What does the correlation coefficient really represent?

Question

What does intuition coefficient mean? If I have an X series, and then a Y series, and if I introduce these two into Weka a multilayer perceptron treating Y as an output signal and X as an input signal, I get a correlation coefficient of 0.76. What does this intuitively represent, and how do I explain this to a business person or non-technical person?

Answer 1

There are several correlation coefficients. The most commonly used, and one called the “one,” is the Pearson product moment correlation.

The correlation coefficient shows the degree of linear dependence of x and y. In other words, the coefficient shows how close the two variables lie along the line.

If the coefficient is 1 or -1, all points lie along the line. If the correlation coefficient is zero, there is no linear relationship between x and y. however, this does not necessarily mean that there is no relationship at all between the two variables. It may, for example, be a non-linear relation.

A positive relationship means that two variables move in the same direction. A higher x value corresponds to a higher y value and vice versa.

A negative relationship means that two variables are moving in opposite directions. A lower x value corresponds to a higher y value and vice versa.

Here you have some examples: