Whether your goal is to identify substitute characteristics or solve a process problem, regression algorithms can produce coefficients for almost any data. However, it doesn’t mean the resulting models are any good.

In machine learning, you divide your data into a training set on which you calculate coefficients and a testing set to check the model’s predictive ability. Testing concerns externally visible results and is not specific to regression.

Validation, on the other hand, is focused on the training set and involves using various regression-specific tools to detect inconsistencies with assumptions. For these purposes, we review methods provided by regression software.

In this post, we explore the meaning and the logic behind the tools provided for this purpose in linear simple and multiple regression in R, with the understanding that similar functions are available from other software and that similar tools exist for other forms of regression.

It is an attempt to clarify the meaning of these numbers and plots and help readers use them. They will be the judges of how successful it is.

The body of the post is about the application of these tools to an example dataset available from Kaggle, with about 30,000 data points. For the curious, some mathematical background is given in the appendix.

Many of the tools are developments from the last 40 years and, therefore, are not covered in the statistics literature from earlier decades.