Month: November 2023

Steven Sanderson performs robust regression:

If you’re familiar with linear regression in R, you’ve probably encountered the traditional lm() function. While this is a powerful tool, it might not be the best choice when dealing with outliers or influential observations. In such cases, robust regression comes to the rescue, and in R, the rlm() function from the MASS package is a valuable resource. In this blog post, we’ll delve into the step-by-step process of performing robust regression in R, using a dataset to illustrate the differences between the base R lm model and the robust rlm model.

The short version of rlm() versus lm() is that Ordinary Least Squares (the form of linear regression we use with lm()) is quite susceptible to outliers. Meanwhile, rlm() uses a technique known as M-estimation, which ends up weighting outlier points different from inliers, making it less susceptible to a small number of outliers wrecking the chart.

Steven Sanderson’s power level is over 9000:

In the realm of statistics, power regression stands out as a versatile tool for exploring the relationship between two variables, where one variable is the power of the other. This type of regression is particularly useful when there’s an inherent nonlinear relationship between the variables, often characterized by an exponential or inverse relationship.

Read on to learn more about the definition of power regression and how to perform it in R using a technique called “swole linear regression.” Or at least that’s what I think the technique should be called. Which is probably why I’m not in charge of naming things.

Tomaz Kastrun messes with R^2:

So, an R-squared of 0.59 might show how well the data fit to the model (hence goodness of fit) and also explains about 59% of the variation in our dependent variable.

Given this logic, we prefer our regression models to have a high R-squared. Yes? Right! And by useless test, with adding random noise to a function, what happens next?

I like Tomaz’s scenario here and think he does a good job demonstrating the outcome. I do, however, struggle with the characterization of “making R^2 useless.” When the error term approaches an enormous value relative to the regressable components, that R^2 is telling you that something else is dominating the relationship between the independent variables and dependent variable. And this is correct: that error term does dominate. I suppose the problem here is philosophical: we call it an error term but what it signifies is “information we don’t understand about the relationship between these variables.” Yes, in this toy example, it was randomly-generated noise. But in a real dataset, it’s not random; it’s inexplicable, at least given the information you know at that time and the mechanisms you use to analyze the relationship.