How to calculate the coordinates of a curve?

Question

JavaScript

Hello!
There is a curve built on 5 points (0.22, 0), (0.36, 0.25), 0.61, 0.5), (0.73, 0.75), (0.84, 1).
It is necessary to find the coordinates of the points on the curve if the x values ​​are known.
I tried to solve SLAE from known points to find the coefficients a, b, c, d in an equation like ax**3 + bx**2 + cx + d = y. I used a ready-made solution , but there are suspicions that this code does not work, because results are not tested.
How can this be done with the least amount of effort?

Answer 1

You need something like this
https://github.com/Tom-Alexander/regression-js
Polynomial regression
I didn't use the library, but that's the point.

Answer 2

Is there an understanding of what kind of function should eventually turn out?
Built your points on the graph:
Whether it is experimental data tending to a linear function - then decide by linear regression.
Either the curve should lie exactly along the points, and then it can be the sum of a sinusoid and a linear one, or a curve of some 6th order.