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This is a rather confused question.

The first issue is the assumption that there is an independent variable and a dependent variable. If your data comprise measurements of the height and mass (weight) of school children, which one is the independent variable? The answer is: neither. It is most likely to be age.


A second issue is the very serious danger of confusing correlation with causality. Yes, statistics may show high correlation but that does not imply causality. A simplistic example from economics: correlation between companies with large profits and large investment in machinery. Profitability is required to enable the company to finance investment. Proper investment helps the company become more competitive and so generate more profits.


Finally, consider the two variables X and Y. X is uniform on the interval [-p, p]; Y = X^2. The regression coefficient between X and Y is 0 but the relationship is far from non-existent. You need some educated guesses to find the correct statistics to make educated guesses!

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Q: What is the statistics are used as a way to make an educated guess about the relationship between the independent variable and the dependent variable?
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