What does the sign of covariance mean?
Look at Y = aX + b.
Then:
Cov(X,Y) = Cov(X,aX + b) = aVar(X).
If a > 0, above the average in X
goes with above the ave in Y.
If a < 0, above the average n X goes with below the ave in Y.
Cov(X,Y) = 0 means that there is no
linear trend which connects X
and Y.
x
y
x
y
a>0
a<0
Ave(Y)
Ave(Y)
Ave(X)
Ave(X)