Problem with least square fit

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In summary, the speaker has a question about data fitting using least square fit with a set of experimental data. They have tried two methods and have observed different results on a log and linear scale. They are seeking advice on the best approach, which may depend on the underlying physics.
  • #1
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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  • #2
Which is better depends on the underlying physics.
 

1. What is the problem with least square fit?

The problem with least square fit is that it assumes that the data points have equal weight and that the errors are normally distributed. This may not always be the case in real-world situations, leading to inaccurate results.

2. Can least square fit be used for all types of data?

No, least square fit is most suitable for linear relationships and may not be appropriate for non-linear data.

3. How do you determine if a least square fit is a good fit?

A good fit can be determined by calculating the coefficient of determination, also known as R-squared value. A high R-squared value (close to 1) indicates a good fit, while a low value (close to 0) indicates a poor fit.

4. What are some alternatives to least square fit?

Alternative methods include weighted least squares, which takes into account the varying weights of data points, and non-linear least squares, which can be used for non-linear relationships.

5. How can you improve the accuracy of a least square fit?

One way to improve accuracy is by increasing the sample size and reducing the amount of measurement error. Additionally, using a more appropriate model or considering outliers in the data can also improve the accuracy of the fit.

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