Show that if Y aXb where a0then CorrXY1or1 Underwhat conditi

Show that if Y =aX+b where a=0,then Corr(X,Y)=1or1. Underwhat conditions will = 1?

Solution

Y = ax+b

For row =1, there is perfect linear positive correlation

Hence a =1 implies there is perfect linear correlation between x and y

Or y = x+b and one unit of increase in X results in one unit increase in Y