How will you interpret the coefficient of correlation?

Answer 1

Correlation is a measure of the strength of a linear relationship between two variables. In theory it ranges between -1 and +1, although in practice, random and observation error make this value smaller.

Near -1, the correlation is very strongly negative, which means that an increase in one variable is accompanied by a decrease in the other.

Near +1, the correlation is very strongly positive, which means that an increase in one variable is accompanied by an increase in the other.

Near 0, the correlation is weak and there is no linear pattern in which the two variables change.

There are two very critical points to remember:

1. Correlation does not measure causation. For example, the number of cars on the road is correlated to my age but my getting older does not cause more cars to be made and cars do not cause me to grow old (at least, not with most drivers!)
2. Correlation will only measure a linear relationship. If you examine a relationship like y = x2, over a symmetric interval, the correlation coefficient will be close to 0. But there is, clearly, a very strong relationship - just that it is not linear.

Finally, the importance of any correlation coefficient is subjective and depends on the context. A correlation coefficient that is high for a sociological study may be considered moderate for a high school physics experiment.