Exercise 8.10Calculator Sales Data

MonthYear 1Year 2

January197296

February211276

March203305

April247308

May239356

June269393

July308363

August262386

September258443

October256308

November261358

December288384

a) Values of l0 and b0 can be find by fit a least squares trend line to half part of data. l0 be the y-intercept and b0 be the slope.

X=11Y=197X'X=1278

1221178650

13203

14247X'Y=29992999

152392048620486

16269

17308l0=204.803

18262b06.940559

19258

110256

111261

112288

Therefore,

b) Excel spreadsheet of Holts trend corrected exponential smoothing for calculator sales, =0.20 & =0.10nalphagammaSSEsquares

240.20.128870.614661255.24411635.42942443

Time PeriodActual (y)LevelGrowth rate ForecastForecast errorSquare Forecast Error

0204.8036.940559441

1197208.79496.645687646211.7436-14.74358974217.3734385

2211214.55246.556876457215.4406-4.44055944119.71856815

3203217.48756.194689977221.1093-18.10932401327.9476161

4247228.34576.661046993223.682123.31785082543.7221667

5239235.80546.740911666235.00683.9932336615.94591506

6269247.83717.269985171242.546326.45367526699.7969348

7308265.68568.327844272255.10752.892955042797.664693

8262271.61088.087574667274.0135-12.01348024144.3237075

9258275.35877.65360749279.6984-21.69835886470.8187773

10256277.60987.113361599283.0123-27.01229458729.6640584

11261279.97866.638897653284.7232-23.72319726562.7900883

12288286.8946.666548544286.61751.3825445371.911429398

13296294.04846.715338286293.56052.4394870865.951097242

14276295.8116.220063313300.7637-24.76374862613.2432456

15305302.62486.279442069302.03112.9689377938.814591618

16308308.72346.261356233308.9043-0.9042918350.817743723

17356323.18787.081660439314.984841.01521031682.247476

18393342.81568.336270595330.269562.73050783935.116609

19363353.52158.573233308351.151911.84813565140.3783183

20386366.87589.051338812362.094723.90527521571.4621828

21443389.341710.39279644375.927167.072881364498.771413

22308381.38768.558106612399.7345-91.734491358415.216904

23358383.55667.919192618389.9457-31.94569971020.527729

24384389.98067.76967757391.4758-7.47575237455.88687356

c) Excel spreadsheet with the values for ,,s, l24 and b24 when SSE is minimized using SolvernalphagammaSSEsquares

240.110028027724.58121205.41657434.71910964

Time PeriodActual (y)LevelGrowth rate ForecastForecast errorSquare Forecast Error

0204.8036.940559441

1197210.12146.940559441211.7436-14.74358974217.3734385

2211216.3956.940559441217.0619-6.06193927636.74710778

3203221.0986.940559441223.3355-20.33551475413.5331602

4247230.12496.940559441228.038618.96140488359.5348751

5239237.27836.940559441237.06541.9345571363.742511311

6269246.94556.940559441244.218924.78114195614.1049964

7308259.84016.940559441253.88654.11395932928.320591

8262266.25476.940559441266.7807-4.78065898922.85470037

9258271.52336.940559441273.1952-15.19521136230.8944484

10256275.99226.940559441278.4639-22.4638698504.6254466

11261280.51956.940559441282.9328-21.9327712481.0464526

12288287.51956.940559441287.46010.5398916050.291482945

13296294.62956.940559441294.46011.539928892.371380985

14276298.75666.940559441301.5701-25.57006608653.8282793

15305305.62056.940559441305.6972-0.6971984450.486085671

16308312.05926.940559441312.561-4.5610464320.80314454

17356323.07086.940559441318.999837.000237631369.017585

18393336.94196.940559441330.011462.988610483967.565051

19363345.98596.940559441343.882519.11753074365.4799816

20386356.56556.940559441352.926533.073504751093.856717

21443372.25266.940559441363.506179.493928766319.28471

22308371.35996.940559441379.1932-71.193200625068.471815

23358376.06696.940559441378.3005-20.30050388412.110458

24384383.11666.940559441383.00740.9925635680.985182437

d) Prediction for January, February and March Year 3.

January year 3 = y25 =

February year 3 = y26

March year 3 = y27