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Meaning of p value in regression analysis

When you run a regression in statistical software, and it gives you the results, please explain to me what the following fields mean:

Prob > F [In particular, how small/large does this have to be to be statistically significant?]

Root MSE

P>|t| [Should the number be smaller than .05 to be significant at 5%?]

Solution Summary

Meaning of p value, F test, t test in regression analysis.