1. The Eurelian Federal Trade Commission annually ranks varieties of domestic cigarettes according to their tar, nicotine, and carbon monoxide (CO) contents. Each of these is considered to be hazardous to health. Past studies have shown that increases in the tar and nicotine contents of a cigarette are accompanied by an increase in the carbon monoxide emitted from the cigarette smoke. Data from last year are given in the following table, together with some MINITAB output.

(a) Fill in the missing numbers of the Analysis-of-Variance table for MODEL I.

(b) Do the data provide sufficient evidence to indicate that the tar and nicotine in the model 1 contribute information for the prediction of CO comparing with Model 3 at 5% significant level?

Model 1: The regression equation is CO 2 3.20219 + 0.96257 tar 2.63166 nicotine 0.13048 weight Predictor Coef StDev T P Constant 3.20219 3.46175 0.93 0.3655 tar 0.96257 0.24224 3.97 0.0007 nicotine 3.90056 -0.67 0.5072 weight 3.88534 0.03 0.9735 821.446 RSq=91.86% RSq(adj)=90.70% Model 2: The regression equation is CO = 3.114 + 0.80419 tar - 0.423 weight Predictor Coef StDev T P Constant 3.114 3.416 0.91 0.372 tar 0.80419 0.05904 13.62 0 | weight -0.423 3.813 0.11 0.913 821.428 RSq291.68% RSq(adj):90.90% Analysis of Variance Source DF SS MS F P Regression 2 494.31 247.15 121.25 0 Residual Error 22 44.84 2.04 Total 24 539.15 Model 3: The regression equation is CO = - 11.8 + 25.1 weight Predictor Coef StDev T P Constant -11.795 9.722 -1.21 0.237 weight 25.068 9.98 2.51 0.019 S=4.289 R-Sq=21.53% R-Sq(adj)=18.10% Analysis of Variance Source DF SS MS F P Regression 1 116.06 116.06 6.31 0.019 Residual Error 23 423.09 18.4 Total 24 539.15