Question

6. You have a x-y relationship as follows 1 2 3 4 5 6 7 8 10 X 17.52 22.76 24.22 36.83 37.65 51.32 68.35 74.59 4.382 1.787 7.757 3nd order polynomial to curve-fit this relationship, i.e. We want to use a yaaxax +a^x (8) (a) Determine the coefficients of the polynomial by solving the following equation a (9) y's az a, (b) Determine the coefficients of the polynomial by using function polyfit (c) Make a plot showing y, y verse x. (d) Find the least squares error between y and y, ie. 11 J-Σ-J) (10) _

use matlab

Answer 1

Matlab Code:

x = 0:10;
y = [4.382 1.787 7.757 17.52 22.76 24.22 36.83 37.65 51.32 68.35 74.59];

%part a - selecting 4 points to solve for the coefficients
X = [x(1) x(4) x(8) x(11)]';
Y = [y(1) y(4) y(8) y(11)]';
A = [ones(4,1) X X.^2 X.^3];
coeffs1 = inv(A)*Y;
yb1 = coeffs1(1)+coeffs1(2).*x+coeffs1(3).*x.^2+coeffs1(4).*x.^3;
lsqerr1 = sum((y-yb1).^2);%least square error for part a
subplot(1,2,1);
plot(x,y); hold on
plot(x,yb1);
legend('y','yb1');

%part b
coeffs2 = polyfit(x,y,3);
yb2 = coeffs2(4)+coeffs2(3).*x+coeffs2(2).*x.^2+coeffs2(1).*x.^3;
lsqerr2 = sum((y-yb2).^2);%least square error for part b
subplot(1,2,2);
plot(x,y); hold on
plot(x,yb2);
legend('y','yb');

Command Window >> lsqerr2 lsqerr2 104.46 |» fx >>

80 80 y yb1 yb 70 60 60 50 50 40 20 20 10 10 0 10 5 C 5 10 LC 70 40 30 LO 30