Question

The accompanying data table show the percentage of tax returns filed electronically in a city from 2000 to 2009. Complete parts a through e below.

Score: 1 of 5 pts 1 of 4 (2 complete) HW Score: 7.27%, 1.45 of 20 pts 16.2.7 ίΞ Question Help | * The accompanying data table show the percentage of tax returns filed electronically in a city from 2000 to 2009. Complete parts a through e below. EEB Click the icon to view the percentage of tax returns filed electronically by year. a) Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with α-0.1 The percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with a 0.1 is Round to the nearest integer as needed.)

B.) Calculate the MAD for the forecast in part a

C.) Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with trend adjustment. set $\alpha$ = 0.4 and $\beta$ = 0.5

D.) Calculate the MAD for the forecast in part c

E.) In which forecast do you have the most confidence in and why?

Answer 1

A) Exponential smoothing with o 0.1 Year PercentageForecast |Y. - F.l 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 27 30 34 42 27.0000 3.0000 27.3000 6.7000 27.9700 14.0300 29.3730 114.6270 30.8357 19.1643 32.7521 21.2479 34.8769 22.1231 37.0892 24.9108 39.5803 24.4197 Total150.2227 50 54 57 62 64 The percentage oftax retum for 2010 using Exponential smoothing with α = 0.1 is F10% (0.1) (64)-(1-0.1) (39.5803-42.0223 Hence the percentage of tax returns for 2010 using Exponential smoothing with α 0.1 is 42.0223 B) MAD for forecast for 2010 using Exponential smoothing with α-0.1 is Σ1Yt-, 150.2227-16.6914

C)Exponential smoothing with trend adjust α-0.4, β-0.5 Year PercentageForecast 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 27 30 34 42 27.0000 3.0000 50 54 57 62 64 27.0000 0.0000 28.2000 0.6000 30.5200 1.4600 35.1120 3.0260 38.6672 3.2906 43.2003 3.9119 47.5202 4.1159 51.3121 3.9539 55.5873 4.1145 31.9800 10.0200 5.8620 8.0422 6.8878 5.3639 6.7340 4.2982 419578 55.2660 9.7018 Total The percentage of tax returm for 2010 using Exponential smoothing with trend adjustment We have to first find Fio- (0.4) (64)+ (1-0.4) (55.5873) 58.9524 Now Tİ,-7, +0.5 (Ao-FIT,)= 4.1 145 +0.5*(58.9524-59.7018)-3.7398 Now FIT10-F1o T1o 58.9524 +3.7398 -62.6922 Hence the percentage of tax returns for 2010 using Exponential smoothing with trend adjustment is 62.6922

D) MAD for forecast for 2010 using Exponential smoothing with trend adjustr entist-nt.ssa ea= 6.1565 MAD->ht' FITI 55.4082 61565 9 E) We have most confidence in Exponential smoothing with trend adjustment forecast. Because it has smaller MAD as compare to Exponential smoothing forecast