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I have some questions about a formula and least square approximation

I have 14 information about the speed of a fluid inside a tube, speed, position and standard deviation. I already made a graphic of these information:

enter image description here (Its x:radios and y:speed)

And now I have to perform a least square approximation on these information, find two variables (k and R) and plot a graph (parabola curve).

These variables are suppose to be used in this formula:

enter image description here

Does anyone have an idea on how to start the second part? I was said that least square would give me these information, but i'm not sure what the k and R are.

I want to know if its possible to use least square to find the k and R, and what is the best way to do it. I saw that Scypy has a somewhat ready module for least square.

Gerry Myerson
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1 Answers1

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Yeah, it can be done and the method that would best solve it is linear regression. Your a0 and a2 coefficient vector can be gotten from the equation (X' is X transpose) a = inv(X'*X)*X'*Y

Here X is the 14 X 2 matrix containing first column containing 1 (r^0) and the second column containing r^2. Y is your function values. You will then have to figure out how to relate a0 and a2 to K and R.

user2544840
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