# The DO Loop

Statistical programming in SAS with an emphasis on SAS/IML programsThe skewness of a distribution indicates whether a distribution is symmetric or not. The Wikipedia article about skewness discusses two common definitions for the sample skewness, including the definition used by SAS. In the middle of the article, you will discover the following sentence: In general, the [estimators]are both biased

A fundamental principle of data analysis is that a statistic is an estimate of a parameter for the population. A statistic is calculated from a random sample. This leads to uncertainty in the estimate: a different random sample would have produced a different statistic. To quantify the uncertainty, SAS procedures

The triangulation theorem for polygons says that every simple polygon can be triangulated. In fact, if the polygon has V vertices, you can decompose it into V-2 non-overlapping triangles. In this article, a "polygon" always means a simple polygon. Also, a "random point" means one that is drawn at random

How can you efficiently generate N random uniform points in a triangular region of the plane? There is a very cool algorithm (which I call the reflection method) that makes the process easy. I no longer remember where I saw this algorithm, but it is different from the "weighted average"

A previous article discusses the confidence band for the mean predicted value in a regression model. The article shows a "graded confidence band plot," which I saw in Claus O. Wilke's online book, Fundamentals of Data Visualization (Section 16.3). It communicates uncertainty in the predictions. A graded band plot is

You've probably seen many graphs that are similar to the one at the right. This plot shows a regression line overlaid on a scatter plot of some data. Given a value for the independent variable (x), the regression line gives the best prediction for the mean of the response variable