Penguins can dive for a very long time. One of the key determinants is how quickly they use the oxygen in their body. The variables recorded are Dive Heart Rate (bpm) and Duration (min). For this homework, you will be asked to perform the appropriate analysis to explore the relationship between the two variables. For most of the questions, you will want to use technology to perform the computations, either Excel, a TI calculator, or the software available with the text.

1. (3 pts) Before you make any graphs or perform any calculations, what kind of association do you expect between the two variables? Explain why this is your expectation.

2. (2 pts) Which variable is the explanatory variable, and which is the response variable? Explain your response.

3. (3 pts) Create a scatterplot of the two variables.

4. (2 pts) Compute the value of the correlation coefficient, r. Round your answer to 3 decimal places.

5. (3 pts) Describe the linear association between the two variables. Explain how you determined the linear association?

6. (3 pts) Compute the equation of the regression line and add the line to the scatterplot. Round coefficients to at least 3 decimal places.

7. (2 pts) Interpret the meaning of the slope of the regression line in this context.

8. (2 pts) Compute the means for each of the variables and verify that that point is on the regression line by plugging the mean value of the explanatory variable into the equation for the regression line.

9. (2 pts) For the eighth dive, compute the predicted value of the response variable.

10. (2 pts) For the eighth dive, compute the residual.

11. (3 pts) Compute R2. (rounded to 3 decimal places). Explain both what this values tells you in terms of how well the line fits the data and in terms of explained variability.

12. (2 pts) How good do you feel about the regression line's ability to predict values. Explain how you made that decision.

Dive Heart Rate (bpm)

103.4

77.6

44.3

54.2

42.9

31.8

42.1

40.2

81

106.3

87.7

45.5

48.6

83.6

37.7

34.1

43.3

40.3

31.5

67.8

48.5

27.5

29.9

22.8

36.3

30.6

28.1

39

28.5

23.5

50.6

48.4

50.8

49.6

Duration (min)

1.1833333

4.7666667

9.1333333

7.25

11.866667

11.283333

6.05

9.8333333

2

2.0666667

2.1166667

10.5

7.4666667

2.5833167

14.48325

8.9666167

8.49995

10.5166

9.2087

1.9333167

3.2999833

13.5166

11.949933

12.583267

9.8166

11.149933

14.68325

5.8166333

9.89995

12.399933

10.783333

11.533333

8.2166667

11.3