Hi,

I have a basic conceptual question regarding the context dependent correlation analysis.
In the context dependent correlation analysis as described on the afni page for CD cor Ana ,
it says to include interaction regressors and the seed regressor in the original regression analysis which has the task related regressors (independent variables) and regressors of no interest.

The question is, if the seed itself is a dependent variable which can be expressed as a linear combination of the independent task variables, when we do the CD cor ana, the variance that is explained by the two task regressors (in a general regression without seed regressor and interaction regressors) is now being split into variance explained by the task regressors and seed regressor.
y=b1x1+b2x2 - before CD cor ana: x1,x2 independent task regressors
y=c1x1+c2x2+c3x3+c4(x1*x3)+c5(x2*x3); x3-seed regressor
if x3=a1x1+a2x2;
then replacing for x3 in the above equation and rearranging terms
y=(c1+a1c3)x1+(c2+a2c3)x2+ c4(x1*x3)+c5(x2*x3)
we are essentially regressing with the above equation in CD cor ana when we include for seed regressor and the interaction terms
but, the variance explained by the seed regressor is not by the seed itself but can be attributed to the task regressors.

Is it that the betas associated with task regressors (in a general regression without seed regressor and interaction regressors)
cannot be equal to the betas associated with the same task regressors when we do the CD cor ana with a seed that can be expressed as a linear combination of the independent task variables?

Pardon me if I am missing something here completely.
I am just trying to understand how the analysis will be affected if the seed region has a similar characteristics as the target region .

Thanks alot again