Fixed tilt linalg.lstsq?

Question

Suppose we have two datasets: x = [1,2,3] y = [2,4,6] Obviously, the linear fit will return slope 2 and intercept 0 and, of course, both procedures in Numpy linalg.lstsq()and polyfit()successfully. But they think of tilt and interception as parameters for the search.

Is it possible to keep the slope fixed and only detect interception?

Answer 1

If the equation is a match y = a*x + b, you can find the hook bthat best matches your data, given a fixed slope a = A, like:

b = np.mean(y - A*x)

b = B , , :

a = np.dot(X, Y-B) / np.dot(X, X)

Answer 2

scipy.optimize.fsolve:

X = np.array([1, 2, 3])
Y = np.array([2, 4, 6])
s = 2

def f(i):
    """Fixed slope 1-deg polynomial residuals"""
    return ((Y - (s*X + i))**2).sum()

, polyfit:

In [37]: np.polyfit(X, Y, 1)
Out[37]: array([  2.00000000e+00,   2.30755522e-15])

In [38]: fsolve(f, x0=1)
Out[38]: array([  1.63883763e-16])

:

In [39]: s = 4

In [40]: fsolve(f, x0=1)
Out[40]: array([-3.99075568])