Why Do Different Least Square Fit Methods Yield Different Results?

[pack2themoon]

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!

 

[mathman]

Which is better depends on the underlying physics.