How does numpy.polyfit return a slope and y-intercept when its documentation says it returns otherwise?

Question

I have seen examples where slope, yintercept = numpy.polyfit(x,y,1) is used to return slope and y-intercept, but the documentation does not mention "slope" or "intercept" anywhere.

The documentation also states three different return options:

• p: ndarray, shape (deg + 1,) or (deg + 1, K)

  Polynomial coefficients, highest power first. If y was 2-D, the coefficients for k-th data set are in p[:,k],

or

• residuals, rank, singular_values, rcond

  These values are only returned if full == True

  • residuals: sum of squared residuals of the least squares fit
  • rank: the effective rank of the scaled Vandermonde
  • singular_values: singular values of the scaled Vandermonde
  • rcond: value of rcond,

or

• v: ndarray, shape (deg + 1, deg + 1) or (deg + 1, deg + 1, K)

  Present only if full == False and cov == True

I have also run code with exactly the previous line and the slope and yintercept variables are filled with a single value each, which does not fit any of the documented returns. Which documentation am I supposed to use, or what am I missing?

Answer 1

slope, yintercept = numpy.polyfit(x, y, 1) 

Both full and cov parameters are False, so it's the first option, "Polynomial coefficients, highest power first". deg is 1, so "p: ndarray, shape (deg + 1,)" is an array of shape (2,).

With tuple assignment,

• slope is p[0], the x^deg-0 = x¹ coefficient,
• yintercept is p[1], the x^deg-1 = x⁰ coefficient.