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 scatterplot that appeared in the article “Treatment of Mixed Hydrogen Sulfide and Organic Vapors in a Rock Medium Biofilter” (Water Environment Research, 2001: 426–435).

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 Σx_i = 384.26, Σy_i = 3149.04, $\sum x_i^2$ = 5099.2412, Σx_iy_i = 37,850.7762, and $\sum y_i^2$= 309,892.6548.

1. a. Does a scatterplot of the data suggest appropriateness of the simple linear regression model?
2. 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.
3. c. Roughly what is the size of a typical deviation of points in the scatterplot from the least squares line?
4. d. What proportion of observed variation in removal efficiency can be attributed to the model relationship?
5. e. Estimate the slope coefficient in a way that conveys information about reliability and precision, and interpret your estimate.
6. 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?