Every now and again you come across an answer to a question that is just so clear that you want to bookmark it so that you can find it again if something like the original question you were googling comes up again. That just happened to me. I was googling "How are linear regression models, ANOVAs, and ANCOVAs related?" because it is a long time since I have had to do those equations by hand and all I remembered was that I learned them together because they relied on the same basic formulae. What those formulae were, I had completely forgotten.
Thanks, SAS, SPSS, Python, and R, for doing all the work for me and letting my brain atrophy.
Here is an answer to my question that is so good that I'm giving it space on my blog. Thanks, Karen Grace-Martin, for tapping this out so the rest of us could have the benefit of your explanation.