13.2 LINEAR REGRESSION AS A GENERAL LINEAR MODEL
When the response variable has a Normal distribution at each set of given predictor variable values, then we are back in the realm of linear regression. In this realm, the link function is simply the identity function, where
![equation](https://static.packt-cdn.com/products/9781119526810/graphics/images/c13-disp-0002.png)
Setting Xβ equal to g(μ) using this identity link gives us Xβ = g(μ) = μ.
Once we have a functional relationship between Xβ and μ, we can work backwards to obtain the final form of the regression model by expanding our abbreviated notation. Doing so gives us the population equation for linear regression:
![equation](https://static.packt-cdn.com/products/9781119526810/graphics/images/c13-disp-0003.png)
from which we can obtain the descriptive form
![equation](https://static.packt-cdn.com/products/9781119526810/graphics/images/c13-disp-0004.png)
which we worked with in Chapter 11.