Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 12 Jul 2011 15:37:16 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Jul/12/t1310499947a2smiqheqa391ep.htm/, Retrieved Wed, 15 May 2024 16:09:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123037, Retrieved Wed, 15 May 2024 16:09:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan den Buys Daphné
Estimated Impact228
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A-stap 32] [2011-07-12 19:37:16] [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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123037&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123037&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123037&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.214234531522304
beta0.107870793533823
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.214234531522304 \tabularnewline
beta & 0.107870793533823 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123037&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]0.214234531522304[/C][/ROW]
[ROW][C]beta[/C][C]0.107870793533823[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123037&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123037&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
alpha0.214234531522304
beta0.107870793533823
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310691081008196.5820519760911.4179480321
1410494951000087.9912499749407.0087500295
1510797751035376.9481782744398.0518217288
1611295471085598.0739223343948.9260776711
1714126831358800.5982935953882.4017064096
1814126831360657.0019873252025.9980126815
1913522441273172.3471629179071.6528370872
2012916501195737.330664595912.6693354975
2113414221256521.7089523284900.2910476772
2214019831298993.11265369102989.887346313
2314126831354240.3757144658442.6242855424
2414429641408421.8497611834542.1502388178
2515338331581849.49354827-48016.4935482666
2614732441531955.86280381-58711.8628038121
2714732441551749.32605794-78505.3260579403
2815641141591892.63000426-27778.6300042579
2918160141964718.54770347-148704.547703471
3018364271911151.19166118-74724.1916611798
3117857341782299.21269293434.787307102
3216645781665431.29312591-853.293125909055
3317554201693578.4649678561841.5350321548
3417554201742206.8811943713213.1188056301
3517651651728792.5784098336372.4215901729
3618160141750859.2350915465154.7649084597
3718560401874721.0558947-18681.0558947015
3818764531799879.4633701576573.5366298498
3918764531827402.3433483649050.6566516396
4019370141952373.86299974-15359.862999738
4121694522293640.62322182-124188.623221816
4222298902306314.1668644-76424.1668644003
4322396032220842.3614459918760.6385540147
4420883222069922.7514434618399.248556542
4521694522166191.049399953260.95060004899
4621391712158191.92154122-19020.9215412238
4720785822150666.43917562-72084.439175623
4822094782171463.6827630638014.3172369446
4922396032223772.6672428415830.3327571559
5021889092223686.78010434-34777.7801043354
5121996102193793.417164965816.58283504471
5222699162258918.5602160110997.4397839936
5325326402551162.58696573-18522.5869657299
5426633522628072.8375713635279.1624286417
5526633522636173.0614799327178.938520065
5626029132453381.85128811149531.148711886
5726936602578225.15631599115434.843684014
5826029132570844.7053552432068.2946447642
5925520922523272.8617324628819.1382675408
6027445092681546.7464398462962.2535601603
6127746342730757.3067228143876.6932771914
6227033782690605.464392712772.5356073049
6328849672709465.76468151175501.235318493
6429562282839902.10592002116325.894079985
6531681033212374.2200082-44271.2200081958
6633087113369327.24536629-60616.245366286
6732892583357319.42456467-68061.4245646675
6832784303230661.1259481747768.8740518303
6933595593324861.6658625434697.3341374639
7033496923211948.28591922137743.714080782
