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#### A.4.5.14 Linear Fit Form

The Linear Fit form () determines a least-squares best fit of a line to the data points, optionally weighted by a given value, and plots the corresponding line.

Example LinearFit plot

Linear Fit configuration panel

The configuration options are:

Weight
  Weighting to apply to each point. If left blank, no weighting (equivalent to unit weighting) is applied. If independent sampling errors `E` are available for each point, a suitable value for this may be `1./(E*E)` (equivalently `pow(E,-2)`).
Thickness
  Line thickness in pixels.
Dash
  Dash pattern. The line is solid by default.
Antialiasing
  If true, pixels are blurred to give the line a smoother appearance.

As well as drawing the line onto the plot, the calculated fitting coefficients are displayed at the bottom of the form configuration panel, under the heading Report. Note the coefficients are calculated by subset, and are only displayed for one subset at a time. To see the calculated values, select the subset of interest in the Subset selector. The reported items are:

Equation
  The equation of the line. The basic linear equation is `y=m*x+c`, but if one or both of the axes are plotted logarithmically, the fit is performed to take account of this, and the equation is displayed accordingly.
c
  The constant intercept of the line on the Y axis.
m
  The line gradient.
Correlation
  Pearson's product moment correlation coefficient.

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TOPCAT - Tool for OPerations on Catalogues And Tables
Starlink User Note253
TOPCAT web page: http://www.starlink.ac.uk/topcat/
Author email: m.b.taylor@bristol.ac.uk
Mailing list: topcat-user@jiscmail.ac.uk