Given two vectors X and Y, I have to find their correlation, i.e. their linear dependence/independence. Both vectors have equal dimension. The result should be a floating point number from [-1.0 .. 1.0].
Example:
X=[-1, 2, 0]
Y=[ 4, 2, -0.3]
Find y = cor(X,Y) such that y belongs to [-1.0 .. 1.0].
It should be a simple construction involving a list-comprehension. No external library is allowed.
UPDATE: ok, if the dot product is enough, then here is my solution:
nX = 1/(sum([x*x for x in X]) ** 0.5)
nY = 1/(sum([y*y for y in Y]) ** 0.5)
cor = sum([(x*nX)*(y*nY) for x,y in zip(X,Y) ])
right?
Sounds like a dot product to me.
Solve the equation for the cosine of the angle between the two vectors, which is always in the range [-1, 1], and you’ll have what you want.
It’s equal to the dot product divided by the magnitudes of two vectors.