Table 17.8 gives the monthly international passenger totals over the last 11 years for an airline company. A plot of these passenger totals reveals an upward trend with increasing seasonal variation, and the natural logarithmic transformation is found to best equalize the seasonal variation [see Figure 17.9(a) and (b)]. Figure 17.9(c) gives the JMP output of a regression analysis of the monthly international passenger totals by using the model

In ye = 60 + 61t + 61/j + 6/2/2 + . . . + 0m11Mi1 + Et TABLE 17.8 Monthly International Passenger Totals (Thousands of Passengers) DS AirPass Year Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 112 118 132 129 121 135 148 148 136 1 15 119 104 126 118 141 135 125 149 170 170 158 133 114 145 150 140 178 163 172 178 199 199 184 162 146 171 166 180 193 181 183 218 230 242 209 191 196 172 194 196 236 235 229 243 264 272 237 204 211 180 188 201 235 227 234 264 302 293 259 229 242 233 203 229 267 269 270 315 364 347 312 284 274 237 8 277 278 317 313 318 374 413 405 355 9 315 306 301 271 356 348 306 355 422 465 467 404 347 10 340 305 318 336 362 348 363 435 491 505 404 11 359 310 360 342 337 406 396 420 472 548 559 463 407 362 405 Source: FAA Statistical Handbook of Civil Aviation (several annual issues). These data were originally presented by Box and Jenkins (1976). We have updated the situ- ation in this exercise to be more modern.FIGURE 17,9 Analysis of the Monthly International Passenger Totals [a) Plot of the passenger totals (b) Plot of the natural logarithms of the passenger totals 800 - 6.5 600 6.0- 400- 5.5 200 5.0- 4.5+ 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 Time Time (c) JMP Output of a regression analysis of the monthly International passenger totals using the dummy variable model Term Estimate Std Error + Ratio Probeltl Lower 95% Upper 95% Predicted Lower 95% Upper 95% Intercept 4.6961806 0.01973 238.02 <.0001 lnpass indly time jan feb mar .0001 apr may jun jul aug sep oct nov r-sq="98.3%" durbin-watson statistic="0.420944(c)" jmp output of a regression analysis the monthly international passenger totals using dummy variable model term estimate std error t ratio probelt lower upper predicted intercept sop s="0.0573917" r-5q r-sqladj here my m2. . mij are appropriately defined variables for january through november let y135 denote in month next year tells us that point forecast and percent prediction interval jugg are. respectively. least squares estimates on find myis. then calculating y13. to decimal places rest places.>