What does correlation coefficient actually represent
What does correlation coefficient intuitively mean? If I have a series of X and then a series of Y, and if I input these two into Weka multilayer perceptron treating Y as the output and X as input, I get a correlation coefficient as 0.76. What does this intuitively represent, and how I explain this to a business man or a non-techie person?
Answer
There are several correlation coefficients. The most commonly used, and the one that is referred to as "the one" is Pearson's product moment correlation.
A correlation coefficient shows the degree of linear dependence of x and y. In other words, the coefficient shows how close two variables lie along a line.
If the coefficient is equal to 1 or -1, all the points lie along a line. If the correlation coefficient is equal to zero, there is no linear relation between x and y. however, this does not necessarily mean that there is no relation at all between the two variables. There could e.g. be a non-linear relation.
A positive relationship means that the two variables move into the same direction. A higher value of x corresponds to higher values of y, and vice versa.
A negative relationship means that the two variables move into the opposite directions. A lower value of x corresponds to higher values of y, and vice versa.
Here you have a handful of examples:
