Correlations
Correlations are ubiquitous. For example, news articles reporting that a research paper found no correlation between X and Y. Also, it is related to (in)dependence, which plays an important role in linear regression. This post will explain the Pearson correlation coefficient. The explanation is mainly based on the book by Hogg et al. (2018).
In the context of a book on mathematical statistics, certain variable names make sense. However, in this post, some variable names are changed to make the information more coherent. One convention which is adhered to is that single values are lowercase, and multiple values are capitalized. Furthermore, since in most empirical research we only need discrete statistics, the continuous versions of formulas are omitted.