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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 17 Aug 2012 05:55:15 -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/2012/Aug/17/t1345197328x5rywop495zj9pp.htm/, Retrieved Sat, 04 May 2024 06:50:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169458, Retrieved Sat, 04 May 2024 06:50:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2012-08-17 09:53:12] [46972ec2bfa5b295f8450f947ab1f239]
-   PD    [Exponential Smoothing] [stap 32 reeks A] [2012-08-17 09:55:15] [7d6606cca1b3596736d7d387043cb02b] [Current]
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Dataseries X:
7175
7049
6923
6670
9225
9099
7175
5898
6024
6024
6150
6416
5645
4873
4240
4240
6670
6923
4999
2823
3974
3974
4873
5391
5265
3974
4620
4366
6543
6024
3974
2443
3848
4240
4620
5125
4100
3215
3595
3721
7049
7049
5125
4873
5645
5265
6290
7568
7821
6024
5518
4999
8466
8720
8074
8720
8593
7568
8720
9998
10516
8973
7948
8720
12048
13073
12820
13325
13199
11921
14098
14616
15375
13073
12174
13199
15641
17818
17299
17299
17553
16666
18970
18970
18578
16400
16793
17046
18716
20893
19349
20121
19475
19096
22045
21399
20500
19223
20500
21146
21918
22943
21918
22550
21779
21653
24854
25120
24095
22298
23829
24474
25246
26398
25246
26145
25753
24348
27296
27296




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169458&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169458&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169458&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.653336794717538
beta0.0529479297781898
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.653336794717538 \tabularnewline
beta & 0.0529479297781898 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169458&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]0.653336794717538[/C][/ROW]
[ROW][C]beta[/C][C]0.0529479297781898[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169458&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169458&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
alpha0.653336794717538
beta0.0529479297781898
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1356456814.02804487179-1169.02804487179
1448735266.03361772966-393.033617729662
1542404345.17875692662-105.178756926623
1642404199.0433039566140.9566960433949
1766706547.5919941447122.408005855303
1869236733.88192810384189.118071896157
1949994879.58979890093119.410201099067
2028233603.09402303204-780.094023032042
2139743162.97504671028811.024953289724
2239743675.03162465166298.968375348337
2348733983.55162831497889.448371685027
2453914838.03914375957552.960856240428
2552654033.764789933371231.23521006663
2639744425.94999741163-451.949997411632
2746203667.3441200697952.655879930305
2843664400.53677056496-34.5367705649587
2965436862.93346862741-319.933468627411
3060246902.9840182814-878.984018281397
3139744409.38031580656-435.380315806563
3224432522.08666661924-79.086666619241
3338483179.28602498548668.713975014515
3442403503.67352140846736.326478591538
3546204400.58190088295219.418099117054
3651254775.43644755026349.563552449745
3741004141.14212677648-41.1421267764772
3832153142.257104393172.7428956069025
3935953255.2472681885339.752731811499
4037213266.45200971549454.547990284506
4170495987.035707740921061.96429225908
4270496821.51887507965227.481124920355
4351255328.25662492925-203.256624929254
4448733847.827618736541025.17238126346
4556455655.61025401861-10.610254018613
4652655706.00449790705-441.004497907054
4762905760.19439865594529.805601344056
4875686499.358626926221068.64137307378
4978216340.70142465041480.2985753496
5060246569.22068461322-545.22068461322
5155186543.56922356257-1025.56922356257
5249995827.85807021621-828.85807021621
5384668001.42148288464464.578517115362
5487208216.5679024865503.432097513498
