In a previous article, I showed how to find the intersection (if it exists) between two line segments in the plane. There are some fun problems in probability theory that involve intersections of line segments. One is "What is the probability that two randomly chosen chords of a circle intersect?"
Suppose you want to find observations in multivariate data that are closest to a numerical target value. For example, for the students in the Sashelp.Class data set, you might want to find the students whose (Age, Height, Weight) values are closest to the triplet (13, 62, 100). The way to
Last week I got the following message: Dear Rick: How can I create a normal distribution within a specified range (min and max)? I need to simulate a normal distribution that fits within a specified range. I realize that a normal distribution is by definition infinite... Are there any alternatives,
This article describes the advantages and disadvantages of principal component regression (PCR). This article also presents alternative techniques to PCR. In a previous article, I showed how to compute a principal component regression in SAS. Recall that principal component regression is a technique for handling near collinearities among the regression
How can you specify weights for a statistical analysis? Hmmm, that's a "weighty" question! Many people on discussion forums ask "What is a weight variable?" and "How do you choose a weight for each observation?" This article gives a brief overview of weight variables in statistics and includes examples of
Pearson's correlation measures the linear association between two variables. Because the correlation is bounded between [-1, 1], the sampling distribution for highly correlated variables is highly skewed. Even for bivariate normal data, the skewness makes it challenging to estimate confidence intervals for the correlation, to run one-sample hypothesis tests ("Is
Last week I blogged about the broken-stick problem in probability, which reminded me that the broken-stick model is one of the many techniques that have been proposed for choosing the number of principal components to retain during a principal component analysis. Recall that for a principal component analysis (PCA) of
Skewness is a measure of the asymmetry of a univariate distribution. I have previously shown how to compute the skewness for data distributions in SAS. The previous article computes Pearson's definition of skewness, which is based on the standardized third central moment of the data. Moment-based statistics are sensitive to
On discussion forums, I often see questions that ask how to Winsorize variables in SAS. For example, here are some typical questions from the SAS Support Community: I want an efficient way of replacing (upper) extreme values with (95th) percentile. I have a data set with around 600 variables and
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,
