In statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, several scatterplot smoothing methods are available to fit a function through the points of a scatterplot

Scatterplot

A scatter plot or scattergraph is a type of mathematical diagram using Cartesian coordinates to display values for two variables for a set of data....

 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 attempts to separate the non-random behaviour in the data from the random fluctuations, removing or reducing these fluctuations, and allows prediction of the response based value of the explanatory variable.

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

• A straight line (simple linear regression
  Simple linear regression
  In statistics, simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable. In other words, simple linear regression fits a straight line through the set of n points in such a way that makes the sum of squared residuals of the model as...
  
  )
• A quadratic
  Quadratic
  In mathematics, the term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree, or equations or formulas that involve such terms...
  
   or a polynomial
  Polynomial
  In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
  
   curve
• Local regression
  Local regression
  LOESS, or LOWESS , is one of many "modern" modeling methods that build on "classical" methods, such as linear and nonlinear 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...
  
  
• Smoothing spline
  Spline
  Spline can refer to:* Spline , a mating feature for rotating elements* Spline , a mathematical function used for interpolation or smoothing* Smoothing spline, a method of smoothing using a spline function...
  
  s

The smoothing curve is chosen so as to provide the best fit in some sense, often defined as the fit that results in the minimum sum of the squared errors (a least squares

Least squares

The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in solving every...

 criterion).

See also

• Additive model
  Additive model
  In statistics, an additive model is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle and is an essential part of the ACE algorithm. The AM uses a one dimensional smoother to build a restricted class of nonparametric regression models. Because of this,...
  
  
• Generalized additive model
  Generalized additive model
  In statistics, the generalized additive model is a statistical model developed by Trevor Hastie and Rob Tibshirani for blending properties of generalized linear models with additive models....