Should linear regression always be forced through the origin?

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SUMMARY

Forcing linear regression through the origin is generally not acceptable unless there is a strong theoretical justification for doing so. The discussion emphasizes that while a better gradient value may be obtained by forcing the regression through the origin, this practice can lead to misleading results. It is crucial to assess the statistical significance of deviations between experimental data and theoretical predictions, particularly when no established functional relationship exists. Ultimately, the integrity of the data should be maintained without artificially constraining the model to fit theoretical expectations.

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garyman
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Wasn't sure which section this should be in, so please move if inappropriate. If a plot between two variables theoretically should pass through the origin, should you force the linear regression through the origin. I seem to get a much better value for my gradient when forced through the origin, and was just wondering if this is acceptable.
 
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I would not force it through the origin, because in reality it might not go through it due to some error.
 
Curve fitting experimental data is not a simple thing. FWIW, we teach all students and post-docs a 1-credit ethics course where this (in addition to other scenarios) is discussed.

If the theory is sound, the curve should be generated by the theory and experimental data compared against it. Deviations from experimental data points and theoretical predictions are then first decided to be statistically significant or not, and then described and (possibly) explained.

If there is no theory (as is sometimes the case in biology, for example), then there's no curve to fit- there is no known functional (quantitative) relationship between the two quantities, although good data may imply a particular relationship.
 
garyman said:
Wasn't sure which section this should be in, so please move if inappropriate. If a plot between two variables theoretically should pass through the origin, should you force the linear regression through the origin. I seem to get a much better value for my gradient when forced through the origin, and was just wondering if this is acceptable.

You should never force your curve fit to pass through a point that is not part of your data. In many cases, if the theoretical description includes a (0,0), then you can simply point out the discrepancy in your data and your theoretical description, and maybe discuss possible reasons on why that occurred (there are many systematic errors that could have caused that). But at no point should you force your data to "obey" the theory.

Zz.
 

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