# Fitting data with broekn stick regression

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Wendy Cameron on 5 Jun 2018
Commented: John D'Errico on 8 Jun 2018
Hi.
I have some grape ripening data (sugar versus heat degrees) and want to try and fit a broken stick regression to it, and am wondering if this can be done in Matlab.
The data is quite simple e.g.
x=[1644 1669 1697 1720 1792 1909];
y=[11.9 11.6 12.6 13.4 13.9 14.6],
Basically grape ripening seems to follow a linear increase until some point and then flattens off on another trajectory. I'm wondering how I might use segmented or broken stick regression in matlab.

Image Analyst on 6 Jun 2018
Yes your data is quite simple. In fact TOO simple.
x=[1644 1669 1697 1720 1792 1909];
y=[11.9 11.6 12.6 13.4 13.9 14.6]
plot(x, y, 'bs-', 'LineWidth', 2);
grid on;
title('Sugar versus heat degrees', 'fontSize', fontSize);
ylabel('Sugar', 'fontSize', fontSize);
xlabel('heat degrees', 'fontSize', fontSize);
I don't see how you can expect to get any kind of meaningful regression out of this very tiny simple set of data.
Anyway, why would you want to lines instead of a formula for a more continuous function? What does two linear formulas get you over one single model formula, except for a more complicated model where you have to check your x value first before plugging it into one of two models? Not sure why two formulas are desired/advantageous over one formula. Please explain why.
John D'Errico on 8 Jun 2018
To reiterate my comment, you simply do not have sufficient information to estimate a broken stick regression, and certainly not to estimate where the breaks occur.

Image Analyst on 8 Jun 2018
Edited: Image Analyst on 8 Jun 2018
Here's one way to do it. See attached script for demo with noisy data.
Basically I fit lines to the left side and right side and kept track of the slope differences as I varied the point (x value, index) at which the sides were separated. The point where the slope different is greatest is where the lines are most dissimilar and where the crossing occurs.
##### 2 CommentsShowHide 1 older comment
Image Analyst on 8 Jun 2018
Then, is it time to "Accept this answer"? Or is it still not working?

JAYANTH BHIMAVARAPU on 5 Jun 2018
You can have a look at this solution: Broken-Stick Regression
Wendy Cameron on 6 Jun 2018
Yes I did see that but I really just can't understand it and can't make it work with my data unfortunately.
Wendy