Covariance and Correlation
~12 mincode completion
Implement correlation(x, y) from the definition, returning r as a float. The n−1 cancels between numerator and denominator, but compute it honestly rather than relying on that.
Examples
A perfect straight line upward
- Input
- correlation([1, 2, 3], [2, 4, 6])
- Output
- 1
A perfect straight line downward
- Input
- correlation([1, 2, 3], [6, 4, 2])
- Output
- -1
A symmetric parabola is perfectly determined and yet uncorrelated
- Input
- correlation([-2, -1, 0, 1, 2], [4, 1, 0, 1, 4])
- Output
- 0
Hints
Hint 1
Take the square root at the end, not inside the sum.
Hint 2
Watch for this: forgets to centre one of the variables.
Requirements
x: array of shape (n,)y: array of shape (n,)Return float in [-1, 1]
Constraints
Allowed library: NumPy only
Time limit: 200 ms, Memory: 64 MB
Try similar problems(4)
Where this shows up
~12 min
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Python
import numpy as np
def correlation(x, y):
"""
Pearson correlation coefficient.
Args:
x: array of shape (n,)
y: array of shape (n,)
Returns:
float in [-1, 1]
"""
# YOUR CODE HERE
pass