Suppose that you compute the coefficients of a polynomial regression by using a certain set of polynomial effects and that I compute coefficients for a different set of polynomial effects. Can I use my coefficients to find your coefficients? The answer is yes, and this article explains how. Standard Polynomial

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I just got back from a great conference in San Diego at the 2010 meeting of the Western Users of SAS Software (WUSS) where I gave several presentations on PROC IML and SAS/IML Studio. If you didn't make it to San Diego, you can still read my 2010 paper on

Sampling with replacement is a useful technique for simulations and for resampling from data. Over at the SAS/IML Discussion Forum, there was a recent question about how to use SAS/IML software to sample with replacement from a set of events. I have previously blogged about efficient sampling, but this topic

This post is about an estimate, but not the statistical kind. It also provides yet another example in which the arithmetic mean is not the appropriate measure for a computation. First, some background. Last week I read a blog post by Peter Flom that reminded me that it is wrong

Today I'm in San Diego at the 2010 meeting of the Western Users of SAS Software (WUSS). I am giving several presentations on SAS/IML and SAS/IML Studio: A tutorial workshop on SAS/IML Studio for the SAS/STAT User. The material in this tutorial is a small sampling of Chapters 4–11 of

In this blog and in the book Statistical Programming with SAS/IML Software, I present tips and techniques for writing efficient SAS/IML programs for data analysis, simulation, matrix computations, and other topics of interest to statistical programmers. When I was writing my book, one of the reviewers commented that he wasn’t

How can you change a programming trick into a programming treat? Try this algorithm: If you develop a clever snippet of code, squirrel it away. This snippet is a "trick." If you use the trick a second time, copy and modify the code. The trick has become a "treat." If

The SAS/IML language provides the QUAD function for evaluating one-dimensional integrals. You can also use the QUAD function to compute a double integral as an iterated integral. A One-Dimensional Integration Suppose you want to evaluate the following integral: To evaluate this integral in the SAS/IML language: Define a function module

I was recently asked how to create a tridiagonal matrix in SAS/IML software. For example, how can you easily specify the following symmetric tridiagonal matrix without typing all of the zeros? proc iml; m = {1 6 0 0 0, 6 2 7 0 0, 0 7 3 8 0,

In a previous post, I discussed how to use the LOC function to eliminate loops over observations. Dale McLerran chimed in to remind me that another way to improve efficiency is to use subscript reduction operators. I ended my previous post by issuing a challenge: can you write an efficient

Today is World Statistics Day, an event set up to "highlight the role of official statistics and the many achievements of the national statistical system." I want to commemorate World Statistics Day by celebrating the role of the US government in data collection and dissemination. Data analysis begins with data.

The IMLPlus language has been available to SAS customers since 2002, but there are still many people who have never heard of it. What is IMLPlus? The documentation SAS/IML Studio for SAS/STAT Users says this about IMLPlus: The programming language in SAS/IML Studio, which is called IMLPlus, is an enhanced

Have you ever been stuck while trying to solve a scrambled-word puzzle? You stare and stare at the letters, but no word reveals itself? You are stumped. Stymied. I hope you didn't get stumped on the word puzzle I posted as an anniversary present for my wife. She breezed through

A few people asked me to explain the significance of the cartoon in the scrambled-word puzzle that I posted as an anniversary present for my wife. The cartoon refers to a famous experiment devised by Sir Ronald A. Fisher.

In a previous post, I discussed how to generate random permutations of N elements. But what if you want to systematically iterate through a list of ALL permutations of N elements? In the SAS DATA step you can use the ALLPERM subroutine in the SAS DATA step. For example, the

Today's post is a puzzle. Why? Well, my wife loves solving word puzzles, and today is our wedding anniversary. Last year, I bought her a Jumble® book. This year, I've created a one-of-a-kind scrambled word puzzle just for her. (But you can play, too!) I created this puzzle by using

Sometimes it is convenient to reshape the data in a matrix. Suppose you have a 1 x 12 matrix. This same data can fit into several matrices with different dimensions: a 2 x 6 matrix, a 3 x 4 matrix, a 4 x 3 matrix, and so on. The SHAPE function enables you to specify the number of

My previous post on creating a random permutation started me thinking about word games. My wife loves to solve the daily Jumble® puzzle that runs in our local paper. The puzzle displays a string of letters like MLYBOS, and you attempt to unscramble the letters to make an ordinary word.

I recently read a paper that described a SAS macro to carry out a permutation test. The permutations were generated by PROC IML. (In fact, an internet search for the terms "SAS/IML" and "permutation test" gives dozens of papers in recent years.) The PROC IML code was not as efficient

A previous post described a simple algorithm for generating Fibonacci numbers. It was noted that the ratio between adjacent terms in the Fibonacci sequence approaches the "Golden Ratio," 1.61803399.... This post explains why. In a discussion with my fellow blogger, David Smith, I made the comment "any two numbers (at

Often, the first step of a SAS/IML program is to use the USE, READ, and CLOSE statements to read data from a SAS data set into a vector or matrix. There are several ways to read data: Read variables into vectors of the same name. Read one or more variables

In a previous blog post about hurricanes, I created a histogram of the occurrence of tropical cyclones in the Atlantic basin during the years 1988–2003. That histogram shows that the peak of hurricane activity occurs in the second week of September, but also that a majority of tropical storms occur

This morning I read an interesting post about the design of the new Twitter Web page. The post included some R code to generate the ratio between adjacent terms in the Fibonacci seqence. The ratio converges to the "Golden Ratio": 1.61803399.... I'm sure that many R gurus will post simpler

The SAS/IML language is a vector language, so statements that operate on a few long vectors run much faster than equivalent statements that involve many scalar quantities. For example, in a previous post, I asserted that the LOC function is much faster than writing a loop, for finding observations that

The Junk Chart blog discusses a potential problem that can arise in grouped bar charts when the two groups have vastly different ranges. One possible solution (which is discussed at the Junk Chart sister blog, Numbers Rule Your World) is to present the data back-back in what is sometimes called

The SAS/IML run-time library contains hundreds of functions and subroutines that you can call to perform statistical analysis. There are also many functions in Base SAS software that you can call from SAS/IML programs. However, one day you might need to compute some quantity for which there is no prewritten

Visualizing the distribution of data is a primary task of data analysis. With all the hurricane activity in the Atlantic this year, I’ve been thinking about ways to visualize the historical distribution of hurricane activity. USA Today on Friday, August 13, 2010, announced that "the heart of hurricane season is

Recently, SAS Global Forum announced the call for papers for the 2011 conference to be held at Caesars Palace in Las Vegas. Since the conference is in Las Vegas, I’ve been thinking a lot about games of chance: blackjack, craps, roulette, and the like. You can analyze these games by

My mother taught me to put things away when I'm finished using them. She doesn't use a computer, but if she did, I know that she'd approve of this tip from my book: Tip: Always close your files and data sets when you are finished reading or writing them. In

Today is the birthday of Bernhard Riemann, a German mathematician who made fundamental contributions to the fields of geometry, analysis, and number theory. Riemann is definitely on my list of the greatest mathematicians of all time, and his conjecture about the distribution of prime numbers is one of the great