The Federal Trade Commission (FTC) annually ranks varieties of domestic cigarettes according to their tar, nicotine, and carbon monoxide content. The U.S.

surgeon general considers each of these three substances hazardous to a smoker’s health.

Past studies have shown that increases in the tar and nicotine content of a cigarette are accompanied by an increase in the carbon monoxide emitted from the cigarette smoke.

Table 12.10 presents data on tar, nicotine, and carbon monoxide content (in milligrams)

and weight (in grams) for a sample of 25 (filter) brands tested in a recent year. Suppose we want to model carbon monoxide content y as a function of tar content x1, nicotine content x2, and weight x3, using the model E1y2 = b0 + b1 x1 + b2 x2 + b3 x3 The model is fitted to the 25 data points in Table 12.10, and a portion of the SAS printout is shown in Figure 12.50. Examine the printout. Do you detect any signs of multicollinearity?

Detecting Multicollinearity—

Modeling Carbon Monoxide Content Example 12.18 Table 12.10 FTC Cigarette Data for Example 12.18 Tar 1x12 Nicotine 1x22 Weight 1x32 Carbon Monoxide (y)

14.1 .86 .9853 13.6 16.0 1.06 1.0938 16.6 29.8 2.03 1.1650 23.5 8.0 .67 .9280 10.2 4.1 .40 .9462 5.4 15.0 1.04 .8885 15.0 8.8 .76 1.0267 9.0 12.4 .95 .9225 12.3 16.6 1.12 .9372 16.3 14.9 1.02 .8858 15.4 13.7 1.01 .9643 13.0 15.1 .90 .9316 14.4 7.8 .57 .9705 10.0 11.4 .78 1.1240 10.2 9.0 .74 .8517 9.5 1.0 .13 .7851 1.5 17.0 1.26 .9186 18.5 12.8 1.08 1.0395 12.6 15.8 .96 .9573 17.5 4.5 .42 .9106 4.9 14.5 1.01 1.0070 15.9 7.3 .61 .9806 8.5 8.6 .69 .9693 10.6 15.2 1.02 .9496 13.9 12.0 .82 1.1184 14.9