Here you go tec:
"Statistical significance does not equate to high correlation. For large enough sample sizes even very low r values (0.1, 0.01, etc) eventually become significant, but these do not equate to high correlation.
...
According to a Sloan Consulting article at ISIXSIGMA.COM site and quote (emphasis added)
“As a rule of thumb a strong correlation or relationship has an r-value range of between 0.85 to 1, or -0.85 to -1. In a moderate correlation, the r-value ranges from 0.75 to 0.85 or, -0.75 to -0.85. In a weak correlation, one that is not a very helpful predictor, r ranges from 0.60 to 0.74 or -0.60 to 0.74. Though an entirely random relationship equals, 0.00, any relationship that has a correlation r-value that is 0.59 and below is not considered to be a reliable predictor.”
According to this Intel Teach Program a correlation between 0 and 0.19 is a very weak one while one between 0.2 and 0.39 weak enough."