Problem:

The table below shows the observed monthly demand data for airline traffic for six years (i.e. airline passengers carried (000's)). A separate spreadsheet is available here:"Airline Passengers"

	2005	2006	2007	2008	2009	2010
January	112	115	145	171	196	204
February	118	126	150	180	196	188
March	132	141	178	193	236	235
April	129	135	163	181	235	227
May	121	125	172	183	229	234
June	135	149	178	218	243	264
July	148	170	199	230	264	302
August	148	170	199	242	272	293
September	136	158	184	209	237	259
October	119	133	162	191	211	229
November	104	114	146	172	180	203
December	118	140	166	194	201	229

We will use the slope as our estimate of the trend; and we will use the intercept as the estimate of the deseasonalized demand for December 2004.

We can now use the estimate of the trend and the estimate of the deseasonalized demand for December 2004 to determine an estimate of the deseasonalized demand for each month. Then our estimate of the deseasonalized demand for month t is given by:

This is effectively the linear model from the regression.

We are now ready to estimate the seasonal factors:

Compute the estimate of the deseasonalized demand for month t as given above.

Divide each monthly demand observation by its corresponding deseasonalized demand estimate to calculate the seasonal factors for each month of observed data. That is, the seasonal factor in month t is where is the demand observation for month t.

Average the factors for each month. That is, average all the factors corresponding January, all the factors corresponding to February, and so on. The resulting averages are the 12 seasonal factors, which should add to exactly 12. If they do not add to 12, then we normalize the factors by multiplying each one by where is the estimate for the seasonal factor, before normalization

Determine the forecast for seasonalized demand in the following months, as of December 2010 (Up to two decimal places):

1.January 2011 ?

2.July 2011 ?

3.February 2012 ?

4.October 2012 ?