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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 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.
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