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:

$x_{(1)} \le x_{(2)} \le \cdots \le x_{(n)}$

If a Q-Q plot is requested (with a PLOT statement of the form PLOT yvariable*NQQ.), the ith-ordered value $x_{(i)}$ is represented by a point with y-coordinate $x_{(i)}$ and x-coordinate $\Phi ^{-1}\left(\frac{i-0.375}{n+0.25}\right)$ , where $\Phi (\cdot )$ 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 $x_{(i)}$ is represented by a point with y-coordinate $\frac{i}{n}$ and x-coordinate $\Phi \left(\frac{x_{(i)}-\mu }{\sigma }\right)$ , 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, $x_{(i)}=\cdots =x_{(i+k-1)}$ ), then only the point $\left(\Phi \left(\frac{x_{(i)}-\mu }{\sigma }\right), \frac{i+k-1}{n}\right)$ is displayed.