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I want to find the mathematical equation that would give me the blue data points in the graph below. enter image description here

I know the equation that would give me equation for the line will be something similar to y=a|m-x|+b but I don't know how to find the equation that'll give me the data points that are shown in blue. Any help is appreciated.

imageprocessingproblem
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    why do you need it? In any case the graph doesn't provide enough informations for a human to find an explicit equation of the blue part. – Davide Trono Jan 25 '21 at 09:18
  • That's a question I was given by my professor. I spent hours on it yesterday but still couldn't find a solution. I need to find two things according to this graph first mathematical equation that represents the data then with linear regression representing the data points (as red line) and transform it into matrix-vector form. Maybe I got the question wrong? @DavideTrono – imageprocessingproblem Jan 25 '21 at 09:25
  • Its likely the question is looking for the absolute value function you cited. If you want a function passing exactly through $p$ points, you are looking to use polynomial interpolation to find a function of degree at most $p-1$. Applying this here would probably give you a function with hundreds of terms. Applying this method to real world data in general (where measurement errors and variance will cause data to look imperfect) causes gross overfitting. – David Diaz Jan 25 '21 at 09:30
  • Here's formula that will roughly reproduce the image: Open microsoft paint, select spray paint, then spray along the red line allowing appropriate departures from the line with each spray. Looks like about fifty sprays. – David Diaz Jan 25 '21 at 09:47
  • Haha I thought the same with you! @DavidDiaz, but then I thought and maybe I should pick a few points of data and generate a piecewise function. What do you say? – imageprocessingproblem Jan 25 '21 at 11:32

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