The REG Procedure

Construction of Q-Q and P-P Plots

If a normal probability-probability or quantile-quantile plot for the variable x is requested, the n nonmissing values of x are first ordered from smallest to largest:

x Subscript left-parenthesis 1 right-parenthesis Baseline less-than-or-equal-to x Subscript left-parenthesis 2 right-parenthesis Baseline less-than-or-equal-to midline-horizontal-ellipsis less-than-or-equal-to x Subscript left-parenthesis n right-parenthesis

If a Q-Q plot is requested (with a PLOT statement of the form PLOT yvariable*NQQ.), the ith-ordered value x Subscript left-parenthesis i right-parenthesis is represented by a point with y-coordinate x Subscript left-parenthesis i right-parenthesis and x-coordinate normal upper Phi Superscript negative 1 Baseline left-parenthesis StartFraction i minus 0.375 Over n plus 0.25 EndFraction right-parenthesis, where normal upper Phi left-parenthesis dot right-parenthesis is the standard normal distribution.

If a P-P plot is requested (with a PLOT statement of the form PLOT yvariable*NPP.), the ith-ordered value x Subscript left-parenthesis i right-parenthesis is represented by a point with y-coordinate StartFraction i Over n EndFraction and x-coordinate normal upper Phi left-parenthesis StartFraction x Subscript left-parenthesis i right-parenthesis Baseline minus mu Over sigma EndFraction right-parenthesis, where mu is the mean of the nonmissing x-values and sigma is the standard deviation. If an x-value has multiplicity k (that is, x Subscript left-parenthesis i right-parenthesis Baseline equals midline-horizontal-ellipsis equals x Subscript left-parenthesis i plus k minus 1 right-parenthesis), then only the point left-parenthesis normal upper Phi left-parenthesis StartFraction x Subscript left-parenthesis i right-parenthesis Baseline minus mu Over sigma EndFraction right-parenthesis comma StartFraction i plus k minus 1 Over n EndFraction right-parenthesis is displayed.

Last updated: December 09, 2022