Least Squares Fitting--Exponential
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المرجع الالكتروني للمعلوماتيه
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www.almerja.com
الجزء والصفحة:
...
28-3-2021
1986
Least Squares Fitting--Exponential
To fit a functional form
 |
(1)
|
take the logarithm of both sides
 |
(2)
|
The best-fit values are then
where 
and 
.
This fit gives greater weights to small 
values so, in order to weight the points equally, it is often better to minimize the function
 |
(5)
|
Applying least squares fitting gives
 |
(6)
|
 |
(7)
|
![[sum_(i=1)^(n)y_i sum_(i=1)^(n)x_iy_i; sum_(i=1)^(n)x_iy_i sum_(i=1)^(n)x_i^2y_i][a; b]=[sum_(i=1)^(n)y_ilny_i; sum_(i=1)^(n)x_iy_ilny_i].](https://mathworld.wolfram.com/images/equations/LeastSquaresFittingExponential/NumberedEquation6.gif) |
(8)
|
Solving for 
and 
,
In the plot above, the short-dashed curve is the fit computed from (◇) and (◇) and the long-dashed curve is the fit computed from (9) and (10).
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