Problem 5.6

Nasser Abbasi

Output

» nma_HW_5_6

solve problem 5.6

Nasser Abbasi

enter the x values:[1 2 3 4 5]

enter the y values:[2470 2510 2410 2350 2240]

enter the polyminal degree to fit to data [1 to 4]:1

a =

1.0e+003 *

2.5820

-0.0620

fitting polynomial degree=1

a(0) = 2582

a(1) = -62

» nma_HW_5_6

solve problem 5.6

Nasser Abbasi

enter the x values:[1 2 3 4 5]

enter the y values:[2470 2510 2410 2350 2240]

enter the polyminal degree to fit to data [1 to 4]:2

a =

1.0e+003 *

2.4520

0.0494

-0.0186

fitting polynomial degree=2

a(0) = 2452

a(1) = 49.4286

a(2) = -18.5714

»

» nma_HW_5_6

solve problem 5.6

Nasser Abbasi

enter the x values:[1 2 3 4 5]

enter the y values:[2470 2510 2410 2350 2240]

enter the polyminal degree to fit to data [1 to 4]:3

a =

1.0e+003 *

2.3260

0.2264

-0.0861

0.0075

fitting polynomial degree=3

a(0) = 2326

a(1) = 226.429

a(2) = -86.0714

a(3) = 7.5

»

» nma_HW_5_6

solve problem 5.6

Nasser Abbasi

enter the x values:[1 2 3 4 5]

enter the y values:[2470 2510 2410 2350 2240]

enter the polyminal degree to fit to data [1 to 4]:4

a =

1.0e+003 *

1.8400

1.1425

-0.6437

0.1425

-0.0112

fitting polynomial degree=4

a(0) = 1840

a(1) = 1142.5

a(2) = -643.75

a(3) = 142.5

a(4) = -11.25

»

SOURCE CODE

function nma_HW_5_6()

%

% solve problem 5.6

% Nasser Abbasi

clear all; help nma_HW_5_6;

x=input('enter the x values:');

y=input('enter the y values:');

deg = input('enter the polyminal degree to fit to data [1 to 4]:');

figure;

plot(1:length(x),y,'or');

title(sprintf('fitting data using polynomial of degree %d',deg));

xlabel('Day number');

ylabel('Dow value');

grid on;

A= makeDesignMatrix(x,deg);

a=inv(A'*A)*A'*y'

%Now, add sixth day to see how the fit will extent to it

x(6)=6;

printCoeff(a);

if(deg==1) % y=a1 + a2 x

Y=a(1)+a(2)*x;

else

if(deg==2) % y=a1+a2 x+ a3 x^2

Y=a(1)+a(2)*x+a(3)*x.^2;

else

if(deg==3) % y=a1 + a2 x +a3 x^2 + a4 x^3

Y=a(1)+a(2)*x+a(3)*x.^2+a(4)*x.^3;

else

if(deg==4) % y=a1 +a2 x + a3 x^2 + a4 x^3 + a5 x^4

Y=a(1)+a(2)*x+a(3)*x.^2+a(4)*x.^3+a(5)*x.^4;

end

end

end

end

%

% now estimate the value at day 6 using the polynomial

%

hold on;

plot(1:6,Y,'--');

legend('actual','fitted data');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function A=makeDesignMatrix(x,deg)

%note: y1=1, y2=x, y3=x^2, y4=x^3, y5=x^4

for(i=1:length(x))

for(j=1:deg+1)

A(i,j)= x(i)^(j-1);

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function printCoeff(a)

fprintf('fitting polynomial degree=%d\n',length(a)-1);

for (i=1:length(a))

fprintf('a(%d) = %g\n',i-1,a(i));

end