Dear all,

This is probably more related to statistics than to [R] but I hope someone
can give me an idea how to solve it nevertheless:

Assume I have a variable y that is a function of x: y=f(x). I know the
average value of y for different intervals of x. For example, I know that
in the interval[0;x1] the average y is y1, in the interval [x1;x2] the
average y is y2 and so forth.

I would like to find a line of minimum curvature so that the average values
of y in each interval correspond to y1, y2, ...

My idea was to use (cubic) splines. But the problem I have seems somewhat
different to what is usually done with splines. As far as I understand it,
splines help to find a curve that passes a set of given points. But I don't
have any points, I only have average values of y per interval.

If you have any suggestions on how to solve this, I'd love to hear them.

Thanks very much in advance,

Michael

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