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 segmen ...
that has the best fit to a series of data points.
Several methods exist, considering:
*Vertical distance:
Simple linear regression
**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 are ...
:
Robust simple linear regression
Robustness is the property of being strong and healthy in constitution. When it is transposed into a system, it refers to the ability of tolerating perturbations that might affect the system’s functional body. In the same line ''robustness'' ca ...
*
Perpendicular distance In geometry, the perpendicular distance between two objects is the distance from one to the other, measured along a line that is perpendicular to one or both.
The distance from a point to a line is the distance to the nearest point on that line. Th ...
:
Orthogonal 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 errors ...
**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 term ...
:
Major axis regression
In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account. It is a generaliz ...
See also
*
Linear least squares
Linear least squares (LLS) is the least squares approximation of linear functions to data.
It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and ...
*
Linear segmented regression
Segmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented ...
*
Linear trend estimation
Linear trend estimation is a statistical technique to aid interpretation of data. When a series of measurements of a process are treated as, for example, a sequences or time series, trend estimation can be used to make and justify statements abo ...
*
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 Bias (statistics), biasing of the linear regression regression slope, slope towards zero (the underestimation of its absolute value), caused by errors in the independent variable.
...
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