# Statistic - Smooth (Function Continuity) (Soft ?)

To smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise.

In mathematical analysis, smoothness has to do with how many derivatives of a function exist and are continuous. The term smooth function is often used technically to mean a function that has derivatives of all orders everywhere in its domain. ie Smoothed conditional means. See wiki/smoothness

## Algorithms

Data smoothing is typically done through the simplest of all density estimators, the histogram.

loess and cubic smoothing splines are probably the two best ways of doing smoothing.

If you set the degrees of freedom to be equal roughly, they look pretty similar too in general.

## Documentation / Reference

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Ggplot - Smooth (Geom_Smooth|Stat_Smooth)

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SVG - Curve (Line)

in SVG. A curved line is just designed with a path element. There are three different path commands that you can use to create smooth curves. bezier curve, an “arc” or part of a circle....
Statistics - (Logit|Logistic) (Function|Transformation)

The logit transform is a S-shaped curve that applies a softer function. It's a soft function of a step function: Never below 0, never above 1 and a smooth transition in between. where: ...
Statistics - Generalized additive model (GAM)

In statistics, a generalized additive model (GAM) is a generalized linear model in which the linear predictor depends linearly on unknown smooth functions of some predictor variables, and interest focuses...
Statistics - LOcal (Weighted) regrESSion (LOESS|LOWESS)

Popular family of methods called local regression that helps fitting non-linear functions just focusing locally on the data. LOESS and LOWESS (locally weighted scatterplot smoothing) are two strongly...
Statistics - Smoothing (cubic) spline

A smoothing spline is a way of fitting splines without having to worry knots. They are a little bit more challenging mathematically as others splines and approaches the problem from a completely different...