12.84. 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 scatter plot that appeared in the article "Treatment of Mixed Hydrogen Sulfide and Organic Vapors in a Rock Medium Biofilter" (Water Environment Research, 2001: 426-435). The data is available on "wastewater.csv". There are 33 observations and the variables are labeled temp and removal:
"","temp","removal"
"1",7.68,98.09
"2",6.51,98.25
"3",6.43,97.82
"4",5.48,97.82
"5",6.57,97.82
"6",10.22,97.93
"7",15.69,98.38
"8",16.77,98.89
"9",17.13,98.96
"10",17.63,98.9
"11",16.72,98.68
"12",15.45,98.69
"13",12.06,98.51
"14",11.44,98.09
"15",10.17,98.25
"16",9.64,98.36
"17",8.55,98.27
"18",7.57,98
"19",6.94,98.09
"20",8.32,98.25
"21",10.5,98.41
"22",16.02,98.51
"23",17.83,98.71
"24",17.03,98.79
"25",16.18,98.87
"26",16.26,98.76
"27",14.44,98.58
"28",12.78,98.73
"29",12.25,98.45
"30",11.69,98.37
"31",11.34,98.36
"32",10.97,98.45
"33",6.53,96.55
1. Identify the dependent and independent variables.
2. Construct a scatterplot of the data.
3. Find the correlation (r).
4. Can we conclude that the population correlation is different from zero? Give the p-value and conclusion.
5. Find the regression equation.
6. What proportion of observed variation in removal efficiency can be attributed to the model relationship?
7. Interpret the intercept (in terms of this problem).
8. Interpret the slope (in terms of this problem).
9. Obtain a point prediction of removal efficiency when temperature = 10.50.
10. Test the null hypothesis of H0: β1 = 0. Give the p-value and conclusion.
11. Create a normal probability plot of the residuals.
12. Create a scatter plot of residuals versus fitted values.
13. Considering the problem description and the graphs from #2, 11 and 12, do these regression assumptions appear to be met? Discuss each assumption separately.
14. For the publication, the authors removed the observation (6.53, 96.55). Why do you think they did this? Calculate the correlation after removing this observation.