Here, changing the units of
corresponds to multiplying all the
values by a certain number. This would change the mean and the standard deviation of
but it would not change the correlation. To see this, imagine dividing every number on the vertical axis by 10. The units of
are now in cm rather than in mm, but the graph has remain exactly the same. The units of
have changed, by the relative distance of the
values about the mean are the same; that is, the Z-scores corresponding to the
values have remained the same.