A Pennsylvania research firm conducted a study in which 30 drivers of ages 18 to 82 years old were sampled. For each one, the maximum distance in feet at which he or she could read a newly design sign was determined. The goal of the study was to explore the relationship between a driver's age and the maximum distance at which signs were legible. The explanatory variable is age, and the response variable is distance. Here's a scatter plot for the data, which shows a negative linear relationship between the age of a driver and the maximum distance at which a highway sign was legible. What about the strength of the relationship? It turns out that the correlation between the two variables is r = -0.793. Since r is less than zero, it confirms that the direction of the relationship is negative. Since r is relatively close to negative one, it suggests that the relationship is moderately strong. In context, the negative correlation confirms that the maximum distance at which a sign is legible generally decreases with age. The correlation only measures the strength of a linear relationship between two variables. It ignores any other type of relationship, no matter how strong it is. For example, consider the relationship between the average fuel usage driving a fixed distance in a car and the speed at which the car drives. Our data describes a fairly simple curvilinear relationship. The amount of fuel consumed decreases rapidly to a minimum, for a car driving 60 kilometers per hour. And then increases gradually for speeds exceeding 60 kilometers per hour. The relationship is very strong as the observations seem to perfectly fit the curve. Although the relationship is strong, the correlation r is equal to -0.172. It indicates a weak linear relationship. This makes sense considering the data fails to adhere closely to a linear form. The correlation is useless for accessing the strength of any type of relationship that is not linear including relationships that are curvilinear such as the one in our example. So beware of interpreting r when it's close to zero as an indicator of a weak relationship. Rather it indicates a weak linear relationship. It's very important to always look at the data in the scatter plot. Since, as in our example, there might be a strong nonlinear relationship that r does not indicate. The same can be said for a large correlation coefficient. It's very important to interpret both the scatter plot and the correlation together. As with the other inferential tools we've discussed, an associated p-value is also calculated for the correlation coefficient. And it's interpreted as significant when it's less than or equal to 0.05. Thus, the correlation coefficient and corresponding p-value will now allow us to evaluate whether or not the relationship between two quantitative variables we observe in a sample holds for the larger population.