7132286923172763.1578580355928.8421419705
7234102533410577.64309332-324.643093320541
7334708473437322.8187131533524.1812868463
7434102533353363.0189426156889.9810573924
7536621543544049.42394826118104.576051739
7637833093625072.41968732158236.580312677
7740653623932372.68370228132989.316297722
7841766504156003.1860662220646.8139337827
7941464924159099.70073077-12607.7007307694
8040858974135945.46397225-50048.4639722491
8141366244221910.34482007-85286.3448200729
8241971854154495.5681338642689.4318661448
8339950563996870.72796679-1814.72796678776
8441562044218518.4816093-62314.481609297
8542577794266991.11993618-9212.11993618216
8642167984170639.846201946158.1537980959
8744793664452085.3371181627280.6628818428
8845700804554961.9169476815118.0830523213
8949538374850975.31305938102861.686940623
9050241384988148.8922569435989.1077430556
9149334184950790.46115794-17372.4611579441
9249841174875716.9448598108400.055140205
9350143984973072.4644310141325.5355689898
9450446785038471.259955336206.74004466832
9548522614791826.6096915860434.3903084174
9650338565009926.6574989523929.3425010489
9751344375137471.61691645-3034.61691644788
9850338565073079.89708376-39223.8970837612
9953268545368646.67093669-41792.670936686
10054176075458539.43212698-40932.4321269765
10158110375873320.69786637-62283.6978663662
10258716315922973.98420792-51342.9842079151
10358910895797258.9130868293830.0869131833
10459926315839504.52016799153126.479832012
10559926315888399.71979881104231.280201185
10660326575937067.4666289795589.5333710331
10758510635709285.84333886141777.156661144
10859419385944184.7854314-2246.78543140274
10960023776058449.76358427-56072.7635842711
11058910895932231.32317341-41142.3231734065
11162142466272990.86552201-58744.8655220084
11262748126371476.91273965-96664.9127396466
11366780216820306.42785883-142285.427858832
11467492836864877.51799775-115594.51799775
11568498646829622.0025826420241.9974173615
11669407396901740.7156275638998.2843724443
11769504516870274.8521625280176.1478374815
11869611526895367.7986868565784.2013131538
11967795636651730.43880333127832.561196665
12069611526768513.49707714192638.502922857

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1069108 & 1008196.58205197 & 60911.4179480321 \tabularnewline
14 & 1049495 & 1000087.99124997 & 49407.0087500295 \tabularnewline
15 & 1079775 & 1035376.94817827 & 44398.0518217288 \tabularnewline
16 & 1129547 & 1085598.07392233 & 43948.9260776711 \tabularnewline
17 & 1412683 & 1358800.59829359 & 53882.4017064096 \tabularnewline
18 & 1412683 & 1360657.00198732 & 52025.9980126815 \tabularnewline
19 & 1352244 & 1273172.34716291 & 79071.6528370872 \tabularnewline
20 & 1291650 & 1195737.3306645 & 95912.6693354975 \tabularnewline
21 & 1341422 & 1256521.70895232 & 84900.2910476772 \tabularnewline
22 & 1401983 & 1298993.11265369 & 102989.887346313 \tabularnewline
23 & 1412683 & 1354240.37571446 & 58442.6242855424 \tabularnewline
24 & 1442964 & 1408421.84976118 & 34542.1502388178 \tabularnewline
25 & 1533833 & 1581849.49354827 & -48016.4935482666 \tabularnewline
26 & 1473244 & 1531955.86280381 & -58711.8628038121 \tabularnewline
27 & 1473244 & 1551749.32605794 & -78505.3260579403 \tabularnewline
28 & 1564114 & 1591892.63000426 & -27778.6300042579 \tabularnewline
29 & 1816014 & 1964718.54770347 & -148704.547703471 \tabularnewline
30 & 1836427 & 1911151.19166118 & -74724.1916611798 \tabularnewline
31 & 1785734 & 1782299.2126929 & 3434.787307102 \tabularnewline
32 & 1664578 & 1665431.29312591 & -853.293125909055 \tabularnewline
33 & 1755420 & 1693578.46496785 & 61841.5350321548 \tabularnewline
34 & 1755420 & 1742206.88119437 & 13213.1188056301 \tabularnewline
35 & 1765165 & 1728792.57840983 & 36372.4215901729 \tabularnewline
36 & 1816014 & 1750859.23509154 & 65154.7649084597 \tabularnewline
37 & 1856040 & 1874721.0558947 & -18681.0558947015 \tabularnewline
38 & 1876453 & 1799879.46337015 & 76573.5366298498 \tabularnewline
39 & 1876453 & 1827402.34334836 & 49050.6566516396 \tabularnewline
40 & 1937014 & 1952373.86299974 & -15359.862999738 \tabularnewline
41 & 2169452 & 2293640.62322182 & -124188.623221816 \tabularnewline
42 & 2229890 & 2306314.1668644 & -76424.1668644003 \tabularnewline
43 & 2239603 & 2220842.36144599 & 18760.6385540147 \tabularnewline
44 & 2088322 & 2069922.75144346 & 18399.248556542 \tabularnewline
45 & 2169452 & 2166191.04939995 & 3260.95060004899 \tabularnewline
46 & 2139171 & 2158191.92154122 & -19020.9215412238 \tabularnewline
47 & 2078582 & 2150666.43917562 & -72084.439175623 \tabularnewline
48 & 2209478 & 2171463.68276306 & 38014.3172369446 \tabularnewline
49 & 2239603 & 2223772.66724284 & 15830.3327571559 \tabularnewline
50 & 2188909 & 2223686.78010434 & -34777.7801043354 \tabularnewline
51 & 2199610 & 2193793.41716496 & 5816.58283504471 \tabularnewline
52 & 2269916 & 2258918.56021601 & 10997.4397839936 \tabularnewline
53 & 2532640 & 2551162.58696573 & -18522.5869657299 \tabularnewline
54 & 2663352 & 2628072.83757136 & 35279.1624286417 \tabularnewline
55 & 2663352 & 2636173.06147993 & 27178.938520065 \tabularnewline
56 & 2602913 & 2453381.85128811 & 149531.148711886 \tabularnewline
57 & 2693660 & 2578225.15631599 & 115434.843684014 \tabularnewline
58 & 2602913 & 2570844.70535524 & 32068.2946447642 \tabularnewline
59 & 2552092 & 2523272.86173246 & 28819.1382675408 \tabularnewline
60 & 2744509 & 2681546.74643984 & 62962.2535601603 \tabularnewline
61 & 2774634 & 2730757.30672281 & 43876.6932771914 \tabularnewline
62 & 2703378 & 2690605.4643927 & 12772.5356073049 \tabularnewline
63 & 2884967 & 2709465.76468151 & 175501.235318493 \tabularnewline
64 & 2956228 & 2839902.10592002 & 116325.894079985 \tabularnewline
65 & 3168103 & 3212374.2200082 & -44271.2200081958 \tabularnewline
66 & 3308711 & 3369327.24536629 & -60616.245366286 \tabularnewline
67 & 3289258 & 3357319.42456467 & -68061.4245646675 \tabularnewline
68 & 3278430 & 3230661.12594817 & 47768.8740518303 \tabularnewline
69 & 3359559 & 3324861.66586254 & 34697.3341374639 \tabularnewline
70 & 3349692 & 3211948.28591922 & 137743.714080782 \tabularnewline
71 & 3228692 & 3172763.15785803 & 55928.8421419705 \tabularnewline
72 & 3410253 & 3410577.64309332 & -324.643093320541 \tabularnewline
73 & 3470847 & 3437322.81871315 & 33524.1812868463 \tabularnewline
74 & 3410253 & 3353363.01894261 & 56889.9810573924 \tabularnewline
75 & 3662154 & 3544049.42394826 & 118104.576051739 \tabularnewline
76 & 3783309 & 3625072.41968732 & 158236.580312677 \tabularnewline
77 & 4065362 & 3932372.68370228 & 132989.316297722 \tabularnewline
78 & 4176650 & 4156003.18606622 & 20646.8139337827 \tabularnewline
79 & 4146492 & 4159099.70073077 & -12607.7007307694 \tabularnewline
80 & 4085897 & 4135945.46397225 & -50048.4639722491 \tabularnewline
81 & 4136624 & 4221910.34482007 & -85286.3448200729 \tabularnewline
82 & 4197185 & 4154495.56813386 & 42689.4318661448 \tabularnewline
83 & 3995056 & 3996870.72796679 & -1814.72796678776 \tabularnewline
84 & 4156204 & 4218518.4816093 & -62314.481609297 \tabularnewline
85 & 4257779 & 4266991.11993618 & -9212.11993618216 \tabularnewline
86 & 4216798 & 4170639.8462019 & 46158.1537980959 \tabularnewline
87 & 4479366 & 4452085.33711816 & 27280.6628818428 \tabularnewline
88 & 4570080 & 4554961.91694768 & 15118.0830523213 \tabularnewline
89 & 4953837 & 4850975.31305938 & 102861.686940623 \tabularnewline
90 & 5024138 & 4988148.89225694 & 35989.1077430556 \tabularnewline
91 & 4933418 & 4950790.46115794 & -17372.4611579441 \tabularnewline
92 & 4984117 & 4875716.9448598 & 108400.055140205 \tabularnewline
93 & 5014398 & 4973072.46443101 & 41325.5355689898 \tabularnewline
94 & 5044678 & 5038471.25995533 & 6206.74004466832 \tabularnewline
95 & 4852261 & 4791826.60969158 & 60434.3903084174 \tabularnewline
96 & 5033856 & 5009926.65749895 & 23929.3425010489 \tabularnewline
97 & 5134437 & 5137471.61691645 & -3034.61691644788 \tabularnewline
98 & 5033856 & 5073079.89708376 & -39223.8970837612 \tabularnewline
99 & 5326854 & 5368646.67093669 & -41792.670936686 \tabularnewline
100 & 5417607 & 5458539.43212698 & -40932.4321269765 \tabularnewline
101 & 5811037 & 5873320.69786637 & -62283.6978663662 \tabularnewline
102 & 5871631 & 5922973.98420792 & -51342.9842079151 \tabularnewline
103 & 5891089 & 5797258.91308682 & 93830.0869131833 \tabularnewline
104 & 5992631 & 5839504.52016799 & 153126.479832012 \tabularnewline
105 & 5992631 & 5888399.71979881 & 104231.280201185 \tabularnewline
106 & 6032657 & 5937067.46662897 & 95589.5333710331 \tabularnewline
107 & 5851063 & 5709285.84333886 & 141777.156661144 \tabularnewline
108 & 5941938 & 5944184.7854314 & -2246.78543140274 \tabularnewline
109 & 6002377 & 6058449.76358427 & -56072.7635842711 \tabularnewline
110 & 5891089 & 5932231.32317341 & -41142.3231734065 \tabularnewline
111 & 6214246 & 6272990.86552201 & -58744.8655220084 \tabularnewline
112 & 6274812 & 6371476.91273965 & -96664.9127396466 \tabularnewline
113 & 6678021 & 6820306.42785883 & -142285.427858832 \tabularnewline
114 & 6749283 & 6864877.51799775 & -115594.51799775 \tabularnewline
115 & 6849864 & 6829622.00258264 & 20241.9974173615 \tabularnewline
116 & 6940739 & 6901740.71562756 & 38998.2843724443 \tabularnewline
117 & 6950451 & 6870274.85216252 & 80176.1478374815 \tabularnewline
118 & 6961152 & 6895367.79868685 & 65784.2013131538 \tabularnewline
119 & 6779563 & 6651730.43880333 & 127832.561196665 \tabularnewline
120 & 6961152 & 6768513.49707714 & 192638.502922857 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123037&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]60911.4179480321[/C][/ROW]
[ROW][C]14[/C][C]1049495[/C][C]1000087.99124997[/C][C]49407.0087500295[/C][/ROW]
[ROW][C]15[/C][C]1079775[/C][C]1035376.94817827[/C][C]44398.0518217288[/C][/ROW]
[ROW][C]16[/C][C]1129547[/C][C]1085598.07392233[/C][C]43948.9260776711[/C][/ROW]
[ROW][C]17[/C][C]1412683[/C][C]1358800.59829359[/C][C]53882.4017064096[/C][/ROW]
[ROW][C]18[/C][C]1412683[/C][C]1360657.00198732[/C][C]52025.9980126815[/C][/ROW]
[ROW][C]19[/C][C]1352244[/C][C]1273172.34716291[/C][C]79071.6528370872[/C][/ROW]
[ROW][C]20[/C][C]1291650[/C][C]1195737.3306645[/C][C]95912.6693354975[/C][/ROW]
[ROW][C]21[/C][C]1341422[/C][C]1256521.70895232[/C][C]84900.2910476772[/C][/ROW]
[ROW][C]22[/C][C]1401983[/C][C]1298993.11265369[/C][C]102989.887346313[/C][/ROW]
[ROW][C]23[/C][C]1412683[/C][C]1354240.37571446[/C][C]58442.6242855424[/C][/ROW]
[ROW][C]24[/C][C]1442964[/C][C]1408421.84976118[/C][C]34542.1502388178[/C][/ROW]
[ROW][C]25[/C][C]1533833[/C][C]1581849.49354827[/C][C]-48016.4935482666[/C][/ROW]
[ROW][C]26[/C][C]1473244[/C][C]1531955.86280381[/C][C]-58711.8628038121[/C][/ROW]
[ROW][C]27[/C][C]1473244[/C][C]1551749.32605794[/C][C]-78505.3260579403[/C][/ROW]
[ROW][C]28[/C][C]1564114[/C][C]1591892.63000426[/C][C]-27778.6300042579[/C][/ROW]
[ROW][C]29[/C][C]1816014[/C][C]1964718.54770347[/C][C]-148704.547703471[/C][/ROW]
[ROW][C]30[/C][C]1836427[/C][C]1911151.19166118[/C][C]-74724.1916611798[/C][/ROW]
[ROW][C]31[/C][C]1785734[/C][C]1782299.2126929[/C][C]3434.787307102[/C][/ROW]
[ROW][C]32[/C][C]1664578[/C][C]1665431.29312591[/C][C]-853.293125909055[/C][/ROW]
[ROW][C]33[/C][C]1755420[/C][C]1693578.46496785[/C][C]61841.5350321548[/C][/ROW]
[ROW][C]34[/C][C]1755420[/C][C]1742206.88119437[/C][C]13213.1188056301[/C][/ROW]
[ROW][C]35[/C][C]1765165[/C][C]1728792.57840983[/C][C]36372.4215901729[/C][/ROW]
[ROW][C]36[/C][C]1816014[/C][C]1750859.23509154[/C][C]65154.7649084597[/C][/ROW]
[ROW][C]37[/C][C]1856040[/C][C]1874721.0558947[/C][C]-18681.0558947015[/C][/ROW]
[ROW][C]38[/C][C]1876453[/C][C]1799879.46337015[/C][C]76573.5366298498[/C][/ROW]
[ROW][C]39[/C][C]1876453[/C][C]1827402.34334836[/C][C]49050.6566516396[/C][/ROW]
[ROW][C]40[/C][C]1937014[/C][C]1952373.86299974[/C][C]-15359.862999738[/C][/ROW]
[ROW][C]41[/C][C]2169452[/C][C]2293640.62322182[/C][C]-124188.623221816[/C][/ROW]
[ROW][C]42[/C][C]2229890[/C][C]2306314.1668644[/C][C]-76424.1668644003[/C][/ROW]
[ROW][C]43[/C][C]2239603[/C][C]2220842.36144599[/C][C]18760.6385540147[/C][/ROW]
[ROW][C]44[/C][C]2088322[/C][C]2069922.75144346[/C][C]18399.248556542[/C][/ROW]
[ROW][C]45[/C][C]2169452[/C][C]2166191.04939995[/C][C]3260.95060004899[/C][/ROW]
[ROW][C]46[/C][C]2139171[/C][C]2158191.92154122[/C][C]-19020.9215412238[/C][/ROW]
[ROW][C]47[/C][C]2078582[/C][C]2150666.43917562[/C][C]-72084.439175623[/C][/ROW]
[ROW][C]48[/C][C]2209478[/C][C]2171463.68276306[/C][C]38014.3172369446[/C][/ROW]
[ROW][C]49[/C][C]2239603[/C][C]2223772.66724284[/C][C]15830.3327571559[/C][/ROW]
[ROW][C]50[/C][C]2188909[/C][C]2223686.78010434[/C][C]-34777.7801043354[/C][/ROW]
[ROW][C]51[/C][C]2199610[/C][C]2193793.41716496[/C][C]5816.58283504471[/C][/ROW]
[ROW][C]52[/C][C]2269916[/C][C]2258918.56021601[/C][C]10997.4397839936[/C][/ROW]
[ROW][C]53[/C][C]2532640[/C][C]2551162.58696573[/C][C]-18522.5869657299[/C][/ROW]
[ROW][C]54[/C][C]2663352[/C][C]2628072.83757136[/C][C]35279.1624286417[/C][/ROW]
[ROW][C]55[/C][C]2663352[/C][C]2636173.06147993[/C][C]27178.938520065[/C][/ROW]
[ROW][C]56[/C][C]2602913[/C][C]2453381.85128811[/C][C]149531.148711886[/C][/ROW]
[ROW][C]57[/C][C]2693660[/C][C]2578225.15631599[/C][C]115434.843684014[/C][/ROW]
[ROW][C]58[/C][C]2602913[/C][C]2570844.70535524[/C][C]32068.2946447642[/C][/ROW]
[ROW][C]59[/C][C]2552092[/C][C]2523272.86173246[/C][C]28819.1382675408[/C][/ROW]
[ROW][C]60[/C][C]2744509[/C][C]2681546.74643984[/C][C]62962.2535601603[/C][/ROW]
[ROW][C]61[/C][C]2774634[/C][C]2730757.30672281[/C][C]43876.6932771914[/C][/ROW]
[ROW][C]62[/C][C]2703378[/C][C]2690605.4643927[/C][C]12772.5356073049[/C][/ROW]
[ROW][C]63[/C][C]2884967[/C][C]2709465.76468151[/C][C]175501.235318493[/C][/ROW]
[ROW][C]64[/C][C]2956228[/C][C]2839902.10592002[/C][C]116325.894079985[/C][/ROW]
[ROW][C]65[/C][C]3168103[/C][C]3212374.2200082[/C][C]-44271.2200081958[/C][/ROW]
[ROW][C]66[/C][C]3308711[/C][C]3369327.24536629[/C][C]-60616.245366286[/C][/ROW]
[ROW][C]67[/C][C]3289258[/C][C]3357319.42456467[/C][C]-68061.4245646675[/C][/ROW]
[ROW][C]68[/C][C]3278430[/C][C]3230661.12594817[/C][C]47768.8740518303[/C][/ROW]
[ROW][C]69[/C][C]3359559[/C][C]3324861.66586254[/C][C]34697.3341374639[/C][/ROW]
[ROW][C]70[/C][C]3349692[/C][C]3211948.28591922[/C][C]137743.714080782[/C][/ROW]
[ROW][C]71[/C][C]3228692[/C][C]3172763.15785803[/C][C]55928.8421419705[/C][/ROW]
[ROW][C]72[/C][C]3410253[/C][C]3410577.64309332[/C][C]-324.643093320541[/C][/ROW]
[ROW][C]73[/C][C]3470847[/C][C]3437322.81871315[/C][C]33524.1812868463[/C][/ROW]
[ROW][C]74[/C][C]3410253[/C][C]3353363.01894261[/C][C]56889.9810573924[/C][/ROW]
[ROW][C]75[/C][C]3662154[/C][C]3544049.42394826[/C][C]118104.576051739[/C][/ROW]
[ROW][C]76[/C][C]3783309[/C][C]3625072.41968732[/C][C]158236.580312677[/C][/ROW]
[ROW][C]77[/C][C]4065362[/C][C]3932372.68370228[/C][C]132989.316297722[/C][/ROW]
[ROW][C]78[/C][C]4176650[/C][C]4156003.18606622[/C][C]20646.8139337827[/C][/ROW]
[ROW][C]79[/C][C]4146492[/C][C]4159099.70073077[/C][C]-12607.7007307694[/C][/ROW]
[ROW][C]80[/C][C]4085897[/C][C]4135945.46397225[/C][C]-50048.4639722491[/C][/ROW]
[ROW][C]81[/C][C]4136624[/C][C]4221910.34482007[/C][C]-85286.3448200729[/C][/ROW]
[ROW][C]82[/C][C]4197185[/C][C]4154495.56813386[/C][C]42689.4318661448[/C][/ROW]
[ROW][C]83[/C][C]3995056[/C][C]3996870.72796679[/C][C]-1814.72796678776[/C][/ROW]
[ROW][C]84[/C][C]4156204[/C][C]4218518.4816093[/C][C]-62314.481609297[/C][/ROW]
[ROW][C]85[/C][C]4257779[/C][C]4266991.11993618[/C][C]-9212.11993618216[/C][/ROW]
[ROW][C]86[/C][C]4216798[/C][C]4170639.8462019[/C][C]46158.1537980959[/C][/ROW]
[ROW][C]87[/C][C]4479366[/C][C]4452085.33711816[/C][C]27280.6628818428[/C][/ROW]
[ROW][C]88[/C][C]4570080[/C][C]4554961.91694768[/C][C]15118.0830523213[/C][/ROW]
[ROW][C]89[/C][C]4953837[/C][C]4850975.31305938[/C][C]102861.686940623[/C][/ROW]
[ROW][C]90[/C][C]5024138[/C][C]4988148.89225694[/C][C]35989.1077430556[/C][/ROW]
[ROW][C]91[/C][C]4933418[/C][C]4950790.46115794[/C][C]-17372.4611579441[/C][/ROW]
[ROW][C]92[/C][C]4984117[/C][C]4875716.9448598[/C][C]108400.055140205[/C][/ROW]
[ROW][C]93[/C][C]5014398[/C][C]4973072.46443101[/C][C]41325.5355689898[/C][/ROW]
[ROW][C]94[/C][C]5044678[/C][C]5038471.25995533[/C][C]6206.74004466832[/C][/ROW]
[ROW][C]95[/C][C]4852261[/C][C]4791826.60969158[/C][C]60434.3903084174[/C][/ROW]
[ROW][C]96[/C][C]5033856[/C][C]5009926.65749895[/C][C]23929.3425010489[/C][/ROW]
[ROW][C]97[/C][C]5134437[/C][C]5137471.61691645[/C][C]-3034.61691644788[/C][/ROW]
[ROW][C]98[/C][C]5033856[/C][C]5073079.89708376[/C][C]-39223.8970837612[/C][/ROW]
[ROW][C]99[/C][C]5326854[/C][C]5368646.67093669[/C][C]-41792.670936686[/C][/ROW]
[ROW][C]100[/C][C]5417607[/C][C]5458539.43212698[/C][C]-40932.4321269765[/C][/ROW]
[ROW][C]101[/C][C]5811037[/C][C]5873320.69786637[/C][C]-62283.6978663662[/C][/ROW]
[ROW][C]102[/C][C]5871631[/C][C]5922973.98420792[/C][C]-51342.9842079151[/C][/ROW]
[ROW][C]103[/C][C]5891089[/C][C]5797258.91308682[/C][C]93830.0869131833[/C][/ROW]
[ROW][C]104[/C][C]5992631[/C][C]5839504.52016799[/C][C]153126.479832012[/C][/ROW]
[ROW][C]105[/C][C]5992631[/C][C]5888399.71979881[/C][C]104231.280201185[/C][/ROW]
[ROW][C]106[/C][C]6032657[/C][C]5937067.46662897[/C][C]95589.5333710331[/C][/ROW]
[ROW][C]107[/C][C]5851063[/C][C]5709285.84333886[/C][C]141777.156661144[/C][/ROW]
[ROW][C]108[/C][C]5941938[/C][C]5944184.7854314[/C][C]-2246.78543140274[/C][/ROW]
[ROW][C]109[/C][C]6002377[/C][C]6058449.76358427[/C][C]-56072.7635842711[/C][/ROW]
[ROW][C]110[/C][C]5891089[/C][C]5932231.32317341[/C][C]-41142.3231734065[/C][/ROW]
[ROW][C]111[/C][C]6214246[/C][C]6272990.86552201[/C][C]-58744.8655220084[/C][/ROW]
[ROW][C]112[/C][C]6274812[/C][C]6371476.91273965[/C][C]-96664.9127396466[/C][/ROW]
[ROW][C]113[/C][C]6678021[/C][C]6820306.42785883[/C][C]-142285.427858832[/C][/ROW]
[ROW][C]114[/C][C]6749283[/C][C]6864877.51799775[/C][C]-115594.51799775[/C][/ROW]
[ROW][C]115[/C][C]6849864[/C][C]6829622.00258264[/C][C]20241.9974173615[/C][/ROW]
[ROW][C]116[/C][C]6940739[/C][C]6901740.71562756[/C][C]38998.2843724443[/C][/ROW]
[ROW][C]117[/C][C]6950451[/C][C]6870274.85216252[/C][C]80176.1478374815[/C][/ROW]
[ROW][C]118[/C][C]6961152[/C][C]6895367.79868685[/C][C]65784.2013131538[/C][/ROW]
[ROW][C]119[/C][C]6779563[/C][C]6651730.43880333[/C][C]127832.561196665[/C][/ROW]
[ROW][C]120[/C][C]6961152[/C][C]6768513.49707714[/C][C]192638.502922857[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123037&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123037&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
1310691081008196.5820519760911.4179480321
1410494951000087.9912499749407.0087500295
1510797751035376.9481782744398.0518217288
1611295471085598.0739223343948.9260776711
1714126831358800.5982935953882.4017064096
1814126831360657.0019873252025.9980126815
1913522441273172.3471629179071.6528370872
2012916501195737.330664595912.6693354975
2113414221256521.7089523284900.2910476772
2214019831298993.11265369102989.887346313
2314126831354240.3757144658442.6242855424
2414429641408421.8497611834542.1502388178
2515338331581849.49354827-48016.4935482666
2614732441531955.86280381-58711.8628038121
2714732441551749.32605794-78505.3260579403
2815641141591892.63000426-27778.6300042579
2918160141964718.54770347-148704.547703471
3018364271911151.19166118-74724.1916611798
3117857341782299.21269293434.787307102
3216645781665431.29312591-853.293125909055
3317554201693578.4649678561841.5350321548
3417554201742206.8811943713213.1188056301
3517651651728792.5784098336372.4215901729
3618160141750859.2350915465154.7649084597
3718560401874721.0558947-18681.0558947015
3818764531799879.4633701576573.5366298498
3918764531827402.3433483649050.6566516396
4019370141952373.86299974-15359.862999738
4121694522293640.62322182-124188.623221816
4222298902306314.1668644-76424.1668644003
4322396032220842.3614459918760.6385540147
4420883222069922.7514434618399.248556542
4521694522166191.049399953260.95060004899
4621391712158191.92154122-19020.9215412238
4720785822150666.43917562-72084.439175623
4822094782171463.6827630638014.3172369446
4922396032223772.6672428415830.3327571559
5021889092223686.78010434-34777.7801043354
5121996102193793.417164965816.58283504471
5222699162258918.5602160110997.4397839936
5325326402551162.58696573-18522.5869657299
5426633522628072.8375713635279.1624286417
5526633522636173.0614799327178.938520065
5626029132453381.85128811149531.148711886
5726936602578225.15631599115434.843684014
5826029132570844.7053552432068.2946447642
5925520922523272.8617324628819.1382675408
6027445092681546.7464398462962.2535601603
6127746342730757.3067228143876.6932771914
6227033782690605.464392712772.5356073049
6328849672709465.76468151175501.235318493
6429562282839902.10592002116325.894079985
6531681033212374.2200082-44271.2200081958
6633087113369327.24536629-60616.245366286
6732892583357319.42456467-68061.4245646675
6832784303230661.1259481747768.8740518303
6933595593324861.6658625434697.3341374639
7033496923211948.28591922137743.714080782
7132286923172763.1578580355928.8421419705
7234102533410577.64309332-324.643093320541
7334708473437322.8187131533524.1812868463
7434102533353363.0189426156889.9810573924
7536621543544049.42394826118104.576051739
7637833093625072.41968732158236.580312677
7740653623932372.68370228132989.316297722
7841766504156003.1860662220646.8139337827
7941464924159099.70073077-12607.7007307694
8040858974135945.46397225-50048.4639722491
8141366244221910.34482007-85286.3448200729
8241971854154495.5681338642689.4318661448
8339950563996870.72796679-1814.72796678776
8441562044218518.4816093-62314.481609297
8542577794266991.11993618-9212.11993618216
8642167984170639.846201946158.1537980959
8744793664452085.3371181627280.6628818428
8845700804554961.9169476815118.0830523213
8949538374850975.31305938102861.686940623
9050241384988148.8922569435989.1077430556
9149334184950790.46115794-17372.4611579441
9249841174875716.9448598108400.055140205
9350143984973072.4644310141325.5355689898
9450446785038471.259955336206.74004466832
9548522614791826.6096915860434.3903084174
9650338565009926.6574989523929.3425010489
9751344375137471.61691645-3034.61691644788
9850338565073079.89708376-39223.8970837612
9953268545368646.67093669-41792.670936686
10054176075458539.43212698-40932.4321269765
10158110375873320.69786637-62283.6978663662
10258716315922973.98420792-51342.9842079151
10358910895797258.9130868293830.0869131833
10459926315839504.52016799153126.479832012
10559926315888399.71979881104231.280201185
10660326575937067.4666289795589.5333710331
10758510635709285.84333886141777.156661144
10859419385944184.7854314-2246.78543140274
10960023776058449.76358427-56072.7635842711
11058910895932231.32317341-41142.3231734065
11162142466272990.86552201-58744.8655220084
11262748126371476.91273965-96664.9127396466
11366780216820306.42785883-142285.427858832
11467492836864877.51799775-115594.51799775
11568498646829622.0025826420241.9974173615
11669407396901740.7156275638998.2843724443
11769504516870274.8521625280176.1478374815
11869611526895367.7986868565784.2013131538
11967795636651730.43880333127832.561196665
12069611526768513.49707714192638.502922857







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1216881996.355045366744536.275499317019456.4345914
1226755440.123519046614380.161814496896500.08522359
1237132048.493211726985859.158225497278237.82819796
1247218220.773220527066814.039736127369627.50670492
1257711802.367933977552392.268007157871212.4678608
1267820963.251267967654607.565366717987318.93716921
1277933891.344186197759873.628352588107909.06001981
1288030337.382368867848144.126808128212530.6379296
1298021473.840170157831681.429821468211266.25051884
1308015465.461798067817704.535465188213226.38813095
1317770967.064347197568306.587014347973627.54168003
1327924234.155420137760860.530513348087607.78032692

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 6881996.35504536 & 6744536.27549931 & 7019456.4345914 \tabularnewline
122 & 6755440.12351904 & 6614380.16181449 & 6896500.08522359 \tabularnewline
123 & 7132048.49321172 & 6985859.15822549 & 7278237.82819796 \tabularnewline
124 & 7218220.77322052 & 7066814.03973612 & 7369627.50670492 \tabularnewline
125 & 7711802.36793397 & 7552392.26800715 & 7871212.4678608 \tabularnewline
126 & 7820963.25126796 & 7654607.56536671 & 7987318.93716921 \tabularnewline
127 & 7933891.34418619 & 7759873.62835258 & 8107909.06001981 \tabularnewline
128 & 8030337.38236886 & 7848144.12680812 & 8212530.6379296 \tabularnewline
129 & 8021473.84017015 & 7831681.42982146 & 8211266.25051884 \tabularnewline
130 & 8015465.46179806 & 7817704.53546518 & 8213226.38813095 \tabularnewline
131 & 7770967.06434719 & 7568306.58701434 & 7973627.54168003 \tabularnewline
132 & 7924234.15542013 & 7760860.53051334 & 8087607.78032692 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123037&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]6881996.35504536[/C][C]6744536.27549931[/C][C]7019456.4345914[/C][/ROW]
[ROW][C]122[/C][C]6755440.12351904[/C][C]6614380.16181449[/C][C]6896500.08522359[/C][/ROW]
[ROW][C]123[/C][C]7132048.49321172[/C][C]6985859.15822549[/C][C]7278237.82819796[/C][/ROW]
[ROW][C]124[/C][C]7218220.77322052[/C][C]7066814.03973612[/C][C]7369627.50670492[/C][/ROW]
[ROW][C]125[/C][C]7711802.36793397[/C][C]7552392.26800715[/C][C]7871212.4678608[/C][/ROW]
[ROW][C]126[/C][C]7820963.25126796[/C][C]7654607.56536671[/C][C]7987318.93716921[/C][/ROW]
[ROW][C]127[/C][C]7933891.34418619[/C][C]7759873.62835258[/C][C]8107909.06001981[/C][/ROW]
[ROW][C]128[/C][C]8030337.38236886[/C][C]7848144.12680812[/C][C]8212530.6379296[/C][/ROW]
[ROW][C]129[/C][C]8021473.84017015[/C][C]7831681.42982146[/C][C]8211266.25051884[/C][/ROW]
[ROW][C]130[/C][C]8015465.46179806[/C][C]7817704.53546518[/C][C]8213226.38813095[/C][/ROW]
[ROW][C]131[/C][C]7770967.06434719[/C][C]7568306.58701434[/C][C]7973627.54168003[/C][/ROW]
[ROW][C]132[/C][C]7924234.15542013[/C][C]7760860.53051334[/C][C]8087607.78032692[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123037&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123037&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
1216881996.355045366744536.275499317019456.4345914
1226755440.123519046614380.161814496896500.08522359
1237132048.493211726985859.158225497278237.82819796
1247218220.773220527066814.039736127369627.50670492
1257711802.367933977552392.268007157871212.4678608
1267820963.251267967654607.565366717987318.93716921
1277933891.344186197759873.628352588107909.06001981
1288030337.382368867848144.126808128212530.6379296
1298021473.840170157831681.429821468211266.25051884
1308015465.461798067817704.535465188213226.38813095
1317770967.064347197568306.587014347973627.54168003
1327924234.155420137760860.530513348087607.78032692



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')