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I want to model a set of a few dozen points on the x-y plane where y can be anywhere from 0 to 100 and x increases by 1 for each point on the y-axis, ex:

(1, 26)

(2, 84)

(3, 2)

etc. . .

Is it possible to accurately model such a random array of points with an equation? Someone once suggested using an 'interpolating polynomial in the Lagrange form', but that does not appear to work well with such a random array of points.

If it can't be done with a known regression technique, here is my question:

Given the points (1, 26) (2, 84) (3, 2) (4, 100) (5, 50), could a function exist - any function of any category - which will hit each point?

Thanks.