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Showing content from https://glowingpython.blogspot.com/2012/03/linear-regression-with-numpy.html below:

The Glowing Python: Linear regression with Numpy

, we have seen 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

.

A linear regression line is of the form w

x+w

=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 (x

, y

), the parameters that we are looking for are w

and w

which minimize the error

and we can compute the parameter vector

= (w

, w

)

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,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:

• Polynomial curve fitting
• Curve fitting using fmin

from numpy import arange,array,ones#,random,linalg
from pylab import plot,show
from scipy import stats

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]

slope, intercept, r_value, p_value, std_err = stats.linregress(xi,y)

print 'r value', r_value
print  'p_value', p_value
print 'standard deviation', std_err

line = slope*xi+intercept
plot(xi,line,'r-',xi,y,'o')
show()

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