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Correlation analysis, and its cousin, regression analysis, are well-known statistical approaches used in the study of relationships among multiple physical properties. The investigation of [[permeability]]-[[porosity]] relationships is a typical example of the use of correlation in geology.

Correlation analysis, and its cousin, regression analysis, are well-known statistical approaches used in the study of relationships among multiple physical properties. The investigation of [[permeability]]-[[porosity]] relationships is a typical example of the use of correlation in geology.

The term ''correlation'' most often refers to the linear association between two quantities or variables, that is, the tendency for one variable, x, to increase or decrease as the other, y, increases or decreases, in a straight-line trend or relationship (Draper and Smith, 1966<ref name=Draper_etal_1966>Draper, N. R., and H. Smith, 1966, Applied regression analysis, 2nd ed.: New York, John Wiley, 709 p.</ref>; Snedecor and Cochran, 1967<ref name=Snedecor_etal_1967>Snedecor, G. W., and W. G. Cochran, 1967, Statistical methods, 6th ed.: Ames, Iowa State Univ. Press, 593 p.</ref>). The ''correlation coefficient'' (also called the Pearson correlation coefficient), r, is a dimensionless numerical index of the strength of that relationship. The sample value of r, which can range from -1 to +1, is computed using the following formula:

The term ''correlation'' most often refers to the linear association between two quantities or variables, that is, the tendency for one variable, x, to increase or decrease as the other, y, increases or decreases, in a straight-line trend or relationship.<ref name=Draper_etal_1966>Draper, N. R., and H. Smith, 1966, Applied regression analysis, 2nd ed.: New York, John Wiley, 709 p.</ref> <ref name=Snedecor_etal_1967>Snedecor, G. W., and W. G. Cochran, 1967, Statistical methods, 6th ed.: Ames, Iowa State Univ. Press, 593 p.</ref> The ''correlation coefficient'' (also called the Pearson correlation coefficient), r, is a dimensionless numerical index of the strength of that relationship. The sample value of r, which can range from -1 to +1, is computed using the following formula:

:<math>\mathbf{Equation}</math>

:<math>r = \frac{\displaystyle \sum_{i} (x_{i}-\bar{x})(y_{i}-\bar{y})}{\sqrt{\displaystyle \sum_i (x_{i}-\bar{x})^2 \cdot \displaystyle \sum_i (y_{i}-\bar{y})^2}}</math>

where the summation is made over the n sample values available and where

where the summation is made over the n sample values available and where