Line fitting

For broader coverage of this topic, see Curve fitting.

"Line of best fit" redirects here. For the music magazine, see The Line of Best Fit.

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.). [1]