Carbon aerosols have been identified as a contributing

Chapter 0, Problem 13.31

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Carbon aerosols have been identified as a contributing factor in a number of air quality problems. In a chemical analysis of diesel engine exhaust, x mass (mg/cm2 ) and y elemental carbon (mg/cm2 ) were recorded (Comparison of Solvent Extraction and Thermal Optical Carbon Analysis Methods: Application to Diesel Vehicle Exhaust Aerosol Environmental Science Technology [1984]: 231234). The estimated regression line for this data set is 31 .737x. The accompanying table gives the observed x and y values and the corresponding standardized residuals. x 164.2 156.9 109.8 111.4 87.0 y 181 156 115 132 96 St. resid. 2.52 0.82 0.27 1.64 0.08x 161.8 230.9 106.5 97.6 79.7 y 170 193 110 94 77 St. resid. 1.72 0.73 0.05 0.77 1.11 x 118.7 248.8 102.4 64.2 89.4 y 106 204 98 76 89 St. resid. 1.07 0.95 0.73 0.20 0.68 x 108.1 89.4 76.4 131.7 100.8 y 102 91 97 128 88 St. resid. 0.75 0.51 0.85 0.00 1.49 x 78.9 387.8 135.0 82.9 117.9 y 86 310 141 90 130 St. resid. 0.27 0.89 0.91 0.18 1.05 a. Construct a standardized residual plot. Are there any unusually large residuals? Do you think that there are any influential observations? b. Is there any pattern in the standardized residual plot that would indicate that the simple linear regression model is not appropriate? c. Based on your plot in Part (a), do you think that it is reasonable to assume that the variance of y is the same at each x value? Explain.