5580746824.061541903771249.93845809623
5687206838.967516258591881.03248374141
5785938996.51196910514-403.51196910514
5875688777.08028498333-1209.08028498333
5987208775.50530522676-55.5053052267613
6099989408.31450811527589.685491884733
61105169152.131361588321363.86863841168
6289738671.06917038019301.930829619811
6379489130.33867870405-1182.33867870405
6487208472.93857032505247.061429674948
651204811927.5875341226120.412465877391
661307312049.20191822491023.79808177512
671282011391.31222456261428.68777543739
681332511883.8183625691441.18163743103
691319913088.8484646643110.151535335683
701192113070.3441222664-1149.34412226638
711409813654.3583871948443.641612805235
721461615000.8688637835-384.868863783513
731537514506.5680318705868.431968129458
741307313446.7592356102-373.759235610238
751217413039.7350708864-865.735070886367
761319913185.357520700713.6424792993457
771564116536.1794863225-895.17948632253
781781816364.88735878021453.11264121982
791729916200.14275411931098.85724588067
801729916542.3775935297756.62240647032
811755316875.9479188945677.052081105521
821666616848.0175734487-182.017573448742
831897018706.5317828371263.468217162874
841897019732.1619221431-762.161922143117
851857819496.8309704276-918.830970427625
861640016847.8851000518-447.88510005179
871679316228.4871869293564.512813070658
881704617669.4726943093-623.472694309254
891871620323.03077076-1607.03077075995
902089320510.1435634687382.856436531343
911934919495.7477788162-146.747778816156
922012118834.84768288711286.15231711289
931947519434.418102675640.5818973243549
941909618618.4560460191477.543953980949
952204521010.74122061451034.25877938552
962139922159.4944100372-760.494410037212
972050021846.0846411751-1346.08464117508
981922319041.6210483364181.378951663552
992050019166.43684057691333.56315942306
1002114620706.7752420545439.224757945492
1012191823759.1658530859-1841.16585308592
1022294324520.5274464705-1577.52744647053
1032191822011.3284040947-93.3284040947146
1042255021853.4927783502696.507221649837
1052177921587.0653213658191.934678634178
1062165320977.73438806675.265611939951
1072485423655.29880975161198.70119024838
1082512024258.1097789864861.890221013608
1092409524826.5802707031-731.580270703118
1102229822999.2871367612-701.287136761217
1112382922962.4873660427866.512633957307
1122447423887.1364571295586.863542870498
1132524626250.050843411-1004.05084341104
1142639827683.2758301766-1285.27583017657
1152524625923.1941511181-677.194151118074
1162614525681.1683621497463.83163785033
1172575325103.2236057073649.776394292701
1182434824991.8235586498-643.823558649779
1192729626974.6563133233321.343686676715
1202729626842.7690618811453.230938118872

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5645 & 6814.02804487179 & -1169.02804487179 \tabularnewline
14 & 4873 & 5266.03361772966 & -393.033617729662 \tabularnewline
15 & 4240 & 4345.17875692662 & -105.178756926623 \tabularnewline
16 & 4240 & 4199.04330395661 & 40.9566960433949 \tabularnewline
17 & 6670 & 6547.5919941447 & 122.408005855303 \tabularnewline
18 & 6923 & 6733.88192810384 & 189.118071896157 \tabularnewline
19 & 4999 & 4879.58979890093 & 119.410201099067 \tabularnewline
20 & 2823 & 3603.09402303204 & -780.094023032042 \tabularnewline
21 & 3974 & 3162.97504671028 & 811.024953289724 \tabularnewline
22 & 3974 & 3675.03162465166 & 298.968375348337 \tabularnewline
23 & 4873 & 3983.55162831497 & 889.448371685027 \tabularnewline
24 & 5391 & 4838.03914375957 & 552.960856240428 \tabularnewline
25 & 5265 & 4033.76478993337 & 1231.23521006663 \tabularnewline
26 & 3974 & 4425.94999741163 & -451.949997411632 \tabularnewline
27 & 4620 & 3667.3441200697 & 952.655879930305 \tabularnewline
28 & 4366 & 4400.53677056496 & -34.5367705649587 \tabularnewline
29 & 6543 & 6862.93346862741 & -319.933468627411 \tabularnewline
30 & 6024 & 6902.9840182814 & -878.984018281397 \tabularnewline
31 & 3974 & 4409.38031580656 & -435.380315806563 \tabularnewline
32 & 2443 & 2522.08666661924 & -79.086666619241 \tabularnewline
33 & 3848 & 3179.28602498548 & 668.713975014515 \tabularnewline
34 & 4240 & 3503.67352140846 & 736.326478591538 \tabularnewline
35 & 4620 & 4400.58190088295 & 219.418099117054 \tabularnewline
36 & 5125 & 4775.43644755026 & 349.563552449745 \tabularnewline
37 & 4100 & 4141.14212677648 & -41.1421267764772 \tabularnewline
38 & 3215 & 3142.2571043931 & 72.7428956069025 \tabularnewline
39 & 3595 & 3255.2472681885 & 339.752731811499 \tabularnewline
40 & 3721 & 3266.45200971549 & 454.547990284506 \tabularnewline
41 & 7049 & 5987.03570774092 & 1061.96429225908 \tabularnewline
42 & 7049 & 6821.51887507965 & 227.481124920355 \tabularnewline
43 & 5125 & 5328.25662492925 & -203.256624929254 \tabularnewline
44 & 4873 & 3847.82761873654 & 1025.17238126346 \tabularnewline
45 & 5645 & 5655.61025401861 & -10.610254018613 \tabularnewline
46 & 5265 & 5706.00449790705 & -441.004497907054 \tabularnewline
47 & 6290 & 5760.19439865594 & 529.805601344056 \tabularnewline
48 & 7568 & 6499.35862692622 & 1068.64137307378 \tabularnewline
49 & 7821 & 6340.7014246504 & 1480.2985753496 \tabularnewline
50 & 6024 & 6569.22068461322 & -545.22068461322 \tabularnewline
51 & 5518 & 6543.56922356257 & -1025.56922356257 \tabularnewline
52 & 4999 & 5827.85807021621 & -828.85807021621 \tabularnewline
53 & 8466 & 8001.42148288464 & 464.578517115362 \tabularnewline
54 & 8720 & 8216.5679024865 & 503.432097513498 \tabularnewline
55 & 8074 & 6824.06154190377 & 1249.93845809623 \tabularnewline
56 & 8720 & 6838.96751625859 & 1881.03248374141 \tabularnewline
57 & 8593 & 8996.51196910514 & -403.51196910514 \tabularnewline
58 & 7568 & 8777.08028498333 & -1209.08028498333 \tabularnewline
59 & 8720 & 8775.50530522676 & -55.5053052267613 \tabularnewline
60 & 9998 & 9408.31450811527 & 589.685491884733 \tabularnewline
61 & 10516 & 9152.13136158832 & 1363.86863841168 \tabularnewline
62 & 8973 & 8671.06917038019 & 301.930829619811 \tabularnewline
63 & 7948 & 9130.33867870405 & -1182.33867870405 \tabularnewline
64 & 8720 & 8472.93857032505 & 247.061429674948 \tabularnewline
65 & 12048 & 11927.5875341226 & 120.412465877391 \tabularnewline
66 & 13073 & 12049.2019182249 & 1023.79808177512 \tabularnewline
67 & 12820 & 11391.3122245626 & 1428.68777543739 \tabularnewline
68 & 13325 & 11883.818362569 & 1441.18163743103 \tabularnewline
69 & 13199 & 13088.8484646643 & 110.151535335683 \tabularnewline
70 & 11921 & 13070.3441222664 & -1149.34412226638 \tabularnewline
71 & 14098 & 13654.3583871948 & 443.641612805235 \tabularnewline
72 & 14616 & 15000.8688637835 & -384.868863783513 \tabularnewline
73 & 15375 & 14506.5680318705 & 868.431968129458 \tabularnewline
74 & 13073 & 13446.7592356102 & -373.759235610238 \tabularnewline
75 & 12174 & 13039.7350708864 & -865.735070886367 \tabularnewline
76 & 13199 & 13185.3575207007 & 13.6424792993457 \tabularnewline
77 & 15641 & 16536.1794863225 & -895.17948632253 \tabularnewline
78 & 17818 & 16364.8873587802 & 1453.11264121982 \tabularnewline
79 & 17299 & 16200.1427541193 & 1098.85724588067 \tabularnewline
80 & 17299 & 16542.3775935297 & 756.62240647032 \tabularnewline
81 & 17553 & 16875.9479188945 & 677.052081105521 \tabularnewline
82 & 16666 & 16848.0175734487 & -182.017573448742 \tabularnewline
83 & 18970 & 18706.5317828371 & 263.468217162874 \tabularnewline
84 & 18970 & 19732.1619221431 & -762.161922143117 \tabularnewline
85 & 18578 & 19496.8309704276 & -918.830970427625 \tabularnewline
86 & 16400 & 16847.8851000518 & -447.88510005179 \tabularnewline
87 & 16793 & 16228.4871869293 & 564.512813070658 \tabularnewline
88 & 17046 & 17669.4726943093 & -623.472694309254 \tabularnewline
89 & 18716 & 20323.03077076 & -1607.03077075995 \tabularnewline
90 & 20893 & 20510.1435634687 & 382.856436531343 \tabularnewline
91 & 19349 & 19495.7477788162 & -146.747778816156 \tabularnewline
92 & 20121 & 18834.8476828871 & 1286.15231711289 \tabularnewline
93 & 19475 & 19434.4181026756 & 40.5818973243549 \tabularnewline
94 & 19096 & 18618.4560460191 & 477.543953980949 \tabularnewline
95 & 22045 & 21010.7412206145 & 1034.25877938552 \tabularnewline
96 & 21399 & 22159.4944100372 & -760.494410037212 \tabularnewline
97 & 20500 & 21846.0846411751 & -1346.08464117508 \tabularnewline
98 & 19223 & 19041.6210483364 & 181.378951663552 \tabularnewline
99 & 20500 & 19166.4368405769 & 1333.56315942306 \tabularnewline
100 & 21146 & 20706.7752420545 & 439.224757945492 \tabularnewline
101 & 21918 & 23759.1658530859 & -1841.16585308592 \tabularnewline
102 & 22943 & 24520.5274464705 & -1577.52744647053 \tabularnewline
103 & 21918 & 22011.3284040947 & -93.3284040947146 \tabularnewline
104 & 22550 & 21853.4927783502 & 696.507221649837 \tabularnewline
105 & 21779 & 21587.0653213658 & 191.934678634178 \tabularnewline
106 & 21653 & 20977.73438806 & 675.265611939951 \tabularnewline
107 & 24854 & 23655.2988097516 & 1198.70119024838 \tabularnewline
108 & 25120 & 24258.1097789864 & 861.890221013608 \tabularnewline
109 & 24095 & 24826.5802707031 & -731.580270703118 \tabularnewline
110 & 22298 & 22999.2871367612 & -701.287136761217 \tabularnewline
111 & 23829 & 22962.4873660427 & 866.512633957307 \tabularnewline
112 & 24474 & 23887.1364571295 & 586.863542870498 \tabularnewline
113 & 25246 & 26250.050843411 & -1004.05084341104 \tabularnewline
114 & 26398 & 27683.2758301766 & -1285.27583017657 \tabularnewline
115 & 25246 & 25923.1941511181 & -677.194151118074 \tabularnewline
116 & 26145 & 25681.1683621497 & 463.83163785033 \tabularnewline
117 & 25753 & 25103.2236057073 & 649.776394292701 \tabularnewline
118 & 24348 & 24991.8235586498 & -643.823558649779 \tabularnewline
119 & 27296 & 26974.6563133233 & 321.343686676715 \tabularnewline
120 & 27296 & 26842.7690618811 & 453.230938118872 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169458&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]5645[/C][C]6814.02804487179[/C][C]-1169.02804487179[/C][/ROW]
[ROW][C]14[/C][C]4873[/C][C]5266.03361772966[/C][C]-393.033617729662[/C][/ROW]
[ROW][C]15[/C][C]4240[/C][C]4345.17875692662[/C][C]-105.178756926623[/C][/ROW]
[ROW][C]16[/C][C]4240[/C][C]4199.04330395661[/C][C]40.9566960433949[/C][/ROW]
[ROW][C]17[/C][C]6670[/C][C]6547.5919941447[/C][C]122.408005855303[/C][/ROW]
[ROW][C]18[/C][C]6923[/C][C]6733.88192810384[/C][C]189.118071896157[/C][/ROW]
[ROW][C]19[/C][C]4999[/C][C]4879.58979890093[/C][C]119.410201099067[/C][/ROW]
[ROW][C]20[/C][C]2823[/C][C]3603.09402303204[/C][C]-780.094023032042[/C][/ROW]
[ROW][C]21[/C][C]3974[/C][C]3162.97504671028[/C][C]811.024953289724[/C][/ROW]
[ROW][C]22[/C][C]3974[/C][C]3675.03162465166[/C][C]298.968375348337[/C][/ROW]
[ROW][C]23[/C][C]4873[/C][C]3983.55162831497[/C][C]889.448371685027[/C][/ROW]
[ROW][C]24[/C][C]5391[/C][C]4838.03914375957[/C][C]552.960856240428[/C][/ROW]
[ROW][C]25[/C][C]5265[/C][C]4033.76478993337[/C][C]1231.23521006663[/C][/ROW]
[ROW][C]26[/C][C]3974[/C][C]4425.94999741163[/C][C]-451.949997411632[/C][/ROW]
[ROW][C]27[/C][C]4620[/C][C]3667.3441200697[/C][C]952.655879930305[/C][/ROW]
[ROW][C]28[/C][C]4366[/C][C]4400.53677056496[/C][C]-34.5367705649587[/C][/ROW]
[ROW][C]29[/C][C]6543[/C][C]6862.93346862741[/C][C]-319.933468627411[/C][/ROW]
[ROW][C]30[/C][C]6024[/C][C]6902.9840182814[/C][C]-878.984018281397[/C][/ROW]
[ROW][C]31[/C][C]3974[/C][C]4409.38031580656[/C][C]-435.380315806563[/C][/ROW]
