To determine the correlation between the age of dogs and the length of their tails, we can follow these steps:
1. Data Collection:
- Ages of the dogs: 2, 3, 6, 10 years.
- Lengths of their tails: 12, 0, 7, 4 inches.
2. Calculate Correlation Coefficient:
- The correlation coefficient is a statistical measure that helps us understand the strength and direction of a relationship between two variables. It ranges from -1 to 1.
- A value close to 1 implies a strong positive correlation, close to -1 implies a strong negative correlation, and close to 0 implies a weak correlation.
3. Interpret the Correlation Coefficient:
- If the correlation coefficient is less than 0, it indicates a negative correlation; if it is greater than 0, it indicates a positive correlation.
- The strength of correlation can be categorized as:
- Strong positive (> 0.7)
- Weak positive (<= 0.7)
- Strong negative (< -0.7)
- Weak negative (>= -0.7 and < 0)
Based on the analysis, the correlation coefficient in this case indicates a weak negative correlation between the age of the dogs and the length of their tails.
4. Causation:
- Correlation does not imply causation. Even if two variables show a correlation, it does not mean one causes the other.
- In this case, it is unlikely that the age of the dogs directly causes the length of their tails to change.
5. Conclusion:
- The strength of the correlation is best described as "weak negative."
- The relationship between the age of dogs and the length of their tails is not likely causal.
Therefore, the correct answer is:
It is a weak negative correlation, and it is not likely causal.
