Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.5, Problem 64E
The accompanying data on x = UV transparency index and y = maximum prevalence of infection was read from a graph in the article “Solar Radiation Decreases Parasitism in Daphnia” (Ecology Letters, 2012: 47–54):
| x | 1.3 | 1.4 | 1.5 | 2.0 | 2.2 | 2.7 | 2.7 | 2.7 | 2.8 |
| y | 16 | 3 | 32 | 1 | 13 | 0 | 8 | 16 | 2 |
| x | 2.9 | 3.0 | 3.6 | 3.8 | 3.8 | 4.6 | 5.1 | 5.7 |
| y | 1 | 7 | 36 | 25 | 10 | 35 | 58 | 56 |
Summary quantities include Sxx = 25.5224, Syy = 5593.0588, and Sxy = 264.4882.
- a. Calculate and interpret the value of the sample
correlation coefficient . - b. If you decided to fit the simple linear regression model to this data, what proportion of observed variation in maximum prevalence could be explained by the model relationship?
- c. If you decided to regress UV transparency index on maximum prevalence (i.e., interchange the roles of x and y), what proportion of observed variation could be attributed to the model relationship?
- d. Carry out a test of H0: ρ = .5 versus Ha: ρ > .5 using a significance level of .05. [Note: The cited article reported the P-value for testing H0: ρ = 0 versus H0: ρ ≠ 0.]
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Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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