One of the chapters that we are especially proud of in Practical Data Science with R is Chapter 7, “Linear and Logistic Regression.” We worked really hard to explain the fundamental principles behind both methods in a clear and easy-to-understand form, and to document diagnostics returned by the R implementations […]
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 […]
Here is an absolutely horrible way to confuse yourself and get an inflated reported R-squared on a simple linear regression model in R. We have written about this before, but we found a new twist on the problem (interactions with categorical variable encoding) which we would like to call out […]
Introduction Suppose we have the task of predicting an outcome y given a number of variables v1,..,vk. We often want to “prune variables” or build models with fewer than all the variables. This can be to speed up modeling, decrease the cost of producing future data, improve robustness, improve explain-ability, […]
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 […]
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? 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 […]
When finishing Worry about correctness and repeatability, not p-values I got to thinking a bit more about what can you actually check when reading a paper, especially when you don’t have access to the raw data. Some of the fellow scientists I admire most have a knack for back of […]
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, […]
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 […]