This article shows how to simulate a data set in SAS that satisfies a least squares regression model for continuous variables. When you simulate to create "synthetic" (or "fake") data, you (the programmer) control the true parameter values, the form of the model, the sample size, and magnitude of the
How can you generate data that contains outliers in a simulation study? The contaminated normal distribution is a simple but useful distribution you can use to simulate outliers. The distribution is easy to explain and understand, and it is also easy to implement in SAS. What is a contaminated normal
In the classic textbook by Johnson and Wichern (Applied Multivariate Statistical Analysis, Third Edition, 1992, p. 164), it says: All measures of goodness-of-fit suffer the same serious drawback. When the sample size is small, only the most aberrant behaviors will be identified as lack of fit. On the other hand,
Somewhere in my past I encountered a panel of histograms for small random samples of normal data. I can't remember the source, but it might have been from John Tukey or William Cleveland. The point of the panel was to emphasize that (because of sampling variation) a small random sample
When simulating data or testing algorithms, it is useful to be able to generate patterns of missing data. This article shows how to generate random and systematic patterns of missing values. In other words, this article shows how to replace nonmissing data with missing data. Generate a random pattern of
Although statisticians often assume normally distributed errors, there are important processes for which the error distribution has a heavy tail. A well-known heavy-tailed distribution is the t distribution, but the t distribution is unsuitable for some applications because it does not have finite moments (means, variance,...) for small parameter values.
The article uses the SAS DATA step and Base SAS procedures to estimate the coverage probability of the confidence interval for the mean of normally distributed data. This discussion is based on Section 5.2 (p. 74–77) of Simulating Data with SAS. What is a confidence interval? Recall that a confidence
I saw an interesting mathematical result in Wired magazine. The original article was about mathematical research into prime numbers, but the article included the following tantalizing fact: If Alice tosses a [fair]coin until she sees a head followed by a tail, and Bob tosses a coin until he sees two
Last week I showed how to generate random points uniformly inside a 2-d circular region. That article showed that the distance of a point to the circle's center cannot be distributed uniformly. Instead, you should use the square root of a uniform variate to generate 2-D distances to the origin.
It is easy to generate random points that are uniformly distributed inside a rectangle. You simply generate independent random uniform values for each coordinate. However, nonrectangular regions are more complicated. An instructive example is to simulate points uniformly inside the ball with a given radius. The two-dimensional case is to
