Error in declination of linear regression

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Discussion Overview

The discussion revolves around the calculation of total error in the declination of a linear regression slope derived from experimental measurements of mass and magnetic field strength. Participants explore the implications of measurement errors on the regression analysis and seek methods to quantify the total error considering both regression residuals and measurement inaccuracies.

Discussion Character

  • Technical explanation, Debate/contested, Experimental/applied

Main Points Raised

  • One participant describes the challenge of calculating the total error in the linear slope due to measurement errors not being accounted for in the initial regression analysis.
  • Another participant questions the feasibility of removing measurement error to obtain a "true" slope, expressing skepticism about the possibility.
  • A further clarification is provided regarding the need to consider both the regression error and the inherent measurement errors, suggesting that the total error will exceed the regression residuals alone.
  • It is noted that regression algorithms typically provide statistical standard deviations for estimated parameters but do not differentiate between sources of variation, implying that the reported errors encompass all variations from both measurements and the regression process.

Areas of Agreement / Disagreement

Participants express differing views on the ability to isolate measurement error from regression results. There is no consensus on a method to accurately calculate the total error that incorporates both sources of error.

Contextual Notes

Limitations include the potential for unaccounted assumptions regarding the nature of measurement errors and the dependence on the definitions of error used in regression analysis.

Who May Find This Useful

This discussion may be useful for students and researchers engaged in experimental physics or data analysis, particularly those dealing with linear regression and measurement error considerations.

UiOStud
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During a lab exercise we measured different masses of a magnetic material on a scale while changing the strength of the magnetic field it was in. Afterwards we plotted the masses and the fieldstrength hoping to find a linear slope. Then we drew a linear slope by using linear regression and found the declination of the slope and it's error. However this error does not take into account that the values of the masses also have an error. How can I fin the total error of the declination with the errorin the measurements in mind?
 
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Are you asking how you can remove the measurement error from your results to get the true slope of the line? I doubt that you can.
 
Okay, let me try to explain in other words. I need to find the exact error in the linear slope I'm drawing. Because the points are not actually perfectly aligned there is an error in my regression. But finding the error from the residuals is not enough because there is an extra error coming from the fact that there is an error in the measurements themselves. The total error will be greater than the one I find only looking at the residuals. How can I find the total error of both the error in measurements and the error of regression?
 
Regression algorithms in statistics packages will give you numbers for the statistical standard deviation of the estimated parameters, like the slope. They will not distinguish between different sources of variation. So the numbers they give will be for the total variation of the measurements and the mass.
 
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