Notes on Linear Regression

Having read the linear regression chapter of Element of Statistical Learning, method is different compared with Pattern Recognition and Machine Learning. After the introduction of least square methods, ESL will talk about the variant of the estimator ( $\hat{\beta}$ ). Well, this is something quite new to me.
The first question is why we need to do this ? What’s the benefits of doing such kind of inference? But more interesting point is, with assumption of truly underlying model is linear model: ESL gives hypothesis testing and interval estimation of the parameters. This is quite new, but the question would be what if the real underlying model isn’t linear. I think this is the most common scenario.
For other point, ESL give a detailed analysis and comparison of different shrinkage method, this is a clear description of “bias variance decomposition”. And also other advanced method like lasso path and LAR algorithm.