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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An article reported data from a study in which both a baseline gasoline mixture and a reformulated gasoline were used. Consider the following observations on age (yr) and NOx emissions (g/kWh):
Engine
1
2
3
4
5
6
7
8
9
10
Age
0
0
2
11
7
16
9
0
12
4
Baseline
1.74
4.38
4.04
1.23
5.30
0.58
3.35
3.44
0.73
1.23
Reformulated
1.85
5.93
5.52
2.67
6.54
0.76
4.94
4.87
0.69
1.39
Construct scatter plots of the baseline NOx emissions versus age.
Construct scatter plots of the reformulated NOx emissions versus age.
What appears to be the nature of the relationship between these two variables?
As age increases, emissions also increase.As age increases, emissions decrease. There is no compelling relationship between the data.
Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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