Unknown parameters

In the normal model for a response, yi,


yi  =  
(explained)
µi

 + 
(unexplained)
εi

the mean, µi, is specified as a function of the valuse of the controlled factors and the known structure of the experimental units (e.g. grouping of the experimental units into blocks) that also involves unknown parameters. If the unknown parameters are α, β, ..., we can therefore write it in the form

µi   =   f (xi, zi, ..., α, β, ...)

Least squares

The unknown parameters are usually estimated to make the errors small. The error sum of squares is

Σ εi 2  =  Σ ( yi  −  f (xi, zi, ..., α, β, ...)2

and the unknown parameters are usually estimated to make this sum of squares as small as possible. This is called the method of least squares.

The remainder of this e-book uses normal models of various kinds and least squares is used to estimate the model parameters.