[ROW][C]32[/C][C]2443[/C][C]2522.08666661924[/C][C]-79.086666619241[/C][/ROW]
[ROW][C]33[/C][C]3848[/C][C]3179.28602498548[/C][C]668.713975014515[/C][/ROW]
[ROW][C]34[/C][C]4240[/C][C]3503.67352140846[/C][C]736.326478591538[/C][/ROW]
[ROW][C]35[/C][C]4620[/C][C]4400.58190088295[/C][C]219.418099117054[/C][/ROW]
[ROW][C]36[/C][C]5125[/C][C]4775.43644755026[/C][C]349.563552449745[/C][/ROW]
[ROW][C]37[/C][C]4100[/C][C]4141.14212677648[/C][C]-41.1421267764772[/C][/ROW]
[ROW][C]38[/C][C]3215[/C][C]3142.2571043931[/C][C]72.7428956069025[/C][/ROW]
[ROW][C]39[/C][C]3595[/C][C]3255.2472681885[/C][C]339.752731811499[/C][/ROW]
[ROW][C]40[/C][C]3721[/C][C]3266.45200971549[/C][C]454.547990284506[/C][/ROW]
[ROW][C]41[/C][C]7049[/C][C]5987.03570774092[/C][C]1061.96429225908[/C][/ROW]
[ROW][C]42[/C][C]7049[/C][C]6821.51887507965[/C][C]227.481124920355[/C][/ROW]
[ROW][C]43[/C][C]5125[/C][C]5328.25662492925[/C][C]-203.256624929254[/C][/ROW]
[ROW][C]44[/C][C]4873[/C][C]3847.82761873654[/C][C]1025.17238126346[/C][/ROW]
[ROW][C]45[/C][C]5645[/C][C]5655.61025401861[/C][C]-10.610254018613[/C][/ROW]
[ROW][C]46[/C][C]5265[/C][C]5706.00449790705[/C][C]-441.004497907054[/C][/ROW]
[ROW][C]47[/C][C]6290[/C][C]5760.19439865594[/C][C]529.805601344056[/C][/ROW]
[ROW][C]48[/C][C]7568[/C][C]6499.35862692622[/C][C]1068.64137307378[/C][/ROW]
[ROW][C]49[/C][C]7821[/C][C]6340.7014246504[/C][C]1480.2985753496[/C][/ROW]
[ROW][C]50[/C][C]6024[/C][C]6569.22068461322[/C][C]-545.22068461322[/C][/ROW]
[ROW][C]51[/C][C]5518[/C][C]6543.56922356257[/C][C]-1025.56922356257[/C][/ROW]
[ROW][C]52[/C][C]4999[/C][C]5827.85807021621[/C][C]-828.85807021621[/C][/ROW]
[ROW][C]53[/C][C]8466[/C][C]8001.42148288464[/C][C]464.578517115362[/C][/ROW]
[ROW][C]54[/C][C]8720[/C][C]8216.5679024865[/C][C]503.432097513498[/C][/ROW]
[ROW][C]55[/C][C]8074[/C][C]6824.06154190377[/C][C]1249.93845809623[/C][/ROW]
[ROW][C]56[/C][C]8720[/C][C]6838.96751625859[/C][C]1881.03248374141[/C][/ROW]
[ROW][C]57[/C][C]8593[/C][C]8996.51196910514[/C][C]-403.51196910514[/C][/ROW]
[ROW][C]58[/C][C]7568[/C][C]8777.08028498333[/C][C]-1209.08028498333[/C][/ROW]
[ROW][C]59[/C][C]8720[/C][C]8775.50530522676[/C][C]-55.5053052267613[/C][/ROW]
[ROW][C]60[/C][C]9998[/C][C]9408.31450811527[/C][C]589.685491884733[/C][/ROW]
[ROW][C]61[/C][C]10516[/C][C]9152.13136158832[/C][C]1363.86863841168[/C][/ROW]
[ROW][C]62[/C][C]8973[/C][C]8671.06917038019[/C][C]301.930829619811[/C][/ROW]
[ROW][C]63[/C][C]7948[/C][C]9130.33867870405[/C][C]-1182.33867870405[/C][/ROW]
[ROW][C]64[/C][C]8720[/C][C]8472.93857032505[/C][C]247.061429674948[/C][/ROW]
[ROW][C]65[/C][C]12048[/C][C]11927.5875341226[/C][C]120.412465877391[/C][/ROW]
[ROW][C]66[/C][C]13073[/C][C]12049.2019182249[/C][C]1023.79808177512[/C][/ROW]
[ROW][C]67[/C][C]12820[/C][C]11391.3122245626[/C][C]1428.68777543739[/C][/ROW]
[ROW][C]68[/C][C]13325[/C][C]11883.818362569[/C][C]1441.18163743103[/C][/ROW]
[ROW][C]69[/C][C]13199[/C][C]13088.8484646643[/C][C]110.151535335683[/C][/ROW]
[ROW][C]70[/C][C]11921[/C][C]13070.3441222664[/C][C]-1149.34412226638[/C][/ROW]
[ROW][C]71[/C][C]14098[/C][C]13654.3583871948[/C][C]443.641612805235[/C][/ROW]
[ROW][C]72[/C][C]14616[/C][C]15000.8688637835[/C][C]-384.868863783513[/C][/ROW]
[ROW][C]73[/C][C]15375[/C][C]14506.5680318705[/C][C]868.431968129458[/C][/ROW]
[ROW][C]74[/C][C]13073[/C][C]13446.7592356102[/C][C]-373.759235610238[/C][/ROW]
[ROW][C]75[/C][C]12174[/C][C]13039.7350708864[/C][C]-865.735070886367[/C][/ROW]
[ROW][C]76[/C][C]13199[/C][C]13185.3575207007[/C][C]13.6424792993457[/C][/ROW]
[ROW][C]77[/C][C]15641[/C][C]16536.1794863225[/C][C]-895.17948632253[/C][/ROW]
[ROW][C]78[/C][C]17818[/C][C]16364.8873587802[/C][C]1453.11264121982[/C][/ROW]
[ROW][C]79[/C][C]17299[/C][C]16200.1427541193[/C][C]1098.85724588067[/C][/ROW]
[ROW][C]80[/C][C]17299[/C][C]16542.3775935297[/C][C]756.62240647032[/C][/ROW]
