Question

French Broad Chocolates developed the following quarterly sales forecasting​ model:

Sales​ = 8.25​ + 0.125 t​ - 2.75 D1​ + 1.25 D2​ + 3.5 D3

where t is time period.​ (time is zero in the fourth quarter of​ 2000, time is 1 in the first quarter of 2001 and 2 in the second quarter of 2001​ etc.) and​ D1, D2, and D3 are quarterly dummy variables.

Forecast French Broad​ Chocolate's sales for each quarter of 2010.

Economics

Answer 1

Year	Quarter	time = t
2000	4th	0
2001	1st	1
2001	2nd	2
2001	3rd	3
2001	4th	4
2002	1st	5
2002	2nd	6
2002	3rd	7
2002	4th	8
2003	1st	9
2003	2nd	10
2003	3rd	11
2003	4th	12
2004	1st	13
2004	2nd	14
2004	3rd	15
2004	4th	16
2005	1st	17
2005	2nd	18
2005	3rd	19
2005	4th	20
2006	1st	21
2006	2nd	22
2006	3rd	23
2006	4th	24
2007	1st	25
2007	2nd	26
2007	3rd	27
2007	4th	28
2008	1st	29
2008	2nd	30
2008	3rd	31
2008	4th	32
2009	1st	33
2009	2nd	34
2009	3rd	35
2009	4th	36
2010	1st	37
2010	2nd	38
2010	3rd	39
2010	4th	40

D1 =1 when quarter is 1st and D1=0 otherwise.

D2=1 when quarter is 2nd and D2 = 0 otherwise.

D3 = 1 when quarter is 3rd and D3 = 0 otherwise.

D1=D2=D3 =0 when quarter is 4th.

Chocolates sales in 1st quarter of 2010

Put, t= 37, D1 =1, D2=D3=0.

Sales​ = 8.25​ + 0.125 t​ - 2.75 D1​ + 1.25 D2​ + 3.5 D3

Sales = 8.25 + 0.125 (37) - 2.75(1) + 1.25(0) +3.5(0)

Sales = 8.25 + 4.625 - 2.75 + 0 + 0

Sales = 10.125

Chocolates sales in 2nd quarter of 2010

Put, t= 38, D2 =1, D1=D3=0.

Sales​ = 8.25​ + 0.125 t​ - 2.75 D1​ + 1.25 D2​ + 3.5 D3

Sales = 8.25 + 0.125 (38) - 2.75(0) + 1.25(1) +3.5(0)

Sales = 8.25 + 4.75 - 0 + 1.25 +0

Sales = 14.25

Chocolates sales in 3rd quarter of 2010

Put, t= 39, D3 =1, D1=D2=0.

Sales​ = 8.25​ + 0.125 t​ - 2.75 D1​ + 1.25 D2​ + 3.5 D3

Sales = 8.25 + 0.125 (39) - 2.75(0) + 1.25(0) +3.5(1)

Sales = 8.25 + 4.875 - 0 + 0 + 3.5

Sales = 16.625

Chocolates sales in 4th quarter of 2010

Put, t= 40, D1= D2=D3=0.

Sales​ = 8.25​ + 0.125 t​ - 2.75 D1​ + 1.25 D2​ + 3.5 D3

Sales = 8.25 + 0.125 (40) - 2.75(0) + 1.25(0) +3.5(0)

Sales = 8.25 + 5 - 0 + 0 + 0

Sales = 13.25