Question

I’ve been using the numpy.polyfit function to do some forecasting. If I put in a degree of 1, it works, but I need to do a second degree polynomial fit. In some cases it works, in other cases the plot of the prediction goes down and then goes up forever. For example:

import matplotlib.pyplot as plt
from numpy import *

x=[1,2,3,4,5,6,7,8,9,10]
y=[100,85,72,66,52,48,39,33,29,32]
fit = polyfit(x, y, degree) 
fitfunction = poly1d(z4)
to_predict=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]

plt.plot(to_predict,fitfunction(to_predict))
plt.show()

After I run that, this shows up (I tried putting a picture up but stackoverflow won’t let me).

I want to force it to go through zero.

How would I do that?

Answer 1

If you don’t need the fit’s error be computed using the original least square formula (i.e. minimizing ∑ |y_i – (ax_i² + bx_i)|²), you could try to perform a linear fit of y/x instead, because (ax² + bx)/x = ax + b.

If you must use the same error metric, construct the coefficient matrices directly and use numpy.linalg.lstsq:

coeff = numpy.transpose([x*x, x])
((a, b), _, _, _) = numpy.linalg.lstsq(coeff, y)
polynomial = numpy.poly1d([a, b, 0])

(Note that your provided data sequence does not look like a parabola having a y-intercept of 0.)