Karl Pearson’s Coefficient of Correlation

Karl Pearson’s Coefficient of Correlation (or Product moment correlation or simple correlation coefficient or covariance method ) is based upon the arithmetic mean and the standard deviation.

According to Karl Pearson, the correlation coefficient of two variables is obtained by dividing the sum of the products of the corresponding deviations of the various items of two series from the respective means by the product of their standard deviations and the number of pairs of observation. Basically, it is based on the covariance of the concerned variables.

Formula is:

Karl Pearson's Coefficient of Correlation (r) = NΣXY−ΣX.ΣY / √NΣX² - (Σx)2 √NΣY² - (ΣY)²

Example: 

Find the value of Karl Pearson’s coefficient correlation from the following table:

Solution:

(r) = NΣXY−ΣX.ΣY / √NΣX2 - (Σx)2 √NΣY2 - (ΣY)2 (r) = 6(20,485) – (247 × 486) / [√[[6(11,409) – (2472)] × [6(40,022) – 4862]]]

Karl Pearson’s Coefficient of Correlation  (r) = 0.5298 

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Rank Coefficient and Karl Pearson’s Coefficient of Correlation: In engineering mathematics, coefficients of correlation are statistical measures that quantify the degree and direction of the relationship between two variables. They are used to determine how one variable may predict or relate to another, which is crucial in various engineering applications such as quality control, signal processing, and system optimization.