# Given a set of date point x and y, estimate three polynomial functions (2nd degree, 3rd degree, 4th degree) that will best fit the data.

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John Doe am 27 Nov. 2021
Kommentiert: Walter Roberson am 27 Nov. 2021
Given a set of date point x and y, estimate three polynomial functions (2nd degree, 3rd degree, 4th degree) that will best fit the data. Compute new set of y data from the three functions and determine which of the three functions will give the least norm difference.
This is what I've came up with, but still not sure if it really satisfy the problem.
x=[0.9 1.5 3 4 6 8 9.5];
y=[0.9 1.5 2.5 5.1 4.5 4.9 6.3];
p=polyfit(x,y,3)
xp=0.9:0.1:9.5;
yp=polyval(p,xp);
plot(x,y,'o',xp,yp)
xlabel('x'); ylabel('y')
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### Antworten (1)

Walter Roberson am 27 Nov. 2021
The question is expecting you to also polyfit with degree 2 and 4, and to polyval with those, and to compute the norm() of the projected values against the actual values, and then to see whether degree 2, degree 3, or degree 4 gave the best fit.
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John Doe am 27 Nov. 2021
Bearbeitet: John Doe am 27 Nov. 2021
Is it like this?
x = [0.9 1.5 3 4 6 8 9.5];
y = [0.9 1.5 2.5 5.1 4.5 4.9 6.3];
p = polyfit(x,y,2);
l = polyfit(x,y,3);
t = polyfit(x,y,4);
xp = 0.9:0.1:9.5;
yp1 = polyval(p,xp);
yp2 = polyval(l,xp);
yp3 = polyval(t,xp);
xlabel('x');
ylabel('y');
plot(x,y,'o',xp,yp1,yp2,yp3)
Walter Roberson am 27 Nov. 2021
x = [0.9 1.5 3 4 6 8 9.5];
y = [0.9 1.5 2.5 5.1 4.5 4.9 6.3];
p = polyfit(x,y,2);
l = polyfit(x,y,3);
t = polyfit(x,y,4);
xp = 0.9:0.1:9.5;
yp1 = polyval(p,xp);
yp2 = polyval(l,xp);
yp3 = polyval(t,xp);
xlabel('x');
ylabel('y');
plot(x,y,'o',xp,yp1,xp,yp2,xp,yp3)

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