The first thing I would do is choose a p-value cutoff that's appropriate for you. .05 works for many applications, but still leaves a 5% chance that the analysis falsely reports a relationship in the data. Picking a lower p-value cutoff will make you more sure in your analysis, but the reality is that in the real world, very very rarely will a regression come up with a p-value of say 0.0001. Try to choose a cutoff that makes you relatively sure, but doesn't handicap your analysis too much. 0.05 or 0.01 are probably good choices.
It is very important that you choose this p-value cutoff once and then never alter it until you've moved onto a different project. If you allow yourself to alter the cutoff on the fly, you open yourself up to many biases.
Once you've chosen your cutoff for the entire project, yes you are correct. A p-value > cutoff should be interpreted as no better than random guesses and the analysis should not be trusted. Of course, there are exceptions to the rule as finance is a game of 51-49% advantages, but generally you should ignore results with p-value > cutoff unless you really know what you're doing.
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