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Line fitting is the process of constructing a
straight line In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher dimension spaces. The word ''line'' may also refer to a line segment ...
that has the best fit to a series of data points. Several methods exist, considering: *Vertical distance:
Simple linear regression In statistics, simple linear regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the ''x'' an ...
**Resistance to
outliers In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter a ...
: Robust simple linear regression * Perpendicular distance: Orthogonal regression **Weighted geometric distance:
Deming regression In statistics, Deming regression, named after W. Edwards Deming, is an errors-in-variables model which tries to find the line of best fit for a two-dimensional dataset. It differs from the simple linear regression in that it accounts for erro ...
*
Scale invariance In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical te ...
: Major axis regression


See also

* Linear least squares * Linear segmented regression * Linear trend estimation *
Polynomial regression In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable ''x'' and the dependent variable ''y'' is modelled as an ''n''th degree polynomial in ''x''. Polynomial regression fi ...
*
Regression dilution Regression dilution, also known as regression attenuation, is the biasing of the linear regression slope towards zero (the underestimation of its absolute value), caused by errors in the independent variable. Consider fitting a straight line for ...


Further reading

*"Fitting lines", chap.1 in LN. Chernov (2010), ''Circular and linear regression: Fitting circles and lines by least squares'', Chapman & Hall/CRC, Monographs on Statistics and Applied Probability, Volume 117 (256 pp.)

{{dabprimary, date=May 2019 Regression analysis Geometric algorithms