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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, 28 May 2010 14:49:02 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/May/28/t1275058186ul19gd6fpj57mps.htm/, Retrieved Sat, 27 Apr 2024 20:50:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76639, Retrieved Sat, 27 Apr 2024 20:50:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact201
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-05-28 14:49:02] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
6550
8728
12026
14395
14587
13791
9498
8251
7049
9545
9364
8456
7237
9374
11837
13784
15926
13821
11143
7975
7610
10015
12759
8816
10677
10947
15200
17010
20900
16205
12143
8997
5568
11474
12256
10583
10862
10965
14405
20379
20128
17816
12268
8642
7962
13932
15936
12628
12267
12470
18944
21259
22015
18581
15175
10306
10792
14752
13754
11738
12181
12965
19990
23125
23541
21247
15189
14767
10895
17130
17697
16611
12674
12760
20249
22135
20677
19933
15388
15113
13401
16135
17562
14720
12225
11608
20985
19692
24081
22114
14220
13434
13598
17187
16119
13713
13210
14251
20139
21725
26099
21084
18024
16722
14385
21342
17180
14577




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76639&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76639&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76639&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.137145889450086
beta0.00517785985442284
gamma0.51043125305572

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.137145889450086 \tabularnewline
beta & 0.00517785985442284 \tabularnewline
gamma & 0.51043125305572 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76639&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]0.137145889450086[/C][/ROW]
[ROW][C]beta[/C][C]0.00517785985442284[/C][/ROW]
[ROW][C]gamma[/C][C]0.51043125305572[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76639&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76639&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
alpha0.137145889450086
beta0.00517785985442284
gamma0.51043125305572







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1372377055.55795940171181.442040598286
1493749209.65373173377164.346268266230
151183711732.6882617630104.311738237036
161378413700.480043520883.519956479202
171592615742.3962939177183.603706082293
181382113555.7523335736265.247666426436
19111439946.74386504421196.25613495580
2079758858.93553571608-883.93553571608
2176107566.7097672439843.2902327560214
221001510152.0549428651-137.054942865141
23127599971.902526544162787.09747345584
2488169441.05644068983-625.05644068983
25106778197.965706392052479.03429360795
261094710663.6571207825283.342879217487
271520013180.67493942082019.32506057923
281701015407.40980615611602.59019384390
292090017708.28283331143191.71716668865
301620515978.8265410794226.173458920628
311214312783.1523910586-640.152391058584
32899710534.6613258750-1537.66132587503
3355689568.03863235537-4000.03863235537
341147411523.4405678943-49.4405678942767
351225612647.2557624707-391.255762470704
361058310179.5213810568403.478618943216
371086210447.1648486553414.835151344701
