
Exactly –1. A perfect downhill (negative) linear relationship

–0.70. A strong downhill (negative) linear relationship

–0.50. A moderate downhill (negative) relationship

–0.30. A weak downhill (negative) linear relationship

0. No linear relationship

+0.30. A weak uphill (positive) linear relationship

+0.50. A moderate uphill (positive) relationship

+0.70. A strong uphill (positive) linear relationship

Exactly +1. A perfect uphill (positive) linear relationship
If the scatterplot doesn’t show that there’s at least somewhat of a linear relationship, the correlation doesn’t mean much. Why measure the amount of linear relationship if there isn’t much of one?
However, you can think of this idea of no linear relationship in two ways: 1) If no relationship at all exists, calculating the correlation doesn’t make sense because correlation only applies to linear relationships, and 2) If a strong relationship exists but it’s not linear, the correlation may be misleading, because in some cases a strong curved relationship exists. That’s why it’s critical to check out the scatterplot first.
Comparing Figures (a) and (c), you see Figure (a) is nearly a perfect uphill straight line, and Figure (c) shows a very strong uphill linear pattern (but not as strong as Figure (a)). Figure (b) is going downhill, but the points are somewhat scattered in a wider band, showing a linear relationship is present, but not as strong as in Figures (a) and (c). Figure (d) doesn’t show much of anything happening (and it shouldn’t, since its correlation is very close to 0).
Many folks make the mistake of thinking that a correlation of –1 is a bad thing, indicating no relationship. Just the opposite is true! A correlation of –1 means the data are lined up in a perfect straight line, the strongest negative linear relationship you can get. The “–” (minus) sign just happens to indicate a negative relationship, a downhill line.
How close is close enough to –1 or +1 to indicate a strong enough linear relationship? Most statisticians like to see correlations beyond at least +0.5 or –0.5 before getting too excited about them. Don’t expect a correlation to always be 0.99 however; remember, these are real data, and real data aren’t perfect.