Question

# French Broad Chocolates developed the following quarterly sales forecasting​ model: Sales​ = 8.25​ + 0.125 t​...

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

 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

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