381096511663.7979604003-698.797960400292
391440514811.0778627426-406.07786274265
402037916520.29878986503858.70121013496
412012819830.747511393297.252488606988
421781616396.42805091771419.57194908227
431226812981.9255246590-713.925524658989
44864210327.0324213861-1685.03242138608
4579628254.59799501542-292.597995015418
461393212459.94454124961472.05545875042
471593613644.49375674192291.50624325811
481262811899.2292618824728.77073811762
491226712221.235000673145.7649993269042
501247012901.2627604665-431.262760466518
511894416218.83201699172725.16798300832
522125920242.71682711281016.2831728872
532201521599.6599758524415.340024147561
541858118680.8012396306-99.801239630564
551517514122.15750977771052.8424902223
561030611287.0075962935-981.007596293519
57107929930.0345236007861.965476399306
581475215077.387399979-325.387399978985
591375416381.5175654954-2627.51756549536
601173813275.0480767129-1537.04807671289
611218112985.5733340186-804.573334018613
621296513338.3625063755-373.362506375493
631999018053.57126989691936.42873010306
642312521215.60259488171909.39740511827
652354122429.95397390041111.04602609963
662124719379.71330417001867.28669582996
671518915599.9880366453-410.988036645305
681476711668.76056472623098.23943527378
691089511686.2773256260-791.277325625988
701713016086.11911149381043.88088850617
711769716567.25670330681129.74329669315
721661114462.16099989862148.83900010144
731267415009.2180471533-2335.21804715328
741276015349.3411978374-2589.34119783743
752024920783.6984438491-534.698443849062
762213523598.9294861054-1463.92948610542
772067724000.6414043071-3323.6414043071
781993320673.7362766254-740.736276625386
791538815529.5294040313-141.529404031309
801511313177.62276241091935.37723758906
811340111318.58572385432082.41427614568
821613516918.8166038724-783.81660387242
831756217183.8308753920378.169124608034
841472015420.6858304150-700.68583041495
851222513596.2037807742-1371.20378077415
861160813951.4636916296-2343.46369162962
872098520319.4872646026665.512735397373
881969222885.9391831898-3193.9391831898
892408122225.96615446741855.03384553261
902211420745.20294313051368.79705686955
911422016154.0401457494-1934.0401457494
921343414469.5752900437-1035.57529004371
931359812264.28381123511333.71618876487
941718716495.3749721818691.625027818169
951611917471.4670840425-1352.46708404247
961371314991.5421999882-1278.54219998819
971321012787.8119087772422.18809122283
981425112957.40853551351293.59146448652
992013921148.6492016738-1009.64920167382
1002172521783.5337733780-58.5337733780252
1012609923777.48660968512321.51339031487
1022108422147.0885534734-1063.08855347341
1031802415766.55625231422257.44374768581
1041672215054.43608326511667.56391673492
1051438514267.0812882495117.918711750523
1062134218051.48336655913290.51663344086
1071718018488.4207925968-1308.42079259681
1081457716051.8193322975-1474.81933229747

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7237 & 7055.55795940171 & 181.442040598286 \tabularnewline
14 & 9374 & 9209.65373173377 & 164.346268266230 \tabularnewline
15 & 11837 & 11732.6882617630 & 104.311738237036 \tabularnewline
16 & 13784 & 13700.4800435208 & 83.519956479202 \tabularnewline
