Basic linear modeling

In this exercise we will run a simple regression on all voxels in a 4D FMRI image.

>>> # import some standard librares
>>> import numpy as np
>>> import numpy.linalg as npl
>>> import matplotlib.pyplot as plt
>>> import nibabel as nib

>>> # Load the image as an image object

>>> # Load the image data as an array
>>> # Drop the first 4 3D volumes from the array
>>> # (We already saw that these were abnormal)

>>> # Load the pre-written convolved time course
>>> # Knock off the first four elements

>>> # Compile the design matrix
>>> # First column is convolved regressor
>>> # Second column all ones

>>> # Reshape the 4D data to voxel by time 2D
>>> # Transpose to give time by voxel 2D
>>> # Calculate the pseudoinverse of the design
>>> # Apply to time by voxel array to get betas

>>> # Tranpose betas to give voxels by 2 array
>>> # Reshape into 4D array, with same 3D shape as original data,
>>> # last dimension length 2

>>> # Show the middle slice from the first beta volume

>>> # Show the middle slice from the second beta volume