An introduction to regression and errors in variables from an algebraic viewpoint

There is a need to make a closer connection between classical response surface methods and their experimental design aspects, including optimal design, and algebraic statistics, based on computational algebraic geometry of ideals of points. This is a programme which was initiated by Pistone and Wynn (Biometrika, 1996) and is expanding rapidly. Particular attention is paid to the problem of errors in variables which can be taken as a statistical version of the ApCoA research programme.