theorem.That fact, and the normal and chi-squared distributions given above form the basis of calculations involving the t-statistic:
The result of fitting a set of data points with a quadratic function Conic fitting a set of points using least-squares approximation. The method of least squares is a parameter estimation method in regression analysis based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the ...
Mean square. In mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable. [1] It may also be defined as the arithmetic mean of the squares of the deviations between a set of numbers and a reference value (e.g., may be a mean or an assumed mean of the ...
Estimator. In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. [1] For example, the sample mean is a commonly used estimator of the population mean.
Mean squared error; Mean absolute error; Mean absolute percentage error; Root-mean-square deviation; Test set; Fraction of variance unexplained References. This page ...