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test 4 How do you calculate the covariance of x and y?

C(X,Y) = E(XY)  E(X)E(Y)

test 4How can you tell if the slope of a best linear predictor is nonzero?

When the covariance or C(X,Y) is not = to '0', then the slope is not = to '0'

test 4When do you have evidence that X causes Y?

Never! We are investigating a statistical relationship which has nothing to do with causality

PS#2 E(X) is?

Expected value of x, which is the sum of each of the individual occurrences of X /divided by the number of observations:
Sum Xi/N 