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How to "easily" interpret the F-statistic degrees of freedom (such as given in R's summary.lm)?

By "easily" I mean that rather than answering with some theoretical treatment on degrees of freedom of the F-statistic, which can be found from the internet, what are the F-statistic's degrees of freedom useful for when trying to infer aspects of a linear model?

E.g. the p-value of F-statistic gives information regarding, whether all the variables contribute significally to the model output. So what can the degrees of freedom be used for?

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  • $\begingroup$ "So what can the degrees of freedom be used for?" I do not think that question has the same merit for the d.f. as it has for the p-value. You may possibly be capable of doing something with the p-value, whereas the d.f. are "just" some feature you need to get right in order to get a statistic that has the desired null distribution. $\endgroup$ Oct 6, 2016 at 11:31

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You don't usually "use" the degrees of freedom for anything. It's needed to work out the p value of the F statistic, since every F distribution (each identified by its two degrees-of-freedom parameters) is different. Since R - like most other statistical software - calculates that p-value for you, you don't necessarily need it for anything else.

However, it depends on what else you might want to do (but there are so many things you might want to do - some of which you might use those df numbers for) that this potentially becomes an overly broad question.

In regression, you can work out the two df parameters yourself before you fit the model; they're:

  1. the number of predictors you fit (not counting the constant) and

  2. the number of observations minus the number of predictors minus 1 (for the constant)

So that part of the output is not adding anything you shouldn't already know.

(I suggest you reconsider your objection to the "theoretical" considerations. They're frequently an essential part of understanding what you're doing.)

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