Regression spline
In this section, we will consider various enhancements/generalizations of the linear regression model. We will begin with a piecewise linear regression model and then consider the polynomial regression extension.
The term spline refers to a thin strip of wood that can be easily bent along a curved line.
Basis functions
In the previous section, we made multiple transformations of the input variable X with 
. In the Data Re-expression section of Chapter 4, Exploratory Analysis, we saw how a useful log transformation gave a better stem-and-leaf display than the original variable itself.
In many applications, it has been found that the transformed variables are more important than the original variable itself. Thus, we need a more generic framework to consider the transformations of the variables. Such a framework is provided by the basis functions.
For a single covariate X, the set of transformations may be defined as follows:
Here, 
is the m th transformation of X, and 
is the...
