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Link Functions versus Data Transforms

In the linear regression section of our book Practical Data Science in R, we use the example of predicting income from a number of demographic variables (age, sex, education and employment type). In the text, we choose to regress against log10(income) rather than directly against income. One obvious reason for […]

Can we try to make an adjustment?

In most of our data science teaching (including our book Practical Data Science with R) we emphasize the deliberately easy problem of “exchangeable prediction.” We define exchangeable prediction as: given a series of observations with two distinguished classes of variables/observations denoted “x”s (denoting control variables, independent variables, experimental variables, or […]

Reading the Gauss-Markov theorem

What is the Gauss-Markov theorem? From “The Cambridge Dictionary of Statistics” B. S. Everitt, 2nd Edition: A theorem that proves that if the error terms in a multiple regression have the same variance and are uncorrelated, then the estimators of the parameters in the model produced by least squares estimation […]

What is meant by regression modeling?

What is meant by regression modeling? Linear Regression is one of the most common statistical modeling techniques. It is very powerful, important, and (at first glance) easy to teach. However, because it is such a broad topic it can be a minefield for teaching and discussion. It is common for […]

My Favorite Graphs

The important criterion for a graph is not simply how fast we can see a result; rather it is whether through the use of the graph we can see something that would have been harder to see otherwise or that could not have been seen at all. — William Cleveland, […]

Correlation and R-Squared

What is R2? In the context of predictive models (usually linear regression), where y is the true outcome, and f is the model’s prediction, the definition that I see most often is: In words, R2 is a measure of how much of the variance in y is explained by the […]