4 ms·

Your data is suspiciously rounded off. Just doing linear regression on that data isn't going to give you a perfect fit either.

• Gibbon1 8y ago
  There is that. And also what I learned in school which is doing linear regression using a function with more degrees of freedom than the data tends to generate garbage. It can match the data points exactly and then be wildly off between them.
  • ska 8y ago
    A classic demonstration of similar effect - any set of N data points in a time series, e.g. (t,f(t)), can be fit by a N-1 order polynomial to pass through each point. So fit a high order poly to a set of points sampled (esp. with a little noise) from a low order poly. You'll get crazy oscillations, and outside the sampling area it will likely diverge fast. Now add a smoothness term and crank it up until you get more reasonable results - regularization. It's a simplification, but informative about some ML techniques.
    • Gibbon1 8y ago
      One of my labs some students curve fitted a sixth order poly onto five data points they collected. The process being measured was y = something something minus ln(x). It fit all five points exactly and smoothly and wildly diverged on either side. The professor was really amused.
      • chestervonwinch 8y ago
        It’s called https://en.m.wikipedia.org/wiki/Runge's_phenomenon https://en.m.wikipedia.org/wiki/Runge's_phenomenon and can be mitigated eg by non-uniform interpolation grids like chebychev nodes.