Which pair of variables is the most likely to have both correlation and causation?
A.
the height of a person and the amount of work he does
B.
the length of a person's commute and the amount of money he earns
C.
the number of hours spent exercising and the number of calories burned
D.
the number of customers at a restaurant and the variety of soups ordered
C. the number of hours spent exercising and the number of calories burned.
The pair of variables that is most likely to have both correlation and causation is option C: the number of hours spent exercising and the number of calories burned.
Correlation refers to a relationship between two variables where they tend to change together. Causation, on the other hand, implies that one variable directly influences the other. In this case, if someone spends more hours exercising, it is likely to cause them to burn more calories, leading to a direct causal relationship. Additionally, there is a strong positive correlation between the number of hours spent exercising and the number of calories burned, as the more hours spent exercising, the higher the number of calories burned.
To determine which pair of variables is the most likely to have both correlation and causation, we need to consider the relationship between the variables and the possibility of a cause-and-effect relationship. Correlation refers to a statistical relationship between two variables, meaning that they tend to change together. Causation, on the other hand, refers to a direct cause-and-effect relationship where one variable directly influences the other.
A. The height of a person and the amount of work he does: These variables may have some correlation, as taller individuals may have larger physical capabilities and be capable of doing more physically demanding work. However, it's unlikely to have a direct causal relationship where height alone causes someone to work more. Other factors, such as skills, motivation, and job opportunities, are likely to influence the amount of work a person does. Thus, while there might be some correlation, causation is less evident.
B. The length of a person's commute and the amount of money he earns: There could be a correlation between these variables, as individuals with longer commutes might be more likely to have higher-paying jobs. However, it's difficult to establish a direct causal relationship in this case. While a longer commute may be indicative of better job opportunities, it doesn't directly cause a person to earn more money.
C. The number of hours spent exercising and the number of calories burned: This pair of variables is likely to have both correlation and causation. As someone spends more hours exercising, they are likely to burn more calories. This relationship holds true because physical activity directly causes calories to be burned. Therefore, there is a correlation between the number of hours spent exercising and the number of calories burned, and there is also a clear causal relationship where exercising directly causes calories to be burned.
D. The number of customers at a restaurant and the variety of soups ordered: Although there might be a correlation between the number of customers at a restaurant and the variety of soups ordered, establishing a direct causal relationship is challenging. While a higher number of customers might increase the demand for a variety of soups, it's unlikely that the presence of customers alone is the direct cause of a wider variety of soups being ordered.
Based on the explanations above, the pair of variables most likely to have both correlation and causation is C: the number of hours spent exercising and the number of calories burned.