# Linear Fitting starting from a value

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Nicola De Noni on 10 Oct 2022
Edited: Torsten on 10 Oct 2022
Hi everyone!
I need to fit these data [100 90 80 70 50 45 40 43 42 40 35] whom are distanced by 10 seconds.
The problem is that I would fit these data starting from the first value (100) in order to understand the slope of the line. Is it possible?
Thanks!

Torsten on 10 Oct 2022
Edited: Torsten on 10 Oct 2022
Sure. Use
l(x) = a*x + 100
as model function and fit the parameter a.
xdata = ...; % your xdata as column vector
ydata = ...; % your ydata as column vector
a = xdata\(ydata-100)
But starting from a certain x-value, the slope seems to change. You should separate the fit into two parts:
l1(x) = a*x + 100 0 <= x<= x1
l2(x) = b*x + [(a-b)*x1 + 100] x1 <= x <= x(end)

Hiro Yoshino on 10 Oct 2022
Edited: Hiro Yoshino on 10 Oct 2022
refline is the easiest way to achieve that.
y = [100 90 80 70 50 45 40 43 42 40 35];
x = 0:10:10*(length(y)-1);
plot(x,y,'o');
refline if you want to know the coefficients:
p = polyfit(x,y,1)
p = 1×2
-0.6391 89.6818
polyfit for reference.
Nicola De Noni on 10 Oct 2022
Thanks @Hiro but i would like that the fitting line passe through the first point 100,0

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