MIMO linear regression

[CdeMills]

Hello,

I'm performing electrical measurements with a device having two channels. I
get measurement sets with two inputs and two outputs, the channels being
closed on two resistors with different values. The output waveforms are
arranged such that their cross-correlation at lag 0 is 0. 

If I arrange some linear model, it's rather simple:
A = [ ones(size(I1)) I1 I2]
th = A\[V1 V2]

this way I get a (3,2) matrix, with two offset terms, two "direct"
resistance terms, and two terms resulting from cross-coupling (current from
channel 1 inducing a voltage on channel 2)

The residuals form a (n, 2) matrix; their covariance matrix is nearly
diagonal, indicating a weak coupling. I would like to probe further and test
wether or not the model coefficients are significant. Textbooks are always
concerned with one output data and many explanatory variables; in my case
there are two output data and noise sources. 

Could you suggest textbooks where this case is analysed ? I searched with
the keyword 'MIMO', but didn't find entries over linear regression.

Regards

Pascal



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