Chapter 4 Covariance, Regression, and Correlation

“Co-relation or correlation of structure ” is a phrase much used in biology, and not least in that branch of it which refers to heredity, and the idea is even more frequently present than the phrase; but I am not aware of any previous attempt to define it clearly, to trace its mode of action in detail, or to show how to measure its degree.(Galton, 1888, p 135) A fundamental question in science is how to measure the relationship between two vari-ables. The answer, developed in the late 19th century, in the the form of the correlation coefficient is arguably the most important contribution to psychological theory and method-ology in the past two centuries. Whether we are examining the effect of education upon later income, of parental height upon the height of offspring, or the likelihood of graduating from college as a function of SAT score, the question remains the same: what is the strength of the relationship? This chapter examines measures of relationship between two variables. Generalizations to the problem of how to measure the relationships between sets of variables (multiple correlation and multiple regression) are left to Chapter 5. In the mid 19th century, the British polymath, Sir Francis Galton, became interested in the intergenerational similarity of physical and psychological traits. In his original stud