The correlation coefficient is what the statisticians conjured up to answer these questions. I won't get into specifics here, but the bottom line is that if you feed your data sets into the formula, it'll spit back out a number between -1 and 1. Positive correlation means that both pieces of data should tend to increase or decrease together. The rushing attempts and rushing yards example above would have a strong positive correlation. More attempts generally means more yards.
Fewer attempts means fewer yards.
If the number is close to negative one, that means there is a strong negative correlation . This indicates that the correlation is strong, but one number tends to increase as the other decreases, and vice versa. An example of this would be to compare every NFL player's vertical leap to his weight. Generally speaking, lower weight means higher leap and vice versa. There are exceptions of course, which means the correlation isn't perfect.