Data Regression with MATLAB
Main.MatlabDataRegression History
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There is additional information on regression in the [[https://apmonitor.github.io/data_science|Data Science online course]].
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(:toggle hide fmincon_minimize button show="MATLAB fmincon Solution":)
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!!!! Excel and Python Solutions
The regression tutorials can also be completed with [[Main/ExcelDataRegression|Excel]] and [[Main/PythonDataRegression|Python]]. Click on the appropriate link for additional information.
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A frequent activity for scientists and engineers is to develop correlations from data. By importing the data into MATLAB, data analysis such as statistics, trending, or calculations can be made to synthesize the information into relevant and actionable information. This tutorial demonstrates how to create a linear or polynomial functions that best approximate the data trend, plot the results, and perform a basic statistical analysis. A script file of the MATLAB source code with sample data is below.
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A frequent activity for scientists and engineers is to develop correlations from data. By importing the data into MATLAB, data analysis such as statistics, trending, or calculations can be made to synthesize the information into relevant and actionable information. This tutorial demonstrates how to create a linear, polynomial, or nonlinear function that best approximates the data trend and how to analyze the solution. Script files of the MATLAB source code with sample data are below.
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!!!!Nonlinear Regression
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!!!!Nonlinear Regression with APM MATLAB
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!!!!Nonlinear Regression with MATLAB fmincon
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(:source lang=matlab:)
% clear session, close plots, clear screen
clear all; close all; clc
% data for regression
xm = [18.3447,79.86538,85.09788,10.5211,44.4556, ...
69.567,8.960,86.197,66.857,16.875, ...
52.2697,93.917,24.35,5.118,25.126, ...
34.037,61.4445,42.704,39.531,29.988];
ym = [5.072,7.1588,7.263,4.255,6.282, ...
6.9118,4.044,7.2595,6.898,4.8744, ...
6.5179,7.3434,5.4316,3.38,5.464, ...
5.90,6.80,6.193,6.070,5.737];
% initial parameter guess
p0 = [1,0.5,1];
% define prediction function
yp = @(p) p(1) + p(2)./xm + p(3).*log(xm);
% define objective function (scaled sum of squared errors)
objective = @(p) sum(((yp(p)-ym)./ym).^2);
disp(['Initial Objective: ' num2str(objective(p0))])
% optimize with fmincon
%[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN]
% = fmincon(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS)
A = [];
b = [];
Aeq = [];
beq = [];
% bounds
lb = []; % ones(3)*0.2;
ub = []; % ones(3)*1.5;
popt = fmincon(objective,p0,A,b,Aeq,beq,lb,ub);
% print results
disp(['Final Objective: ' num2str(objective(popt))])
disp(['Optimal parameters: ' num2str(popt)])
% plot results
plot(xm,ym,'ro')
hold on
plot(xm,yp(p0),'bx')
plot(xm,yp(popt),'gs')
legend('measured','initial predicted','optimal predicted')
ylabel('y')
xlabel('x')
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* [[Attach:MATLAB_nonlinear_regression.zip|MATLAB Nonlinear Regression Example Source Code]]
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!!!!Linear and Polynomial Regression
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!!!!Nonlinear Regression
(:html:)
<iframe width="560" height="315" src="https://www.youtube.com/embed/CejquWoc210" frameborder="0" allowfullscreen></iframe>
(:htmlend:)
Both regression tutorials can also be completed with [[Main/ExcelDataRegression|Excel]] and [[Main/PythonDataRegression|Python]]. Click on the appropriate link for additional information.
(:html:)
<iframe width="560" height="315" src="https://www.youtube.com/embed/CejquWoc210" frameborder="0" allowfullscreen></iframe>
(:htmlend:)
Both regression tutorials can also be completed with [[Main/ExcelDataRegression|Excel]] and [[Main/PythonDataRegression|Python]]. Click on the appropriate link for additional information.
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!!!!Python Data Regression
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!!!!MATLAB Data Regression
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(:title Data Regression with MATLAB:)
(:keywords data regression, MATLAB, nonlinear, polynomial, linear regression, university course:)
(:description Data Regression with MATLAB - Problem-Solving Techniques for Chemical Engineers at Brigham Young University:)
!!!!Python Data Regression
A frequent activity for scientists and engineers is to develop correlations from data. By importing the data into MATLAB, data analysis such as statistics, trending, or calculations can be made to synthesize the information into relevant and actionable information. This tutorial demonstrates how to create a linear or polynomial functions that best approximate the data trend, plot the results, and perform a basic statistical analysis. A script file of the MATLAB source code with sample data is below.
* [[Attach:MATLAB_data_regression.zip|MATLAB Data Regression Example Source Code]]
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This regression tutorial can also be completed with [[Main/ExcelDataRegression|Excel]] and [[Main/PythonDataRegression|Python]]. Click on the appropriate link for additional information.
----
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(:keywords data regression, MATLAB, nonlinear, polynomial, linear regression, university course:)
(:description Data Regression with MATLAB - Problem-Solving Techniques for Chemical Engineers at Brigham Young University:)
!!!!Python Data Regression
A frequent activity for scientists and engineers is to develop correlations from data. By importing the data into MATLAB, data analysis such as statistics, trending, or calculations can be made to synthesize the information into relevant and actionable information. This tutorial demonstrates how to create a linear or polynomial functions that best approximate the data trend, plot the results, and perform a basic statistical analysis. A script file of the MATLAB source code with sample data is below.
* [[Attach:MATLAB_data_regression.zip|MATLAB Data Regression Example Source Code]]
(:html:)
<iframe width="560" height="315" src="https://www.youtube.com/embed/ro5ftxuD6is" frameborder="0" allowfullscreen></iframe>
(:htmlend:)
This regression tutorial can also be completed with [[Main/ExcelDataRegression|Excel]] and [[Main/PythonDataRegression|Python]]. Click on the appropriate link for additional information.
----
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