How to fit linear plateau equation ?

I want to fit linear equation with plateau condition.

y=a(x+n)+b

These are the data in which I Want to fit:

x=[0,80,100,120,150],

y=[1865,3608,4057,4343,4389]

I don not know how to find the plateau value of yield.

[John D'Errico]

You don'thow to do something impossible? Something that makes no sense at all? GOOD THING!

The relation

y=a(x+n)+b

is a straight line. There is no plateau described by it at all.

So you need to exaplin what it is that you need to do. Of course, having only 5 data points means that nothing you will do is likely to make much sense.

[madhuri dubey]

Ok the another data data set is

x= x=[0,40,80,100,120,150,170,200],

y=[1865,2855,3608,4057,4343,4389,4415,4478]

I don't know how to fit plateau condition in linear equation that is why i asked to help. The plateau condition are given here;

x < xc(Ymax) ;

y=yp, x >= xc(Ymax)

[John D'Errico]

I give up.

Answer 1

[Bruno Luong]

You can use this FEX file (BSFK)

The code is by default use QUADPROG from MATLAB, but can also work with QPAS project by Adrian Wills for user who has not access to optimization toolbox as showed below:

x=[0,40,80,100,120,150,170,200];
y=[1865,2855,3608,4057,4343,4389,4415,4478];

opt = struct('KnotRemoval','none','sigma',1,'qpengine','qpas');
pp = BSFK(x,y,2,2,[],opt);

% prepare graphical data
xi = linspace(min(x),max(x));
yi = ppval(pp,xi);
xb = pp.breaks(2);
yb = ppval(pp,xb);

clf
plot(x,y,'or',xi,yi,'-b');
xline(pp.breaks(2));
text(xb,yb,sprintf('(%g,%g)',xb,yb));

[Bruno Luong]

The equation of the plateau obtained with BSFK is

y(x) = pp.coefs(2,2) + pp.coefs(2,1)*(x-pp.breaks(2))
 = 4326.29 + 1.664956 * (x - 111.97931945)

[John D'Errico]

Note that the upper line segment is not held constant in your solution, as it seems the OP wants.

[Bruno Luong]

I don't know exactly what he wants, I did not follow the thread closely.

I give the code if he is not happy then I hope he'll come back with further request.

If the plateau must be constant I can enfore the derivative to 0.