qqplot (Quantile-Quantile Plot) in Python



Interpretations

  • All quantile points lie on or at a straight line at an angle of 45 degrees from the x-axis. This indicates that the two samples have similar distributions. 

    And in practice it is always impossible to get such a 100% clear straight line, but the graph looks like this. Here the points lie almost on a straight line. 
  • Y-quantiles are below x-quantiles. This indicates that the y values ​​tend to be lower than the x values. 

    And in practice it is not always possible to get 100 percent as shown above, but the graph looks as shown below. Here you can see that most of the points are below the line, and a few points are above the line. Hence, we can say that the distributions are not the same. 
  • X-quantiles are lower than y-quantiles. This indicates that the x values ​​tend to be lower than the y values. 
  • Indicates that there is a breakpoint up to which the y-quantiles are below the x-quantiles, and after this point, the y-quantiles are higher than the x-quantiles. 

Quantile — Quantile plot using statsmodel in Python —

import numpy as np

import statsmodels.api as sm

import pylab as py

 
# np.random generates different random numbers
# whenever the code is executed
# Note: when executing the same code
# the graph looks different than below.

 
# Random data points generated

data_points = < code class = "plain"> np.random.normal ( 0 , 1 , 100

 

sm.qqplot (data_points, line = `45` )

py.show ()

Output: