# Basic linear modelingΒΆ

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
```