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# Correlation and Regression Questions

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In this problem set you will get some practice performing a linear regression analysis. If you use Statdisk or Excel to perform any portion of these analyses, please include the results, label them, and refer to them accordingly in your interpretations.

Listed below are the overhead widths (in cm) of seals measured from photographs and the weights of the seals (in kg). The data are based on "Mass Estimation of Weddell Seals Using Techniques of Photogrammetry," by R. Garrott of Montana State University. The goal of the study is to explore the relationship between the overhead widths and the weights of the seals and to determine whether there is enough evidence to conclude that it is reasonable to use the overhead width to estimate the weight of a seal.

Overhead Width (cm) 7.2 7.4 9.8 9.4 8.8 8.4
Weight (kg) 116 154 245 202 200 191

1. Find the correlation coefficient and the critical value of r at the 5% significance level. Is there sufficient evidence to conclude that there is a linear relationship between the overhead width and the weight of the seals? Explain this using the value of the correlation coefficient and the critical value of r.

2. Find the explained variation. Explain the meaning of the explained variation in the context of this situation.

3. Find the unexplained variation. Explain the meaning of the unexplained variation in the context of this situation.

4. Find the total variation. Demonstrate and explain the relationship between the explained variation, the unexplained variation, and the total variation in the context of this situation.

5. Find the coefficient of determination. Demonstrate and explain the relationship between the explained variation, the total variation, and the coefficient of determination in the context of this situation. Explain the meaning of the coefficient of determination in the context of this situation.

6. Find the standard error of estimate.

7. Write the equation for the regression line. Explain the meaning of the slope of this line in the context of this situation. Find the predicted weight in kg of a seal given that the width from an overhead photograph is 9.0 cm.

8. Use the prediction interval spreadsheet to find both a 95% prediction interval estimate and a 95% confidence interval estimate of the weight in kg of a seal given that the width from an overhead photograph is 9.0 cm. Explain the meaning of these interval estimates in the context of this situation. Explain the difference between a 95% prediction interval estimate and a 95% confidence interval estimate for any given situation.