Question

Coca-Cola Revenues ($ millions), 2005–2010
Quarter	2005	2006	2007	2008	2009	2010
Qtr1	5,200	5,117	6,075	7,380	7,150	7,800
Qtr2	6,304	6,465	7,705	9,045	8,220	8,659
Qtr3	6,031	6,410	7,662	8,305	8,025	8,411
Qtr4	5,545	5,905	7,303	7,040	7,480	10,479

(a-1) Use MegaStat or Minitab to deseasonalize Coca-Cola’s quarterly data. (Round your answers to 3 decimal places.)

	1	2	3	4
2005
2006
2007
2008
2009
2010
mean

(a-2) State the adjusted four quarterly indexes. (Round your answers to 3 decimal places.)

Q1	Q2	Q3	Q4

(a-3) What is the trend model for the deseasonalized time series? (Round your answers to 2 decimal places.)

y_t =  x_t +

(b) State the model found when performing a regression using seasonal binaries. (A negative value should be indicated by a minus sign. Round your answers to 4 decimal places.)

y_t =  +  t +  Q1 +  Q2 +  Q3

(c) Use the regression equation to make a prediction for each quarter in 2011. (Enter your answers in millions rounded to 3 decimal places.)

Quarter	Predicted
Q1
Q2
Q3
Q4

Answer 1

(a)

				Centered
				Moving	Ratio to	Seasonal	2005
t	Year	Quarter	2005	Average	CMA	Indexes	Deseasonalized
1	1	1	5,200			0.927	5,609.9
2	1	2	6,304			1.087	5,801.2
3	1	3	6,031	5759.625	1.047	1.047	5,762.0
4	1	4	5,545	5769.375	0.961	0.940	5,900.7
5	2	1	5,117	5836.875	0.877	0.927	5,520.4
6	2	2	6,465	5929.250	1.090	1.087	5,949.4
7	2	3	6,410	6094.000	1.052	1.047	6,124.1
8	2	4	5,905	6368.750	0.927	0.940	6,283.8
9	3	1	6,075	6680.250	0.909	0.927	6,553.9
10	3	2	7,705	7011.500	1.099	1.087	7,090.5
11	3	3	7,662	7349.375	1.043	1.047	7,320.3
12	3	4	7,303	7680.000	0.951	0.940	7,771.4
13	4	1	7,380	7927.875	0.931	0.927	7,961.8
14	4	2	9,045	7975.375	1.134	1.087	8,323.6
15	4	3	8,305	7913.750	1.049	1.047	7,934.6
16	4	4	7,040	7781.875	0.905	0.940	7,491.6
17	5	1	7,150	7643.750	0.935	0.927	7,713.6
18	5	2	8,220	7663.750	1.073	1.087	7,564.4
19	5	3	8,025	7800.000	1.029	1.047	7,667.1
20	5	4	7,480	7936.125	0.943	0.940	7,959.8
21	6	1	7,800	8039.250	0.970	0.927	8,414.9
22	6	2	8,659	8462.375	1.023	1.087	7,968.4
23	6	3	8,411			1.047	8,035.9
24	6	4	10,479			0.940	11,151.2

	Calculation of Seasonal Indexes
	1	2	3	4
1			1.047	0.961
2	0.877	1.090	1.052	0.927
3	0.909	1.099	1.043	0.951
4	0.931	1.134	1.049	0.905
5	0.935	1.073	1.029	0.943
6	0.970	1.023
mean:	0.925	1.084	1.044	0.937	3.990
adjusted:	0.927	1.087	1.047	0.940	4.000

y = 156.81x + 5284.7

(b) y_t = 5,159.4000 + 152.3286 t - 381.3476 Q1 + 745.6571 Q2 + 334.3286 Q3

(c)

Quarter	Predicted
Q1	8586.267
Q2	9865.600
Q3	9606.600
Q4	9424.600