## Definition of the regression function $$r(x)$$

$$r(x)=E[Y|X=x]$$ where conditional expectation is defined here.

The regression for discrete $$Y$$ is called classification.

## Regression analysis

Regression analysis consists in estimating $$r(x)$$.

If we define $$\epsilon$$ as $$\epsilon = Y -r(x)$$, then the regression model can be expressed as

$Y=r(x)+\epsilon$

with $$E[\epsilon]=0$$.

$$r(x)$$ corresponds to the deterministic part.

• Demonstration

## References

Wasserman, L. All of statistics (2004). Springer Science & Business Media.