A researcher is proposing that exercise makes a person more energized as a result they require less sleep. He carries out a survey on the number of hours of exercise per week and the average hours of sleep needed per night in order to feel well-rested. The results are shown on page 2 for the  8 participants. Average hours of sleep needed/night 4 5.2 2 3.4 8 10 1.5 6 Hours of exercise/week 8.6 8.1 9 8.5 7.4 6.8 9.4 7.7 Sketch a scatter plot for the data, is the relationship linear? What is the correlation between the two variables? Calculate the coefficient of determination and explain.

Question

A researcher is proposing that exercise makes a person more energized as a result they require less sleep. He carries out a survey on the number of hours of exercise per week and the average hours of sleep needed per night in order to feel well-rested. The results are shown on page 2 for the  8 participants.

Average hours of sleep needed/night

4

5.2

2

3.4

8

10

1.5

6

Hours of

exercise/week

8.6

8.1

9

8.5

7.4

6.8

9.4

7.7

  1. Sketch a scatter plot for the data, is the relationship linear?
  2. What is the correlation between the two variables?
  3. Calculate the coefficient of determination and explain.

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