How to Calculate Error in Slope and Intercept for Least Squares Fit?

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    Error Fitting Square
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Discussion Overview

The discussion revolves around calculating the error in the slope and intercept of a least squares fit for a graph representing the photoelectric effect, specifically focusing on the relationship between voltage and frequency. Participants explore how to quantify the uncertainties associated with the slope and intercept based on given errors in measurements.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant presents a scenario involving measurements of voltage and frequency, seeking to calculate the errors in the slope (m) and intercept (a) of the linear fit equation Vo = m f + a.
  • The slope is given as h/e = 4.59*10^(-15)V/Hz, and the intercept as W/e = 2.11eV, with specified errors for voltage and frequency measurements.
  • Several participants reference a specific equation from a book to assist in the calculations, indicating that it may provide relevant formulas for error propagation in least squares fitting.
  • There is an acknowledgment of the usefulness of the provided link to the book, suggesting it contains valuable information for the calculations being discussed.

Areas of Agreement / Disagreement

There appears to be no explicit disagreement among participants regarding the approach to calculating the errors, but the discussion is primarily focused on referencing external resources rather than resolving the initial query.

Contextual Notes

The discussion does not clarify the specific equations or methods for error calculation, nor does it address any assumptions or limitations inherent in the data or the fitting process.

Ramapaa
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I have some data to calculate the photoelectric effect, and with my measurements I have made a graph using the least square fitting for voltage vs. frequencies. If I have an error of x for all voltages (V) and y for all frequencies f.
How do I calculate the error of the values m and a if my fitting is Vo= m f + a?

If needed here I post the data I have
The slope m is h/e = 4.59*10^(-15)V/Hz
and the constant a is the working function in electronvolts W/e=2.11eV
And the errors
for voltages are x= 0.05V
for frequencies y= 2*10^11
and I am using 5 data pairs.
 
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