MATLAB: How to find the coefficients for an equation having the experimental data

coefficients

I'm trying to write a code that uses observed data to generate the coefficients of a function.

Here's my data:

tc = [10,12,14,16,18,20,22,24,26,28,30,32,34,36,38]; % Temperature (Celsius)

tk = tc + 273.15; % Temperature (Kelvin)

pbar = [6.149,6.585,7.045,7.529,8.035,8.57,9.134,9.722,10.34,10.99,11.67,12.37,13.11,13.89,14.7]; % Pressure (bar)

pkpa = pbar * 100; % Pressure (kPa)

And here is my equation:

A = ln(pkpa) + B/tk;

How do I find A and B that best fit the data?

Best Answer

Rearrange as lnP = A - B/T --> -B/T + A which has form of mx+b for x=1/T, m=-B, b=A.

>> b=polyfit(1./tk,log(pkpa),1);  % fit the form
>> yhat=polyval(b,1./tk);         % evaluate in Matlab form
>> plot(tk,pkpa,'*-')             % plot raw data
>> hold all
>> plot(tk,exp(yhat),'r-')        % add fit
>> B=-b(1);                       % convert to you nomenclature
>> A=b(2);
>> polyval([-B A],1/tk(1))==yhat(1)         % compare results to show same
ans =
   1
>>

NB: Remember must take exp to convert to actual units of P since fitted ln(P)

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MATLAB: How to plot residual and fitting curve

This works well:

a=[6.91 8.26 2.21 1.19 2.32 8.41 7.3 4.32 2 3.42 3.21 7.54 8.72 2.38 3.1 8.18 5.47 1.27 6.09 7.98 7.69 5.39 7.35 7.33 5.3];
b=[17.52 1.77 14.97 7.5 15.09 9.4 17.36 22.69 12.87 19.16 19.06 14.75 9.83 17.61 18.63 11.15 23.89 10.75 22.33 14.29 16.77 22.41 16.63 17.42 21.37];
% First need to sort a otherwise when we go to plot it, it will look like a mess!
[a, sortOrder] = sort(a, 'ascend');
b = b(sortOrder); % Need to sort b the same way.
% First compute the linear fit.
linearCoeffs = polyfit(a, b, 1);
Slope = linearCoeffs(2)
Intercept = linearCoeffs(1)
% Plot training data and fitted data.

subplot(2, 1, 1);
aFitted = a; % Evalutate the fit as the same x coordinates.

bFitted = polyval(linearCoeffs, aFitted);
plot(a, b, 'rd', 'MarkerSize', 10);
hold on;
plot(aFitted, bFitted, 'b-', 'LineWidth', 2);
grid on;
xlabel('a', 'FontSize', 20);
ylabel('b', 'FontSize', 20);
% Plot residuals as lines from actual data to fitted line.

for k = 1 : length(a)
  yActual = b(k);
  yFit = bFitted(k);
  x = a(k);
  line([x, x], [yFit, yActual], 'Color', 'm');
end
% Do the same for a quadratic fit.
quadraticCoeffs = polyfit(a, b, 2);
% Plot training data and fitted data.
subplot(2, 1, 2);
aFitted = a; % Evalutate the fit as the same x coordinates.
bFitted = polyval(quadraticCoeffs, aFitted);
plot(a, b, 'rd', 'MarkerSize', 10);
hold on;
plot(aFitted, bFitted, 'b-', 'LineWidth', 2);
grid on;
xlabel('a', 'FontSize', 20);
ylabel('b', 'FontSize', 20);
% Plot residuals as lines from actual data to fitted line.
for k = 1 : length(a)
  yActual = b(k);
  yFit = bFitted(k);
  x = a(k);
  line([x, x], [yFit, yActual], 'Color', 'm');
end

MATLAB: Add lsline or trend line to log-log graph

This works:

wet=[120 49 30 21 12 10 9 7 4];
dry=[49 12 5 1 1 1 0 0 0 ];
x1=[1 2 3 4 5 6 7 8 9];
scatter(x1,wet);
set(gca,'XScale','log');
set(gca,'YScale','log');
b = polyfit(log(x1), log(wet), 1);
wetfit = exp(b(2)) .* x1.^b(1);
hold on
plot(x1, wetfit)
hold off

producing:

Best Answer

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MATLAB: How to plot residual and fitting curve

MATLAB: Add lsline or trend line to log-log graph

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