The F value in regression is the result of a test where the null hypothesis is that all of the regression coefficients are equal to zero. In other words, the model has no predictive capability. Basically, the f-test compares your model with zero predictor variables (the intercept only model), and decides whether your added coefficients improved the model. If you get a significant result, then whatever coefficients you included in your model improved the model's fit.
P-value
If the p-value is small (less than your alpha level), you can reject the null hypothesis. Only then should you consider the f-value. If you don't reject the null, ignore the f-value.
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