# Interpreting the f ratio in linear regression in r

The last string of my output in r is:

F-statistic: 181.4 on 15 and 2380 DF, p-value: < 2.2e-16

How do I interpret this result?

While I understand that the f value is a ratio that compares the systematic variance to the amount of unsystematic variance i.e. “the ratio of the model to its error” (Fields et al., 2012 p.400), I do not understand how to interpret the string.

Mathematically, $F=\frac{\frac{\text{Sum Squares Model}}{\text{df Model}}}{\frac{\text{Sum Squares Error}}{\text{df Error}}}$.