Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 Jul 2014 12:32:40 +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/2014/Jul/28/t1406547376atmc9t87ctp06sq.htm/, Retrieved Tue, 14 May 2024 09:58:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235353, Retrieved Tue, 14 May 2024 09:58:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact196
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-07-28 11:32:40] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1069108
1059362
1049495
1029082
1231089
1220388
1069108
968521
978233
978233
989056
1008514
1069108
1049495
1079775
1129547
1412683
1412683
1352244
1291650
1341422
1401983
1412683
1442964
1533833
1473244
1473244
1564114
1816014
1836427
1785734
1664578
1755420
1755420
1765165
1816014
1856040
1876453
1876453
1937014
2169452
2229890
2239603
2088322
2169452
2139171
2078582
2209478
2239603
2188909
2199610
2269916
2532640
2663352
2663352
2602913
2693660
2602913
2552092
2744509
2774634
2703378
2884967
2956228
3168103
3308711
3289258
3278430
3359559
3349692
3228692
3410253
3470847
3410253
3662154
3783309
4065362
4176650
4146492
4085897
4136624
4197185
3995056
4156204
4257779
4216798
4479366
4570080
4953837
5024138
4933418
4984117
5014398
5044678
4852261
5033856
5134437
5033856
5326854
5417607
5811037
5871631
5891089
5992631
5992631
6032657
5851063
5941938
6002377
5891089
6214246
6274812
6678021
6749283
6849864
6940739
6950451
6961152
6779563
6961152




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235353&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235353&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235353&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.214234531495479
beta0.107870793560161
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.214234531495479 \tabularnewline
beta & 0.107870793560161 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235353&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]0.214234531495479[/C][/ROW]
[ROW][C]beta[/C][C]0.107870793560161[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235353&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235353&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
alpha0.214234531495479
beta0.107870793560161
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310691081008196.5820519760911.4179480316
1410494951000087.9912485649407.0087514367
1510797751035376.9481761644398.0518238381
1611295471085598.0739199443948.9260800593
1714126831358800.5982907153882.4017092886
1814126831360657.0019847352025.9980152664
1913522441273172.3471609179071.6528390904
2012916501195737.330662495912.6693376033
2113414221256521.7089496384900.2910503731
2214019831298993.11265117102989.88734883
2314126831354240.3757119158442.6242880856
2414429641408421.8497600334542.1502399726
2515338331581849.49355158-48016.4935515777
2614732441531955.86281126-58711.8628112569
2714732441551749.32606805-78505.3260680519
2815641141591892.63001636-27778.6300163562
2918160141964718.54771749-148704.547717491
3018364271911151.19167632-74724.1916763249
3117857341782299.212706783434.78729321552
3216645781665431.29313694-853.293136936845
3317554201693578.4649763261841.5350236769
3417554201742206.8811994413213.1188005591
3517651651728792.5784114136372.4215885925
3618160141750859.2350892865154.764910721
3718560401874721.05588692-18681.0558869184
3818764531799879.4633619776573.5366380285
3918764531827402.3433378949050.6566621056
4019370141952373.86299081-15359.8629908061
4121694522293640.62321204-124188.623212043
4222298902306314.16686143-76424.1668614261
4322396032220842.3614500518760.6385499495
4420883222069922.7514496118399.2485503901
4521694522166191.049409943260.9505900587
4621391712158191.92155145-19020.921551452
4720785822150666.43918628-72084.4391862843
4822094782171463.6827750138014.3172249864
4922396032223772.6672483315830.3327516741
5021889092223686.78010783-34777.7801078325
5121996102193793.417166135816.58283387171
5222699162258918.5602123810997.4397876193
5325326402551162.58695427-18522.58695427
5426633522628072.8375579935279.1624420066
5526633522636173.0614692127178.938530785
5626029132453381.85128126149531.148718741
5726936602578225.15630908115434.843690925
5826029132570844.7053496832068.2946503181
5925520922523272.8617290228819.1382709825
6027445092681546.746442762962.2535572951
6127746342730757.306727743876.6932722973
6227033782690605.4643974412772.5356025631
6328849672709465.76468788175501.235312118
6429562282839902.10592264116325.894077357
6531681033212374.2200067-44271.2200067015
6633087113369327.24536691-60616.2453669133
6732892583357319.4245671-68061.4245670973
6832784303230661.1259565447768.8740434605
6933595593324861.6658706934697.3341293135
7033496923211948.28592409137743.714075906
7132286923172763.1578582855928.8421417219
7234102533410577.6430949-324.643094903789
7334708473437322.8187170733524.1812829268
7434102533353363.0189462656889.9810537375
7536621543544049.42395763118104.576042367
7637833093625072.41969593158236.580304073
7740653623932372.68370269132989.31629731
7841766504156003.1860610520646.8139389493
7941464924159099.700725-12607.7007249957
8040858974135945.46397286-50048.4639728596
8141366244221910.34482604-85286.3448260371
8241971854154495.5681472442689.4318527612
8339950563996870.72797755-1814.72797755012
8441562044218518.48161805-62314.4816180533
8542577794266991.11994609-9212.11994608678
8642167984170639.846211546158.1537884977
8744793664452085.3371300627280.6628699442
8845700804554961.9169624515118.0830375459
8949538374850975.31307336102861.686926641
9050241384988148.8922618335989.1077381689
9149334184950790.46115599-17372.461155992
9249841174875716.94485442108400.055145579
9350143984973072.4644203441325.5355796628
9450446785038471.259949236206.74005076569
9548522614791826.6096885960434.3903114107
9650338565009926.6574945523929.3425054532
9751344375137471.61691463-3034.61691462994
9850338565073079.89708688-39223.8970868774
9953268545368646.67094468-41792.6709446814
10054176075458539.43213902-40932.4321390186
10158110375873320.69788492-62283.6978849182
10258716315922973.98422629-51342.9842262911
10358910895797258.9131003493830.0868996559
10459926315839504.52017729153126.479822708
10559926315888399.71979947104231.280200526
10660326575937067.4666241295589.5333758807
10758510635709285.84333298141777.156667016
10859419385944184.78542166-2246.78542166017
10960023776058449.76357532-56072.763575322
11058910895932231.32316689-41142.3231668891
11162142466272990.86551801-58744.8655180056
11262748126371476.91273958-96664.9127395824
11366780216820306.42786416-142285.427864162
11467492836864877.51800887-115594.518008865
11568498646829622.0026009920241.997399007
11669407396901740.715648638998.284351401
11769504516870274.852180580176.1478195004
11869611526895367.7986992865784.2013007235
11967795636651730.43881223127832.561187767
12069611526768513.49707615192638.502923845

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1069108 & 1008196.58205197 & 60911.4179480316 \tabularnewline
14 & 1049495 & 1000087.99124856 & 49407.0087514367 \tabularnewline
15 & 1079775 & 1035376.94817616 & 44398.0518238381 \tabularnewline
16 & 1129547 & 1085598.07391994 & 43948.9260800593 \tabularnewline
17 & 1412683 & 1358800.59829071 & 53882.4017092886 \tabularnewline
18 & 1412683 & 1360657.00198473 & 52025.9980152664 \tabularnewline
19 & 1352244 & 1273172.34716091 & 79071.6528390904 \tabularnewline
20 & 1291650 & 1195737.3306624 & 95912.6693376033 \tabularnewline
21 & 1341422 & 1256521.70894963 & 84900.2910503731 \tabularnewline
22 & 1401983 & 1298993.11265117 & 102989.88734883 \tabularnewline
23 & 1412683 & 1354240.37571191 & 58442.6242880856 \tabularnewline
24 & 1442964 & 1408421.84976003 & 34542.1502399726 \tabularnewline
25 & 1533833 & 1581849.49355158 & -48016.4935515777 \tabularnewline
26 & 1473244 & 1531955.86281126 & -58711.8628112569 \tabularnewline
27 & 1473244 & 1551749.32606805 & -78505.3260680519 \tabularnewline
28 & 1564114 & 1591892.63001636 & -27778.6300163562 \tabularnewline
29 & 1816014 & 1964718.54771749 & -148704.547717491 \tabularnewline
30 & 1836427 & 1911151.19167632 & -74724.1916763249 \tabularnewline
31 & 1785734 & 1782299.21270678 & 3434.78729321552 \tabularnewline
32 & 1664578 & 1665431.29313694 & -853.293136936845 \tabularnewline
33 & 1755420 & 1693578.46497632 & 61841.5350236769 \tabularnewline
34 & 1755420 & 1742206.88119944 & 13213.1188005591 \tabularnewline
35 & 1765165 & 1728792.57841141 & 36372.4215885925 \tabularnewline
36 & 1816014 & 1750859.23508928 & 65154.764910721 \tabularnewline
37 & 1856040 & 1874721.05588692 & -18681.0558869184 \tabularnewline
38 & 1876453 & 1799879.46336197 & 76573.5366380285 \tabularnewline
39 & 1876453 & 1827402.34333789 & 49050.6566621056 \tabularnewline
40 & 1937014 & 1952373.86299081 & -15359.8629908061 \tabularnewline
41 & 2169452 & 2293640.62321204 & -124188.623212043 \tabularnewline
42 & 2229890 & 2306314.16686143 & -76424.1668614261 \tabularnewline
43 & 2239603 & 2220842.36145005 & 18760.6385499495 \tabularnewline
44 & 2088322 & 2069922.75144961 & 18399.2485503901 \tabularnewline
45 & 2169452 & 2166191.04940994 & 3260.9505900587 \tabularnewline
46 & 2139171 & 2158191.92155145 & -19020.921551452 \tabularnewline
47 & 2078582 & 2150666.43918628 & -72084.4391862843 \tabularnewline
48 & 2209478 & 2171463.68277501 & 38014.3172249864 \tabularnewline
49 & 2239603 & 2223772.66724833 & 15830.3327516741 \tabularnewline
50 & 2188909 & 2223686.78010783 & -34777.7801078325 \tabularnewline
51 & 2199610 & 2193793.41716613 & 5816.58283387171 \tabularnewline
52 & 2269916 & 2258918.56021238 & 10997.4397876193 \tabularnewline
53 & 2532640 & 2551162.58695427 & -18522.58695427 \tabularnewline
54 & 2663352 & 2628072.83755799 & 35279.1624420066 \tabularnewline
55 & 2663352 & 2636173.06146921 & 27178.938530785 \tabularnewline
56 & 2602913 & 2453381.85128126 & 149531.148718741 \tabularnewline
57 & 2693660 & 2578225.15630908 & 115434.843690925 \tabularnewline
58 & 2602913 & 2570844.70534968 & 32068.2946503181 \tabularnewline
59 & 2552092 & 2523272.86172902 & 28819.1382709825 \tabularnewline
60 & 2744509 & 2681546.7464427 & 62962.2535572951 \tabularnewline
61 & 2774634 & 2730757.3067277 & 43876.6932722973 \tabularnewline
62 & 2703378 & 2690605.46439744 & 12772.5356025631 \tabularnewline
63 & 2884967 & 2709465.76468788 & 175501.235312118 \tabularnewline
64 & 2956228 & 2839902.10592264 & 116325.894077357 \tabularnewline
65 & 3168103 & 3212374.2200067 & -44271.2200067015 \tabularnewline
66 & 3308711 & 3369327.24536691 & -60616.2453669133 \tabularnewline
67 & 3289258 & 3357319.4245671 & -68061.4245670973 \tabularnewline
68 & 3278430 & 3230661.12595654 & 47768.8740434605 \tabularnewline
69 & 3359559 & 3324861.66587069 & 34697.3341293135 \tabularnewline
70 & 3349692 & 3211948.28592409 & 137743.714075906 \tabularnewline
71 & 3228692 & 3172763.15785828 & 55928.8421417219 \tabularnewline
72 & 3410253 & 3410577.6430949 & -324.643094903789 \tabularnewline
73 & 3470847 & 3437322.81871707 & 33524.1812829268 \tabularnewline
74 & 3410253 & 3353363.01894626 & 56889.9810537375 \tabularnewline
75 & 3662154 & 3544049.42395763 & 118104.576042367 \tabularnewline
76 & 3783309 & 3625072.41969593 & 158236.580304073 \tabularnewline
77 & 4065362 & 3932372.68370269 & 132989.31629731 \tabularnewline
78 & 4176650 & 4156003.18606105 & 20646.8139389493 \tabularnewline
79 & 4146492 & 4159099.700725 & -12607.7007249957 \tabularnewline
80 & 4085897 & 4135945.46397286 & -50048.4639728596 \tabularnewline
81 & 4136624 & 4221910.34482604 & -85286.3448260371 \tabularnewline
82 & 4197185 & 4154495.56814724 & 42689.4318527612 \tabularnewline
83 & 3995056 & 3996870.72797755 & -1814.72797755012 \tabularnewline
84 & 4156204 & 4218518.48161805 & -62314.4816180533 \tabularnewline
85 & 4257779 & 4266991.11994609 & -9212.11994608678 \tabularnewline
86 & 4216798 & 4170639.8462115 & 46158.1537884977 \tabularnewline
87 & 4479366 & 4452085.33713006 & 27280.6628699442 \tabularnewline
88 & 4570080 & 4554961.91696245 & 15118.0830375459 \tabularnewline
89 & 4953837 & 4850975.31307336 & 102861.686926641 \tabularnewline
90 & 5024138 & 4988148.89226183 & 35989.1077381689 \tabularnewline
91 & 4933418 & 4950790.46115599 & -17372.461155992 \tabularnewline
92 & 4984117 & 4875716.94485442 & 108400.055145579 \tabularnewline
93 & 5014398 & 4973072.46442034 & 41325.5355796628 \tabularnewline
94 & 5044678 & 5038471.25994923 & 6206.74005076569 \tabularnewline
95 & 4852261 & 4791826.60968859 & 60434.3903114107 \tabularnewline
96 & 5033856 & 5009926.65749455 & 23929.3425054532 \tabularnewline
97 & 5134437 & 5137471.61691463 & -3034.61691462994 \tabularnewline
98 & 5033856 & 5073079.89708688 & -39223.8970868774 \tabularnewline
99 & 5326854 & 5368646.67094468 & -41792.6709446814 \tabularnewline
100 & 5417607 & 5458539.43213902 & -40932.4321390186 \tabularnewline
101 & 5811037 & 5873320.69788492 & -62283.6978849182 \tabularnewline
102 & 5871631 & 5922973.98422629 & -51342.9842262911 \tabularnewline
103 & 5891089 & 5797258.91310034 & 93830.0868996559 \tabularnewline
104 & 5992631 & 5839504.52017729 & 153126.479822708 \tabularnewline
105 & 5992631 & 5888399.71979947 & 104231.280200526 \tabularnewline
106 & 6032657 & 5937067.46662412 & 95589.5333758807 \tabularnewline
107 & 5851063 & 5709285.84333298 & 141777.156667016 \tabularnewline
108 & 5941938 & 5944184.78542166 & -2246.78542166017 \tabularnewline
109 & 6002377 & 6058449.76357532 & -56072.763575322 \tabularnewline
110 & 5891089 & 5932231.32316689 & -41142.3231668891 \tabularnewline
111 & 6214246 & 6272990.86551801 & -58744.8655180056 \tabularnewline
112 & 6274812 & 6371476.91273958 & -96664.9127395824 \tabularnewline
113 & 6678021 & 6820306.42786416 & -142285.427864162 \tabularnewline
114 & 6749283 & 6864877.51800887 & -115594.518008865 \tabularnewline
115 & 6849864 & 6829622.00260099 & 20241.997399007 \tabularnewline
116 & 6940739 & 6901740.7156486 & 38998.284351401 \tabularnewline
117 & 6950451 & 6870274.8521805 & 80176.1478195004 \tabularnewline
118 & 6961152 & 6895367.79869928 & 65784.2013007235 \tabularnewline
119 & 6779563 & 6651730.43881223 & 127832.561187767 \tabularnewline
120 & 6961152 & 6768513.49707615 & 192638.502923845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235353&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]1069108[/C][C]1008196.58205197[/C][C]60911.4179480316[/C][/ROW]
[ROW][C]14[/C][C]1049495[/C][C]1000087.99124856[/C][C]49407.0087514367[/C][/ROW]
[ROW][C]15[/C][C]1079775[/C][C]1035376.94817616[/C][C]44398.0518238381[/C][/ROW]
[ROW][C]16[/C][C]1129547[/C][C]1085598.07391994[/C][C]43948.9260800593[/C][/ROW]
[ROW][C]17[/C][C]1412683[/C][C]1358800.59829071[/C][C]53882.4017092886[/C][/ROW]
[ROW][C]18[/C][C]1412683[/C][C]1360657.00198473[/C][C]52025.9980152664[/C][/ROW]
[ROW][C]19[/C][C]1352244[/C][C]1273172.34716091[/C][C]79071.6528390904[/C][/ROW]
[ROW][C]20[/C][C]1291650[/C][C]1195737.3306624[/C][C]95912.6693376033[/C][/ROW]
[ROW][C]21[/C][C]1341422[/C][C]1256521.70894963[/C][C]84900.2910503731[/C][/ROW]
[ROW][C]22[/C][C]1401983[/C][C]1298993.11265117[/C][C]102989.88734883[/C][/ROW]
[ROW][C]23[/C][C]1412683[/C][C]1354240.37571191[/C][C]58442.6242880856[/C][/ROW]
[ROW][C]24[/C][C]1442964[/C][C]1408421.84976003[/C][C]34542.1502399726[/C][/ROW]
[ROW][C]25[/C][C]1533833[/C][C]1581849.49355158[/C][C]-48016.4935515777[/C][/ROW]
[ROW][C]26[/C][C]1473244[/C][C]1531955.86281126[/C][C]-58711.8628112569[/C][/ROW]
[ROW][C]27[/C][C]1473244[/C][C]1551749.32606805[/C][C]-78505.3260680519[/C][/ROW]
[ROW][C]28[/C][C]1564114[/C][C]1591892.63001636[/C][C]-27778.6300163562[/C][/ROW]
[ROW][C]29[/C][C]1816014[/C][C]1964718.54771749[/C][C]-148704.547717491[/C][/ROW]
[ROW][C]30[/C][C]1836427[/C][C]1911151.19167632[/C][C]-74724.1916763249[/C][/ROW]
[ROW][C]31[/C][C]1785734[/C][C]1782299.21270678[/C][C]3434.78729321552[/C][/ROW]
[ROW][C]32[/C][C]1664578[/C][C]1665431.29313694[/C][C]-853.293136936845[/C][/ROW]
[ROW][C]33[/C][C]1755420[/C][C]1693578.46497632[/C][C]61841.5350236769[/C][/ROW]
[ROW][C]34[/C][C]1755420[/C][C]1742206.88119944[/C][C]13213.1188005591[/C][/ROW]
[ROW][C]35[/C][C]1765165[/C][C]1728792.57841141[/C][C]36372.4215885925[/C][/ROW]
[ROW][C]36[/C][C]1816014[/C][C]1750859.23508928[/C][C]65154.764910721[/C][/ROW]
[ROW][C]37[/C][C]1856040[/C][C]1874721.05588692[/C][C]-18681.0558869184[/C][/ROW]
[ROW][C]38[/C][C]1876453[/C][C]1799879.46336197[/C][C]76573.5366380285[/C][/ROW]
[ROW][C]39[/C][C]1876453[/C][C]1827402.34333789[/C][C]49050.6566621056[/C][/ROW]
[ROW][C]40[/C][C]1937014[/C][C]1952373.86299081[/C][C]-15359.8629908061[/C][/ROW]
[ROW][C]41[/C][C]2169452[/C][C]2293640.62321204[/C][C]-124188.623212043[/C][/ROW]
[ROW][C]42[/C][C]2229890[/C][C]2306314.16686143[/C][C]-76424.1668614261[/C][/ROW]
[ROW][C]43[/C][C]2239603[/C][C]2220842.36145005[/C][C]18760.6385499495[/C][/ROW]
[ROW][C]44[/C][C]2088322[/C][C]2069922.75144961[/C][C]18399.2485503901[/C][/ROW]
[ROW][C]45[/C][C]2169452[/C][C]2166191.04940994[/C][C]3260.9505900587[/C][/ROW]
[ROW][C]46[/C][C]2139171[/C][C]2158191.92155145[/C][C]-19020.921551452[/C][/ROW]
[ROW][C]47[/C][C]2078582[/C][C]2150666.43918628[/C][C]-72084.4391862843[/C][/ROW]
[ROW][C]48[/C][C]2209478[/C][C]2171463.68277501[/C][C]38014.3172249864[/C][/ROW]
[ROW][C]49[/C][C]2239603[/C][C]2223772.66724833[/C][C]15830.3327516741[/C][/ROW]
[ROW][C]50[/C][C]2188909[/C][C]2223686.78010783[/C][C]-34777.7801078325[/C][/ROW]
[ROW][C]51[/C][C]2199610[/C][C]2193793.41716613[/C][C]5816.58283387171[/C][/ROW]
[ROW][C]52[/C][C]2269916[/C][C]2258918.56021238[/C][C]10997.4397876193[/C][/ROW]
[ROW][C]53[/C][C]2532640[/C][C]2551162.58695427[/C][C]-18522.58695427[/C][/ROW]
[ROW][C]54[/C][C]2663352[/C][C]2628072.83755799[/C][C]35279.1624420066[/C][/ROW]
[ROW][C]55[/C][C]2663352[/C][C]2636173.06146921[/C][C]27178.938530785[/C][/ROW]
[ROW][C]56[/C][C]2602913[/C][C]2453381.85128126[/C][C]149531.148718741[/C][/ROW]
[ROW][C]57[/C][C]2693660[/C][C]2578225.15630908[/C][C]115434.843690925[/C][/ROW]
[ROW][C]58[/C][C]2602913[/C][C]2570844.70534968[/C][C]32068.2946503181[/C][/ROW]
[ROW][C]59[/C][C]2552092[/C][C]2523272.86172902[/C][C]28819.1382709825[/C][/ROW]
[ROW][C]60[/C][C]2744509[/C][C]2681546.7464427[/C][C]62962.2535572951[/C][/ROW]
[ROW][C]61[/C][C]2774634[/C][C]2730757.3067277[/C][C]43876.6932722973[/C][/ROW]
[ROW][C]62[/C][C]2703378[/C][C]2690605.46439744[/C][C]12772.5356025631[/C][/ROW]
[ROW][C]63[/C][C]2884967[/C][C]2709465.76468788[/C][C]175501.235312118[/C][/ROW]
[ROW][C]64[/C][C]2956228[/C][C]2839902.10592264[/C][C]116325.894077357[/C][/ROW]
[ROW][C]65[/C][C]3168103[/C][C]3212374.2200067[/C][C]-44271.2200067015[/C][/ROW]
[ROW][C]66[/C][C]3308711[/C][C]3369327.24536691[/C][C]-60616.2453669133[/C][/ROW]
[ROW][C]67[/C][C]3289258[/C][C]3357319.4245671[/C][C]-68061.4245670973[/C][/ROW]
[ROW][C]68[/C][C]3278430[/C][C]3230661.12595654[/C][C]47768.8740434605[/C][/ROW]
[ROW][C]69[/C][C]3359559[/C][C]3324861.66587069[/C][C]34697.3341293135[/C][/ROW]
[ROW][C]70[/C][C]3349692[/C][C]3211948.28592409[/C][C]137743.714075906[/C][/ROW]
[ROW][C]71[/C][C]3228692[/C][C]3172763.15785828[/C][C]55928.8421417219[/C][/ROW]
[ROW][C]72[/C][C]3410253[/C][C]3410577.6430949[/C][C]-324.643094903789[/C][/ROW]
[ROW][C]73[/C][C]3470847[/C][C]3437322.81871707[/C][C]33524.1812829268[/C][/ROW]
[ROW][C]74[/C][C]3410253[/C][C]3353363.01894626[/C][C]56889.9810537375[/C][/ROW]
[ROW][C]75[/C][C]3662154[/C][C]3544049.42395763[/C][C]118104.576042367[/C][/ROW]
[ROW][C]76[/C][C]3783309[/C][C]3625072.41969593[/C][C]158236.580304073[/C][/ROW]
[ROW][C]77[/C][C]4065362[/C][C]3932372.68370269[/C][C]132989.31629731[/C][/ROW]
[ROW][C]78[/C][C]4176650[/C][C]4156003.18606105[/C][C]20646.8139389493[/C][/ROW]
[ROW][C]79[/C][C]4146492[/C][C]4159099.700725[/C][C]-12607.7007249957[/C][/ROW]
[ROW][C]80[/C][C]4085897[/C][C]4135945.46397286[/C][C]-50048.4639728596[/C][/ROW]
[ROW][C]81[/C][C]4136624[/C][C]4221910.34482604[/C][C]-85286.3448260371[/C][/ROW]
[ROW][C]82[/C][C]4197185[/C][C]4154495.56814724[/C][C]42689.4318527612[/C][/ROW]
[ROW][C]83[/C][C]3995056[/C][C]3996870.72797755[/C][C]-1814.72797755012[/C][/ROW]
[ROW][C]84[/C][C]4156204[/C][C]4218518.48161805[/C][C]-62314.4816180533[/C][/ROW]
[ROW][C]85[/C][C]4257779[/C][C]4266991.11994609[/C][C]-9212.11994608678[/C][/ROW]
[ROW][C]86[/C][C]4216798[/C][C]4170639.8462115[/C][C]46158.1537884977[/C][/ROW]
[ROW][C]87[/C][C]4479366[/C][C]4452085.33713006[/C][C]27280.6628699442[/C][/ROW]
[ROW][C]88[/C][C]4570080[/C][C]4554961.91696245[/C][C]15118.0830375459[/C][/ROW]
[ROW][C]89[/C][C]4953837[/C][C]4850975.31307336[/C][C]102861.686926641[/C][/ROW]
[ROW][C]90[/C][C]5024138[/C][C]4988148.89226183[/C][C]35989.1077381689[/C][/ROW]
[ROW][C]91[/C][C]4933418[/C][C]4950790.46115599[/C][C]-17372.461155992[/C][/ROW]
[ROW][C]92[/C][C]4984117[/C][C]4875716.94485442[/C][C]108400.055145579[/C][/ROW]
[ROW][C]93[/C][C]5014398[/C][C]4973072.46442034[/C][C]41325.5355796628[/C][/ROW]
[ROW][C]94[/C][C]5044678[/C][C]5038471.25994923[/C][C]6206.74005076569[/C][/ROW]
[ROW][C]95[/C][C]4852261[/C][C]4791826.60968859[/C][C]60434.3903114107[/C][/ROW]
[ROW][C]96[/C][C]5033856[/C][C]5009926.65749455[/C][C]23929.3425054532[/C][/ROW]
[ROW][C]97[/C][C]5134437[/C][C]5137471.61691463[/C][C]-3034.61691462994[/C][/ROW]
[ROW][C]98[/C][C]5033856[/C][C]5073079.89708688[/C][C]-39223.8970868774[/C][/ROW]
[ROW][C]99[/C][C]5326854[/C][C]5368646.67094468[/C][C]-41792.6709446814[/C][/ROW]
[ROW][C]100[/C][C]5417607[/C][C]5458539.43213902[/C][C]-40932.4321390186[/C][/ROW]
[ROW][C]101[/C][C]5811037[/C][C]5873320.69788492[/C][C]-62283.6978849182[/C][/ROW]
[ROW][C]102[/C][C]5871631[/C][C]5922973.98422629[/C][C]-51342.9842262911[/C][/ROW]
[ROW][C]103[/C][C]5891089[/C][C]5797258.91310034[/C][C]93830.0868996559[/C][/ROW]
[ROW][C]104[/C][C]5992631[/C][C]5839504.52017729[/C][C]153126.479822708[/C][/ROW]
[ROW][C]105[/C][C]5992631[/C][C]5888399.71979947[/C][C]104231.280200526[/C][/ROW]
[ROW][C]106[/C][C]6032657[/C][C]5937067.46662412[/C][C]95589.5333758807[/C][/ROW]
[ROW][C]107[/C][C]5851063[/C][C]5709285.84333298[/C][C]141777.156667016[/C][/ROW]
[ROW][C]108[/C][C]5941938[/C][C]5944184.78542166[/C][C]-2246.78542166017[/C][/ROW]
[ROW][C]109[/C][C]6002377[/C][C]6058449.76357532[/C][C]-56072.763575322[/C][/ROW]
[ROW][C]110[/C][C]5891089[/C][C]5932231.32316689[/C][C]-41142.3231668891[/C][/ROW]
[ROW][C]111[/C][C]6214246[/C][C]6272990.86551801[/C][C]-58744.8655180056[/C][/ROW]
[ROW][C]112[/C][C]6274812[/C][C]6371476.91273958[/C][C]-96664.9127395824[/C][/ROW]
[ROW][C]113[/C][C]6678021[/C][C]6820306.42786416[/C][C]-142285.427864162[/C][/ROW]
[ROW][C]114[/C][C]6749283[/C][C]6864877.51800887[/C][C]-115594.518008865[/C][/ROW]
[ROW][C]115[/C][C]6849864[/C][C]6829622.00260099[/C][C]20241.997399007[/C][/ROW]
[ROW][C]116[/C][C]6940739[/C][C]6901740.7156486[/C][C]38998.284351401[/C][/ROW]
[ROW][C]117[/C][C]6950451[/C][C]6870274.8521805[/C][C]80176.1478195004[/C][/ROW]
[ROW][C]118[/C][C]6961152[/C][C]6895367.79869928[/C][C]65784.2013007235[/C][/ROW]
[ROW][C]119[/C][C]6779563[/C][C]6651730.43881223[/C][C]127832.561187767[/C][/ROW]
[ROW][C]120[/C][C]6961152[/C][C]6768513.49707615[/C][C]192638.502923845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235353&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235353&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
1310691081008196.5820519760911.4179480316
1410494951000087.9912485649407.0087514367
1510797751035376.9481761644398.0518238381
1611295471085598.0739199443948.9260800593
1714126831358800.5982907153882.4017092886
1814126831360657.0019847352025.9980152664
1913522441273172.3471609179071.6528390904
2012916501195737.330662495912.6693376033
2113414221256521.7089496384900.2910503731
