residual sum of squares

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  • 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.