Why Do Different Least Square Fit Methods Yield Different Results?

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SUMMARY

This discussion centers on the differences in results obtained from two least squares fitting methods applied to experimental data sets. The first method involves performing a linear least squares fit on the logarithm of the dependent variable (log(yi)), while the second method directly minimizes the sum of squared differences (sigma (yi-y)^2) in the linear scale. The results indicate that the first method provides a better fit on a logarithmic scale, whereas the second method is more accurate on a linear scale. The choice of method should be guided by the underlying physics of the data being analyzed.

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pack2themoon
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Hi everyone, very excited to be here and this my first post.

I have a question about data fitting by using least square fit, and the problem is:
I have a experimental data set(xi, yi), and I want to fit it to single exponential y,
now i tried two ways:
1. do linear least square fit to (xi, log(yi))
2. directly search minimal for sigma (yi-y)^2

The resulted fittings are different, the 1st one only looks fit on log scale, and the 2nd only looks fit on linear scale.

Can you give me any hint what is the root of the problem? and which way makes physical sense?

Thank you!
 
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