InfoIn statistics, the residual sum of squares (RSS) is the sum of squares of residuals.more...It is also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE). It is a measure of the discrepancy between the data and an estimation model. A small RSS indicates a tight fit of the model to the data.

Hence the residual sum of squares has been completely decomposed into two components.Consider fitting a line with one predictor variable.…

Mallows's C p addresses the issue of overfitting, in which model selection statistics such as the residual sum of squares always get smaller as more variables are added to a model.Thus, if we aim to select the model giving the smallest residual sum of squares, the model including all variables would always be selected.…

A small RSS indicates a tight fit of the model to the data.In general, total sum of squares = explained sum of squares + residual sum of squares.For a proof of this in the multivariate ordinary least squares (OLS) case, see partitioning in the general OLS model.…

In general: total sum of squares = explained sum of squares + residual sum of squares.

From all these auxiliary regressions, one selects the one that yields the smallest residual sum of squares.

This is often used for deciding how many predictor variables to use in regression.Without cross-validation, adding predictors always reduces the residual sum of squares (or possibly leaves it unchanged).In contrast, the cross-validated mean-square error will tend to decrease if valuable predictors are added, but increase if worthless predictors are added.…

To have a lack-of-fit sum of squares that differs from the residual sum of squares, one must observe more than one y-value for each of one or more of the x-values.

Note that the residual sum of squares can be further partitioned as the lack-of-fit sum of squares plus the sum of squares due to pure error.

For wide classes of linear models, the total sum of squares equals the explained sum of squares plus the residual sum of squares.For a proof of this in the multivariate OLS case, see partitioning in the general OLS model.…

Mallows's C p has been shown to be equivalent to Akaike Information Criterion in the special case of Gaussian linear regression.Mallows's C p addresses the issue of overfitting, in which model selection statistics such as the residual sum of squares always get smaller as more variables are added to a model.Thus, if we aim to select the model giving the smallest residual sum of squares, the model including all variables would always be selected.…

At each stage in the process, after a new variable is added, a test is made to check if some variables can be deleted without appreciably increasing the residual sum of squares (RSS).The procedure terminates when the measure is (locally) maximized, or when the available improvement falls below some critical value.…

Such new data is usually not available at the time of model building, so instead we use GCV to estimate what performance would be on new data.The raw residual sum-of-squares (RSS) on the training data is inadequate for comparing models, because the RSS always increases as MARS terms are dropped.…

In statistics, the predicted residual sum of squares (PRESS) statistic is a form of cross-validation used in regression analysis to provide a summary measure of the fit of a model to a sample of observations that were not themselves used to estimate the model.It is calculated as the sums of squares of the prediction residuals for those observations.…