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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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In bioinformatics, the root mean square deviation of atomic positions is the measure of the average distance between the atoms of superimposed proteins. In structure based drug design, the RMSD is a measure of the difference between a crystal conformation of the ligand conformation and a docking prediction.
In statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable (s). It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the ...
Percentage error; Mean absolute percentage error; Mean squared error; Mean squared prediction error; Minimum mean-square error; Squared deviations; Peak signal-to-noise ratio; Root mean square deviation; Errors and residuals in statistics
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:
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 ...
For the special case when both and are scalars, the above relations simplify to ^ = (¯) + ¯ = (¯) + ¯, = = (), where = is the Pearson's correlation coefficient between and .. The above two equations allows us to interpret the correlation coefficient either as normalized slope of linear regression