Question: While older adults are often viewed as weak and feeble, there is an increasing body of evidence that resilience, the ability to moderate the negative effects of physiological stress and promote positive adaptation, is a defining characteristic of old age and a hallmark of successful aging. Using data from a sample of 500 adults between the ages of 18 and 80, you decide to explore this association for yourself. Age was measured in years and resilience was measured using the Wagnild and Young Resilience Scale, which has scores ranging from 25 to 175, with higher scores indicating more resilience. Use the Stata output provided below to help answer the following questions.

1. Briefly (1-2 sentences) explain why it is appropriate to calculate the correlation coefficient for these data.
2. Briefly (1-2 sentences) explain a potential limitation of the correlation coefficient within the context of this study.
3. What is the estimated correlation coefficient for the relationship between age and scores on the Wagnild and Young Resilience Scale? Provide an interpretation of this value.
4. Do you think there is evidence of a strong linear relationship between age and scores on the Wagnild and Young Resilience Scale? Why or why not?
5. What percent of the variation in someone’s score on the Wagnild and Young Resilience Scale can be explained by their age?
6. You would now like to know if the association between age and scores on the Wagnild and Young Resilience Scale is statistically significant at the 5% level of significance. To begin, st ate the null and alternative hypotheses to test the claim that there is a linear association between age and scores on the Wagnild and Young Resilience Scale. Make sure you define any variables that you use. It is not sufficient to just use Greek letters without defining them!
7. Convert the data to the appropriate test statistic and calculate the degrees of freedom.
8. Compare the test statistic from g) to the critical value of the appropriate known distribution and calculate the corresponding p-value range (based on the Sullivan table). Based on this, will you reject or fail to reject the null hypothesis?
9. Interpret your findings in the context of the study using a 5% level of significance.

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