Should linear regression always be forced through the origin?

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Discussion Overview

The discussion centers around the appropriateness of forcing linear regression through the origin when plotting two variables that theoretically should intersect at that point. Participants explore the implications of this practice in the context of data fitting, theoretical predictions, and potential errors in experimental data.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant suggests that forcing the regression through the origin yields a better gradient value, questioning the acceptability of this approach.
  • Another participant argues against forcing the regression through the origin, citing the possibility of real-world data not passing through that point due to errors.
  • A third participant emphasizes the complexity of curve fitting and mentions that deviations from theoretical predictions should be statistically assessed and explained, particularly when no clear theoretical model exists.
  • A later reply reiterates that one should not force a curve fit to pass through a point not represented in the data, suggesting that discrepancies should be acknowledged and discussed rather than ignored.

Areas of Agreement / Disagreement

Participants express differing views on whether linear regression should be forced through the origin. There is no consensus, as some advocate for this practice under certain conditions while others strongly oppose it, highlighting the potential for systematic errors and the importance of theoretical alignment.

Contextual Notes

Participants note that the appropriateness of forcing a regression through the origin may depend on the theoretical framework and the nature of the experimental data, with some emphasizing the need for statistical significance in deviations.

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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