Dear Joelle,
> what reasoning we have behind this shape?
Well, it's the time course resulting from convolving a stimulus on/off function with the canonical HRF response. If you have different assumptions then it doesn't make sense to rely on the canonical HRF of course.
> What is the point of having a constant term in the model?
The intercept is the mean of the measured data ("implicit baseline") when all predictors are 0. We need an intercept because when all predictors are 0 the voxels within the EPI images are not 0 but have some positive value still (due to the hydrogen nuclei within the tisse, independent of any BOLD effect).
> then such short rest periods doesnt allow for the signal to return to baseline
Yes.
> What would [1 -1] then test, with the 1 over the task column and the -1 over the constant column?
As stated, in a simple linear regression it's slope vs. intercept, in fMRI it's beta of the task regressor vs. beta of the constant term. It's statistically valid, but it (likely) lacks a meaning. If you look at the last beta image in your analysis folder you might get an idea why, also see above what the intercept means.
> My goal is to see which regions are activated during the task compared to during rest.
As you don't explicitely model rest the correct contrast is [1 0] for positive activations during task and [-1 0] for negative activations during task. As stated previously, the design is highly inefficient though, so it wouldn't be surprising if you fail to detect expected effects.
Best
Helmut
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