How to make segmented regression line and determine the breakpoints?

Hi,

I have a data set which shows multiple distinct linear lines as shown in the figure. I have to plot equations mx+y in such a way that the slope is always positive and where there is change in gradient, breakpoint is determined. I tried to do it but I am sure how it is done in Matlab.

Any suggestions would be helpful. I have attached the dataset.

Thank you in advance.

Answer 1

[Image Analyst]

The way I do it is to pick a dividing point and then slide that along fitting a line to each side. The dividing point that has the biggest difference in the slopes of the two lines is the dividing point to use. Then just fit the two lines on either side of that. Full demo is attached.

Answer 2

[dpb]

I've answered this several time in the past, but never think to keep a link...

https://www.mathworks.com/matlabcentral/answers/134225-data-fitting-and-slop

Ah! There's the one...

https://www.mathworks.com/matlabcentral/answers/164913-difficulty-in-fitting-two-lines-with-polynomials?s_tid=srchtitle#answer_161148

Following is most of text from above...

Piecewise linear regression is fairly easy to code anyway...the algebra to add the condition to match the two at the breakpoint is

y = a1 + b1 x, x<=c,
y = a2 + b2 x, x>c.

Match breakpoint, or

a1 + b1 c = a2 + b2 c. 

Rearrange this to isolate (say) a2 as

a2 = a1 + b1 c - b2 c --> a1 + c(b1-b2) = aprime

Now have

y = a1     + b1 x, x<=c,
y = aprime + b2 x, x>c.

This is easy-peasy to code in Matlab and use as target for nlinfit --

function y=piecewise(coef,x)
% return piecewise linear fit given a1,b1,c,b2 as coefficient array and vector x
% c is breakpoint, a1 is intercept of first section, b1,b2 are two segment slopes
a1=coef(1); b1=coef(2);  % reduce parentheses clutter....
c=coef(3); b2=coef(4);
ix=x>c;                  % location > breakpoint
y(ix)=[a1+c*(b1-b2)+b2*x(ix)];
y(~ix)=[a1+b1*x(~ix)];
y=y(:);

Use this as

coeff=nlinfit(X,Y,@piecewise,coeff0);

[Harshita Garg]

Thank you