print 'y x1 x2 x3 x4 x5 x6 x7'
for t in texts:
print "{:>7.1f}{:>10.2f}{:>9.2f}{:>9.2f}{:>10.2f}{:>7.2f}{:>7.2f}{:>9.2f}" /
.format(t.y,t.x1,t.x2,t.x3,t.x4,t.x5,t.x6,t.x7)
(output for above:) y x1 x2 x3 x4 x5 x6 x7
-6.0 -4.95 -5.87 -0.76 14.73 4.02 0.20 0.45
-5.0 -4.55 -4.52 -0.71 13.74 4.47 0.16 0.50
-10.0 -10.96 -11.64 -0.98 15.49 4.18 0.19 0.53
-5.0 -1.08 -3.36 0.75 24.72 4.96 0.16 0.60
-8.0 -6.52 -7.45 -0.86 16.59 4.29 0.10 0.48
-3.0 -0.81 -2.36 -0.50 22.44 4.81 0.15 0.53
-6.0 -7.01 -7.33 -0.33 13.93 4.32 0.21 0.50
-8.0 -4.46 -7.65 -0.94 11.40 4.43 0.16 0.49
-8.0 -11.54 -10.03 -1.03 18.18 4.28 0.21 0.55
How would I regress these in python, to get the linear regression formula:
Y = a1x1 + a2x2 + a3x3 + a4x4 + a5x5 + a6x6 + +a7x7 + c
from sklearn import linear_model
clf = linear_model.LinearRegression()
clf.fit([[getattr(t, 'x%d' % i) for i in range(1, 8)] for t in texts],
[t.y for t in texts])
Then clf.coef_ will have the regression coefficients.
sklearn.linear_model also has similar interfaces to do various kinds of regularizations on the regression.
from scipy.optimize import curve_fit
import scipy
def fn(x, a, b, c):
return a + b*x[0] + c*x[1]
# y(x0,x1) data:
# x0=0 1 2
# ___________
# x1=0 |0 1 2
# x1=1 |1 2 3
# x1=2 |2 3 4
x = scipy.array([[0,1,2,0,1,2,0,1,2,],[0,0,0,1,1,1,2,2,2]])
y = scipy.array([0,1,2,1,2,3,2,3,4])
popt, pcov = curve_fit(fn, x, y)
print popt
import numpy as np
y = np.array([-6, -5, -10, -5, -8, -3, -6, -8, -8])
X = np.array(
[
[-4.95, -4.55, -10.96, -1.08, -6.52, -0.81, -7.01, -4.46, -11.54],
[-5.87, -4.52, -11.64, -3.36, -7.45, -2.36, -7.33, -7.65, -10.03],
[-0.76, -0.71, -0.98, 0.75, -0.86, -0.50, -0.33, -0.94, -1.03],
[14.73, 13.74, 15.49, 24.72, 16.59, 22.44, 13.93, 11.40, 18.18],
[4.02, 4.47, 4.18, 4.96, 4.29, 4.81, 4.32, 4.43, 4.28],
[0.20, 0.16, 0.19, 0.16, 0.10, 0.15, 0.21, 0.16, 0.21],
[0.45, 0.50, 0.53, 0.60, 0.48, 0.53, 0.50, 0.49, 0.55],
]
)
X = X.T # transpose so input vectors are along the rows
X = np.c_[X, np.ones(X.shape[0])] # add bias term
beta_hat = np.linalg.lstsq(X, y, rcond=None)[0]
print(beta_hat)
RESULT:
[ -0.49104607 0.83271938 0.0860167 0.1326091 6.85681762 22.98163883 -41.08437805 -19.08085066]