Script illustrating how to do a linear regression and plot the confidence band of the fit

The script below illustrates how to carry out a simple linear regression of data stored in an ASCII file, plot the linear fit and the 2 sigma confidence band.

The script invokes the confband method described here to plot the confidence bands. The confband is assumed to be lying inside the "nemmen" module (not yet publicly available, sorry) but you can place it in any module you want.

I got the test data here to perform the fitting.

After running the script you should get the following plot:

where the best-fit line is displayed in green and the shaded area is in gray.

The script below is also available at Github Gist.

   
 import numpy, pylab, scipy  
 import nemmen  
   
 # Data taken from http://orion.math.iastate.edu/burkardt/data/regression/x01.txt.  
 # I removed the header from the file and left only the data in 'testdata.dat'.  
 xdata,ydata = numpy.loadtxt('testdata.dat',unpack=True,usecols=(1,2))  
 xdata=numpy.log10(xdata) # take the logs  
 ydata=numpy.log10(ydata)  
   
 # Linear fit  
 a, b, r, p, err = scipy.stats.linregress(xdata,ydata)  
   
 # Generates arrays with the fit  
 x=numpy.linspace(xdata.min(),xdata.max(),100)  
 y=a*x+b  
   
 # Calculates the 2 sigma confidence band contours for the fit  
 lcb,ucb,xcb=nemmen.confband(xdata,ydata,a,b,conf=0.95)  
   
 # Plots the fit and data  
 pylab.clf()  
 pylab.plot(xdata,ydata,'o')  
 pylab.plot(x,y)  
   
 # Plots the confidence band as shaded area  
 pylab.fill_between(xcb, lcb, ucb, alpha=0.3, facecolor='gray')  
   
 pylab.show()  
 pylab.draw()