Questions: Question 7 10 pts 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? - Fire must be the cause of coughing. - Temperature is a possible lurking variable that is behind this relationship. - There is a pretty strong positive linear relationship between sales of firewood and cough drops.

Solution Steps

To interpret the correlation value of \( r = 0.85 \), we need to understand what correlation means. A correlation value close to 1 indicates a strong positive linear relationship between two variables. However, correlation does not imply causation, so we cannot conclude that one variable causes the other. Instead, we can consider the possibility of a lurking variable that might influence both variables.

The given correlation value is \( r = 0.85 \). This value indicates a strong positive linear relationship between the two variables: weekly sales of firewood and cough drops. A correlation value close to 1 suggests that as one variable increases, the other variable also tends to increase.

While \( r = 0.85 \) shows a strong positive linear relationship, it does not imply causation. Therefore, we cannot conclude that "Fire must be the cause of coughing." Instead, we should consider other possible explanations, such as a lurking variable that might influence both variables.

One plausible lurking variable could be temperature. During colder months, people are more likely to buy firewood for heating and cough drops for colds, which could explain the observed correlation.

Based on the correlation value and the possible lurking variable, the correct interpretations are:

1. Temperature is a possible lurking variable that is behind this relationship.
2. There is a pretty strong positive linear relationship between sales of firewood and cough drops.

Final Answer