What is correlation and how to interpret the coefficient value

In our world, everything is interconnected, somewhere it can be seen with the naked eye, and somewhere people do not even suspect the existence of such dependence. Nevertheless, in statistics, when they mean mutual dependence, the term "correlation" is often used. It can often be found in the economic literature. Let's try to understand together what the essence of this concept is, what are the coefficients and how to interpret the obtained values.

The concept of

So what is correlation? Typically, this term implies a statistical relationship between two or more parameters. If the value of one or several of them changes, this inevitably affects the size of the others. For the mathematical determination of the strength of such interdependence, it is customary to use different coefficients. It should be noted that in the case when the change in one parameter does not lead to a regular change in the other but affects some statistical characteristic of this parameter, such a relationship is not correlative, but simply statistical.

History of the term

In order to better understand what a correlation is, let's plunge into history a little. This term appeared in the XVIII century due to the efforts of the French paleontologist Georges Cuvier. This scientist developed the so-called "law of correlation" of organs and parts of living beings, which allowed to restore the appearance of an ancient fossil animal, having only some of its remains. In statistics, this word has come into use since 1886 with the light hand of English statistics and biologist Francis Galton. The very title of the term already contains its decoding: not simply and not only the relationship is "relation", but the relations that have something in common - "co-relation". However, only Galton's pupil, biologist and mathematician K. Pearson (1857 - 1936) was able to clearly explain mathematically what a correlation was. It was he who first deduced the exact formula for calculating the corresponding coefficients.

Paired correlation

This is the relationship between two concrete quantities. For example, it is proved that the annual advertising costs in the United States are very closely related to the value of the gross domestic product. It is estimated that between these values in the period from 1956 to 1977 the correlation coefficient was 0.9699. Another example is the number of visits to the online store and the volume of its sales. A close relationship is revealed between such quantities as the volume of beer sales and air temperature, the average monthly temperature for a particular place in the current and previous year, etc. How to treat the coefficient of pair correlation? We note at once that it takes a value from -1 to 1, with a negative number denoting the inverse, and a positive one indicating a direct dependence. The more the module of the result of calculations, the stronger the values affect each other. A zero value indicates a lack of dependency, a value less than 0.5 indicates a weak relationship, and otherwise a pronounced relationship.

Pearson's Correlation

Depending on the scale on which the variables are measured, one or another indicator (the Fechner coefficient, Spearman, Kendall, etc.) is used for calculations. When investigating interval values, the indicator, invented by Karl Pearson, is most often used. This coefficient shows the degree of linear relationships between the two parameters. When they talk about the correlation, they often mean it. This indicator has become so popular that its formula is in Excel and, if desired, you can, in practice, understand what a correlation is, without going into the subtleties of complex formulas. The syntax of this function is: PEARSON (array1, array2). As the first and second arrays, the corresponding ranges of numbers are usually substituted.