Computing FMRI Activations: Coecients and t-Statistics by Detrending and Multiple Regression

Detrending is often performed when analyzing FMRI data in order to remove any linear (or higher-order) drift and offset from the signal. When performing simple linear regression after detrending, the results obtained are not identical to those obtained by multiple linear regression. In fact, even if there is no error in the data, detrending and simple linear regression are unable to determine exactly the correct coefficients in simulations. In addition, the choice of reference function, whether it be a square wave of ones and zeros or negative ones and ones, also affects the obtained result. Particular care should be taken when detrending and using a zero-one square wave as a reference function. The t-statistics for such a case do not give an accurate estimation of the error in the data, yielding too many false negatives. ∗Biophysics Research Institute, Medical College of Wisconsin †Division of Biostatistics, Medical College of Wisconsin ‡ Corresponding author: Biophysics Research Institute Medical College of Wisconsin 8701 Watertown Plank Rd. Milwaukee, WI 53226 Phone: 414-456-4027 Email: dbrowe@mcw.edu