Find The Deference of a curve and a line with some flexibility

[absamr]

hi i have a series of 2d vector every time it's deferent and i want a formula to define that is it a curve or a line. but i don't want it to be really accurate and i want it to have some flexibility.these are examples of what i want

 

[Dr.Peterson]

hi i have a series of 2d vector every time it's deferent and i want a formula to define that is it a curve or a line. but i don't want it to be really accurate and i want it to have some flexibility.these are examples of what i want
View attachment 10474

It isn't at all clear what you want.

I suspect that you have a list of coordinate pairs for points (which could be described as position vectors), and you want to determine what line or curve (e.g. parabola) passes through those points, allowing for some error.

This is called linear or quadratic regression. The easiest way to do it would be to enter the coordinates into a spreadsheet (Excel or similar), and ask it for what it calls a "trendline". (You can specify various kinds of functions to use.) Or you can look up the term and learn how to do it yourself.

If this doesn't sound like what you want, please give as much detail as you can -- show us your data, and tell us what result you want (e.g. an equation like y = x^2, or just a statement, "yes, the points are on a line", or whatever).