Scatterplot smoothing

In statistics, several scatterplot smoothing methods are available to fit a function through the points of a scatterplot to best represent the relationship between the variables.

Scatterplots may be smoothed by fitting a line to the data points in a diagram. This line attempts to display the non-random component of the association between the variables in a 2D scatter plot.

Smoothing is normally accomplished by using any one of the techniques mentioned below.

• A straight line
• A quadratic or a polynomial curve
• Smoothing splines

Of these, the smoothing splines technique is applied when greater flexibility is needed in the nonlinear behaviour. The curve is fitted in such a way that provides the best fit, often defined as the fit that results in the minimum sum of the squared errors (least squares criterion).

The use of smoothing separates the non-random data from the random fluctuations and allows prediction of the response based value of the explanatory variable.

See also

• Local regression
• Additive model
• Generalized additive model