Line fitting

Line fitting is the process of constructing a straight line that has the best fit to a series of data points. Several methods exist, considering: *Vertical distance: Simple linear regression *Resistance to outliers: Robust simple linear regression *Perpendicular distance: Orthogonal regression (this is not scale-invariant i.e. changing the measurement units leads to a different line.) *Weighted geometric distance: Deming regression *Scale invariant approach: Major axis regression This allows for measurement error in both variables, and gives an equivalent equation if the measurement units are altered.

Line fitting is the process of constructing a straight line that has the best fit to a series of data points. Several methods exist, considering: Vertical distance: Simple linear regression Resistance to outliers: Robust simple linear regression Perpendicular distance: Orthogonal regression (this is not scale-invariant i.e. changing the measurement units leads to a different line.) Weighted geometric distance: Deming regression Scale invariant approach: Major axis regression This allows for measurement error in both variables, and gives an equivalent equation if the measurement units are altered. ==See also== Linear least squares Linear segmented regression Linear trend estimation Polynomial regression Regression dilution ==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.). *"[https://foto.aalto.fi/seura/julkaisut/pjf/pjf_e/2005/Inkila_2005_PJF.pdf Homogeneous Least-Squares Problem", Keijo Inkilä (2005), The Photogrammetric Journal of Finland, 19(2):34–42

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