I would not call y the observed BOLD response, but rather the observed
MRI signal. It is a combination of many things, which one tries to model
as well as possible (using linear regression with 3dDeconvolve, for
example). Often it might be expressed as some linear sum of baseline,
motion, responses to known stimuli, and remaining noise.
The 'y' in that equation is the EPI time series input to 3dDeconvolve
(one time series per voxel). One would define the X matrix as well as
possible (by giving 3dDeoncolve sitmulus times and corresponding basis
functions, a polynomial baseline degree, and possibly many regressors of
no interest, such as motion paramters).
The output from 3dDeconvolve is the B vector (one per voxel), as well as
optionally the e (error) vector, among other things.
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I suggest you read through the analysis tutorial here:
http://afni.nimh.nih.gov/pub/dist/edu/data/CD.expanded/AFNI_data6/FT_analysis/tutorial
Start by reading the overview: t00_overview.txt
and then focus on the regression, starting with t15_regression.txt .
- rick