Question

Problem: The relationship between a variable g and time t for a certain process is given by: go=p, In +e 2 sin(0.3t) A set of 25 experimental data pairs were obtained. We want to calculate the optimal values of the relationship parameters P. and p, in the least-squares sense. Write a MATLAB script that solves the curve fitting problem using the least-squares method. Requirements: 1. Your script must calculate the values of the parameters P, and p, and display their values using 4 digits after the decimal point, as follows: The calculated coefficients are: pl - p2 = ... 2. Your script must calculate the coefficient of determination R2 and display it in a formatted fashion, using 5 digits after the decimal point, as follows: Calculated R2 = 3. On the same set of axes, plot a comparison of the original data and the fit function. The fit function must be plotted with a resolution of no less than 100 points. a) Add proper labels to the axes of the figure. b) Add proper legend.

Answer 1

`Hey,

Note: If you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

Please note in order to run the program you should have t2pb2data.mat file in your current directory as mentioned in question

clc
clear all
close all
format long
A=load('t2pb2data.mat');
t=A(:,1);
g=A(:,2);
A=[log(1./t(:).^3) sin(0.3*t)];
b=g(:);
C=A\b;
p1=C(1);
p2=-log(C(2));
f=@(t) p1*log(1./t.^3)+exp(-p2)*sin(0.3*t);
fprintf('The calculated coefficients are: \n');
fprintf('p1=%.4f\np2=%.4f\n',p1,p2);
SSR=sum((g-f(t)).^2);
SST=sum((g-mean(g)).^2);
R2=1-SSR/SST;
fprintf('R2=%.5f\n',R2);
tt=linspace(min(t),max(t),101);
yy=f(tt);
plot(tt,yy,t,g,'o');
xlabel('t');
ylabel('g(t)');
title('Plot of fit g(t)');
legend('g(t)','raw data');

- O X Pradeep PUBLISH VIEW do E C . Search Documentation E Bulleted List Preformatted Text Numbered List E Code Image Display Latex INSERT BLOCK MARKUP Publish PUBLISH ох googleLinks.m X HomeworkLib2.m X testcm x ahk.m X nse_filt.m x + 1 MATLAB R2018a HOME PLOTS APPS EDITOR B Bold Hyperlink Italic Save Section Section Inline Latex with Title M Monospaced FILE INSERT SECTION INSERT INLINE MARKUP Da O: Windows System32 Current Folder Name 0409 1029 1033 1036 1040 1045 1046 1049 1055 3082 Advancedinstallers af-ZA am-et AppLocker appraiser Details Editor - C:\Users\PRADEEP KALRA\Documents\MATLAB\saveee.m saveee. m bisectionmethodbypradeep.m x eulerSystem.m x f=@(t) pl*log (1./t. 3) +exp(-p2)*sin(0.3*t); fprintf('The calculated coefficients are: \n') fprintf('pl=& .4f\np2=$.4f\n',pl,p2); SSR=sum((g-f(t)).^2); SST=sum ((g-mean(g)).^2); R2=1-SSR/SST; fprintf('R2=$.5f\n',R2); tt=linspace (min(t),max(t),101); yy=f(tt); plot(tt, vy,t,g,'o'); xlabel('t'); ylabel('g(t)'); title('Plot of fit g(t)'); legend('g(t)', 'raw data'); Command Window The calculated coefficients are: pl=-2.0195 p2=-0.9675 R2=-0.22359 IIIIIIIIIIIII Workspace Name HA C Value 100x2 double 100x1 double [-2.0195;2.6314] @(t)p1*log(1./t.^3)+... 100x1 double -2.0195 -0.9675 -0.2236 1.2221e+03 Hg p2 R2 SSR script In 26 Col 27 ENG 1:26 AM ? IN 04/16/20 Type here to search op ^ D

Kindly revert for any queries

Thanks.