problem_1_data.asv

% part a
xa=[1 2 3 4 5]';
ya=[2.2 2.8 3.6 4.5 5.5]';
Z=[ones(size(xa)) xa xa.^1]; 
[ a, fx, r2 ] = least_squares( Z, ya );
% part b

xb=[3 4 5 7 8 9 11 12]';
yb=[1.6 3.6 4.4 3.4 2.2 2.8 3.8 4.6]';
Z=[ones(size(xb)) xb xb.^2 xb.^3]; 
[ a, fx, r2 ] = least_squares( Z, yb );
% part c

xc=[0.5 1 2 3 4 5 6 7 9]';
yc=[6 4.4 3.2 2.7 2.2 1.9 1.7 1.4 1.1]';
Z=[exp(-1.5*xc), exp(-.3*xc),exp(-.05*xc)];
[ a3, fx3, r23 ] = least_squares( Z, yc );