Most data come from one of two sources, either from observational studies and surveys , in which the researcher simply observes the data as they are, or from controlled experiments , in which the researcher assigns subjects to various treatments. Often the relationship between two variables is of interest. One way of summarizing a relationship between two variables is through regression . Regression may or may not be a good summary, though, so there are many things to watch out for when using regression. As might be expected, there is a logical relationship between correlation and regression .
Formal statistics begins with the study of probability and random variables .
Random variables can be summarized by their expected value and standard error . Two important types of random variables are the normal and binomial distributions. Given a set of data, it is natural to ask about the Truth behind the data. These are questions of inference about parameters. Of course, the inferences depend on whether the data are numerical data from one population , numerical data from two populations , or if the data are proportions from one or two populations .