Editing Bootstrap aggregating (section)

== Example: ozone data ==
To illustrate the basic principles of bagging, below is an analysis on the relationship between [[ozone]] and temperature (data from [[Peter Rousseeuw|Rousseeuw]] and Leroy{{clarify|date=May 2021}} (1986), analysis done in [[R (programming language)|R]]).

The relationship between temperature and ozone appears to be nonlinear in this dataset, based on the scatter plot. To mathematically describe this relationship, [[local regression|LOESS]] smoothers (with bandwidth 0.5) are used. Rather than building a single smoother for the complete dataset, 100 [[bootstrap (statistics)|bootstrap]] samples were drawn. Each sample is composed of a random subset of the original data and maintains a semblance of the master set's distribution and variability. For each bootstrap sample, a LOESS smoother was fit. Predictions from these 100 smoothers were then made across the range of the data. The black lines represent these initial predictions. The lines lack agreement in their predictions and tend to overfit their data points: evident by the wobbly flow of the lines.

[[image:ozone.png|center]]

By taking the average of 100 smoothers, each corresponding to a subset of the original dataset, we arrive at one bagged predictor (red line). The red line's flow is stable and does not overly conform to any data point(s).