The HPREG Procedure

Diagnostic Statistics

This section gathers the formulas for the statistics available in the OUTPUT statement. All the statistics available in the OUTPUT statement are conditional on the selected model and do not take into account the variability introduced by doing model selection.

The model to be fit is bold upper Y equals bold upper X bold-italic beta plus bold-italic epsilon, and the parameter estimate is denoted by bold b equals left-parenthesis bold upper X prime bold upper X bold right-parenthesis Superscript bold minus Baseline bold upper X prime bold upper Y. The subscript i denotes values for the ith observation, and the parenthetical subscript left-parenthesis i right-parenthesis means that the statistic is computed by using all observations except the ith observation.

The ALPHA= option in the PROC HPREG statement is used to set the alpha value for the confidence limit statistics.

Table 6 contains the diagnostic statistics and their formulas. Each statistic is computed for each observation.

Table 6: Formulas and Definitions for Diagnostic Statistics

MODEL Option
or Statistic Formula
PRED (ModifyingAbove bold upper Y With caret Subscript i) bold upper X Subscript i Baseline bold b
RES (r Subscript i) bold upper Y Subscript i Baseline minus ModifyingAbove bold upper Y With caret Subscript i
H (h Subscript i) bold x Subscript i Baseline left-parenthesis bold upper X prime bold upper X right-parenthesis Superscript minus Baseline bold x prime Subscript i
STDP StartRoot h Subscript i Baseline ModifyingAbove sigma With caret squared EndRoot
STDI StartRoot left-parenthesis 1 plus h Subscript i Baseline right-parenthesis ModifyingAbove sigma With caret squared EndRoot
STDR StartRoot left-parenthesis 1 minus h Subscript i Baseline right-parenthesis ModifyingAbove sigma With caret squared EndRoot
LCL ModifyingAbove upper Y With caret Subscript i Baseline minus t Subscript StartFraction alpha Over 2 EndFractionSTDI
LCLM ModifyingAbove upper Y With caret Subscript i Baseline minus t Subscript StartFraction alpha Over 2 EndFractionSTDP
UCL ModifyingAbove upper Y With caret Subscript i Baseline plus t Subscript StartFraction alpha Over 2 EndFractionSTDI
UCLM ModifyingAbove upper Y With caret Subscript i Baseline plus t Subscript StartFraction alpha Over 2 EndFractionSTDP
STUDENT StartFraction r Subscript i Baseline Over STDR Subscript i Baseline EndFraction
RSTUDENT StartFraction r Subscript i Baseline Over ModifyingAbove sigma With caret Subscript left-parenthesis i right-parenthesis Baseline StartRoot 1 minus h Subscript i Baseline EndRoot EndFraction
COOKD StartFraction 1 Over p EndFraction STUDENT squared StartFraction STDP squared Over STDR squared EndFraction
COVRATIO StartFraction det left-parenthesis ModifyingAbove sigma With caret squared Subscript left-parenthesis i right-parenthesis Baseline left-parenthesis bold x prime Subscript left-parenthesis i right-parenthesis Baseline bold x Subscript left-parenthesis i right-parenthesis Baseline right-parenthesis Superscript negative 1 Baseline Over det left-parenthesis ModifyingAbove sigma With caret squared left-parenthesis bold upper X prime bold upper X right-parenthesis Superscript negative 1 Baseline right-parenthesis EndFraction
DFFITS StartFraction left-parenthesis ModifyingAbove bold upper Y With caret Subscript i Baseline minus ModifyingAbove bold upper Y With caret Subscript left-parenthesis i right-parenthesis Baseline right-parenthesis Over left-parenthesis ModifyingAbove sigma With caret Subscript left-parenthesis i right-parenthesis Baseline StartRoot h Subscript i Baseline EndRoot right-parenthesis EndFraction
PRESS(predr Subscript i) StartFraction r Subscript i Baseline Over 1 minus h Subscript i Baseline EndFraction


Last updated: December 09, 2022