year Percentage 2000 28 2001 32 2002 37 2003 43 2004 47 2005 52 2006 56...

year	Percentage
2000	28
2001	32
2002	37
2003	43
2004	47
2005	52
2006	56
2007	58
2008	61
2009	66

Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with trend adjustment. Set

alphaα =0.5 and β=0.6

Solutions

Expert Solution

Unadjusted forecast =(Percentage of prior period)+(1 - ) Forecast of the prior period.

(Unadjusted forecast of the first period is same as the actual).

Trend for the next period =(Forecast of that next period - Forecast of the prior period)+(1 - )Trend of the prior period.

(Trend of the first period =0).

Adjusted forecast =Unadjusted forecast + Trend.

Year	Percentage	Unadjusted forecast ( =0.5)	Trend ( =0.6)	Adjusted forecast
2000	28	28	0	28
2001	32	0.5(28)+0.5(28) =28	0.6(28-28)+0.4(0) =0	28
2002	37	0.5(32)+0.5(28) =30	0.6(30-28)+0.4(0) =1.2	31.2
2003	43	0.5(37)+0.5(30) =33.5	0.6(33.5-30)+0.4(1.2) =2.58	36.08
2004	47	0.5(43)+0.5(33.5) =38.25	0.6(38.25-33.5)+0.4(2.58) =3.882	42.132
2005	52	0.5(47)+0.5(38.25) =42.625	0.6(42.625-38.25)+0.4(3.882) =4.1778	46.8028
2006	56	0.5(52)+0.5(42.625) =47.3125	0.6(47.3125-42.625)+0.4(4.1778) =4.48362	51.79612
2007	58	0.5(56)+0.5(47.3125) =51.65625	0.6(51.65625-47.3125)+0.4(4.48362) =4.399698	56.055948
2008	61	0.5(58)+0.5(51.65625) =54.828125	0.6(54.828125-51.65625)+0.4(4.399698) =3.6630042	58.4911292
2009	66	0.5(61)+0.5(54.828125) =57.9140625	0.6(57.9140625-54.828125)+0.4(3.6630042) =3.31676418	61.23082668
2010		0.5(66)+0.5(57.9140625) =61.95703125	0.6(61.95703125-57.9140625)+0.4(3.31676418) =3.752486922	65.70951817

Thus, the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with trend adjustment =65.70951817

milcah answered 9 months ago

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