2214019831298993.11265117102989.88734883
2314126831354240.3757119158442.6242880856
2414429641408421.8497600334542.1502399726
2515338331581849.49355158-48016.4935515777
2614732441531955.86281126-58711.8628112569
2714732441551749.32606805-78505.3260680519
2815641141591892.63001636-27778.6300163562
2918160141964718.54771749-148704.547717491
3018364271911151.19167632-74724.1916763249
3117857341782299.212706783434.78729321552
3216645781665431.29313694-853.293136936845
3317554201693578.4649763261841.5350236769
3417554201742206.8811994413213.1188005591
3517651651728792.5784114136372.4215885925
3618160141750859.2350892865154.764910721
3718560401874721.05588692-18681.0558869184
3818764531799879.4633619776573.5366380285
3918764531827402.3433378949050.6566621056
4019370141952373.86299081-15359.8629908061
4121694522293640.62321204-124188.623212043
4222298902306314.16686143-76424.1668614261
4322396032220842.3614500518760.6385499495
4420883222069922.7514496118399.2485503901
4521694522166191.049409943260.9505900587
4621391712158191.92155145-19020.921551452
4720785822150666.43918628-72084.4391862843
4822094782171463.6827750138014.3172249864
4922396032223772.6672483315830.3327516741
5021889092223686.78010783-34777.7801078325
5121996102193793.417166135816.58283387171
5222699162258918.5602123810997.4397876193
5325326402551162.58695427-18522.58695427
5426633522628072.8375579935279.1624420066
5526633522636173.0614692127178.938530785
5626029132453381.85128126149531.148718741
5726936602578225.15630908115434.843690925
5826029132570844.7053496832068.2946503181
5925520922523272.8617290228819.1382709825
6027445092681546.746442762962.2535572951
6127746342730757.306727743876.6932722973
6227033782690605.4643974412772.5356025631
6328849672709465.76468788175501.235312118
6429562282839902.10592264116325.894077357
6531681033212374.2200067-44271.2200067015
6633087113369327.24536691-60616.2453669133
6732892583357319.4245671-68061.4245670973
6832784303230661.1259565447768.8740434605
6933595593324861.6658706934697.3341293135
7033496923211948.28592409137743.714075906
7132286923172763.1578582855928.8421417219
7234102533410577.6430949-324.643094903789
7334708473437322.8187170733524.1812829268
7434102533353363.0189462656889.9810537375
7536621543544049.42395763118104.576042367
7637833093625072.41969593158236.580304073
7740653623932372.68370269132989.31629731
7841766504156003.1860610520646.8139389493
7941464924159099.700725-12607.7007249957
8040858974135945.46397286-50048.4639728596
8141366244221910.34482604-85286.3448260371
8241971854154495.5681472442689.4318527612
8339950563996870.72797755-1814.72797755012
8441562044218518.48161805-62314.4816180533
8542577794266991.11994609-9212.11994608678
8642167984170639.846211546158.1537884977
8744793664452085.3371300627280.6628699442
8845700804554961.9169624515118.0830375459
8949538374850975.31307336102861.686926641
9050241384988148.8922618335989.1077381689
9149334184950790.46115599-17372.461155992
9249841174875716.94485442108400.055145579
9350143984973072.4644203441325.5355796628
9450446785038471.259949236206.74005076569
9548522614791826.6096885960434.3903114107
9650338565009926.6574945523929.3425054532
9751344375137471.61691463-3034.61691462994
9850338565073079.89708688-39223.8970868774
9953268545368646.67094468-41792.6709446814
10054176075458539.43213902-40932.4321390186
10158110375873320.69788492-62283.6978849182
10258716315922973.98422629-51342.9842262911
10358910895797258.9131003493830.0868996559
10459926315839504.52017729153126.479822708
10559926315888399.71979947104231.280200526
10660326575937067.4666241295589.5333758807
10758510635709285.84333298141777.156667016
10859419385944184.78542166-2246.78542166017
10960023776058449.76357532-56072.763575322
11058910895932231.32316689-41142.3231668891
11162142466272990.86551801-58744.8655180056
11262748126371476.91273958-96664.9127395824
11366780216820306.42786416-142285.427864162
11467492836864877.51800887-115594.518008865
11568498646829622.0026009920241.997399007
11669407396901740.715648638998.284351401
11769504516870274.852180580176.1478195004
11869611526895367.7986992865784.2013007235
11967795636651730.43881223127832.561187767
12069611526768513.49707615192638.502923845







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1216881996.355033746744536.275485947019456.43458153
1226755440.123503126614380.16179756896500.08520873
1237132048.493190416985859.158203887278237.82817695
1247218220.773194397066814.039710257369627.50667853
1257711802.367901677552392.26797587871212.46782753
1267820963.251233627654607.565333637987318.93713362
1277933891.344156537759873.628324298107909.05998877
1288030337.382345667848144.126786238212530.63790508
1298021473.840154727831681.429807078211266.25050236
1308015465.461788657817704.535456458213226.38812084
1317770967.064345187568306.587012467973627.5416779
1327924234.155424467760860.530518678087607.78033025

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 6881996.35503374 & 6744536.27548594 & 7019456.43458153 \tabularnewline
122 & 6755440.12350312 & 6614380.1617975 & 6896500.08520873 \tabularnewline
123 & 7132048.49319041 & 6985859.15820388 & 7278237.82817695 \tabularnewline
124 & 7218220.77319439 & 7066814.03971025 & 7369627.50667853 \tabularnewline
125 & 7711802.36790167 & 7552392.2679758 & 7871212.46782753 \tabularnewline
126 & 7820963.25123362 & 7654607.56533363 & 7987318.93713362 \tabularnewline
127 & 7933891.34415653 & 7759873.62832429 & 8107909.05998877 \tabularnewline
128 & 8030337.38234566 & 7848144.12678623 & 8212530.63790508 \tabularnewline
129 & 8021473.84015472 & 7831681.42980707 & 8211266.25050236 \tabularnewline
130 & 8015465.46178865 & 7817704.53545645 & 8213226.38812084 \tabularnewline
131 & 7770967.06434518 & 7568306.58701246 & 7973627.5416779 \tabularnewline
132 & 7924234.15542446 & 7760860.53051867 & 8087607.78033025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235353&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]121[/C][C]6881996.35503374[/C][C]6744536.27548594[/C][C]7019456.43458153[/C][/ROW]
[ROW][C]122[/C][C]6755440.12350312[/C][C]6614380.1617975[/C][C]6896500.08520873[/C][/ROW]
[ROW][C]123[/C][C]7132048.49319041[/C][C]6985859.15820388[/C][C]7278237.82817695[/C][/ROW]
[ROW][C]124[/C][C]7218220.77319439[/C][C]7066814.03971025[/C][C]7369627.50667853[/C][/ROW]
[ROW][C]125[/C][C]7711802.36790167[/C][C]7552392.2679758[/C][C]7871212.46782753[/C][/ROW]
[ROW][C]126[/C][C]7820963.25123362[/C][C]7654607.56533363[/C][C]7987318.93713362[/C][/ROW]
[ROW][C]127[/C][C]7933891.34415653[/C][C]7759873.62832429[/C][C]8107909.05998877[/C][/ROW]
[ROW][C]128[/C][C]8030337.38234566[/C][C]7848144.12678623[/C][C]8212530.63790508[/C][/ROW]
[ROW][C]129[/C][C]8021473.84015472[/C][C]7831681.42980707[/C][C]8211266.25050236[/C][/ROW]
[ROW][C]130[/C][C]8015465.46178865[/C][C]7817704.53545645[/C][C]8213226.38812084[/C][/ROW]
[ROW][C]131[/C][C]7770967.06434518[/C][C]7568306.58701246[/C][C]7973627.5416779[/C][/ROW]
[ROW][C]132[/C][C]7924234.15542446[/C][C]7760860.53051867[/C][C]8087607.78033025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235353&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235353&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
1216881996.355033746744536.275485947019456.43458153
1226755440.123503126614380.16179756896500.08520873
1237132048.493190416985859.158203887278237.82817695
1247218220.773194397066814.039710257369627.50667853
1257711802.367901677552392.26797587871212.46782753
1267820963.251233627654607.565333637987318.93713362
1277933891.344156537759873.628324298107909.05998877
1288030337.382345667848144.126786238212530.63790508
1298021473.840154727831681.429807078211266.25050236
1308015465.461788657817704.535456458213226.38812084
1317770967.064345187568306.587012467973627.5416779
1327924234.155424467760860.530518678087607.78033025



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')