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FactChecker

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I do disagree. How accurately a variable can be measured is not the significant issue. The head/tail result of a coin toss can be measured with great accuracy but that does not make that result the independent variable. The decision of whether to model Y=aX+b+##\epsilon## versus X=a'Y+b'+##\epsilon##' is a matter of how you will use the data, what SSE you want to minimize, and whether you want the standard statistical theory and results to apply to your use. How the data will be used should determine which linear regression to do.Yes, this is correct.

@FactChecker can confirm, but I don’t think that he is disagreeing with me. He is just showing you why the two choices are not equivalent.

It's essential to be minimizing the correct errors. The regression of X as a linear function of Y is guaranteed to minimize ##\sum (x_i-\hat {x_i})^2##.

The two approaches are easy to compare. Just do both regressions and see which one has the smaller SSE for that sample using ##y_i## to estimate ##x_i##.

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