[ROW][C]81[/C][C]17553[/C][C]16875.9479188945[/C][C]677.052081105521[/C][/ROW]
[ROW][C]82[/C][C]16666[/C][C]16848.0175734487[/C][C]-182.017573448742[/C][/ROW]
[ROW][C]83[/C][C]18970[/C][C]18706.5317828371[/C][C]263.468217162874[/C][/ROW]
[ROW][C]84[/C][C]18970[/C][C]19732.1619221431[/C][C]-762.161922143117[/C][/ROW]
[ROW][C]85[/C][C]18578[/C][C]19496.8309704276[/C][C]-918.830970427625[/C][/ROW]
[ROW][C]86[/C][C]16400[/C][C]16847.8851000518[/C][C]-447.88510005179[/C][/ROW]
[ROW][C]87[/C][C]16793[/C][C]16228.4871869293[/C][C]564.512813070658[/C][/ROW]
[ROW][C]88[/C][C]17046[/C][C]17669.4726943093[/C][C]-623.472694309254[/C][/ROW]
[ROW][C]89[/C][C]18716[/C][C]20323.03077076[/C][C]-1607.03077075995[/C][/ROW]
[ROW][C]90[/C][C]20893[/C][C]20510.1435634687[/C][C]382.856436531343[/C][/ROW]
[ROW][C]91[/C][C]19349[/C][C]19495.7477788162[/C][C]-146.747778816156[/C][/ROW]
[ROW][C]92[/C][C]20121[/C][C]18834.8476828871[/C][C]1286.15231711289[/C][/ROW]
[ROW][C]93[/C][C]19475[/C][C]19434.4181026756[/C][C]40.5818973243549[/C][/ROW]
[ROW][C]94[/C][C]19096[/C][C]18618.4560460191[/C][C]477.543953980949[/C][/ROW]
[ROW][C]95[/C][C]22045[/C][C]21010.7412206145[/C][C]1034.25877938552[/C][/ROW]
[ROW][C]96[/C][C]21399[/C][C]22159.4944100372[/C][C]-760.494410037212[/C][/ROW]
[ROW][C]97[/C][C]20500[/C][C]21846.0846411751[/C][C]-1346.08464117508[/C][/ROW]
[ROW][C]98[/C][C]19223[/C][C]19041.6210483364[/C][C]181.378951663552[/C][/ROW]
[ROW][C]99[/C][C]20500[/C][C]19166.4368405769[/C][C]1333.56315942306[/C][/ROW]
[ROW][C]100[/C][C]21146[/C][C]20706.7752420545[/C][C]439.224757945492[/C][/ROW]
[ROW][C]101[/C][C]21918[/C][C]23759.1658530859[/C][C]-1841.16585308592[/C][/ROW]
[ROW][C]102[/C][C]22943[/C][C]24520.5274464705[/C][C]-1577.52744647053[/C][/ROW]
[ROW][C]103[/C][C]21918[/C][C]22011.3284040947[/C][C]-93.3284040947146[/C][/ROW]
[ROW][C]104[/C][C]22550[/C][C]21853.4927783502[/C][C]696.507221649837[/C][/ROW]
[ROW][C]105[/C][C]21779[/C][C]21587.0653213658[/C][C]191.934678634178[/C][/ROW]
[ROW][C]106[/C][C]21653[/C][C]20977.73438806[/C][C]675.265611939951[/C][/ROW]
[ROW][C]107[/C][C]24854[/C][C]23655.2988097516[/C][C]1198.70119024838[/C][/ROW]
[ROW][C]108[/C][C]25120[/C][C]24258.1097789864[/C][C]861.890221013608[/C][/ROW]
[ROW][C]109[/C][C]24095[/C][C]24826.5802707031[/C][C]-731.580270703118[/C][/ROW]
[ROW][C]110[/C][C]22298[/C][C]22999.2871367612[/C][C]-701.287136761217[/C][/ROW]
[ROW][C]111[/C][C]23829[/C][C]22962.4873660427[/C][C]866.512633957307[/C][/ROW]
[ROW][C]112[/C][C]24474[/C][C]23887.1364571295[/C][C]586.863542870498[/C][/ROW]
[ROW][C]113[/C][C]25246[/C][C]26250.050843411[/C][C]-1004.05084341104[/C][/ROW]
[ROW][C]114[/C][C]26398[/C][C]27683.2758301766[/C][C]-1285.27583017657[/C][/ROW]
[ROW][C]115[/C][C]25246[/C][C]25923.1941511181[/C][C]-677.194151118074[/C][/ROW]
[ROW][C]116[/C][C]26145[/C][C]25681.1683621497[/C][C]463.83163785033[/C][/ROW]
[ROW][C]117[/C][C]25753[/C][C]25103.2236057073[/C][C]649.776394292701[/C][/ROW]
[ROW][C]118[/C][C]24348[/C][C]24991.8235586498[/C][C]-643.823558649779[/C][/ROW]
[ROW][C]119[/C][C]27296[/C][C]26974.6563133233[/C][C]321.343686676715[/C][/ROW]
[ROW][C]120[/C][C]27296[/C][C]26842.7690618811[/C][C]453.230938118872[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169458&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169458&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
1356456814.02804487179-1169.02804487179
1448735266.03361772966-393.033617729662
1542404345.17875692662-105.178756926623
1642404199.0433039566140.9566960433949
1766706547.5919941447122.408005855303
1869236733.88192810384189.118071896157
1949994879.58979890093119.410201099067
2028233603.09402303204-780.094023032042
2139743162.97504671028811.024953289724
2239743675.03162465166298.968375348337
