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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 model, such as a linear ...
Models that are over-parameterised (over-fitted) would tend to give small residuals for observations included in the model-fitting but large residuals for observations that are excluded. The PRESS statistic has been extensively used in lazy learning and locally linear learning to speed-up the assessment and the selection of the neighbourhood size.
If one runs a regression on some data, then the deviations of the dependent variable observations from the fitted function are the residuals. If the linear model is applicable, a scatterplot of residuals plotted against the independent variable should be random about zero with no trend to the residuals. [5]
Residual plots plot the difference between the actual data and the model's predictions: correlations in the residual plots may indicate a flaw in the model. Cross validation is a method of model validation that iteratively refits the model, each time leaving out just a small sample and comparing whether the samples left out are predicted by the ...
This makes the fitted model likely to pass close to a high leverage observation. [1] Hence high-leverage points have the potential to cause large changes in the parameter estimates when they are deleted i.e., to be influential points. Although an influential point will typically have high leverage, a high leverage point is not necessarily an ...
An illustrative plot of a fit to data (green curve in top panel, data in red) plus a plot of residuals: red points in bottom plot. Dashed curve in bottom panel is a straight line fit to the residuals. If the functional form is correct then there should be little or no trend to the residuals - as seen here.
The residuals from the least squares linear fit to this plot are identical to the residuals from the least squares fit of the original model (Y against all the independent variables including Xi). The influences of individual data values on the estimation of a coefficient are easy to see in this plot.
The variable on the x axis is just the observation number as it appeared in the data set. Rousseeuw and Leroy (1986) contains many such plots. The horizontal reference lines are at 2 and −2, so that any observed scaled residual beyond these boundaries can be considered to be an outlier.