Let's say I want to predict the crop yield of a field. Sure, looking at the yield in previous years would help. But the yield is just a nonlinear projection of a point in high-dimensional space that has dimensions like weather, water availability, pest infestations, farmer skill, etc. All of these dimensions are incredibly relevant to forecasting, but once we've projected our points onto the yield axis, most of this information is gone. So if you want to take advantage of this information, you need to do your fitting in the original high-dimensional space.