17 & 15926 & 15742.3962939177 & 183.603706082293 \tabularnewline
18 & 13821 & 13555.7523335736 & 265.247666426436 \tabularnewline
19 & 11143 & 9946.7438650442 & 1196.25613495580 \tabularnewline
20 & 7975 & 8858.93553571608 & -883.93553571608 \tabularnewline
21 & 7610 & 7566.70976724398 & 43.2902327560214 \tabularnewline
22 & 10015 & 10152.0549428651 & -137.054942865141 \tabularnewline
23 & 12759 & 9971.90252654416 & 2787.09747345584 \tabularnewline
24 & 8816 & 9441.05644068983 & -625.05644068983 \tabularnewline
25 & 10677 & 8197.96570639205 & 2479.03429360795 \tabularnewline
26 & 10947 & 10663.6571207825 & 283.342879217487 \tabularnewline
27 & 15200 & 13180.6749394208 & 2019.32506057923 \tabularnewline
28 & 17010 & 15407.4098061561 & 1602.59019384390 \tabularnewline
29 & 20900 & 17708.2828333114 & 3191.71716668865 \tabularnewline
30 & 16205 & 15978.8265410794 & 226.173458920628 \tabularnewline
31 & 12143 & 12783.1523910586 & -640.152391058584 \tabularnewline
32 & 8997 & 10534.6613258750 & -1537.66132587503 \tabularnewline
33 & 5568 & 9568.03863235537 & -4000.03863235537 \tabularnewline
34 & 11474 & 11523.4405678943 & -49.4405678942767 \tabularnewline
35 & 12256 & 12647.2557624707 & -391.255762470704 \tabularnewline
36 & 10583 & 10179.5213810568 & 403.478618943216 \tabularnewline
37 & 10862 & 10447.1648486553 & 414.835151344701 \tabularnewline
38 & 10965 & 11663.7979604003 & -698.797960400292 \tabularnewline
39 & 14405 & 14811.0778627426 & -406.07786274265 \tabularnewline
40 & 20379 & 16520.2987898650 & 3858.70121013496 \tabularnewline
41 & 20128 & 19830.747511393 & 297.252488606988 \tabularnewline
42 & 17816 & 16396.4280509177 & 1419.57194908227 \tabularnewline
43 & 12268 & 12981.9255246590 & -713.925524658989 \tabularnewline
44 & 8642 & 10327.0324213861 & -1685.03242138608 \tabularnewline
45 & 7962 & 8254.59799501542 & -292.597995015418 \tabularnewline
46 & 13932 & 12459.9445412496 & 1472.05545875042 \tabularnewline
47 & 15936 & 13644.4937567419 & 2291.50624325811 \tabularnewline
48 & 12628 & 11899.2292618824 & 728.77073811762 \tabularnewline
49 & 12267 & 12221.2350006731 & 45.7649993269042 \tabularnewline
50 & 12470 & 12901.2627604665 & -431.262760466518 \tabularnewline
51 & 18944 & 16218.8320169917 & 2725.16798300832 \tabularnewline
52 & 21259 & 20242.7168271128 & 1016.2831728872 \tabularnewline
53 & 22015 & 21599.6599758524 & 415.340024147561 \tabularnewline
54 & 18581 & 18680.8012396306 & -99.801239630564 \tabularnewline
55 & 15175 & 14122.1575097777 & 1052.8424902223 \tabularnewline
56 & 10306 & 11287.0075962935 & -981.007596293519 \tabularnewline
57 & 10792 & 9930.0345236007 & 861.965476399306 \tabularnewline
58 & 14752 & 15077.387399979 & -325.387399978985 \tabularnewline
59 & 13754 & 16381.5175654954 & -2627.51756549536 \tabularnewline
60 & 11738 & 13275.0480767129 & -1537.04807671289 \tabularnewline
61 & 12181 & 12985.5733340186 & -804.573334018613 \tabularnewline
62 & 12965 & 13338.3625063755 & -373.362506375493 \tabularnewline
63 & 19990 & 18053.5712698969 & 1936.42873010306 \tabularnewline
64 & 23125 & 21215.6025948817 & 1909.39740511827 \tabularnewline
