Imagining a Linear Regression model with more than 3 dimensions I'm just getting started with Machine Learning and this is really bugging me now.
Assuming we could use more than 2 feature variables to train a Multiple Linear Regression model, how can we imagine the geometry of the model?
Let me elaborate.
For a linear regression model with a feature variable and a response variable, we come up with an equation of a line (y = mx + c) and for a multivariate linear regression model with 2 predictor variables, we can figure out the equation of a plane (a(x-x1)+ b(y-y1) + c (z-z1) = 0).
How can we imagine the model in 4 dimensions or more, since we are humans and as a layman, we cannot imagine higher dimensions like physicists?
Humans live in a 3 dimensional world. Consequently it can be hard for us to visualise anything beyond 3 dimensions. For 4 dimensions, we can perhaps think about time as the next dimension, so we might think about how a 3 dimensional image changes over time. Even that is quite tricky, so for 5 dimensions and above it is basically impossible.
Rather than trying to visualise a model in terms of geometry, it may be better to understand how models work by using linear algebra (ie matrix algebra)