The Least-Squares Method

Data optimization in Thermo‑Calc is based on the least-squares method for fitting values calculated on the basis of a model with observed quantities. The software is accordingly trying to find the optimizing variable values that lead the minimized sum of the squares of the differences between the calculated values and the observed quantities (that is, of the errors or residuals).

The least-squares method works best under the following conditions:

• The observed quantities have a Gaussian probability distribution.
• The observed quantities are only subject to random errors.
• The different observations (experiments) are uncorrelated
• The standard deviation of each observation can be estimated.
• The number of observations is large.
• The models used give precise predictions.

Of course, these conditions are usually not all met in a normal thermodynamic assessment. But even in non-ideal conditions, there is no known method that works better than the least-squares method.