What does correlation coefficient actually represent [closed]

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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?

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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: