What is and how to interpret the correlation coefficient

In our world, everything is interconnected, somewhere it can be seen with the naked eye, but where some people do not even know of the existence of such a relationship.Nevertheless, statistics, when they mean interdependence, often use the term "correlation".It often can be found in the economic literature.Let's try to understand what is the essence of this concept, what are the factors and how to interpret the values ​​obtained.


So, what is the correlation?Generally, this term is meant a statistical relationship between two or more parameters.If you change the value of one or more of them, this inevitably affects the value of the others.For the mathematical definition of force such interdependence is common to use a variety of factors.It should be noted that in the case where a change in one parameter does not lead to a natural change in the other, but the impact on any of the statistical characteristic parameter, such a relationship is not a correlation, but just statistical.

term history

In order to better understand what the correlation, let's delve into the story.The term appeared in the XVIII century, thanks to the efforts of the French paleontologist Georges Cuvier.This scientist developed the so-called "law of correlation" organs and parts of living beings, which allows you to restore the appearance of an ancient fossil animals, having the presence of only a few of his remains.In statistics, this word came into use since 1886, with a light hand of the English statistics and biologist Francis Galton.The very title of the term has found its interpretation: not just, and not only the connection - «relation», and relations with each other is something shared - «co-relation».However, clearly explain mathematically that such a correlation could only disciple of Galton, a biologist and mathematician Karl Pearson (1857 - 1936).It was he who first brought the exact formula for the calculation of the relevant coefficients.

Pair correlation

This term relationship between two specific values.For example, it is proved that the annual cost of advertising in the United States are closely related to the size 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 - the number of visits to the online store and the volume of its sales.The close relationship found between these values, as sales of beer and the air temperature, the average temperature for the specific location in the current and previous year, and so on. D. How to interpret the correlation coefficient?Just note that it takes a value between -1 and 1, and a negative number indicates the reverse, as positive - a direct correlation.The more the results of the counting module, the greater the value of influencing each other.A value of zero indicates the lack of dependence, the value of less than 0.5 indicates a weak and otherwise - of a distinct relationship.

Pearson correlation

Depending on what scale measured variables used for the calculation of a particular indicator (Fechner coefficient, Spearman, Kendall, and so on. D.).When examined interval values ​​are most commonly used indicator, invented by Karl Pearson.This ratio indicates the degree of linear relationship between the two parameters.When people talk about correlations, most of it and have in mind.This figure has become so popular that it has the formula in Excel, and if desired can be very practical to understand what correlation, without going into the intricacies of complex formulas.The syntax of this function is of the form: PEARSON (array1, array2).As the first and second arrays typically supplies the appropriate number ranges.