Y will always be less extreme.
The key to understanding this simply is this equation.
This is what tells us that the standard scores have a regression coefficient â¤ 1.
We said it's 1, and so because it's not 1 it must be less than that.
That means the standard score shrinks.
If the standard score shrinks that means if it's negative it moves this way.
If it's positive it moves this way.
That means there is more area under here,
so this has to be a little more area than this.
Therefore, y will always be less extreme.
This is the concept of regression.
That is regression to the mean.
If someone is exceptional in one thing,
we will always predict that person to be a bit less exceptional
in that other thing if there is any error.