imaging-03

Aim

In this unit we want to work through an example of linear regression, in particular the estimation part.

Linear regression in action

First, I will walk/talk you through an example of how to load in some data, get a timecourse from a single voxel at a time, the designMatrix and then show the linear regression bit in action.

go to subfolder and you can also have a look at the PDF file I produced from the analysis script using the publish() feature in Matlab.

Turning this into a function

If we have time, we can also think about how we can take the logic of the code I wrote in the script into a function that takes as inputs

• the name of a data file y_filename
• the name of the design matrix file X_filename
• the [x, y, z] coordinate in image coords

Specification

The function linRegress() should be of the following form:

• b = linRegress( y_filename, X_filename, coords)

• loads in y_filename (a nifti file) which provides data and information about timing

  • uses information in y_filename to make a vector of numbers that specify time (call one t_seeconds, another t_volumes) discussion point in your groups! why?? how??

• gets a 1d vector y from the data stored in y_filename using the coords variable (hint: how are x,y,z stored, how can we get them out??). consider reusing code we wrote last time?!

• loads in design matrix from X_filename

• finds: beta = X\y; using backslash operation

• reports beta values on command line (disp, sprintf, fprintf)

• plots modelfit = X*beta on top of timecourse plot (same figure)

Ultimately, running the following should work

cd('facesVhouses');
b = linRegress( 'filtered_func_data.nii', 'designMatrix.txt', [18, 14, 4])
cd('..'); % come back up one folder

Notes

To orient you with some of the calculations, consider the following plot: