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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Dec 2016 16:47:16 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/19/t1482162485zdwwre5yjc0saqf.htm/, Retrieved Sat, 18 May 2024 03:33:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301398, Retrieved Sat, 18 May 2024 03:33:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-19 15:47:16] [2e2b863c9581eba851d0277c64dc678f] [Current]
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Dataseries X:
3440
3620
3600
4140
4820
3940
3860
4680
5000
4480
4600
3660
3660
3780
4140
4000
4340
6440
3880
4780
4960
5340
4640
4180
3860
3760
3860
3460
3620
7220
4480
4440
4940
4820
4420
3940
3560
3660
4140
3680
4540
3820
5680
4520
4640
4820
4740
3900
3300
3520
3840
3500
3300
3840
4000
4180
5020
4540
4520
3680
3580
3500
3440
3560
3320
3220
4180
4460
4420
4620
4220
3660
3440
3700
3500
3240
3200
4180
4100
4120
4240
4020
3780
3560
3360
3240
3540
3300
3280
4200
3340
3900
4380
4120
3780
3380
3260
3320
3380
3100
3240
3100
3240
3640
4140
4240
4040
3760




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301398&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301398&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301398&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0305208666978793
beta0.620762252890875
gamma0.485055819380812

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0305208666978793 \tabularnewline
beta & 0.620762252890875 \tabularnewline
gamma & 0.485055819380812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301398&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.0305208666978793[/C][/ROW]
[ROW][C]beta[/C][C]0.620762252890875[/C][/ROW]
[ROW][C]gamma[/C][C]0.485055819380812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301398&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301398&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0305208666978793
beta0.620762252890875
gamma0.485055819380812







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1336603342.85790598291317.142094017091
1437803506.03142696105273.968573038948
1541403915.5779185792224.422081420801
1640003796.19748774613203.80251225387
1743404156.71568001729183.284319982709
1864406294.24684768854145.75315231146
1938804104.2273335893-224.227333589296
2047804955.334104716-175.334104715997
2149605291.27789086978-331.277890869784
2253404788.68567968488551.314320315119
2346405005.97626018864-365.97626018864
2441804018.33647701929161.663522980708
2538604118.16683771941-258.166837719407
2637604250.85337413608-490.853374136082
2738604606.64140965414-746.641409654138
2834604422.41281556225-962.412815562255
2936204690.07896287328-1070.07896287328
3072206700.35140344221519.64859655779
3144804283.48761850212196.512381497875
3244405114.12725689977-674.127256899766
3349405295.76382182996-355.763821829955
3448205141.24984725163-321.249847251631
3544204817.80523030731-397.805230307314
3639403993.96784271513-53.9678427151321
3735603802.35614319321-242.356143193212
3836603738.96864748773-78.9686474877317
3941403907.71131034274232.288689657259
4036803591.108947110188.8910528899005
4145403799.36511037925740.63488962075
4238206605.9134969984-2785.9134969984
4356803867.017584509681812.98241549032
4445204299.01144600298220.988553997024
4546404636.075396190233.92460380977172
4648204493.98119531822326.018804681781
4747404151.76630092337588.233699076633
4839003535.87022011046364.129779889542
4933003292.507202760277.49279723972768
5035203342.39007630626177.609923693744
5138403699.00570606492140.994293935081
5235003344.12706186242155.872938137582
5333003894.12319270934-594.123192709338
5438405009.49246584956-1169.49246584956
5540004521.1173557868-521.117355786795
5641804127.5612012937452.4387987062555
5750204348.53906798365671.460932016345
5845404382.06406039426157.935939605744
5945204158.62167195097361.378328049032
6036803426.71411227554253.285887724458
6135803006.45644489618573.543555103816
6235003158.53549928146341.464500718541
6334403510.95996801559-70.9599680155889
6435603160.61968238821399.380317611789
6533203373.98528910454-53.9852891045412
6632204254.12956158334-1034.12956158334
6741804096.2076061451483.7923938548593
6844604023.71259950488436.287400495121
6944204587.65755388534-167.657553885342
7046204378.34353076077241.656469239228
7142204278.96914240535-58.9691424053508
7236603501.28128341704158.718716582955
7334403244.82700378105195.172996218955
7437003285.14166615408414.858333845916
7535003456.1728172674943.827182732507
7632403342.99880029462-102.998800294624
7732003330.80197285261-130.801972852608
7841803749.19850578534430.801494214658
7941004190.95794877589-90.9579487758892
8041204304.84582061619-184.845820616187
8142404580.01422378067-340.014223780671
8240204568.8417438333-548.841743833301
8337804299.91556933511-519.91556933511
8435603597.73863087514-37.7386308751434
8533603335.9202254184924.0797745815057
8632403454.56800936052-214.568009360516
8735403400.23300713798139.766992862019
8833003191.08215108582108.917848914183
8932803146.43386845416133.566131545843
9042003816.15793523856383.842064761442
9133403989.40019459574-649.400194595739
9239004009.78687052981-109.786870529814
9343804183.39390387672196.606096123276
9441204069.6809441585850.3190558414167
9537803823.27893145381-43.2789314538063
9633803362.0589147197817.9410852802221
9732603131.73015130445128.269848695546
9833203144.02748676933175.97251323067
9933803278.33200148197101.667998518032
10031003062.8829608334837.1170391665196
10132403035.64528018544204.354719814562
10231003834.57481593884-734.57481593884
10332403475.96086115984-235.960861159842
10436403758.7156974999-118.715697499899
10541404071.9584597468568.0415402531517
10642403878.9205825646361.079417435399
10740403597.26706417115442.732935828855
10837603188.15584649623571.84415350377

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3660 & 3342.85790598291 & 317.142094017091 \tabularnewline
14 & 3780 & 3506.03142696105 & 273.968573038948 \tabularnewline
15 & 4140 & 3915.5779185792 & 224.422081420801 \tabularnewline
16 & 4000 & 3796.19748774613 & 203.80251225387 \tabularnewline
17 & 4340 & 4156.71568001729 & 183.284319982709 \tabularnewline
18 & 6440 & 6294.24684768854 & 145.75315231146 \tabularnewline
19 & 3880 & 4104.2273335893 & -224.227333589296 \tabularnewline
20 & 4780 & 4955.334104716 & -175.334104715997 \tabularnewline
21 & 4960 & 5291.27789086978 & -331.277890869784 \tabularnewline
22 & 5340 & 4788.68567968488 & 551.314320315119 \tabularnewline
23 & 4640 & 5005.97626018864 & -365.97626018864 \tabularnewline
24 & 4180 & 4018.33647701929 & 161.663522980708 \tabularnewline
25 & 3860 & 4118.16683771941 & -258.166837719407 \tabularnewline
26 & 3760 & 4250.85337413608 & -490.853374136082 \tabularnewline
27 & 3860 & 4606.64140965414 & -746.641409654138 \tabularnewline
