Python最小二乘回归QS

Question

Why doesn't this code work? I am trying to do multi-variate regression. Four equations of the form:

Ax + By + c = d

A + 2B + C = 0.2 etc.

A = np.array([[ 0.,  1, 1.],
   [ 1.,  2, 1.],
   [ 2.,  3, 1.],
   [ 3.,  4, 1.]])

y = np.array([-1, 0.2, 0.9, 2.1])
m, c = np.linalg.lstsq(A, y)[0]
print m, c

What am I doing wrong?

Answer 1

I assume that you took m, c = np.linalg.lstsq(A, y)[0] line from the lstsq example .
In the example they are solving linear regression problem with one variable and constant. As the result, np.linalg.lstsq(A, y) for this problem returns four-element tuple (array([ 1. , -0.95]), array([ 0.05]), 2, array([ 4.10003045, 1.09075677])) (first element – solution, second – residuals, third – the coefficient matrix rank, last element – singular values of coefficient matrix). So, np.linalg.lstsq(A, y)[0] (in the example) returns array with two elements which can be unpacked the way they are doing it: m, c = np.linalg.lstsq(A, y)[0] ( m = 1., c = -0.95 ).

You are solving regression with two variables and constant. Therefore, np.linalg.lstsq(A, y)[0] will return array with three elements and if you want to unpack it the way it was in the example you can do it this way:

x1, x2, c = np.linalg.lstsq(A, y)[0]

But more convenient way would be (in my opinion):

x, residuals, rank, s = np.linalg.lstsq(A, y) #lstsq func always return four-element tuple

print 'solution is %s.' % str(x)
print 'matrix A rank is %d.' % rank
print 'residuals are %s.' % str(residuals)
print 'singular values of A are %s.' % str(s)

print 'first variable is %f.' % x[0]
print 'second variable is %f.' % x[1]
print 'constant is %f.' % x[2]