# statistics

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The tourist industry is subject to enormous seasonal variation. A hotel in North Queensland has recorded its occupancy rate for each quarter during the past 5 years. These data are shown in the accompanying table.

Table 1: Occupancy rate

Year 2004 2005 2006 2007 2008
Quarter 1 0.561 0.575 0.594 0.622 0.665
Quarter 2 0.702 0.738 0.738 0.708 0.835
Quarter 3 0.800 0.868 0.729 0.806 0.873
Quarter 4 0.568 0.605 0.600 0.632 0.670

What is the centered moving average that would correspond to Quarter 2 in 2006?

What is the adjusted seasonal index for Quarter 2 ______ % ?

The trend line for this decomposition model has been calculated to be (at 3 decimal places) Y = 0.650 + 0.004 T where T represents time. What is the coefficient of determination (R2) for this trend line?

1) 0.0932 (9.32%)
2) 0.3448 (34.48%)
3) 0.4554 (45.54%)
4) 0.7882 (78.82%)

What would be the forecast in Quarter 2, 2009 using the trend line previously given (i.e. Y = 0.650 + 0.004 T) and the relevant adjusted seasonal index?

If we exponentially smooth the data in Table 1 with the a smoothing constant of 0.1, the smoothed value for Quarter 3 in 2004 would be?

If we exponentially smooth the data in Table 1 with the a smoothing constant of 0.1, the forecast for Quarter 1 in 2009 would be?