28 & 3460 & 4422.41281556225 & -962.412815562255 \tabularnewline
29 & 3620 & 4690.07896287328 & -1070.07896287328 \tabularnewline
30 & 7220 & 6700.35140344221 & 519.64859655779 \tabularnewline
31 & 4480 & 4283.48761850212 & 196.512381497875 \tabularnewline
32 & 4440 & 5114.12725689977 & -674.127256899766 \tabularnewline
33 & 4940 & 5295.76382182996 & -355.763821829955 \tabularnewline
34 & 4820 & 5141.24984725163 & -321.249847251631 \tabularnewline
35 & 4420 & 4817.80523030731 & -397.805230307314 \tabularnewline
36 & 3940 & 3993.96784271513 & -53.9678427151321 \tabularnewline
37 & 3560 & 3802.35614319321 & -242.356143193212 \tabularnewline
38 & 3660 & 3738.96864748773 & -78.9686474877317 \tabularnewline
39 & 4140 & 3907.71131034274 & 232.288689657259 \tabularnewline
40 & 3680 & 3591.1089471101 & 88.8910528899005 \tabularnewline
41 & 4540 & 3799.36511037925 & 740.63488962075 \tabularnewline
42 & 3820 & 6605.9134969984 & -2785.9134969984 \tabularnewline
43 & 5680 & 3867.01758450968 & 1812.98241549032 \tabularnewline
44 & 4520 & 4299.01144600298 & 220.988553997024 \tabularnewline
45 & 4640 & 4636.07539619023 & 3.92460380977172 \tabularnewline
46 & 4820 & 4493.98119531822 & 326.018804681781 \tabularnewline
47 & 4740 & 4151.76630092337 & 588.233699076633 \tabularnewline
48 & 3900 & 3535.87022011046 & 364.129779889542 \tabularnewline
49 & 3300 & 3292.50720276027 & 7.49279723972768 \tabularnewline
50 & 3520 & 3342.39007630626 & 177.609923693744 \tabularnewline
51 & 3840 & 3699.00570606492 & 140.994293935081 \tabularnewline
52 & 3500 & 3344.12706186242 & 155.872938137582 \tabularnewline
53 & 3300 & 3894.12319270934 & -594.123192709338 \tabularnewline
54 & 3840 & 5009.49246584956 & -1169.49246584956 \tabularnewline
55 & 4000 & 4521.1173557868 & -521.117355786795 \tabularnewline
56 & 4180 & 4127.56120129374 & 52.4387987062555 \tabularnewline
57 & 5020 & 4348.53906798365 & 671.460932016345 \tabularnewline
58 & 4540 & 4382.06406039426 & 157.935939605744 \tabularnewline
59 & 4520 & 4158.62167195097 & 361.378328049032 \tabularnewline
60 & 3680 & 3426.71411227554 & 253.285887724458 \tabularnewline
61 & 3580 & 3006.45644489618 & 573.543555103816 \tabularnewline
62 & 3500 & 3158.53549928146 & 341.464500718541 \tabularnewline
63 & 3440 & 3510.95996801559 & -70.9599680155889 \tabularnewline
64 & 3560 & 3160.61968238821 & 399.380317611789 \tabularnewline
65 & 3320 & 3373.98528910454 & -53.9852891045412 \tabularnewline
66 & 3220 & 4254.12956158334 & -1034.12956158334 \tabularnewline
67 & 4180 & 4096.20760614514 & 83.7923938548593 \tabularnewline
68 & 4460 & 4023.71259950488 & 436.287400495121 \tabularnewline
69 & 4420 & 4587.65755388534 & -167.657553885342 \tabularnewline
70 & 4620 & 4378.34353076077 & 241.656469239228 \tabularnewline
71 & 4220 & 4278.96914240535 & -58.9691424053508 \tabularnewline
72 & 3660 & 3501.28128341704 & 158.718716582955 \tabularnewline
73 & 3440 & 3244.82700378105 & 195.172996218955 \tabularnewline
74 & 3700 & 3285.14166615408 & 414.858333845916 \tabularnewline
75 & 3500 & 3456.17281726749 & 43.827182732507 \tabularnewline
76 & 3240 & 3342.99880029462 & -102.998800294624 \tabularnewline
77 & 3200 & 3330.80197285261 & -130.801972852608 \tabularnewline
78 & 4180 & 3749.19850578534 & 430.801494214658 \tabularnewline
79 & 4100 & 4190.95794877589 & -90.9579487758892 \tabularnewline
80 & 4120 & 4304.84582061619 & -184.845820616187 \tabularnewline
81 & 4240 & 4580.01422378067 & -340.014223780671 \tabularnewline
82 & 4020 & 4568.8417438333 & -548.841743833301 \tabularnewline
83 & 3780 & 4299.91556933511 & -519.91556933511 \tabularnewline
84 & 3560 & 3597.73863087514 & -37.7386308751434 \tabularnewline
85 & 3360 & 3335.92022541849 & 24.0797745815057 \tabularnewline
86 & 3240 & 3454.56800936052 & -214.568009360516 \tabularnewline
87 & 3540 & 3400.23300713798 & 139.766992862019 \tabularnewline
88 & 3300 & 3191.08215108582 & 108.917848914183 \tabularnewline
89 & 3280 & 3146.43386845416 & 133.566131545843 \tabularnewline
90 & 4200 & 3816.15793523856 & 383.842064761442 \tabularnewline
91 & 3340 & 3989.40019459574 & -649.400194595739 \tabularnewline
92 & 3900 & 4009.78687052981 & -109.786870529814 \tabularnewline
93 & 4380 & 4183.39390387672 & 196.606096123276 \tabularnewline
94 & 4120 & 4069.68094415858 & 50.3190558414167 \tabularnewline
95 & 3780 & 3823.27893145381 & -43.2789314538063 \tabularnewline
96 & 3380 & 3362.05891471978 & 17.9410852802221 \tabularnewline
97 & 3260 & 3131.73015130445 & 128.269848695546 \tabularnewline
98 & 3320 & 3144.02748676933 & 175.97251323067 \tabularnewline
99 & 3380 & 3278.33200148197 & 101.667998518032 \tabularnewline
100 & 3100 & 3062.88296083348 & 37.1170391665196 \tabularnewline
101 & 3240 & 3035.64528018544 & 204.354719814562 \tabularnewline
102 & 3100 & 3834.57481593884 & -734.57481593884 \tabularnewline
103 & 3240 & 3475.96086115984 & -235.960861159842 \tabularnewline
104 & 3640 & 3758.7156974999 & -118.715697499899 \tabularnewline
105 & 4140 & 4071.95845974685 & 68.0415402531517 \tabularnewline
106 & 4240 & 3878.9205825646 & 361.079417435399 \tabularnewline
107 & 4040 & 3597.26706417115 & 442.732935828855 \tabularnewline
108 & 3760 & 3188.15584649623 & 571.84415350377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301398&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]3660[/C][C]3342.85790598291[/C][C]317.142094017091[/C][/ROW]
[ROW][C]14[/C][C]3780[/C][C]3506.03142696105[/C][C]273.968573038948[/C][/ROW]
[ROW][C]15[/C][C]4140[/C][C]3915.5779185792[/C][C]224.422081420801[/C][/ROW]
[ROW][C]16[/C][C]4000[/C][C]3796.19748774613[/C][C]203.80251225387[/C][/ROW]
[ROW][C]17[/C][C]4340[/C][C]4156.71568001729[/C][C]183.284319982709[/C][/ROW]
[ROW][C]18[/C][C]6440[/C][C]6294.24684768854[/C][C]145.75315231146[/C][/ROW]
[ROW][C]19[/C][C]3880[/C][C]4104.2273335893[/C][C]-224.227333589296[/C][/ROW]
[ROW][C]20[/C][C]4780[/C][C]4955.334104716[/C][C]-175.334104715997[/C][/ROW]
[ROW][C]21[/C][C]4960[/C][C]5291.27789086978[/C][C]-331.277890869784[/C][/ROW]
[ROW][C]22[/C][C]5340[/C][C]4788.68567968488[/C][C]551.314320315119[/C][/ROW]
[ROW][C]23[/C][C]4640[/C][C]5005.97626018864[/C][C]-365.97626018864[/C][/ROW]
[ROW][C]24[/C][C]4180[/C][C]4018.33647701929[/C][C]161.663522980708[/C][/ROW]
[ROW][C]25[/C][C]3860[/C][C]4118.16683771941[/C][C]-258.166837719407[/C][/ROW]
[ROW][C]26[/C][C]3760[/C][C]4250.85337413608[/C][C]-490.853374136082[/C][/ROW]
[ROW][C]27[/C][C]3860[/C][C]4606.64140965414[/C][C]-746.641409654138[/C][/ROW]
[ROW][C]28[/C][C]3460[/C][C]4422.41281556225[/C][C]-962.412815562255[/C][/ROW]
[ROW][C]29[/C][C]3620[/C][C]4690.07896287328[/C][C]-1070.07896287328[/C][/ROW]
[ROW][C]30[/C][C]7220[/C][C]6700.35140344221[/C][C]519.64859655779[/C][/ROW]
[ROW][C]31[/C][C]4480[/C][C]4283.48761850212[/C][C]196.512381497875[/C][/ROW]