65 & 23541 & 22429.9539739004 & 1111.04602609963 \tabularnewline
66 & 21247 & 19379.7133041700 & 1867.28669582996 \tabularnewline
67 & 15189 & 15599.9880366453 & -410.988036645305 \tabularnewline
68 & 14767 & 11668.7605647262 & 3098.23943527378 \tabularnewline
69 & 10895 & 11686.2773256260 & -791.277325625988 \tabularnewline
70 & 17130 & 16086.1191114938 & 1043.88088850617 \tabularnewline
71 & 17697 & 16567.2567033068 & 1129.74329669315 \tabularnewline
72 & 16611 & 14462.1609998986 & 2148.83900010144 \tabularnewline
73 & 12674 & 15009.2180471533 & -2335.21804715328 \tabularnewline
74 & 12760 & 15349.3411978374 & -2589.34119783743 \tabularnewline
75 & 20249 & 20783.6984438491 & -534.698443849062 \tabularnewline
76 & 22135 & 23598.9294861054 & -1463.92948610542 \tabularnewline
77 & 20677 & 24000.6414043071 & -3323.6414043071 \tabularnewline
78 & 19933 & 20673.7362766254 & -740.736276625386 \tabularnewline
79 & 15388 & 15529.5294040313 & -141.529404031309 \tabularnewline
80 & 15113 & 13177.6227624109 & 1935.37723758906 \tabularnewline
81 & 13401 & 11318.5857238543 & 2082.41427614568 \tabularnewline
82 & 16135 & 16918.8166038724 & -783.81660387242 \tabularnewline
83 & 17562 & 17183.8308753920 & 378.169124608034 \tabularnewline
84 & 14720 & 15420.6858304150 & -700.68583041495 \tabularnewline
85 & 12225 & 13596.2037807742 & -1371.20378077415 \tabularnewline
86 & 11608 & 13951.4636916296 & -2343.46369162962 \tabularnewline
87 & 20985 & 20319.4872646026 & 665.512735397373 \tabularnewline
88 & 19692 & 22885.9391831898 & -3193.9391831898 \tabularnewline
89 & 24081 & 22225.9661544674 & 1855.03384553261 \tabularnewline
90 & 22114 & 20745.2029431305 & 1368.79705686955 \tabularnewline
91 & 14220 & 16154.0401457494 & -1934.0401457494 \tabularnewline
92 & 13434 & 14469.5752900437 & -1035.57529004371 \tabularnewline
93 & 13598 & 12264.2838112351 & 1333.71618876487 \tabularnewline
94 & 17187 & 16495.3749721818 & 691.625027818169 \tabularnewline
95 & 16119 & 17471.4670840425 & -1352.46708404247 \tabularnewline
96 & 13713 & 14991.5421999882 & -1278.54219998819 \tabularnewline
97 & 13210 & 12787.8119087772 & 422.18809122283 \tabularnewline
98 & 14251 & 12957.4085355135 & 1293.59146448652 \tabularnewline
99 & 20139 & 21148.6492016738 & -1009.64920167382 \tabularnewline
100 & 21725 & 21783.5337733780 & -58.5337733780252 \tabularnewline
101 & 26099 & 23777.4866096851 & 2321.51339031487 \tabularnewline
102 & 21084 & 22147.0885534734 & -1063.08855347341 \tabularnewline
103 & 18024 & 15766.5562523142 & 2257.44374768581 \tabularnewline
104 & 16722 & 15054.4360832651 & 1667.56391673492 \tabularnewline
105 & 14385 & 14267.0812882495 & 117.918711750523 \tabularnewline
106 & 21342 & 18051.4833665591 & 3290.51663344086 \tabularnewline
107 & 17180 & 18488.4207925968 & -1308.42079259681 \tabularnewline
108 & 14577 & 16051.8193322975 & -1474.81933229747 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76639&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]7237[/C][C]7055.55795940171[/C][C]181.442040598286[/C][/ROW]
[ROW][C]14[/C][C]9374[/C][C]9209.65373173377[/C][C]164.346268266230[/C][/ROW]
[ROW][C]15[/C][C]11837[/C][C]11732.6882617630[/C][C]104.311738237036[/C][/ROW]
