What does the p-value in the ANOVA table of multiple regression results indicate?

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The P value is the probability, assuming no effect or difference (null hypothesis), of obtaining a result equal to or more extreme than what was observed. The P-value of the ANOVA table indicates that under the assumption that all the group means are equal, the probability of having the observed results. If the P value is smaller than an extremely low value, say 0.01, the probability of observing the group difference as the sample is lower than 1% if the group means are equal in the population, and we can reject the null hypothesis.