Two of the most widely used measures of association are *covariance* and *correlation*. These measures are closely related to each other; in fact, you can think of correlation as a modified version of covariance.

Correlation is easier to interpret because its value is always between –1 and 1. For example, a correlation of 0.9 indicates a very strong relationship in which two variables nearly always move in the same direction; a correlation of –0.1 shows a very weak relationship in which there is a slight tendency for two variables to move in opposite directions.

With covariance, there is no minimum or maximum value, so the values are more difficult to interpret. For example, a covariance of 50 may show a strong or weak relationship; this depends on the units in which covariance is measured.

Correlation is a measure of the strength and direction of two *related* variables. Two variables are said to be related if they can be expressed with the following equation:

*Y* = m*X* + b

*X* and *Y* are variables; m and b are constants. For example, suppose that the relationship between two variables is:

*Y* = 3*X* + 4

In this case, 3 is the *coefficient* of *X*, which means that an increase of *X* by 1 causes *Y* to increase by 3. Equivalently, a decrease of *X* by 1 causes *Y* to decrease by 3. The 4 in this equation indicates that *Y* equals 4 when *X* equals 0.

Note that even though correlation can be computed for any pair, this doesn't mean they are *linearly related*. For example, you could have a high correlation with a small slope, and a low correlation with a large slope, as shown in the following graphs.

Covariance and correlation show that variables can have a positive relationship, a negative relationship, or no relationship at all. With covariance and correlation, there are three cases that may arise:

**If two variables increase or decrease at the same time, the covariance and correlation between them is**For example, the covariance and correlation between the stock prices of two oil companies is positive because many of the same factors affect the stock prices in the same way.*positive*.**If two variables move in opposite directions, the covariance and correlation between them is**For example, the covariance and correlation between interest rates and new home sales is negative because rising interest rates increase the cost of purchasing a new home, which in turn reduces new home sales. The opposite occurs with falling interest rates.*negative*.**If two variables are unrelated to each other, the covariance and correlation between them is**For example, the covariance and correlation between gold prices and new car sales is zero because the two have nothing to do with each other.*zero*(or very close to zero).