For linear regression models, there is a class of statistics that I call deletion diagnostics or leave-one-out statistics. These observation-wise statistics address the question, "If I delete the i_th observation and refit the model, what happens to the statistics for the model?" For example: The PRESS statistic is similar to

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Recoding variables can be tedious, but it is often a necessary part of data analysis. Almost every SAS programmer has written a DATA step that uses IF-THEN/ELSE logic or the SELECT-WHEN statements to recode variables. Although creating a new variable is effective, it is also inefficient because you have to

A family of curves is generated by an equation that has one or more parameters. To visualize the family, you might want to display a graph that overlays four of five curves that have different parameter values, as shown to the right. The graph shows members of a family of

Statistical programmers and analysts often use two kinds of rectangular data sets, popularly known as wide data and long data. Some analytical procedures require that the data be in wide form; others require long form. (The "long format" is sometimes called "narrow" or "tall" data.) Fortunately, the statistical graphics procedures

Knowing how to visualize a regression model is a valuable skill. A good visualization can help you to interpret a model and understand how its predictions depend on explanatory factors in the model. Visualization is especially important in understanding interactions between factors. Recently I read about work by Jacob A.

Modern statistical software provides many options for computing robust statistics. For example, SAS can compute robust univariate statistics by using PROC UNIVARIATE, robust linear regression by using PROC ROBUSTREG, and robust multivariate statistics such as robust principal component analysis. Much of the research on robust regression was conducted in the

The eigenvalues of a matrix are not easy to compute. It is remarkable, therefore, that with relatively simple mental arithmetic, you can obtain bounds for the eigenvalues of a matrix of any size. The bounds are provided by using a marvelous mathematical result known as Gershgorin's Disc Theorem. For certain

Recently I wrote about how to compute the Kolmogorov D statistic, which is used to determine whether a sample has a particular distribution. One of the beautiful facts about modern computational statistics is that if you can compute a statistic, you can use simulation to estimate the sampling distribution of

Have you ever run a statistical test to determine whether data are normally distributed? If so, you have probably used Kolmogorov's D statistic. Kolmogorov's D statistic (also called the Kolmogorov-Smirnov statistic) enables you to test whether the empirical distribution of data is different than a reference distribution. The reference distribution

In SAS/IML programs, a common task is to write values in a matrix to a SAS data set. For some programs, the values you want to write are in a matrix and you use the CREATE FROM/APPEND FROM syntax to create the data set, as follows: proc iml; X =