# Correlation Coefficient and P-value

1. What is the r value for the relationship between Hamstring strength index 60°/s and the Shuttle run test? Is this r value significant? Provide a rationale for your answer.

2. Consider r = 1.00 and r = −1.00. Which r value is stronger? Provide a rationale for your answer.

3. Describe the direction of the relationship between the Hamstring strength index 60°/s and the Shuttle run test.

4. Without using numbers, describe the relationship between the Hamstring strength index 120°/s and the Triple hop index.

5. Which variable has the weakest relationship with the Quadriceps strength index 120°/s? Provide a rationale for your answer.

6. Which of the following sets of variables has the strongest relationship?

a. Hamstring strength index 120°/s and the Hop index

b. Quadriceps strength index 60°/s and the Carioca test

c. Quadriceps strength index 120°/s and the Side step test

d. Quadriceps strength index 60°/s and the Triple hop index

7. In Table 5, two r values are reported as r = −0.498 and r = −0.528. Describe each r value in words, indicating which would be more statistically significant, and provide a rationale for your answer.

8. The researchers stated that the study showed a positive, significant correlation between Quadriceps strength indices and pre- and postoperative functional stability. Considering the data presented in the Table 5, do you agree with their statement? Provide a rationale for your answer.

9. The researchers stated that no significant relationship could be described between Hamstring strength indices 60°/s and functional stability. Given the data in Table 5, explain why not.

10. Consider the relationship reported for the Quadriceps strength index 120°/s and the Hop index (r = 0.744**, p = 0.000). What do these r and p values indicate related to statistical significance and clinical importance?

Questions to be answered: Please refer to table 5 in the attachment that I have provided

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#### Solution Summary

This solution is comprised of a detailed explanation of correlation output given in exercise 23. All 10 questions were answered regarding correlation coefficient and p-values.

Regression Analysis and Correlation Coefficient

Please answer the 11 following questions about the attached problem. Please note that there are 4 attachments for this pb (the table is in two parts).

(c) Find the regression coefficients a and b.

(d) Place the regression line on the scatter diagram.

(e) Give s^2 xy and s xy.

(f) Compute the missing predicted values, residuals, and normal deviates for the given portion of the table.

(g) Plot the residual plot.

(h) Interpret the residual plot.

(i) Plot the residual normal probability plot.

(j) Interpret the residual normal probability plot.

(k) iii. Compute the t -statistic for testing beta = 0. What can you say about its p-

value?

(m) Construct the anova table and use Table A.7 to give information about the p-

value.

(p) Compute the correlation coefficient r.

(q) ii. Construct the 95% confidence interval for r.