The following scatter plot summarizes the shoulder height of dogs, in inches (in.) and the percentage of dogs surviving 10 - 15 years.

Question

Which of the following statements about correlation and causation are true within this context? Select all that apply.
-There is a moderately strong, positive association between the shoulder height in dogs and the percentage of dogs living to age 10 - 15.
The data does not provide evidence that a smaller shoulder height causes dogs to survive 10 - 15 years.

There is a moderately strong, negative association between the shoulder height in dogs and the percentage of dogs living to age
There is a moderately strong, negative association between the shoulder height in dogs and the percentage of dogs living to age 10 minus 15 point

Since there is a moderately strong correlation, the data provides evidence that a smaller shoulder height causes dogs to survive
years.
Since there is a moderately strong correlation, the data provides evidence that a smaller shoulder height causes dogs to survive 10 minus 15 years.

Since there is a moderately strong correlation, dogs that have a smaller shoulder height tend to survive
years.
Since there is a moderately strong correlation, dogs that have a smaller shoulder height tend to survive 10 minus 15 years.

Causation can be established in this context because there is a clear relationship between the variables studied.
Causation can be established in this context because there is a clear relationship between the variables studied.
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Answer 1

Based on the information provided, the following statements can be assessed for their truthfulness in the context of correlation and causation related to the shoulder height of dogs and their survival rates:

1. There is a moderately strong, positive association between the shoulder height in dogs and the percentage of dogs living to age 10 - 15.

   • False (If there's a negative association, this cannot be true).

2. The data does not provide evidence that a smaller shoulder height causes dogs to survive 10 - 15 years.

   • True (Correlation does not imply causation).

3. There is a moderately strong, negative association between the shoulder height in dogs and the percentage of dogs living to age 10 - 15.

   • True (If there is indeed a negative correlation).

4. Since there is a moderately strong correlation, the data provides evidence that a smaller shoulder height causes dogs to survive 10 - 15 years.

   • False (Correlation alone does not imply causation).

5. Since there is a moderately strong correlation, dogs that have a smaller shoulder height tend to survive 10 - 15 years.

   • False (If the relationship is negative, smaller shoulder height would correlate with lower survival rates, not higher).

6. Causation can be established in this context because there is a clear relationship between the variables studied.

   • False (Even with a correlation, causation cannot be concluded without further evidence).

Based on these assessments, the true statements are:

• The data does not provide evidence that a smaller shoulder height causes dogs to survive 10 - 15 years.
• There is a moderately strong, negative association between the shoulder height in dogs and the percentage of dogs living to age 10 - 15.