How to do a nonlinear fit using least squares

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Andrew
Andrew 2019 年 9 月 14 日
コメント済み: Star Strider 2019 年 9 月 15 日
I have a set of data points giving me the values for the second virial coefficient, for various values of T, of the virial expansion which is an equation that corrects the ideal gas law for empirical deviations:
I'm trying to do a least squares fit to determine how well the van der Waals equation predicts using MATLAB.
The equation you derive for B using van der Waals' equation ends up being:
where a and b are unknown constants I need to determine and R is just the ideal gas constant.
Now my data points for true values are here:
B = [-160 -35 -4.2 9 16.9 21.3]*10^-6 ;
T = [100 200 300 400 500 600]; (kelvin)
How can I write some code which will use the least squares method to generate estimates for a and b using the given data points?
My problem is that this is essentially a equation which I'm not sure how to represent in MATLAB.
I can only find options for quadratic, cubic, polynomial fit etc.

採用された回答

Star Strider
Star Strider 2019 年 9 月 15 日
編集済み: Star Strider 2019 年 9 月 15 日
This is actually a linear problem, so a linear approximation will estimate the parameters correctly:
R = 8.314462; % J K^−1 mol
B = [-160 -35 -4.2 9 16.9 21.3];
T = [100 200 300 400 500 600];
ab = [ones(size(B(:))) - 1./(R*T(:))] \ B(:); % Linear Approximation Parameter Estimation
Bfit = [ones(size(B(:))) - 1./(R*T(:))] * ab; % Linear Fit
figure
plot(T, B, 'pg')
hold on
plot(T, Bfit,'-r')
hold off
grid
xlabel('T')
ylabel('B')
legend('Data','Linear Least-Squares Fit', 'Location','E')
The parameters are:
a = 64.2001320479734
b = 182307.574287957
EDIT —
Added plot figure:
How to do a nonlinear fit using least squares - 2019 09 14.png
  8 件のコメント
Andrew
Andrew 2019 年 9 月 15 日
got it. Thanks for the clarification!
Star Strider
Star Strider 2019 年 9 月 15 日
My pleasure!

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その他の回答 (1 件)

Jackson Burns
Jackson Burns 2019 年 9 月 15 日
Attached is code generated by cftool using a custom equation. Hope this helps!
  5 件のコメント
Jackson Burns
Jackson Burns 2019 年 9 月 15 日
If you're making this call in a function, it will tell you that result is unused if you don't later on reference result or return it from the function.
Andrew
Andrew 2019 年 9 月 15 日
got it. Thanks!

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