So this is a polynomial curve of unknown degree and coefficients,

>>8297168
Take differential equations.

>>8297168
use le computer software

>>8297168
what does "the best fit" mean? if you want a degree n polynomial fit, pick n points, and fit a polynomial with lagrange interpolation. you're probably going to overfit if you make n too high, but just try different values increasing n to make it more precise

>>8297327
what the fuck are you talking about

>>8297330
the best fit obviously means the polynomial that looks most like the polynomial in the picture, hopefully near-identical to the polynomial in the picture

>>8297406
it usually isn't that. I would expect the actual best fit no to consider those weird spikes. the best fit for real data is usually not the actual minimization of the error. that's called "overfitting"

>>8297168
If you want the meme answer, pick n to be the number of data points you have minus one, and then you have exactly one polynomial that goes through all of them.

Maybe try randomly picking half the data as the "training set" and the other half as the "test set" and pick the n which has the least error on the test set, to prevent overfitting.

>>8297411
oh yeah ignore those spikes, they're at the square numbers, the function returns zero at every perfect square

>>8297473
give me the data and ill fit it for you.

>>8297477
http://pastebin.com/HtSnk2Mm

>>8297168
Lrn2lagrange-polynomial