A correlation of r = 0.85 is found between weekly sales of firewood and cough drops over a 1-year period. Which of the following is a correct interpretation of this correlation value? There is a pretty strong positive linear relationship between sales of firewood and cough drops. Temperature is a possible lurking variable that is behind this relationship. Fire must be the cause of coughing.
Question
A correlation of r = 0.85 is found between weekly sales of firewood and cough drops over a 1-year period. Which of the following is a correct interpretation of this correlation value? There is a pretty strong positive linear relationship between sales of firewood and cough drops. Temperature is a possible lurking variable that is behind this relationship. Fire must be the cause of coughing.
Solution
The correlation value of r = 0.85 indeed indicates a strong positive linear relationship between the sales of firewood and cough drops. This means that as the sales of firewood increase, the sales of cough drops also tend to increase, and vice versa.
The mention of temperature as a possible lurking variable is a plausible interpretation. A lurking variable is an extraneous variable that is not included in the correlation analysis but could influence the relationship between the two variables. In this case, colder temperatures could lead to increased sales of both firewood (for heating) and cough drops (for cold-related coughs), thus influencing the observed correlation.
However, the statement "Fire must be the cause of coughing" is not a correct interpretation based on the correlation value. Correlation does not imply causation. Just because two variables are correlated
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