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From: Nathan Jensen on 6 Jul 2010 10:15
Disclaimer: I am sorry for the long question, and confusing layout of it.

Given data:

x=[0 1.63 5.615 6.255 6.82 7.34 7.83 8.3 8.755 8.965];
y=[28.71 28.71 90.75 114.75 138.75 162.75 186.75 210.75 234.75 245.868];

Required output:

A curve of good fit (this term is loosely defined at the moment, perhaps an R^2 value) that fits only points 2-10, with an initial slope at point 2 (1.63, 28.71) of 0.

Caveats:

-The slope (derivative of position curve) at point 2 (1.63, 28.71), must be 0 or as close to 0 as possible.
-The only points that I really need to focus on are points 2-10. In reality, for the situation that has been presented me, any x value less than 1.63 will always have a y value of 28.71, thus the fitted curve only needs to work with x(2):x(end).
-For other situations, the x values will change, but the y values will not.
-I do not yet have the curve fitting toolbox, but I may in the future.

First attempt:

x=[0 1.63 5.615 6.255 6.82 7.34 7.83 8.3 8.755 8.965];
y=[28.71 28.71 90.75 114.75 138.75 162.75 186.75 210.75 234.75 245.868];
x0=x(2);
options=optimset('TolX',1e-5,'TolFun',1e-8,'MaxFunEvals',inf);
myx=fminsearch(@(a) sum((a(1)*(x-x0).^2+a(2)*(x-x0).^3+a(3)*(x-x0).^4+a(4)-y).^2), [0,0,0,0],options);
x2=(x(1) : (x(end)-x(1))/1000 : x(end));
y2=myx(1)*(x2-x0).^2+myx(2)*(x2-x0).^3+myx(3)*(x2-x0).^4+myx(4);
plot(x2,y2,'k-');
hold on
plot(x,y,'r*');

My question to you:

How can I write a function that takes in given x values, and plots a curve of good fit, with the given requirements? Is there a better way to do it than the one that I have already done?

Thank you,

Nathan
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