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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.
For statistical inference, sums-of-squares can still be formed: the model sum-of-squares is ‖ ‖; the residual sum-of-squares is ‖ ‖. However, because H does not correspond to an ordinary least-squares fit (i.e. is not an orthogonal projection), these sums-of-squares no longer have (scaled, non-central) chi-squared distributions, and ...
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 ...
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 ...
t. e. Okun's law in macroeconomics states that in an economy the GDP growth should depend linearly on the changes in the unemployment rate. Here the ordinary least squares method is used to construct the regression line describing this law. In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the ...
The residue of a differential form can be expressed in terms of traces of endomorphisms on the fraction field of the completed local rings ^, which leads to a conceptual proof of the formula. A more recent exposition along similar lines, using more explicitly the notion of Tate vector spaces , is given by Clausen (2009) .
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 ...