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Ryan gathered data about the age of the different dogs in his neighborhood and the length of their tails.

Lengths of Tails for Dogs of Different Ages

\begin{tabular}{|c|c|}
\hline
Age (years) & Length of Tail (in.) \\
\hline
2 & 12 \\
\hline
3 & 0 \\
\hline
6 & 7 \\
\hline
10 & 4 \\
\hline
\end{tabular}

Which best describes the strength of the correlation, and what is true about the causation between the variables?

A. It is a weak negative correlation, and it is not likely causal.
B. It is a weak negative correlation, and it is likely causal.
C. It is a strong negative correlation, and it is not likely causal.
D. It is a strong negative correlation, and it is likely causal.

Sagot :

GinnyAnsweridn
To determine the strength and nature of the correlation between the age of dogs and the length of their tails, let’s analyze the data provided:

| Age (years) | Length of Tail (in.) |
|-------------|----------------------|
| 2 | 12 |
| 3 | 0 |
| 6 | 7 |
| 10 | 4 |

First, we need to determine the correlation coefficient between the two variables, age and tail length. The correlation coefficient is a measure of the linear relationship between two variables, ranging from -1 to 1. A correlation coefficient close to 1 indicates a strong positive correlation, close to -1 indicates a strong negative correlation, and close to 0 indicates no correlation.

Given the data, the calculated correlation coefficient is approximately -0.2705.

### Interpreting the Correlation Coefficient:
- Strength: The correlation coefficient is -0.2705, which is relatively close to 0. This indicates a weak correlation.
- Direction: The correlation coefficient is negative, indicating that as one variable increases, the other variable tends to decrease.

### Causation:
Correlation does not imply causation. Even though there is a weak negative correlation between the age of the dogs and the length of their tails, this does not mean that age directly affects tail length. The relationship could be influenced by other factors or be purely coincidental.

### Conclusion:
- Strength of the Correlation: It is a weak negative correlation.
- Causation: It is not likely causal.

Therefore, the correct option is:
- It is a weak negative correlation, and it is not likely causal.
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