Correlation: Facts and Fallacies
In Chapter 4 we discussed correlation as an important tool in identifying and assessing hidden risk (event risk not evident in the track record). There is, however, considerable misunderstanding about what correlation does and does not show. In this chapter, we take a closer look at correlation and some of the ways it is often misinterpreted.
The correlation coefficient, typically denoted by the letter r, measures the degree of linear relationship between two variables. The correlation coefficient ranges from −1.0 to +1.0. The closer the correlation coefficient is to +1.0, the closer the relationship is between the two variables. A perfect correlation of 1.0 would occur only in artificial situations. For example, the heights of a group of people measured in inches and the heights of the same group of people measured in feet would be perfectly correlated. The closer the correlation coefficient is to −1.0, the stronger the inverse correlation is between the two variables. For example, average winter temperatures in the U.S. Northeast and heating oil usage in that region would be inversely related variables (variables with a negative correlation coefficient). If two variables have a correlation coefficient near zero, it indicates that there is no significant (linear) relationship between the variables. It is important to understand that the correlation coefficient only indicates the degree of correlation between two variables ...