2348733983.55162831497889.448371685027
2453914838.03914375957552.960856240428
2552654033.764789933371231.23521006663
2639744425.94999741163-451.949997411632
2746203667.3441200697952.655879930305
2843664400.53677056496-34.5367705649587
2965436862.93346862741-319.933468627411
3060246902.9840182814-878.984018281397
3139744409.38031580656-435.380315806563
3224432522.08666661924-79.086666619241
3338483179.28602498548668.713975014515
3442403503.67352140846736.326478591538
3546204400.58190088295219.418099117054
3651254775.43644755026349.563552449745
3741004141.14212677648-41.1421267764772
3832153142.257104393172.7428956069025
3935953255.2472681885339.752731811499
4037213266.45200971549454.547990284506
4170495987.035707740921061.96429225908
4270496821.51887507965227.481124920355
4351255328.25662492925-203.256624929254
4448733847.827618736541025.17238126346
4556455655.61025401861-10.610254018613
4652655706.00449790705-441.004497907054
4762905760.19439865594529.805601344056
4875686499.358626926221068.64137307378
4978216340.70142465041480.2985753496
5060246569.22068461322-545.22068461322
5155186543.56922356257-1025.56922356257
5249995827.85807021621-828.85807021621
5384668001.42148288464464.578517115362
5487208216.5679024865503.432097513498
5580746824.061541903771249.93845809623
5687206838.967516258591881.03248374141
5785938996.51196910514-403.51196910514
5875688777.08028498333-1209.08028498333
5987208775.50530522676-55.5053052267613
6099989408.31450811527589.685491884733
61105169152.131361588321363.86863841168
6289738671.06917038019301.930829619811
6379489130.33867870405-1182.33867870405
6487208472.93857032505247.061429674948
651204811927.5875341226120.412465877391
661307312049.20191822491023.79808177512
671282011391.31222456261428.68777543739
681332511883.8183625691441.18163743103
691319913088.8484646643110.151535335683
701192113070.3441222664-1149.34412226638
711409813654.3583871948443.641612805235
721461615000.8688637835-384.868863783513
731537514506.5680318705868.431968129458
741307313446.7592356102-373.759235610238
751217413039.7350708864-865.735070886367
761319913185.357520700713.6424792993457
771564116536.1794863225-895.17948632253
781781816364.88735878021453.11264121982
791729916200.14275411931098.85724588067
801729916542.3775935297756.62240647032
811755316875.9479188945677.052081105521
821666616848.0175734487-182.017573448742
831897018706.5317828371263.468217162874
841897019732.1619221431-762.161922143117
851857819496.8309704276-918.830970427625
861640016847.8851000518-447.88510005179
871679316228.4871869293564.512813070658
881704617669.4726943093-623.472694309254
891871620323.03077076-1607.03077075995
902089320510.1435634687382.856436531343
911934919495.7477788162-146.747778816156
922012118834.84768288711286.15231711289
931947519434.418102675640.5818973243549
941909618618.4560460191477.543953980949
952204521010.74122061451034.25877938552
962139922159.4944100372-760.494410037212
972050021846.0846411751-1346.08464117508
981922319041.6210483364181.378951663552
992050019166.43684057691333.56315942306
1002114620706.7752420545439.224757945492
1012191823759.1658530859-1841.16585308592
1022294324520.5274464705-1577.52744647053
1032191822011.3284040947-93.3284040947146
1042255021853.4927783502696.507221649837
1052177921587.0653213658191.934678634178
1062165320977.73438806675.265611939951
1072485423655.29880975161198.70119024838
1082512024258.1097789864861.890221013608
1092409524826.5802707031-731.580270703118
1102229822999.2871367612-701.287136761217
1112382922962.4873660427866.512633957307
1122447423887.1364571295586.863542870498
1132524626250.050843411-1004.05084341104
1142639827683.2758301766-1285.27583017657
1152524625923.1941511181-677.194151118074
1162614525681.1683621497463.83163785033
1172575325103.2236057073649.776394292701
