To determine the correlation between the ages of dogs and the lengths of their tails, we need to follow these steps:
1. Data Collection: We have the following data:
- Ages of the dogs (in years): 2, 3, 6, 10
- Lengths of their tails (in inches): 12, 0, 7, 4
2. Calculate Correlation Coefficient: The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where:
- A value of 1 indicates a perfect positive linear relationship.
- A value of -1 indicates a perfect negative linear relationship.
- A value around 0 indicates no linear relationship.
3. Interpreting the Correlation Coefficient: Based on the given solution, the correlation coefficient between the ages and tail lengths is approximately -0.270. This is a negative correlation because the value is less than zero, indicating that as the age increases, the length of the tail decreases. However, the magnitude of this coefficient is less than 0.7, so it is considered weak.
4. Correlation Strength: Given that the absolute value of the correlation coefficient (-0.270) is less than 0.7, it indicates a weak correlation.
5. Causal Relationship: Even though we observe a weak negative correlation, this does not imply causation. Causation would mean that changes in the age directly cause changes in the length of the tail. However, in this context, age and tail length are likely influenced by other factors, and the weak correlation makes it unlikely to assume a causal relationship.
Based on these observations, the appropriate conclusion about the type of correlation and causation between the age of dogs and the length of their tails is:
- It is a weak negative correlation, and it is not likely causal.
So the correct statement is:
- It is a weak negative correlation, and it is not likely causal.