[ROW][C]32[/C][C]4440[/C][C]5114.12725689977[/C][C]-674.127256899766[/C][/ROW]
[ROW][C]33[/C][C]4940[/C][C]5295.76382182996[/C][C]-355.763821829955[/C][/ROW]
[ROW][C]34[/C][C]4820[/C][C]5141.24984725163[/C][C]-321.249847251631[/C][/ROW]
[ROW][C]35[/C][C]4420[/C][C]4817.80523030731[/C][C]-397.805230307314[/C][/ROW]
[ROW][C]36[/C][C]3940[/C][C]3993.96784271513[/C][C]-53.9678427151321[/C][/ROW]
[ROW][C]37[/C][C]3560[/C][C]3802.35614319321[/C][C]-242.356143193212[/C][/ROW]
[ROW][C]38[/C][C]3660[/C][C]3738.96864748773[/C][C]-78.9686474877317[/C][/ROW]
[ROW][C]39[/C][C]4140[/C][C]3907.71131034274[/C][C]232.288689657259[/C][/ROW]
[ROW][C]40[/C][C]3680[/C][C]3591.1089471101[/C][C]88.8910528899005[/C][/ROW]
[ROW][C]41[/C][C]4540[/C][C]3799.36511037925[/C][C]740.63488962075[/C][/ROW]
[ROW][C]42[/C][C]3820[/C][C]6605.9134969984[/C][C]-2785.9134969984[/C][/ROW]
[ROW][C]43[/C][C]5680[/C][C]3867.01758450968[/C][C]1812.98241549032[/C][/ROW]
[ROW][C]44[/C][C]4520[/C][C]4299.01144600298[/C][C]220.988553997024[/C][/ROW]
[ROW][C]45[/C][C]4640[/C][C]4636.07539619023[/C][C]3.92460380977172[/C][/ROW]
[ROW][C]46[/C][C]4820[/C][C]4493.98119531822[/C][C]326.018804681781[/C][/ROW]
[ROW][C]47[/C][C]4740[/C][C]4151.76630092337[/C][C]588.233699076633[/C][/ROW]
[ROW][C]48[/C][C]3900[/C][C]3535.87022011046[/C][C]364.129779889542[/C][/ROW]
[ROW][C]49[/C][C]3300[/C][C]3292.50720276027[/C][C]7.49279723972768[/C][/ROW]
[ROW][C]50[/C][C]3520[/C][C]3342.39007630626[/C][C]177.609923693744[/C][/ROW]
[ROW][C]51[/C][C]3840[/C][C]3699.00570606492[/C][C]140.994293935081[/C][/ROW]
[ROW][C]52[/C][C]3500[/C][C]3344.12706186242[/C][C]155.872938137582[/C][/ROW]
[ROW][C]53[/C][C]3300[/C][C]3894.12319270934[/C][C]-594.123192709338[/C][/ROW]
[ROW][C]54[/C][C]3840[/C][C]5009.49246584956[/C][C]-1169.49246584956[/C][/ROW]
[ROW][C]55[/C][C]4000[/C][C]4521.1173557868[/C][C]-521.117355786795[/C][/ROW]
[ROW][C]56[/C][C]4180[/C][C]4127.56120129374[/C][C]52.4387987062555[/C][/ROW]
[ROW][C]57[/C][C]5020[/C][C]4348.53906798365[/C][C]671.460932016345[/C][/ROW]
[ROW][C]58[/C][C]4540[/C][C]4382.06406039426[/C][C]157.935939605744[/C][/ROW]
[ROW][C]59[/C][C]4520[/C][C]4158.62167195097[/C][C]361.378328049032[/C][/ROW]
[ROW][C]60[/C][C]3680[/C][C]3426.71411227554[/C][C]253.285887724458[/C][/ROW]
[ROW][C]61[/C][C]3580[/C][C]3006.45644489618[/C][C]573.543555103816[/C][/ROW]
[ROW][C]62[/C][C]3500[/C][C]3158.53549928146[/C][C]341.464500718541[/C][/ROW]
[ROW][C]63[/C][C]3440[/C][C]3510.95996801559[/C][C]-70.9599680155889[/C][/ROW]
[ROW][C]64[/C][C]3560[/C][C]3160.61968238821[/C][C]399.380317611789[/C][/ROW]
[ROW][C]65[/C][C]3320[/C][C]3373.98528910454[/C][C]-53.9852891045412[/C][/ROW]
[ROW][C]66[/C][C]3220[/C][C]4254.12956158334[/C][C]-1034.12956158334[/C][/ROW]
[ROW][C]67[/C][C]4180[/C][C]4096.20760614514[/C][C]83.7923938548593[/C][/ROW]
[ROW][C]68[/C][C]4460[/C][C]4023.71259950488[/C][C]436.287400495121[/C][/ROW]
[ROW][C]69[/C][C]4420[/C][C]4587.65755388534[/C][C]-167.657553885342[/C][/ROW]
[ROW][C]70[/C][C]4620[/C][C]4378.34353076077[/C][C]241.656469239228[/C][/ROW]
[ROW][C]71[/C][C]4220[/C][C]4278.96914240535[/C][C]-58.9691424053508[/C][/ROW]
[ROW][C]72[/C][C]3660[/C][C]3501.28128341704[/C][C]158.718716582955[/C][/ROW]
[ROW][C]73[/C][C]3440[/C][C]3244.82700378105[/C][C]195.172996218955[/C][/ROW]
[ROW][C]74[/C][C]3700[/C][C]3285.14166615408[/C][C]414.858333845916[/C][/ROW]
[ROW][C]75[/C][C]3500[/C][C]3456.17281726749[/C][C]43.827182732507[/C][/ROW]
[ROW][C]76[/C][C]3240[/C][C]3342.99880029462[/C][C]-102.998800294624[/C][/ROW]
[ROW][C]77[/C][C]3200[/C][C]3330.80197285261[/C][C]-130.801972852608[/C][/ROW]
[ROW][C]78[/C][C]4180[/C][C]3749.19850578534[/C][C]430.801494214658[/C][/ROW]
[ROW][C]79[/C][C]4100[/C][C]4190.95794877589[/C][C]-90.9579487758892[/C][/ROW]
[ROW][C]80[/C][C]4120[/C][C]4304.84582061619[/C][C]-184.845820616187[/C][/ROW]
[ROW][C]81[/C][C]4240[/C][C]4580.01422378067[/C][C]-340.014223780671[/C][/ROW]
[ROW][C]82[/C][C]4020[/C][C]4568.8417438333[/C][C]-548.841743833301[/C][/ROW]
[ROW][C]83[/C][C]3780[/C][C]4299.91556933511[/C][C]-519.91556933511[/C][/ROW]
[ROW][C]84[/C][C]3560[/C][C]3597.73863087514[/C][C]-37.7386308751434[/C][/ROW]
[ROW][C]85[/C][C]3360[/C][C]3335.92022541849[/C][C]24.0797745815057[/C][/ROW]
[ROW][C]86[/C][C]3240[/C][C]3454.56800936052[/C][C]-214.568009360516[/C][/ROW]
[ROW][C]87[/C][C]3540[/C][C]3400.23300713798[/C][C]139.766992862019[/C][/ROW]
[ROW][C]88[/C][C]3300[/C][C]3191.08215108582[/C][C]108.917848914183[/C][/ROW]
[ROW][C]89[/C][C]3280[/C][C]3146.43386845416[/C][C]133.566131545843[/C][/ROW]
[ROW][C]90[/C][C]4200[/C][C]3816.15793523856[/C][C]383.842064761442[/C][/ROW]
[ROW][C]91[/C][C]3340[/C][C]3989.40019459574[/C][C]-649.400194595739[/C][/ROW]
[ROW][C]92[/C][C]3900[/C][C]4009.78687052981[/C][C]-109.786870529814[/C][/ROW]
[ROW][C]93[/C][C]4380[/C][C]4183.39390387672[/C][C]196.606096123276[/C][/ROW]
[ROW][C]94[/C][C]4120[/C][C]4069.68094415858[/C][C]50.3190558414167[/C][/ROW]
[ROW][C]95[/C][C]3780[/C][C]3823.27893145381[/C][C]-43.2789314538063[/C][/ROW]
[ROW][C]96[/C][C]3380[/C][C]3362.05891471978[/C][C]17.9410852802221[/C][/ROW]
[ROW][C]97[/C][C]3260[/C][C]3131.73015130445[/C][C]128.269848695546[/C][/ROW]
[ROW][C]98[/C][C]3320[/C][C]3144.02748676933[/C][C]175.97251323067[/C][/ROW]
[ROW][C]99[/C][C]3380[/C][C]3278.33200148197[/C][C]101.667998518032[/C][/ROW]
[ROW][C]100[/C][C]3100[/C][C]3062.88296083348[/C][C]37.1170391665196[/C][/ROW]
[ROW][C]101[/C][C]3240[/C][C]3035.64528018544[/C][C]204.354719814562[/C][/ROW]
[ROW][C]102[/C][C]3100[/C][C]3834.57481593884[/C][C]-734.57481593884[/C][/ROW]
[ROW][C]103[/C][C]3240[/C][C]3475.96086115984[/C][C]-235.960861159842[/C][/ROW]
[ROW][C]104[/C][C]3640[/C][C]3758.7156974999[/C][C]-118.715697499899[/C][/ROW]
[ROW][C]105[/C][C]4140[/C][C]4071.95845974685[/C][C]68.0415402531517[/C][/ROW]
[ROW][C]106[/C][C]4240[/C][C]3878.9205825646[/C][C]361.079417435399[/C][/ROW]
[ROW][C]107[/C][C]4040[/C][C]3597.26706417115[/C][C]442.732935828855[/C][/ROW]
[ROW][C]108[/C][C]3760[/C][C]3188.15584649623[/C][C]571.84415350377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301398&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301398&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1336603342.85790598291317.142094017091
1437803506.03142696105273.968573038948
1541403915.5779185792224.422081420801
1640003796.19748774613203.80251225387
1743404156.71568001729183.284319982709
1864406294.24684768854145.75315231146
1938804104.2273335893-224.227333589296
2047804955.334104716-175.334104715997
2149605291.27789086978-331.277890869784
2253404788.68567968488551.314320315119
2346405005.97626018864-365.97626018864
2441804018.33647701929161.663522980708
2538604118.16683771941-258.166837719407
2637604250.85337413608-490.853374136082
2738604606.64140965414-746.641409654138
2834604422.41281556225-962.412815562255
