88. Snowpacks contain a wide spectrum of pollutants that may represent environmental hazards. The article Atmospheric PAH Deposition: Deposition Velocities and Washout Ratios (J. Environ. Engrg., 2002: 186—195) focused on the deposition of polyaromatic hydrocarbons. The authors proposed a multiple regression model for relating deposition over a speci ed time period (y, in mg/m2) to two rather complicated predictors x1 (mg-sec/m3) and x2

(mg/m2) de ned in terms of PAH air concentrations for various species, total time, and total amount of precipitation. Here is data on the species uoranthene and corresponding MINITAB output:

yˆ  .66573, sY ˆ  01785 obs x1 x2 fith 1 92017 .0026900 278.78 2 51830 .0030000 124.53 3 17236 .0000196 22.65 4 15776 .0000360 28.68 5 33462 .0004960 32.66 6 243500 .0038900 604.70 7 67793 .0011200 27.69 8 23471 .0006400 14.18 9 13948 .0004850 20.64 10 8824 .0003660 20.60 11 7699 .0002290 16.61 12 15791 .0014100 15.08 13 10239 .0004100 18.05 14 43835 .0000960 99.71 15 49793 .0000896 58.97 16 40656 .0026000 172.58 17 50774 .0009530 44.25 The regression equation is fith  33.5  0.00205 x1  29836 x2 Predictor Coef SE Coef T P Constant 33.46 14.90 2.25 0.041 x1 0.0020548 0.0002945 6.98 0.000 x2 29836 13654 2.19 0.046 S  44.28 R-Sq  92.3% R-Sq(adj)  91.2%

Analysis of Variance Source DF SS MS F P Regression 2 330989 165495 84.39 0.000 Residual Error 14 27454 1961 Total 16 358443 Formulate questions and perform appropriate analyses.

Construct the appropriate residual plots, including plots against the predictors. Based on these plots, justify adding a quadratic term, and t the model with this additional term. Is this term statistically signi cant, and does it help the appearance of the diagnostic plots?

d. Use the MSE and c11 to get a 95% con dence interval for b1.

e. Carry out a t test for the hypothesis H0: b10 against a two-tailed alternative, and interpret the result.

f. Form the analysis of variance table and carry out the F test for the hypothesis H0: b1b20.
Find R2 and interpret.