A recent issue of Astronomy magazine mentioned Kepler's third law of planetary motion, which states "the square of a planet's orbital period is proportional to the cube of its average distance from the Sun" (Astronomy, Dec 2016, p. 17). The article included a graph (shown at the right) that shows

## Tag: **Data Analysis**

Who was the oldest person elected president of the United States? How about the youngest? Who was the oldest when he left office? Let's look at some data. Wikipedia has a page that presents a table of the presidents of the US by age. It lists the dates for which

Occasionally on a discussion forum, a statistical programmer will ask a question like the following: I am trying to fit a parametric distribution to my data. The sample has a long tail, so I have tried the lognormal, Weibull, and gamma distributions, but nothing seems to fit. Please help!! In

Every year near Halloween I write an article in which I demonstrate a simple programming trick that is a real treat to use. This year's trick (which features the CMISS function and the crossproducts matrix in SAS/IML) enables you to count the number of observations that are missing for pairs

A previous post discusses how the loess regression algorithm is implemented in SAS. The LOESS procedure in SAS/STAT software provides the data analyst with options to control the loess algorithm and fit nonparametric smoothing curves through points in a scatter plot. Although PROC LOESS satisfies 99.99% of SAS users who

Loess regression is a nonparametric technique that uses local weighted regression to fit a smooth curve through points in a scatter plot. Loess curves are can reveal trends and cycles in data that might be difficult to model with a parametric curve. Loess regression is one of several algorithms in

How far away is the nearest hospital? How far is the nearest restaurant? The nearest gas station? These are commonly asked questions whose answers depend on the location of the person asking the question. Recently I showed an algorithm that enables you to find the distance between a set of

What is weighted regression? How does it differ from ordinary (unweighted) regression? This article describes how to compute and score weighted regression models. Visualize a weighted regression Technically, an "unweighted" regression should be called an "equally weighted " regression since each ordinary least squares (OLS) regression weights each observation equally.

The recent releases of SAS 9.4 have featured major enhancements to the ODS statistical graphics procedures such as PROC SGPLOT. In fact, PROC SGPLOT (and the underlying Graph Template Language (GTL)) are so versatile and powerful that you might forget to consider whether you can create a graph automatically by

Last week I showed how to find the nearest neighbors for a set of d-dimensional points. A SAS user wrote to ask whether something similar could be done when you have two distinct groups of points and you want to find the elements in the second group that are closest

My son is taking an AP Statistics course in high school this year. AP Statistics is one of the fastest-growing AP courses, so I welcome the chance to see topics and techniques in the course. Last week I was pleased to see that they teach data exploration techniques, such as

Last week I showed how to compute nearest-neighbor distances for a set of numerical observations. Nearest-neighbor distances are used in many statistical computations, including the analysis of spatial point patterns. This article describes how the distribution of nearest-neighbor distances can help you determine whether spatial data are uniformly distributed or

Last week I wrote about how to compute sample quantiles and weighted quantiles in SAS. As part of that article, I needed to draw some step functions. Recall that a step function is a piecewise constant function that jumps by a certain amount at a finite number of points. Graph

Many univariate descriptive statistics are intuitive. However, weighted statistic are less intuitive. A weight variable changes the computation of a statistic by giving more weight to some observations than to others. This article shows how to compute and visualize weighted percentiles, also known as a weighted quantiles, as computed by

Last week I showed some features of SAS formats, including the fact that you can use formats to bin a continuous variable without creating a new variable in the DATA step. During the discussion I mentioned that it can be confusing to look at the output of a formatted variable

In a scatter plot, the regions where observations are packed tightly are areas of high density. A contour plot or heat map of a bivariate kernel density estimate (KDE) is one way to visualize regions of high density. A SAS customer asked whether it is possible to use SAS to

When I read Robert Allison's article about the cost of a taxi ride in New York City, I was struck by the scatter plot (shown at right; click to enlarge) that plots the tip amount against the total bill for 12 million taxi rides. The graph clearly reveals diagonal and

You can visualize missing data. It sounds like an oxymoron, but it is true. How can you draw graphs of something that is missing? In a previous article, I showed how you can use PROC MI in SAS/STAT software to create a table that shows patterns of missing data in

Missing data can be informative. Sometimes missing values in one variable are related to missing values in another variable. Other times missing values in one variable are independent of missing values in other variables. As part of the exploratory phase of data analysis, you should investigate whether there are patterns

In SAS procedures, the WHERE clause is a useful way to filter observations so that the procedure receives only a subset of the data to analyze. The IML procedure supports the WHERE clause in two separate statements. On the USE statement, the WHERE clause acts as a global filter. The

Descriptive univariate statistics are the foundation of data analysis. Before you create a statistical model for new data, you should examine descriptive univariate statistics such as the mean, standard deviation, quantiles, and the number of nonmissing observations. In SAS, there is an easy way to create a data set that

Last weekend was the 2016 NCAA Division I wrestling tournament. In collegiate wrestling there are ten weight classes. The top eight wrestlers in each weight class are awarded the title "All-American" to acknowledge that they are the best wrestlers in the country. I saw a blog post on the InterMat

My previous blog post shows how to use PROC LOGISTIC and spline effects to predict the probability that an NBA player scores from various locations on a court. The LOGISTIC procedure fits parametric models, which means that the procedure estimates parameters for every explanatory effect in the model. Spline bases

Last week Robert Allison showed how to download NBA data into SAS and create graphs such as the location where Stephen Curry took shots in the 2015-16 season to date. The graph at left shows the kind of graphs that Robert created. I've reversed the colors from Robert's version, so

Most SAS regression procedures support the "stars and bars" operators, which enable you to create models that include main effects and all higher-order interaction effects. You can also easily create models that include all n-way interactions up to a specified value of n. However, it can be a challenge to

Last week I showed how to create dummy variables in SAS by using the GLMMOD procedure. The procedure enables you to create design matrices that encode continuous variables, categorical variables, and their interactions. You can use dummy variables to replace categorical variables in procedures that do not support a CLASS

SAS programmers sometimes ask, "How do I create a design matrix in SAS?" A design matrix is a numerical matrix that represents the explanatory variables in regression models. In simple models, the design matrix contains one column for each continuous variable and multiple columns (called dummy variables) for each classification

Last week I showed how to use PROC EXPAND to compute moving averages and other rolling statistics in SAS. Unfortunately, PROC EXPAND is part of SAS/ETS software and not every SAS site has a license for SAS/ETS. For simple moving averages, you can write a DATA step program, as discussed

A common question on SAS discussion forums is how to compute a moving average in SAS. This article shows how to use PROC EXPAND and contains links to articles that use the DATA step or macros to compute moving averages in SAS. In a previous post, I explained how to

A moving average (also called a rolling average) is a statistical technique that is used to smooth a time series. Moving averages are used in finance, economics, and quality control. You can overlay a moving average curve on a time series to visualize how each value compares to a rolling