Welcome to the world of manifold regression! In part 2 we will apply manifold regression to a case study involving fMRI brain imaging data. See part 1 for an introduction to these models.
If you want to skip past the data preparation steps, and go right into the manifold regression, click here
Getting Data
First, we need a set of data to work from. There are many great fMRI imaging datasets available on the OpenNeuro website.

Welcome to the world of manifold regression! In part 1 we will introduce the basic concepts, overview the theory behind regression on manifolds, develop an intuition for these models, and discuss their applications. See part 2 for a step by step statistical analysis applying these models.
What is regression? We will consider regular linear regression (RLR) as an analogy to help understand manifold regression. In RLR, we consider pairs of observations \((x,y)\), with \(x\) the independent variable, and \(y\) the dependent variable.

Getting bored with the plots you can make using the base R plot? Probably time to spice things up with ggplot!
You can read through this article, or you can watch the tutorial video below (or both!).
Let’s get started. First load the ggplot2 library, since thats what we’re here to learn!
library(ggplot2) We’re going to be looking at the msleep dataset (same one we were looking at in the last tutorial )

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