I want to calculate multiple linear regression with numpy. I need to regress my dependent variable (y) against several independent variables (x1, x2, x3, etc.).
For example, with this data:
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
20.64, 0.0, 296, 54.7, 0, 519, 2, 24.0
25.12, 0.0, 387, 54.7, 1, 678, 2, 24.0
19.22, 0.0, 535, 54.7, 0, 296, 2, 24.0
18.99, 0.0, 519, 18.97, 0, 296, 2, 54.9
18.89, 0.0, 296, 18.97, 0, 535, 2, 54.9
25.51, 0.0, 678, 18.97, 1, 387, 2, 54.9
20.19, 0.0, 296, 25.51, 0, 519, 2, 54.9
20.75, 0.0, 535, 25.51, 0, 296, 2, 54.9
24.13, 0.0, 387, 25.51, 1, 678, 2, 54.9
19.24, 0.0, 519, 0, 0, 296, 2, 55.0
20.90, 0.0, 296, 0, 0, 535, 2, 55.0
25.30, 0.0, 678, 0, 1, 387, 2, 55.0
20.78, 0.0, 296, 0, 0, 519, 2, 55.2
23.01, 0.0, 535, 0, 0, 296, 2, 55.2
25.20, 0.0, 387, 0, 1, 678, 2, 55.2
19.12, 0.0, 519, 0, 0, 296, 2, 55.3
20.03, 0.0, 296, 0, 0, 535, 2, 55.3
25.22, 0.0, 678, 0, 1, 387, 2, 55.3
I have created this function that I think it gives the coefficients A from Y = a1x1 + a2x2 + a3x3 + a4x4 + a5x5 + a6x6 + +a7x7 + c.
def calculate_linear_regression_numpy(xx, yy):
""" calculate multiple linear regression """
import numpy as np
from numpy import linalg
A = np.column_stack((xx, np.ones(len(xx))))
coeffs = linalg.lstsq(A, yy)[0] # obtaining the parameters
return coeffs
xx is a list that contains each row of x's, and yy is a list that contains all y.
The A is this:
00 = {ndarray} [ 0. 296. 519. 2. 0. 24. 54.7 1. ]
01 = {ndarray} [ 0. 296. 535. 2. 0. 24. 54.7 1. ]
02 = {ndarray} [ 0. 387. 678. 2. 1. 24. 54.7 1. ]
03 = {ndarray} [ 0. 296. 519. 2. 0. 54.9 18.97957206 1. ]
04 = {ndarray} [ 0. 296. 535. 2. 0. 54.9 18.97957206 1. ]
05 = {ndarray} [ 0. 387. 678. 2. 1. 54.9 18.97957206 1. ]
06 = {ndarray} [ 0. 296. 519. 2. 0. 54.9 25.518085 1. ]
07 = {ndarray} [ 0. 296. 535. 2. 0. 54.9 25.518085 1. ]
08 = {ndarray} [ 0. 387. 678. 2. 1. 54.9 25.518085 1. ]
09 = {ndarray} [ 0. 296. 519. 2. 0. 55. 0. 1.]
10 = {ndarray} [ 0. 296. 535. 2. 0. 55. 0. 1.]
11 = {ndarray} [ 0. 387. 678. 2. 1. 55. 0. 1.]
12 = {ndarray} [ 0. 296. 519. 2. 0. 55.2 0. 1. ]
13 = {ndarray} [ 0. 296. 535. 2. 0. 55.2 0. 1. ]
14 = {ndarray} [ 0. 387. 678. 2. 1. 55.2 0. 1. ]
15 = {ndarray} [ 0. 296. 519. 2. 0. 55.3 0. 1. ]
16 = {ndarray} [ 0. 296. 535. 2. 0. 55.3 0. 1. ]
17 = {ndarray} [ 0. 387. 678. 2. 1. 55.3 0. 1. ]
And the np.dot(A,coeffs) is this:
[ 19.69873196 20.33871176 24.95249051 19.59198545
20.23196525 24.845744 19.41602911 20.05600891 24.66978766
20.09928377 20.73926357 25.35304232 20.09237109 20.73235089
25.34612964 20.08891474 20.72889454 25.34267329]
At the return of the function, the coeffs, contains this 8 values.
[0.0, -0.0010535377771944548, 0.039998737474281849, 0.62111016637058492, -1.0101687709958682, -0.034563440146209781, -0.026910757873959575, 0.31055508318529385]
I don't know if the coeffs[0] or the coeffs[7] is the c from the equation Y defined above.
I take this coeffs and I calculate the new Ŷ multiplying the coeffs with the new ẍ's, like this:
Ŷ=a1ẍ1 + a2ẍ2 + a3ẍ3 + a4ẍ4 + a5ẍ5 + a6ẍ6 + +a7ẍ7 + c
Am I calculating Ŷ correctly? And what should I do when I get a Ŷ with a negative number? Which term is the c (a[0] or a[7])?
