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Residual sum of squares. In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared estimate of errors (SSE), is the sum of the squares of residuals (deviations predicted from actual empirical values of data). It is a measure of the discrepancy between the data and an estimation ...
It is calculated as the sum of squares of the prediction residuals for those observations. [ 1 ] [ 2 ] [ 3 ] Specifically, the PRESS statistic is an exhaustive form of cross-validation, as it tests all the possible ways that the original data can be divided into a training and a validation set.
If that sum of squares is divided by n, the number of observations, the result is the mean of the squared residuals. Since this is a biased estimate of the variance of the unobserved errors, the bias is removed by dividing the sum of the squared residuals by df = n − p − 1, instead of n , where df is the number of degrees of freedom ( n ...
The sum of squares of residuals, also called the residual sum of squares: The total sum of squares (proportional to the variance of the data): The most general definition of the coefficient of determination is. In the best case, the modeled values exactly match the observed values, which results in and R2 = 1.
Reduced chi-squared statistic. In statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating [1] and variance of unit weight in the context of weighted least squares. [2][3] Its square root is called regression standard error, [4 ...
The explained sum of squares, defined as the sum of squared deviations of the predicted values from the observed mean of y, is. Using in this, and simplifying to obtain , gives the result that TSS = ESS + RSS if and only if . The left side of this is times the sum of the elements of y, and the right side is times the sum of the elements of , so ...
In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing. It is a generalization of the idea of using the sum of squares of residuals (SSR) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood. It plays an important role in exponential ...
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least squares include inverting the ...