[ROW][C]16[/C][C]13784[/C][C]13700.4800435208[/C][C]83.519956479202[/C][/ROW]
[ROW][C]17[/C][C]15926[/C][C]15742.3962939177[/C][C]183.603706082293[/C][/ROW]
[ROW][C]18[/C][C]13821[/C][C]13555.7523335736[/C][C]265.247666426436[/C][/ROW]
[ROW][C]19[/C][C]11143[/C][C]9946.7438650442[/C][C]1196.25613495580[/C][/ROW]
[ROW][C]20[/C][C]7975[/C][C]8858.93553571608[/C][C]-883.93553571608[/C][/ROW]
[ROW][C]21[/C][C]7610[/C][C]7566.70976724398[/C][C]43.2902327560214[/C][/ROW]
[ROW][C]22[/C][C]10015[/C][C]10152.0549428651[/C][C]-137.054942865141[/C][/ROW]
[ROW][C]23[/C][C]12759[/C][C]9971.90252654416[/C][C]2787.09747345584[/C][/ROW]
[ROW][C]24[/C][C]8816[/C][C]9441.05644068983[/C][C]-625.05644068983[/C][/ROW]
[ROW][C]25[/C][C]10677[/C][C]8197.96570639205[/C][C]2479.03429360795[/C][/ROW]
[ROW][C]26[/C][C]10947[/C][C]10663.6571207825[/C][C]283.342879217487[/C][/ROW]
[ROW][C]27[/C][C]15200[/C][C]13180.6749394208[/C][C]2019.32506057923[/C][/ROW]
[ROW][C]28[/C][C]17010[/C][C]15407.4098061561[/C][C]1602.59019384390[/C][/ROW]
[ROW][C]29[/C][C]20900[/C][C]17708.2828333114[/C][C]3191.71716668865[/C][/ROW]
[ROW][C]30[/C][C]16205[/C][C]15978.8265410794[/C][C]226.173458920628[/C][/ROW]
[ROW][C]31[/C][C]12143[/C][C]12783.1523910586[/C][C]-640.152391058584[/C][/ROW]
[ROW][C]32[/C][C]8997[/C][C]10534.6613258750[/C][C]-1537.66132587503[/C][/ROW]
[ROW][C]33[/C][C]5568[/C][C]9568.03863235537[/C][C]-4000.03863235537[/C][/ROW]
[ROW][C]34[/C][C]11474[/C][C]11523.4405678943[/C][C]-49.4405678942767[/C][/ROW]
[ROW][C]35[/C][C]12256[/C][C]12647.2557624707[/C][C]-391.255762470704[/C][/ROW]
[ROW][C]36[/C][C]10583[/C][C]10179.5213810568[/C][C]403.478618943216[/C][/ROW]
[ROW][C]37[/C][C]10862[/C][C]10447.1648486553[/C][C]414.835151344701[/C][/ROW]
[ROW][C]38[/C][C]10965[/C][C]11663.7979604003[/C][C]-698.797960400292[/C][/ROW]
[ROW][C]39[/C][C]14405[/C][C]14811.0778627426[/C][C]-406.07786274265[/C][/ROW]
[ROW][C]40[/C][C]20379[/C][C]16520.2987898650[/C][C]3858.70121013496[/C][/ROW]
[ROW][C]41[/C][C]20128[/C][C]19830.747511393[/C][C]297.252488606988[/C][/ROW]
[ROW][C]42[/C][C]17816[/C][C]16396.4280509177[/C][C]1419.57194908227[/C][/ROW]
[ROW][C]43[/C][C]12268[/C][C]12981.9255246590[/C][C]-713.925524658989[/C][/ROW]
[ROW][C]44[/C][C]8642[/C][C]10327.0324213861[/C][C]-1685.03242138608[/C][/ROW]
[ROW][C]45[/C][C]7962[/C][C]8254.59799501542[/C][C]-292.597995015418[/C][/ROW]
[ROW][C]46[/C][C]13932[/C][C]12459.9445412496[/C][C]1472.05545875042[/C][/ROW]
[ROW][C]47[/C][C]15936[/C][C]13644.4937567419[/C][C]2291.50624325811[/C][/ROW]
[ROW][C]48[/C][C]12628[/C][C]11899.2292618824[/C][C]728.77073811762[/C][/ROW]
[ROW][C]49[/C][C]12267[/C][C]12221.2350006731[/C][C]45.7649993269042[/C][/ROW]
[ROW][C]50[/C][C]12470[/C][C]12901.2627604665[/C][C]-431.262760466518[/C][/ROW]
[ROW][C]51[/C][C]18944[/C][C]16218.8320169917[/C][C]2725.16798300832[/C][/ROW]
[ROW][C]52[/C][C]21259[/C][C]20242.7168271128[/C][C]1016.2831728872[/C][/ROW]
[ROW][C]53[/C][C]22015[/C][C]21599.6599758524[/C][C]415.340024147561[/C][/ROW]
[ROW][C]54[/C][C]18581[/C][C]18680.8012396306[/C][C]-99.801239630564[/C][/ROW]
[ROW][C]55[/C][C]15175[/C][C]14122.1575097777[/C][C]1052.8424902223[/C][/ROW]
