from math import sqrt
 
def correlation_coefficient(word):
  alphabet = 'abcdefghijklmnopqrstuvwxyz'
 
  x = list(range(len(word)))
  y = list(map(alphabet.index, word))
  n = len(word)
 
  top = n * sum(a*b for a, b in zip(x, y)) - sum(x) * sum(y)
  bottom = (sqrt(n * sum(a ** 2 for a in x) - sum(x) ** 2)
          * sqrt(n * sum(a ** 2 for a in y) - sum(y) ** 2))
 
  r = top / bottom
  return r
 
print(correlation_coefficient('forty')) # => 0.9644068036349517
print(correlation_coefficient('bells')) # => 0.9717931994369533
print(correlation_coefficient('correlation')) # => 0.13063589827847785

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