480 CHAPTER 9 Correlation and Regression Correlation and Causation The fact that two variables are strongly correlated does not in itself imply a cause-and-effect relationship between the variables. More in-depth study is usually needed to determine whether there is a causal relationship between the variables. When there is a significant correlation between two variables, a researcher should consider these possibilities. 1. Is there a direct cause-and-effect relationship between the variables? That is, does x cause y? For instance, consider the relationship between gross domestic products and carbon dioxide emissions that has been discussed throughout this section. It is reasonable to conclude, from the given data, that countries with higher gross domestic products will have higher carbon dioxide emissions. 2. Is there a reverse cause-and-effect relationship between the variables? That is, does y cause x? For instance, consider the Old Faithful data that have been discussed throughout this section. These variables have a positive linear correlation, and it is possible to conclude that the duration of an eruption affects the time before the next eruption. However, it is also possible that the time between eruptions affects the duration of the next eruption. 3. Is it possible that the relationship between the variables can be caused by a third variable or perhaps a combination of several other variables? For instance, consider the salaries and average home game attendances for the teams in Major League Baseball listed on page 469. Although these variables have a positive linear correlation, it is doubtful that just because a team’s salary decreases, the average attendance per home game will also decrease. The relationship is probably due to other variables, such as the economy, the players on the team, and whether or not the team is winning games. Variables that have an effect on the variables being studied but are not included in the study are called lurking variables. 4. Is it possible that the relationship between two variables may be a coincidence? For instance, although it may be possible to find a significant correlation between the number of animal species living in certain regions and the number of people who own more than two cars in those regions, it is highly unlikely that the variables are directly related. The relationship is probably due to coincidence. Determining which of the cases above is valid for a data set can be difficult. For instance, consider this example. A person breaks out in a rash after eating shrimp at a certain restaurant. This happens every time the person eats shrimp at the restaurant. The natural conclusion is that the person is allergic to shrimp. However, upon further study by an allergist, it is found that the person is not allergic to shrimp, but to a type of seasoning the chef is putting into the shrimp. Picturing the World The scatter plot shows the results of a survey conducted by students in a high school statistics class. In the survey, 125 high school students were asked their grade point average (GPA) and the number of caffeine drinks they consumed each day. 0 2 4 6 8101214 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 GPA (5-point scale) Caffeine drinks (cups per day) x y What type of correlation, if any, does the scatter plot show between caffeine consumption and GPA?
RkJQdWJsaXNoZXIy NjM5ODQ=