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Analytics | Learn SAS | Programming Tips

Rick WicklinAugust 14, 2023 2

Bootstrap confidence intervals for the predicted mean in a regression model

In ordinary least squares regression, there is an explicit formula for the confidence limit of the predicted mean. That is, for any observed value of the explanatory variables, you can create a 95% confidence interval (CI) for the predicted response. This formula assumes that the model is correctly specified and

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Analytics | Programming Tips

Rick WicklinJuly 24, 2023 4

Modifications of the Wilcoxon signed rank test and exact p-values

In a previous article, I discussed the Wilcoxon signed rank test, which is a nonparametric test for the location of the median. The Wikipedia article about the signed rank test mentions a variation of the test due to Pratt (1959). Whereas the standard Wilcoxon test excludes values that equal μ0

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Analytics | Learn SAS | Programming Tips

Rick WicklinJuly 19, 2023 1

On the computation of the Wilcoxon signed rank statistic

Wilcoxon's signed rank test is a popular nonparametric alternative to a paired t test. In a paired t test, you analyze measurements for subjects before and after some treatment or intervention. You analyze the difference in the measurements for each subject, and test whether the mean difference is significantly different

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Analytics | Learn SAS

Rick WicklinJuly 17, 2023 0

Standardize regression coefficients for models that include categorical variables

A previous article discusses standardized coefficients in linear regression models and shows how to compute standardized regression coefficients in SAS by using the STB option on the MODEL statement in PROC REG. It also discusses how to interpret a standardized regression coefficient. Recently, a SAS user wanted to know how

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Analytics | Learn SAS | Programming Tips

Rick WicklinJune 28, 2023 2

Compute the geometric median in SAS

Given a set of N points in k-dimensional space, can you find the location that minimizes the sum of the distances to the points? The location that minimizes the distances is called the geometric median of the points. For univariate data, the "points" are merely a set of numbers \(\{p_1,

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Analytics | Learn SAS

Rick WicklinJune 26, 2023 0

Compute the geometric median of a triangle

While writing an article about labeling a polygon by using the centroid, I almost made a false claim about the centroid. I almost claimed that that the centroid is the point in a polygon that minimizes the sum of the distances to the vertices. It is not. The point that

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Analytics | Learn SAS

Rick WicklinJune 21, 2023 2

Barycentric coordinates for a triangle

A colleague asked how to compute the barycentric coordinates of a point inside a triangle. Given a triangle in the plane with vertices p1, p2, and p3, every point in the triangle can be represented as a convex combination of the vertices: c1*p1 + c2*p2 + c3*p3, where c1,c2,c3 ≥

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Analytics | Learn SAS

Rick WicklinJune 7, 2023 0

Visualize the Spearman rank correlation

A previous article explains the Spearman rank correlation, which is a robust cousin to the more familiar Pearson correlation. I've also discussed why you might want to use rank correlation, and how to interpret the strength of a rank correlation. This article gives a short example that helps you to

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Analytics | Data Visualization

Rick WicklinMay 15, 2023 3

What is the silhouette statistic in cluster analysis?

Assigning observations into clusters can be challenging. One challenge is deciding how many clusters are in the data. Another is identifying which observations are potentially misclassified because they are on the boundary between two different clusters. Ralph Abbey's 2019 paper ("How to Evaluate Different Clustering Results") is a good way

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Analytics | Programming Tips

Rick WicklinMay 3, 2023 3

The exponential of a matrix

In SAS, you can approximate the exponential of a matrix by using the EXPMATRIX function in SAS IML software. This article discusses the exponential of a matrix: what it is, how to compute it, why it is useful, and why you should think of it as a linear map that

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