this post was submitted on 16 Jan 2024
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doesn't this lead to a lot of extraneous variables that are actually linearly dependent on a smaller set? or worse -- overconstraining?
This isn't a universal definition of degrees of freedom, it's just "degrees of freedom as it applies in an undergraduate level stats course," which is typically for the t distribution. It's n-1 because you assume all your observations are independent of one another. In other contexts (ANOVA, e.g.), the calculation is different.
I get that, just thought it was a strange definition given what degrees of freedom actually refers to