A common issue in data analysis is to discern between model-driven results and data-driven results. Model driven results is when we produce a curve fit using a parametric equation, based on a relationship between our variables. For this purpose, we assume some knowledge about the underlying process. Data driven result is when we produce a curve fit using a non-parametric equation. The only thing that we have to work with is the data. We don't have any information about the "true" relationship between the variables.
In case of a data set consisting of only two variables, X and Y, the Matlab Central website provides a code, based on localized regression and cross validation (the code requires the Curve Fitting Toolbox and the Statistics Toolbox).
The code, named LOWESS, also provides Confidence Intervals based on Paired Bootstrap.
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| Non-Parametric LOWESS fit with confidence intervals using a "paired bootstrap". |
Links:
- Matlab Central
- LOWESS code
- Kurt Schmidheiny Lecture Notes (including Bootstrap)
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