# Regression Effect

Whenever there is ANY spread about the linear regression line, for any $x$ above ${\bar x}$, the $y$ values will increase by less than the increase in $x$.

For example, for $x$ one standard deviation above $\bar{x}$, the corresponding predicted $y$ value (y-hat)  will be less than one standard deviation above $\bar{y}$.

Similarly, for $x$ one standard deviation less than $\bar{x}$, the corresponding predicted $y$ (y-hat) will decrease by less than one standard deviation below $\bar{y}$.

This is called the regression effect.

It happens because part of the unexplained variation in $y$ is explained by the change of $x$ (the regression).

The regression line is ALWAYS flatter than the SD-line. (Both lines pass through the point of averages, $(\bar{x},\bar{y})$.