What is an efficient way to evaluate a multivariate quadratic polynomial in p variables? The answer is to use matrix computations! A multivariate quadratic polynomial can be written as the sum of a purely quadratic term (degree 2), a purely linear term (degree 1), and a constant term (degree 0).
In a linear regression model, the predicted values are on the same scale as the response variable. You can plot the observed and predicted responses to visualize how well the model agrees with the data, However, for generalized linear models, there is a potential source of confusion. Recall that a
My colleague, Mike Drutar, recently showed how to create a "strip plot" that shows the distribution of temperatures for each calendar month at a particular location. Mike created the strip plot in SAS Visual Analytics by using a point-and-click interface. This article shows how to create a similar graph by
Biplots are two-dimensional plots that help to visualize relationships in high dimensional data. A previous article discusses how to interpret biplots for continuous variables. The biplot projects observations and variables onto the span of the first two principal components. The observations are plotted as markers; the variables are plotted as
In grade school, students learn how to round numbers to the nearest integer. In later years, students learn variations, such as rounding up and rounding down by using the greatest integer function and least integer function, respectively. My sister, who is an engineer, learned a rounding method that rounds half-integers
Principal component analysis (PCA) is an important tool for understanding relationships in continuous multivariate data. When the first two principal components (PCs) explain a significant portion of the variance in the data, you can visualize the data by projecting the observations onto the span of the first two PCs. In
Understanding multivariate statistics requires mastery of high-dimensional geometry and concepts in linear algebra such as matrix factorizations, basis vectors, and linear subspaces. Graphs can help to summarize what a multivariate analysis is telling us about the data. This article looks at four graphs that are often part of a principal
Every year at Halloween, I post an article that shows a SAS trick that is a real treat. This article shows how to use the INTNX function to find dates that are related to a specified date. The INTNX function is a sweet treat, indeed. I previously wrote an article
A common task in SAS programming is to specify a list of variables that satisfy some pattern. You can specify lists for the KEEP= or DROP= data set options, and you can use lists of variables on many SAS statements such as the VAR and MODEL statements. Although SAS has
In response to a recent article about how to compute the cosine similarity of observations, a reader asked whether it is practical (or even possible) to perform these types of computations on data sets that have many thousands of observations. The problem is that the cosine similarity matrix is an
