Validate Algorithm Statistically: Questions & Answers

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I understand a bit about math, but it's been over 30 years since I've been to college. I have a question about where to find information mostly. My prolbem is that I have an algorithm that guesses the results of a process. The process has as best I can figure about 10 degrees of freedom.

1) how many times would I need to run the algorithim against the process to statistically validate the algorithm?

2) where would I find an Internet source that discusses this type of statistical validation? none of the google terms I come up with work for me.

I understand I can prove it by showing the math of how the algorithm was constructed, but that only works if you know the "why" behind the algorithm.
 
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1. No less than 30.
2. Look up statistical regression analysis.
 
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