Question

Example 1: Least Squares Fit to a Data Set by a Linear Function. Compute the coefficients of the best linear least-squares fit to the following data. x2.4 3.6 3.64 4.7 5.3 y| 33.8 34.7 35.5 36.0 37.5 38.1 Plot both the linear function and the data points on the same axis system Solution We can solve the problem with the following MATLAB commands x[2.4;3.6; 3.6;4.1;4.7;5.3]; y-L33.8;34.7;35.5;36.0;37.5;38.1 X [ones ( size (x)),x); % build the matrix X for linear model % build vector of x -values % build vector of y -values % right hand side of the Normal Equations % Left hand side of the Normal Equations % Cholesky decomposition Uchol (S); % solve the normal equations using Cholesky decomposition plot(x,y,'o') q2:0.1:6; fit-c(1)+c (2)#4; hold on plot (q,fit, 'r'); % plot the data points % define a vector for plotting the linear fit % define the linear fit % plot the linear fit together with the data points Running the script file produces the output 29.6821 1.5826 and the following figure.

Answer 1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

clear all
clc
format short e
dat=load('gco2.dat');
year=dat(:,1);
conc=dat(:,2);
A=[ones(length(year),1) year];
b=conc;
x=A\b;
disp('For linear fit')
c1=x(1)
c2=x(2)
q=min(year):max(year);
yy=polyval(x(end:-1:1),q);
plot(year,conc,'o',q,yy,'LineWidth',2);
A=[ones(length(year),1) year year.^2];
b=conc;
x=A\b;
disp('For quadratic fit')
c1=x(1)
c2=x(2)
c3=x(3)
yy=polyval(x(end:-1:1),q);
hold on;
plot(q,yy,'LineWidth',2);
legend('data points','Linear fit','quadratic fit','location','northwest');

Kindly revert for any queries

Thanks.