Error in declination of linear regression

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SUMMARY

The discussion focuses on the challenge of calculating the total error in the declination of a linear regression slope when both measurement errors and regression errors are present. Participants highlight that standard regression algorithms in statistical packages do not separate these sources of variation, providing only a combined statistical standard deviation for the slope. The need for a method to accurately quantify the total error, considering both measurement inaccuracies and regression residuals, is emphasized.

PREREQUISITES
  • Understanding of linear regression analysis
  • Familiarity with statistical standard deviation concepts
  • Knowledge of error propagation techniques
  • Experience with statistical software packages (e.g., R, Python's SciPy)
NEXT STEPS
  • Research error propagation methods in linear regression
  • Learn how to use R's 'lm' function for regression analysis
  • Explore Python's SciPy library for statistical analysis
  • Investigate techniques for isolating measurement error in experimental data
USEFUL FOR

This discussion is beneficial for data analysts, researchers conducting experiments, and statisticians who need to accurately assess the reliability of regression results in the presence of measurement errors.

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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