Construction of Q-Q and P-P Plots

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:

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

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

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