# Reporting mean regression results across several samples - appropriate?

I'd like to compare two maps (A and B, these are 3-dimensional images from an MRI scanner) acquired from a set of 30 subjects. Each map is composed of a number of spatial units ("voxels"). The value of each voxel is one observation (there's about 10,000 per map). I'm running a linear regression analysis of the relationship between the paired voxels in maps A and B (A is the dependent variable Y, B is the independent variable X). I'm doing a regression analysis separately for each of the 30 subjects because pooling them would violate the assumption of independence of Y (I think, please correct me if I'm wrong). When it comes to summarising the results across all subjects, is it appropriate to report the mean + standard deviation of R-squared and the standardised regression coefficients? I'm especially unsure about the latter (the regression coefficients).

Thanks in advance.

Ahmed

• Why don't you pool the 30 samples and treat the data set as one? This would increase power and give weighted average effects. You could include interactions or random effects to see differences in coefficients across groups (samples). – tomka Sep 5 '16 at 9:30
• Thanks @tomka. I wanted to do this initially, but the problem is, I think the assumption of the independence of Y observations would be violated in that case. Each "sample" is a single subject, each observation is a spatial unit in MRI space (a "voxel"). If I pool all the data, I will have observations from the same subject, which (I've been told) is not correct for a regression analysis. I'm happy to hear opposing views/justifications though. – Ahmed Sep 5 '16 at 10:06
• I think in this case it is necessary to adjust your question. I think this background information is needed to find the best solution. You may want to include detailed information on the substantial background, the sampling of units, and the (nested/spatial) structure of the data. – tomka Sep 5 '16 at 10:09
• I think now it's clearer. I still think you could pool and control for within subject correlation by a mixed effects model. However even when analysing the maps separately per subject the spatial correlation needs to be taken into account. – tomka Sep 5 '16 at 11:22