Giuseppe Vettigli works at the Cybernetics Institute of the Italian National Reasearch Council. He is mainly focused on scientific software design and development. His main interests are in Artificial Intelligence, Data Mining and Multimedia applications. He is a Linux user and his favorite programming languages are Java and Python. You can check his blog about Python programming or follow him on Twitter. Giuseppe is a DZone MVB and is not an employee of DZone and has posted 34 posts at DZone. You can read more from them at their website. View Full User Profile

Linear Regression Using Numpy

03.26.2012
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A few posts ago, we saw how to use the function numpy.linalg.lstsq(...) to solve an over-determined system. This time, we'll use it to estimate the parameters of a regression line.

A linear regression line is of the form w1x+w2=y and it is the line that minimizes the sum of the squares of the distance from each data point to the line. So, given n pairs of data (xi, yi), the parameters that we are looking for are w1 and w2 which minimize the error



and we can compute the parameter vector w = (w1 , w2)T as the least-squares solution of the following over-determined system



Let's use numpy to compute the regression line:
from numpy import arange,array,ones,random,linalg
from pylab import plot,show

xi = arange(0,9)
A = array([ xi, ones(9)])
# linearly generated sequence
y = [19, 20, 20.5, 21.5, 22, 23, 23, 25.5, 24]
w = linalg.lstsq(A.T,y)[0] # obtaining the parameters

# plotting the line
line = w[0]*xi+w[1] # regression line
plot(xi,line,'r-',xi,y,'o')
show()
We can see the result in the plot below.



You can find more about data fitting using numpy in the following posts:

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