let's just go through what co-variance is if we have our axes here and we've got the uh mean of one trait and the mean of the other trait and we've got various data points in our correlation coari is the sum of the deviations from the mean uh of trait uh of the uh trait X and trait Y and it's the sum of the products of those so so this point here deviates from the mean of trade X by a large negative amount okay and similarly it deviates from the mean of trait y by a large negative amount okay so if we multiply say this is minus 5 and this is - 10 okay so we have- 10 * - 5 okay = 50 then over here this point here is like + 10 on the X goale and it's plus 2 in the Y scale then so it's uh + 2 * + 10 = 20 if we sum these because that's what we're doing in the numerator term if we sum those then uh we'll get a positive value we Su them for all of those data points the deviations in each direction for all B points okay then we'll get a positive value in the numerator if we imagine that again with our means for X and Y but the the relationship is negative then uh this data point has a positive deviation from this mean and a negative deviation from this mean so then we might have minus 20 * plus 10 and similarly we would have minus 20 and + 10 okay - 20 * + 10 is -00 and and so you can see that the numerator is negative