Table 16.8 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 16.9(a) and (b)]. Figure 16.9(c) gives the MINITAB output of a regression analysis of the monthly international passenger totals by using the model
In yt = β0 + β1t + βM1M1 + βM2M2 + ∙ ∙ ∙ + βM11M11 + e,
Here M1, M2,..., M11 are appropriately defined dummy variables for January (month 1) through November (month 11). Let y133 denote the international passenger totals in month 133 (January of next year). The MINITAB output tells us that a point forecast of and a 95 percent prediction interval for In y133 are, respectively. 6.08610 and [5.96593. 6.20627). Using the least squares point estimates on the MINITAB output, show how the point forecast has been calculated. Then, by calculating e608610 and e5,96593, e620627], find a point forecast of and a 95 percent prediction interval for y133.