## residual sum of squares

13 examples (0.03 sec)
• Info In statistics, the residual sum of squares (RSS) is the sum of squares of residuals. more...
• Hence the residual sum of squares has been completely decomposed into two components.
• Thus, if we aim to select the model giving the smallest residual sum of squares, the model including all variables would always be selected.
• In general, total sum of squares = explained sum of squares + residual sum of squares.
• 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.
• Without cross-validation, adding predictors always reduces the residual sum of squares (or possibly leaves it unchanged).
• 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.
• 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.
• 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 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.