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Correlation and Regression

In science, law, and life one often wants to know the relationship between one thing and another.

In the 2 x 2 tables discussed previously, we were interested in, for example, the relation between trial mode (judge or jury) and case outcome (win or lose). The measure of relation for such nominal data is necessarily limited by their categorical nature.

For quantitative data, measures of relation seem even more natural. Do the number of hours that one studies help explain the grades obtained?

The term correlation is often used to denote some form of association. Perhaps we think there is a correlation between number of hours studied and grade point average (GPA). Or between SAT scores (or high-school GPA) and college grades.

Correlation in statistics often refers to a measure of linear association between two quantitative variables. A unit increase in one variable increases or decreases by a fixed amount the other variable. For example, 50 hours of additional study in a semester may, on average, increase GPA by .1; or a 50 point higher score on the SAT may correlate with a GPA in college that is .1 higher.

Accordingly, a technique widely used is simple linear regression, which estimates the best straight line to summarize the relation between two quantitative variables. See a simple illustration.