1182434824991.8235586498-643.823558649779
1192729626974.6563133233321.343686676715
1202729626842.7690618811453.230938118872







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12126532.984826696824963.404755581628102.5648978119
12225160.60395657223255.488574589327065.7193385547
12326116.18131670123899.077450507728333.2851828942
12426338.488592775923822.99012077828853.9870647738
12527706.89750345524901.205110374930512.5898965351
12629673.774006450626582.823111030732764.7249018704
12728983.82970355625610.429101631132357.2303054809
12829622.837331646525968.337569351333277.3370939417
12928833.315159233824898.028095872732768.602222595
13027853.471828904423636.947780009432069.9958777994
13130618.320903530326119.539177030535117.10263003
13230337.88699627625555.391169523135120.3828230289

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 26532.9848266968 & 24963.4047555816 & 28102.5648978119 \tabularnewline
122 & 25160.603956572 & 23255.4885745893 & 27065.7193385547 \tabularnewline
123 & 26116.181316701 & 23899.0774505077 & 28333.2851828942 \tabularnewline
124 & 26338.4885927759 & 23822.990120778 & 28853.9870647738 \tabularnewline
125 & 27706.897503455 & 24901.2051103749 & 30512.5898965351 \tabularnewline
126 & 29673.7740064506 & 26582.8231110307 & 32764.7249018704 \tabularnewline
127 & 28983.829703556 & 25610.4291016311 & 32357.2303054809 \tabularnewline
128 & 29622.8373316465 & 25968.3375693513 & 33277.3370939417 \tabularnewline
129 & 28833.3151592338 & 24898.0280958727 & 32768.602222595 \tabularnewline
130 & 27853.4718289044 & 23636.9477800094 & 32069.9958777994 \tabularnewline
131 & 30618.3209035303 & 26119.5391770305 & 35117.10263003 \tabularnewline
132 & 30337.886996276 & 25555.3911695231 & 35120.3828230289 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169458&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]26532.9848266968[/C][C]24963.4047555816[/C][C]28102.5648978119[/C][/ROW]
[ROW][C]122[/C][C]25160.603956572[/C][C]23255.4885745893[/C][C]27065.7193385547[/C][/ROW]
[ROW][C]123[/C][C]26116.181316701[/C][C]23899.0774505077[/C][C]28333.2851828942[/C][/ROW]
[ROW][C]124[/C][C]26338.4885927759[/C][C]23822.990120778[/C][C]28853.9870647738[/C][/ROW]
[ROW][C]125[/C][C]27706.897503455[/C][C]24901.2051103749[/C][C]30512.5898965351[/C][/ROW]
[ROW][C]126[/C][C]29673.7740064506[/C][C]26582.8231110307[/C][C]32764.7249018704[/C][/ROW]
[ROW][C]127[/C][C]28983.829703556[/C][C]25610.4291016311[/C][C]32357.2303054809[/C][/ROW]
[ROW][C]128[/C][C]29622.8373316465[/C][C]25968.3375693513[/C][C]33277.3370939417[/C][/ROW]
[ROW][C]129[/C][C]28833.3151592338[/C][C]24898.0280958727[/C][C]32768.602222595[/C][/ROW]
[ROW][C]130[/C][C]27853.4718289044[/C][C]23636.9477800094[/C][C]32069.9958777994[/C][/ROW]
[ROW][C]131[/C][C]30618.3209035303[/C][C]26119.5391770305[/C][C]35117.10263003[/C][/ROW]
[ROW][C]132[/C][C]30337.886996276[/C][C]25555.3911695231[/C][C]35120.3828230289[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169458&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169458&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
12126532.984826696824963.404755581628102.5648978119
12225160.60395657223255.488574589327065.7193385547
12326116.18131670123899.077450507728333.2851828942
12426338.488592775923822.99012077828853.9870647738
12527706.89750345524901.205110374930512.5898965351
12629673.774006450626582.823111030732764.7249018704
12728983.82970355625610.429101631132357.2303054809
12829622.837331646525968.337569351333277.3370939417
12928833.315159233824898.028095872732768.602222595
13027853.471828904423636.947780009432069.9958777994
13130618.320903530326119.539177030535117.10263003
13230337.88699627625555.391169523135120.3828230289



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')