What is correlation and how to interpret the value of the coefficient

In our world everything is interconnected, where it is visible to the naked eye, but somewhere people even do not suspect about existence of such dependence. However, in statistics, when referring to mutual dependence, often use the term "correlation". It can be often found in the economic literature. Let's try to understand what is the essence of this concept, what are the ratios and how to interpret the resulting values.

The Concept

So, what is the correlation? As a rule, this term means a statistical relationship between two or more parameters. If you change the value of one or more of them, it inevitably affects the value of others. To mathematically determine the strength of such interdependence is common to use a variety of factors. It should be noted that in the case when changing one parameter does not lead to a natural change in the other, but the effect on any statistical description of this parameter, the link is not correlation, but just the statistics.

History of the term

In order to better understand what the correlation is, let's plunge  into the story. This term appeared in the XVIII century thanks to the efforts of the French paleontologist Georges Cuvier. This scientist developed the so-called “the law of correlation" of the organs and parts of living creatures, which allowed to restore the look of an ancient fossil animal, having only some of his remains. In statistics, this word came into use in 1886 with a light hand statistics and English biologist Francis Galton. In the name of the term already contains its meaning: not just and not only a connection – “relations”, and the relationship between having a cross joint – “co-relation”. However, to clearly explain mathematically that such a correlation could only disciple of Galton, a biologist and mathematician K. Pearson (1857 – 1936). It was he who first brought the exact formula to calculate the coefficients.

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The pair correlation

The So-called relationship between two specific variables. For example, it is proved that the annual cost of advertising in the United States are very 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 amounted to 0,9699. Another example – the number of visits to the online store and the volume of its sales. The close relationship identified between these variables, as sales of beer and air temperature, the average temperature for a specific location in the current and previous year etc. How to interpret correlation coefficient? Just note that it takes the value from -1 to 1, where negative number indicates the opposite, and positive – a direct relationship. The larger the module the calculation result is, the stronger the magnitude of influence each other. A value of zero indicates a lack of dependence, a value less than 0.5 indicates a weak, but otherwise - on a pronounced relationship.

Pearson Correlation

Depending on what scale the measured variables used for calculation one or another indicator (the coefficient of Fechner, Spearman, Kendall, etc.). When examined interval values, the most commonly used indicator, invented by Karl Pearson. This ratio indicates the degree of linear relationship between two parameters. When people talk about correlation with respect to most of its mean. This figure became so popular that his formula in Excel and, if desired, can be very difficult to find what correlation, not going into details of complex formulas. Syntax this function has the form: PEARSON(array1, array2). As the first and second arrays normally insert the appropriate number ranges.