correlation.py

import math
import numpy as np

data_X = [5,6,8,12,15,18,10]
data_Y = [1,4,6,8,10,12,14]

def mean(x):
        return  sum(x)/len(x)

def de_mean(data):
# convert x by subtracting its mean ( so the result has mean 0)
        x_bar = mean(data)
        return [x_i - x_bar for x_i in data]

def sum_of_square(v):
        return np.dot(v,v)


def covariance(x,y):
        n = len(x)
        return np.dot(de_mean(x), de_mean(y)) / (n-1)

def variance(data):
        n = len(data)
        deviations = de_mean(data)
        return sum_of_square(deviations) / (n-1)


def standard_deviation(data):
        return math.sqrt(variance(data))

def correlation(x,y):
        stdev_x = standard_deviation(x)
        stdev_y = standard_deviation(y)
        if stdev_x > 0 and stdev_y > 0:
            return covariance(x,y) / stdev_x / stdev_y
        else:
            return 0


print(correlation(data_X,data_Y))