6
¥Regression Model (General Linear System)
_Simple Regression Model (one regressor): Y(t) = a0+a1t+b r(t)+e(t)
"Run 3dDeconvolve with regressor r(t), a time series IRF
_Deconvolution and Regression Model (one stimulus with a lag of p TRÕs):  
"Y(t) = a0+a1t+b0f(t)+b1f(t-TR)É+bpf(t-p*TR)+e(t)
"Run 3dDeconvolve with stimulus files (containing 0Õs and 1Õs)
¥Model in Matrix Format: Y = Xb + e
_X: design matrix - more rows (TRÕs) than columns (baseline parameters + beta weights).          
_          a0     a1       b                                       a0    a1     b0    É    bp
"             ------------------                      ------------------------
q1     1     r(0)                         1   p     fp     É    f0 
q1     2     r(1)                                      1   p+1 fp+1 É f1
q    .  .  .         .  .  .
q1   N-1    r(N-1)                                1   N-1 fN-1 É fN-p-1

_e: random (system) error N(0, s2)


Basics about Regression