Statistical Applications for Environmental Analysis and Risk Assessment

Chapter 11Correlation, Covariance, Geostatistics

11.1 Introduction and Overview

Different from the serial or autocorrelation described in Chapter 10, which refers to the correlation between individual data values of a single variable from the same data sample or population (i.e., univariate data), the bivariate correlation and multiple correlation described in this chapter refer to the degree of association between two variables, and involving more than two variables. That association is typically quantified by a correlation coefficient, which indicates whether one variable is increasing or decreasing as the other increases or whether there is essentially no connection between the two variables (i.e., they are independent or uncorrelated). It is also possible for a group of variables (usually referred to as the predictor or X variables) to jointly relate to another variable (usually referred to as the response or Y variable), in which case the association is described as multiple correlation. In this case also, the correlation between any pair of variables, given the presence of the remaining variables, is described as partial correlation. Multiple and partial correlations are described as part of multiple regression in Section 15.8.

Positive correlation (i.e., the two variables are both increasing or decreasing in concert) ranges from a minimum value of zero for the correlation coefficient to a maximum of 1, while for negative correlation (i.e., as one variable increases, ...