It can be said, as my Spreadsheet Modeling and Decision Analysis text says, that there are two essential elements of a statistical relationship:

1) A tendency for the dependent variable Y to vary with the independent variable(s) in a systematic way. This systematic variation can be mathematically established as a function, f(x1, x2....xk), where x are the independent variables.

2) An element of unsystematic or random variation in the dependent variable, irrespective of the independent variable. This 'error' term should always be taken into account along with the systematic variation. Obviously, the desire is to achieve an error term as low as possible.

It can also be said, as the Elementary Concepts of Statistics that I pulled off of the web says, that "Statistics does nothing else but help us evaluate relations between variables. Actually, all of the hundreds of statistical procedures that exist can be interpreted in terms of evaluating various kinds of inter-variable relations. (The procedures are interpretations.)

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