2936204690.07896287328-1070.07896287328
3072206700.35140344221519.64859655779
3144804283.48761850212196.512381497875
3244405114.12725689977-674.127256899766
3349405295.76382182996-355.763821829955
3448205141.24984725163-321.249847251631
3544204817.80523030731-397.805230307314
3639403993.96784271513-53.9678427151321
3735603802.35614319321-242.356143193212
3836603738.96864748773-78.9686474877317
3941403907.71131034274232.288689657259
4036803591.108947110188.8910528899005
4145403799.36511037925740.63488962075
4238206605.9134969984-2785.9134969984
4356803867.017584509681812.98241549032
4445204299.01144600298220.988553997024
4546404636.075396190233.92460380977172
4648204493.98119531822326.018804681781
4747404151.76630092337588.233699076633
4839003535.87022011046364.129779889542
4933003292.507202760277.49279723972768
5035203342.39007630626177.609923693744
5138403699.00570606492140.994293935081
5235003344.12706186242155.872938137582
5333003894.12319270934-594.123192709338
5438405009.49246584956-1169.49246584956
5540004521.1173557868-521.117355786795
5641804127.5612012937452.4387987062555
5750204348.53906798365671.460932016345
5845404382.06406039426157.935939605744
5945204158.62167195097361.378328049032
6036803426.71411227554253.285887724458
6135803006.45644489618573.543555103816
6235003158.53549928146341.464500718541
6334403510.95996801559-70.9599680155889
6435603160.61968238821399.380317611789
6533203373.98528910454-53.9852891045412
6632204254.12956158334-1034.12956158334
6741804096.2076061451483.7923938548593
6844604023.71259950488436.287400495121
6944204587.65755388534-167.657553885342
7046204378.34353076077241.656469239228
7142204278.96914240535-58.9691424053508
7236603501.28128341704158.718716582955
7334403244.82700378105195.172996218955
7437003285.14166615408414.858333845916
7535003456.1728172674943.827182732507
7632403342.99880029462-102.998800294624
7732003330.80197285261-130.801972852608
7841803749.19850578534430.801494214658
7941004190.95794877589-90.9579487758892
8041204304.84582061619-184.845820616187
8142404580.01422378067-340.014223780671
8240204568.8417438333-548.841743833301
8337804299.91556933511-519.91556933511
8435603597.73863087514-37.7386308751434
8533603335.9202254184924.0797745815057
8632403454.56800936052-214.568009360516
8735403400.23300713798139.766992862019
8833003191.08215108582108.917848914183
8932803146.43386845416133.566131545843
9042003816.15793523856383.842064761442
9133403989.40019459574-649.400194595739
9239004009.78687052981-109.786870529814
9343804183.39390387672196.606096123276
9441204069.6809441585850.3190558414167
9537803823.27893145381-43.2789314538063
9633803362.0589147197817.9410852802221
9732603131.73015130445128.269848695546
9833203144.02748676933175.97251323067
9933803278.33200148197101.667998518032
10031003062.8829608334837.1170391665196
10132403035.64528018544204.354719814562
10231003834.57481593884-734.57481593884
10332403475.96086115984-235.960861159842
10436403758.7156974999-118.715697499899
10541404071.9584597468568.0415402531517
10642403878.9205825646361.079417435399
10740403597.26706417115442.732935828855
10837603188.15584649623571.84415350377







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1093045.595801400072032.596837368144058.59476543199
1103092.961103413662078.723497040774107.19870978654
1113200.169588744572183.567026920944216.7721505682
1122962.552758462781942.105727250023982.99978967554
