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, Problem 84SE
In biofiltration of wastewater, air discharged from a treatment facility is passed through a damp porous membrane that causes contaminants to dissolve in water and be transformed into harmless products. The accompanying data on x = inlet temperature (°C) and y = removal efficiency (%) was the basis for a
| Obs | Temp | Removal % | Obs | Temp | Removal % |
| 1 | 7.68 | 98.09 | 17 | 8.55 | 98.27 |
| 2 | 6.51 | 98.25 | 18 | 7.57 | 98.00 |
| 3 | 6.43 | 97.82 | 19 | 6.94 | 98.09 |
| 4 | 5.48 | 97.82 | 20 | 8.32 | 98.25 |
| 5 | 6.57 | 97.82 | 21 | 10.50 | 98.41 |
| 6 | 10.22 | 97.93 | 22 | 16.02 | 98.51 |
| 7 | 15.69 | 98.38 | 23 | 17.83 | 98.71 |
| 8 | 16.77 | 98.89 | 24 | 17.03 | 98.79 |
| 9 | 17.13 | 98.96 | 25 | 16.18 | 98.87 |
| 10 | 17.63 | 98.90 | 26 | 16.26 | 98.76 |
| 11 | 16.72 | 98.68 | 27 | 14.44 | 98.58 |
| 12 | 15.45 | 98.69 | 28 | 12.78 | 98.73 |
| 13 | 12.06 | 98.51 | 29 | 12.25 | 98.45 |
| 14 | 11.44 | 98.09 | 30 | 11.69 | 98.37 |
| 15 | 10.17 | 98.25 | 31 | 11.34 | 98.36 |
| 16 | 9.64 | 98.36 | 32 | 10.97 | 98.45 |
Calculated summary quantities are Σxi = 384.26, Σyi = 3149.04,
- a. Does a scatterplot of the data suggest appropriateness of the simple linear regression model?
- b. Fit the simple linear regression model, obtain a point prediction of removal efficiency when temperature = 10.50, and calculate the value of the corresponding residual.
- c. Roughly what is the size of a typical deviation of points in the scatterplot from the least squares line?
- d. What proportion of observed variation in removal efficiency can be attributed to the model relationship?
- e. Estimate the slope coefficient in a way that conveys information about reliability and precision, and interpret your estimate.
- f. Personal communication with the authors of the article revealed that there was one additional observation that was not included in their scatterplot: (6.53, 96.55). What impact does this additional observation have on the equation of the least squares line and the values of s and r2?
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Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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