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The general linear model: what you need to know P.M.E.Altham, Statistical Laboratory, University of Cambridge.
 

Summary: The general linear model: what you need to know
P.M.E.Altham, Statistical Laboratory, University of Cambridge.
October 14, 2004
Note: this set of basic notes contains deliberate gaps, for you to ll in.
The models
y i = + x i +  i ;
y i = + x i + x i
2 +  i
and
y ij =  + i + j +  ij
may all be seen as special cases of the model
y i = T x i +  i
for i = 1; :::; n where we assume that ( i ; i = 1; :::; n) form a random sample
from N(0;  2 ). Here y i is the `dependent' variable, x i is the known covariate,
the unknown parameter, of dimension say p, and  i is the unknown `error': we
assume that ( i ; i = 1; :::; n)  NID(0; 2 ), ie ( i ; i = 1; :::; n) form a random
sample from N(0;  2 ). The parameter  2 is also unknown. We rewrite this
model as
Y = X + ;
where   Nn (0;  2 I) (a multivariate- normal distribution).

  

Source: Altham, Pat - Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge

 

Collections: Mathematics