Correlation

In mathematics, we use functions and equations to describe relationships between two sets of numbers. An example would be y = 2x + 1. This equation tells us that y is always exactly 2x + 1; there is a perfect relationship between the two sets of numbers. If we know x, we can always find y and vice versa. In the real world, however, relationships are rarely perfect. Would you, for example, be able to calculate a person's weight if you knew the person's height? Probably not. Yet, there is a relationship between height and weight, but the relationship is not perfect. How could we use mathematics to deal with imperfect relationships like the one between height and weight?

One way is to use a statistic that is called correlation. Are you familiar with the word correlation? What do you think it means?

Correlation, as used in mathematics, describes the strength of a relationship. If, for example, there were a perfect relationship between height and weight such that when one is big the other is also big, the correlation between the two would be +1. If there were a perfect relationship between the two, but if one is big, the other is small, the correlation would be -1. If there is no relationship between two sets of numbers, the correlation is 0.

Another way to describe correlation is to say that if the two sets of numbers can be plotted on a graph such that we can draw a straight line connecting all the points, then the correlation is +1 if the straight line has a positive slope, -1 if the straight line has a negative slope. If the points do not exactly lie on a straight line, the correlation is between -1 and 1. If the shape the points form is nowhere close to resembling a straight line, the correlation is 0. Can you think of two sets of numbers such that the correlation between them is close to +1? Can you think of two sets of numbers such that the correlation between them is close to 0? How about -1?