Given a rectangular grid with unit spacing, what is the expected distance between two random vertices, where distance is measured in the L1 metric? (Here "random" means "uniformly at random.") I recently needed this answer for some small grids, such as the one to the right, which is a 7 x 6
The SGPLOT procedure in SAS makes it easy to create graphs that overlay various groups in the data. Many statements support the GROUP= option, which specifies that the graph should overlay group information. For example, you can create side-by-side bar charts and box plots, and you can overlay multiple scatter
This article shows how to score (evaluate) a quantile regression model on new data. SAS supports several procedures for quantile regression, including the QUANTREG, QUANTSELECT, and HPQUANTSELECT procedures. The first two procedures do not support any of the modern methods for scoring regression models, so you must use the "missing
Which president of the United States is ranked the greatest by presidential historians? This article visualizes the results of the 2018 Presidential Greatness Survey, which was created and administered by B. Rottinghaus and J. Vaughn. They analyzed 166 responses from experts in political science who ranked the 44 US presidents
If you use PROC SGPLOT to create ODS graphics, "ATTRS" are everywhere. ATTRS is an abbreviation of "attributes." Most options that change the attributes of a graphical element end with the ATTRS suffix. For example, the MARKERATTRS option modifies attributes of markers, the LINEATTRS option modifies attributes of lines, and
A previous article showed how to use a calibration plot to visualize the goodness-of-fit for a logistic regression model. It is common to overlay a scatter plot of the binary response on a predicted probability plot (below, left) and on a calibration plot (below, right): The SAS program that creates
This article shows how to construct a butterfly plot in SAS. A butterfly plot (also called a butterfly chart) is a comparative bar chart or histogram that displays the distribution of a variable for two subpopulations. A butterfly plot for the cholesterol readings of 5,057 patients in a medical study
In my article about how to construct calibration plots for logistic regression models in SAS, I mentioned that there are several popular variations of the calibration plot. The previous article showed how to construct a loess-based calibration curve. Austin and Steyerberg (2013) recommend the loess-based curve on the basis of
A logistic regression model is a way to predict the probability of a binary response based on values of explanatory variables. It is important to be able to assess the accuracy of a predictive model. This article shows how to construct a calibration plot in SAS. A calibration plot is
Order matters. When you create a graph that has a categorical axis (such as a bar chart), it is important to consider the order in which the categories appear. Most software defaults to alphabetical order, which typically gives no insight into how the categories relate to each other. Alphabetical order
