To analyze the data Ryan gathered about the ages of dogs and the lengths of their tails, we would primarily focus on calculating the correlation coefficient. The correlation coefficient quantifies the degree to which two variables are related.
Given the data points:
- Age: [2, 3, 6, 10] (years)
- Tail length: [12, 0, 7, 4] (inches)
We compute the correlation coefficient between these two variables to understand the nature of their relationship. The range of the correlation coefficient (typically denoted by 'r') is from -1 to 1, where:
- 1 indicates a perfect positive correlation,
- -1 indicates a perfect negative correlation,
- 0 indicates no correlation.
After performing the necessary calculations (which we do not show here), we find the correlation coefficient to be approximately -0.2705.
Interpreting the correlation coefficient (-0.2705):
1. Strength of Correlation:
- A correlation coefficient between -0.5 and 0 is generally considered to indicate a weak negative correlation.
- Since -0.2705 is within this range, the strength of the correlation is weak negative.
2. Causation:
- Correlation does not imply causation. In this case, since we have a weak negative correlation, it suggests that there is not a strong linear relationship between the two variables, making it unlikely that changes in one variable would directly cause changes in the other. In other words, there isn't enough evidence to claim a likely causal relationship.
As a result, the appropriate description of the relationship between these variables is:
"It is a weak negative correlation, and it is not likely causal."
