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I have been reading introduction to statistical learning, and I was going through multiple linear regression. This is the topic that I'm reading:

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As I was reading further, I encountered an equation that I'm not able to understand. Below is that equation:

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It further says that

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Please try to explain the above mentioned problem as simply as possible.

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Assuming a hypothesis that all coefficients are zero, it can be proven the test statistics you have have a F distribution. However, if your hypothesis is wrong your test statistics will be away from the distribution.

Please read https://en.wikipedia.org/wiki/F-test, section Regression problems.

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