1133023.413167057461997.299747693034049.5265864219
1143381.288019651032347.359932607284415.21610669478
1153300.200703829172256.005096842374344.39631081597
1163670.395366898132613.202394152574727.5883396437
1174102.436900233983029.272635128575175.60116533938
1184071.187302239352978.871027854745163.50357662397
1193836.133398656492721.317900654054950.94889665893
1203485.058606074422344.271817666024625.84539448282

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 3045.59580140007 & 2032.59683736814 & 4058.59476543199 \tabularnewline
110 & 3092.96110341366 & 2078.72349704077 & 4107.19870978654 \tabularnewline
111 & 3200.16958874457 & 2183.56702692094 & 4216.7721505682 \tabularnewline
112 & 2962.55275846278 & 1942.10572725002 & 3982.99978967554 \tabularnewline
113 & 3023.41316705746 & 1997.29974769303 & 4049.5265864219 \tabularnewline
114 & 3381.28801965103 & 2347.35993260728 & 4415.21610669478 \tabularnewline
115 & 3300.20070382917 & 2256.00509684237 & 4344.39631081597 \tabularnewline
116 & 3670.39536689813 & 2613.20239415257 & 4727.5883396437 \tabularnewline
117 & 4102.43690023398 & 3029.27263512857 & 5175.60116533938 \tabularnewline
118 & 4071.18730223935 & 2978.87102785474 & 5163.50357662397 \tabularnewline
119 & 3836.13339865649 & 2721.31790065405 & 4950.94889665893 \tabularnewline
120 & 3485.05860607442 & 2344.27181766602 & 4625.84539448282 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301398&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]3045.59580140007[/C][C]2032.59683736814[/C][C]4058.59476543199[/C][/ROW]
[ROW][C]110[/C][C]3092.96110341366[/C][C]2078.72349704077[/C][C]4107.19870978654[/C][/ROW]
[ROW][C]111[/C][C]3200.16958874457[/C][C]2183.56702692094[/C][C]4216.7721505682[/C][/ROW]
[ROW][C]112[/C][C]2962.55275846278[/C][C]1942.10572725002[/C][C]3982.99978967554[/C][/ROW]
[ROW][C]113[/C][C]3023.41316705746[/C][C]1997.29974769303[/C][C]4049.5265864219[/C][/ROW]
[ROW][C]114[/C][C]3381.28801965103[/C][C]2347.35993260728[/C][C]4415.21610669478[/C][/ROW]
[ROW][C]115[/C][C]3300.20070382917[/C][C]2256.00509684237[/C][C]4344.39631081597[/C][/ROW]
[ROW][C]116[/C][C]3670.39536689813[/C][C]2613.20239415257[/C][C]4727.5883396437[/C][/ROW]
[ROW][C]117[/C][C]4102.43690023398[/C][C]3029.27263512857[/C][C]5175.60116533938[/C][/ROW]
[ROW][C]118[/C][C]4071.18730223935[/C][C]2978.87102785474[/C][C]5163.50357662397[/C][/ROW]
[ROW][C]119[/C][C]3836.13339865649[/C][C]2721.31790065405[/C][C]4950.94889665893[/C][/ROW]
[ROW][C]120[/C][C]3485.05860607442[/C][C]2344.27181766602[/C][C]4625.84539448282[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301398&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301398&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1093045.595801400072032.596837368144058.59476543199
1103092.961103413662078.723497040774107.19870978654
1113200.169588744572183.567026920944216.7721505682
1122962.552758462781942.105727250023982.99978967554
1133023.413167057461997.299747693034049.5265864219
1143381.288019651032347.359932607284415.21610669478
1153300.200703829172256.005096842374344.39631081597
1163670.395366898132613.202394152574727.5883396437
1174102.436900233983029.272635128575175.60116533938
1184071.187302239352978.871027854745163.50357662397
1193836.133398656492721.317900654054950.94889665893
1203485.058606074422344.271817666024625.84539448282



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')