echo off;
% NUMERICAL METHODS: MATLAB Programs, (c) John H. Mathews 1994
% To accompany the text:
% NUMERICAL METHODS for Mathematics, Science and Engineering, 2nd Ed, 1992
% Prentice Hall, Englewood Cliffs, New Jersey, 07632, U.S.A.
% This free software is complements of the author.

% Algorithm 5.1 (Least Squares Line).
% Section 5.1, Least-Squares Line, Page 264
echo on; clc; format short; hold off; clear

% This program finds the least squares line, given a set of

% data points { (x , y ), (x , y ) ,..., (x , y ) }.
% 1 1 2 2 n n

% The abscissas and ordinates are stored in X and Y, respectively.

% X = [x , x ,..., x ]; Y = [y , y ,..., y ];
% 1 2 n 1 2 n

% Remark. lsline.m is used for Algorithm 5.1

pause % Press any key to continue.

clc;
% Place the abscissas for the points in X.

% Place the ordinates for the points in Y.

X = [-1 0 1 2 3 4 5 6];

Y = [10 9 7 5 4 3 0 -1];

[A B] = lsline(X,Y);

pause % Press any key to graph data points.

clc; clg;
a = min(X)-0.20; b = max(X)+0.20;
c = min(Y)-0.35; d = max(Y)+0.35;
axis([a b c d]);...
plot(X,Y,'or');...
hold on;...
plot([a b],[0 0],'b',[0 0],[c d],'b');...
xlabel('x');...
ylabel('y');...
title('The given x-y data points.');...
grid;...
axis;...
hold off;...
shg; pause % Press any key to continue.

points = [X;Y]; format short;
clc,disp(''),disp('The given x-y data points.'),...
disp(' x y'),disp(points'),...

pause % Press any key to continue.

clc; clg;
a = -1;
b = 7;
c = -2;
d = 12;
Xs = [a b];
Ys = A*Xs + B;
axis([a b c d]);...
plot(X,Y,'or',Xs,Ys,'-g');...
hold on;...
plot([a b],[0 0],'b',[0 0],[c d],'b');...
xlabel('x');...
ylabel('y');...
Mx1 = 'Least squares line: f(x) = ';...
Mx2 = [Mx1,num2str(A),' x'];...
if B > 0,
Mx3 = [Mx2,' + ',num2str(B)];
else
Mx3 = [Mx2,' - ',num2str(abs(B))];
end;...
title(Mx3);...
grid;...
axis;...
hold off;...
shg; pause % Press any key to continue.

Mx4 = 'The given x-y data points.';
clc,echo off,diary output,...
disp(''),disp(Mx3),disp(Mx4),...
disp(' x y'),disp(points'),diary off, echo on
pause % Press any key to continue.
points = [X;Y;A*X+B;Y-(A*X+B)]';
Mx5=' x(k) y(k) f(x(k)) error';
clc,echo off,diary output,disp(''),disp(Mx3),...
disp(''),disp(Mx5),disp(points),diary off,echo on