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19.3 General linear models

In generalization of the linear regression model the functional form of

for a general linear model is assumed to be given by r known functionsfj(x1,…,xk), j = 1(1)r in the form of

with unknown parameters θ0, θ1,…,θr, and linear independent functions f1(·),…,fr(·). The functions fj(x1,…,xk) can be written in compact form as fj(x), and using the notation

the general linear model (19.9) takes the form

As in the linear regression model usually the variances are assumed to be identical, i.e.

In order to estimate the parameters θ0, θ1,…,θr and σ2 observations are taken, i.e. the data are of the same type as for linear regression models:

Based on these data, and using the notation xi = (xi1,…,xik) the data matrix F is defined by

In order to estimate the regression ...

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