“Well, here goes nothing.”
Dr. Lora Baines, Tron
At the end of this session you should be able to
While the linear regression models assume a linear relationship between a dependent (e.g. y) and one ore more independent variables (e.g. x), non-linear models do not have this restriction. As a drawback, non-linear models can be quite complicated to define if one is looking for a non-linear model which describes the entire data set but local regression models do not have this drawback.
Non-parametric local regression models (loess) use simple linear or quadratic models (i.e. polynomial functions of first or second degree) which are used for a local weighted fit on the data set using a moving window. For example, if the span of this window is set to 7, then only the neighboring 3 lower and higher values are considered for the fit of the central value. A cubic (i.e. x3) weighing function ensures that the actual central value has the largest influence on the fit with decreasing weights towards the end of each sides span.
Regarding validation of such models, a look at its residual standard error gives you a first idea. However, to get a better idea of the reliability of the model when it comes to prediction, the leave-one-out approach from L06 is a better starting point.