Local regression: Difference between revisions

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'''LOESS''' is one of many "modern" [[statistical model|modeling methods]] that build on [[classical statistics|"classical" methods]], such as linear and nonlinear [[Regression analysis|least squares regression]]. Modern regression methods are designed to address situations in which the classical procedures do not perform well or cannot be effectively applied without undue labor. LOESS combines much of the simplicity of linear least squares regression with the flexibility of [[Non-linear_regressionlinear regression|nonlinear regression]]. It does this by fitting simple models to localized subsets of the data to build up a function that describes the deterministic part of the variation in the data, point by point. In fact, one of the chief attractions of this method is that the data analyst is not required to specify a global function of any form to fit a model to the data, only to fit segments of the data.

The trade-off for these features is increased computation. Because it is so computationally intensive, LOESS would have been practically impossible to use in the era when least squares regression was being developed. Most other modern methods for process modeling are similar to LOESS in this respect. These methods have been consciously designed to use our current computational ability to the fullest possible advantage to achieve goals not easily achieved by traditional approaches.

Plotting a smooth curve through a set of data points using this statistical technique is called a '''Loess Curve''', particularilyparticularly when each smoothed value is given by a weighted quadratic least squares regression over the span of values of the y-axis [[scattergram]] criterion variable. When each smoothed value is given by a weighted linear least squares regression over the span, this is known as a '''Lowess curve'''; however, some authorities treat '''Lowess''' and Loess as synonyms.

==Definition of a LOESS model==