  In the last few decades both the volume of high-quality observing data on
variable stars and common access to them have boomed; however the standard used
methods of data processing and interpretation have lagged behind this progress.
The most popular method of data treatment remains for many decades Linear
Regression (LR) based on the principles of Least Squares Method (LSM) or
linearized LSM. Unfortunately, we have to state that the method of linear
regression is not as a rule used accordingly namely in the evaluation of
uncertainties of the LR parameters and estimates of the uncertainty of the LR
predictions.
  We present the matrix version of basic relations of LR and the true estimate
of the uncertainty of the LR predictions. We define properties of the
orthogonal LR models and show how to transform general LR models into
orthogonal ones. We give relations for orthogonal models for common polynomial
series.
