Line of best fit

What is a line of best fit? What is it used for?

For some parameters such as straightness, evenness and also accuracy, the linear part of the measured value can be ignored when stating the measuring result. This way, for example, a linear table mounted at an angle in the system would result in a straightness measurement with an evenly increasing deviation. This deviation would, however, be eliminated by simple straightening, meaning by adjusting the linear table during system installation. The same applies for evenness, where a wedge-shaped base plate leads to a linear fault rate. Also here, the linear table would be adjusted accordingly during installation and thus the fault would be eliminated.

In the case of turntables, this correctable fault rate would correspond to the full periodic sine which would be recorded when measuring wobble and eccentricity. To determine the line of best fit, the incline of the straight line which best matches the measuring results is identified. This is done using the least-squares method. The incline of the straight line is the value for which the sum of squares of all measuring values becomes minimal. This detected straight line is then deducted from the measured values.