[ROW][C]56[/C][C]10306[/C][C]11287.0075962935[/C][C]-981.007596293519[/C][/ROW]
[ROW][C]57[/C][C]10792[/C][C]9930.0345236007[/C][C]861.965476399306[/C][/ROW]
[ROW][C]58[/C][C]14752[/C][C]15077.387399979[/C][C]-325.387399978985[/C][/ROW]
[ROW][C]59[/C][C]13754[/C][C]16381.5175654954[/C][C]-2627.51756549536[/C][/ROW]
[ROW][C]60[/C][C]11738[/C][C]13275.0480767129[/C][C]-1537.04807671289[/C][/ROW]
[ROW][C]61[/C][C]12181[/C][C]12985.5733340186[/C][C]-804.573334018613[/C][/ROW]
[ROW][C]62[/C][C]12965[/C][C]13338.3625063755[/C][C]-373.362506375493[/C][/ROW]
[ROW][C]63[/C][C]19990[/C][C]18053.5712698969[/C][C]1936.42873010306[/C][/ROW]
[ROW][C]64[/C][C]23125[/C][C]21215.6025948817[/C][C]1909.39740511827[/C][/ROW]
[ROW][C]65[/C][C]23541[/C][C]22429.9539739004[/C][C]1111.04602609963[/C][/ROW]
[ROW][C]66[/C][C]21247[/C][C]19379.7133041700[/C][C]1867.28669582996[/C][/ROW]
[ROW][C]67[/C][C]15189[/C][C]15599.9880366453[/C][C]-410.988036645305[/C][/ROW]
[ROW][C]68[/C][C]14767[/C][C]11668.7605647262[/C][C]3098.23943527378[/C][/ROW]
[ROW][C]69[/C][C]10895[/C][C]11686.2773256260[/C][C]-791.277325625988[/C][/ROW]
[ROW][C]70[/C][C]17130[/C][C]16086.1191114938[/C][C]1043.88088850617[/C][/ROW]
[ROW][C]71[/C][C]17697[/C][C]16567.2567033068[/C][C]1129.74329669315[/C][/ROW]
[ROW][C]72[/C][C]16611[/C][C]14462.1609998986[/C][C]2148.83900010144[/C][/ROW]
[ROW][C]73[/C][C]12674[/C][C]15009.2180471533[/C][C]-2335.21804715328[/C][/ROW]
[ROW][C]74[/C][C]12760[/C][C]15349.3411978374[/C][C]-2589.34119783743[/C][/ROW]
[ROW][C]75[/C][C]20249[/C][C]20783.6984438491[/C][C]-534.698443849062[/C][/ROW]
[ROW][C]76[/C][C]22135[/C][C]23598.9294861054[/C][C]-1463.92948610542[/C][/ROW]
[ROW][C]77[/C][C]20677[/C][C]24000.6414043071[/C][C]-3323.6414043071[/C][/ROW]
[ROW][C]78[/C][C]19933[/C][C]20673.7362766254[/C][C]-740.736276625386[/C][/ROW]
[ROW][C]79[/C][C]15388[/C][C]15529.5294040313[/C][C]-141.529404031309[/C][/ROW]
[ROW][C]80[/C][C]15113[/C][C]13177.6227624109[/C][C]1935.37723758906[/C][/ROW]
[ROW][C]81[/C][C]13401[/C][C]11318.5857238543[/C][C]2082.41427614568[/C][/ROW]
[ROW][C]82[/C][C]16135[/C][C]16918.8166038724[/C][C]-783.81660387242[/C][/ROW]
[ROW][C]83[/C][C]17562[/C][C]17183.8308753920[/C][C]378.169124608034[/C][/ROW]
[ROW][C]84[/C][C]14720[/C][C]15420.6858304150[/C][C]-700.68583041495[/C][/ROW]
[ROW][C]85[/C][C]12225[/C][C]13596.2037807742[/C][C]-1371.20378077415[/C][/ROW]
[ROW][C]86[/C][C]11608[/C][C]13951.4636916296[/C][C]-2343.46369162962[/C][/ROW]
[ROW][C]87[/C][C]20985[/C][C]20319.4872646026[/C][C]665.512735397373[/C][/ROW]
[ROW][C]88[/C][C]19692[/C][C]22885.9391831898[/C][C]-3193.9391831898[/C][/ROW]
[ROW][C]89[/C][C]24081[/C][C]22225.9661544674[/C][C]1855.03384553261[/C][/ROW]
[ROW][C]90[/C][C]22114[/C][C]20745.2029431305[/C][C]1368.79705686955[/C][/ROW]
[ROW][C]91[/C][C]14220[/C][C]16154.0401457494[/C][C]-1934.0401457494[/C][/ROW]
[ROW][C]92[/C][C]13434[/C][C]14469.5752900437[/C][C]-1035.57529004371[/C][/ROW]
[ROW][C]93[/C][C]13598[/C][C]12264.2838112351[/C][C]1333.71618876487[/C][/ROW]
[ROW][C]94[/C][C]17187[/C][C]16495.3749721818[/C][C]691.625027818169[/C][/ROW]
[ROW][C]95[/C][C]16119[/C][C]17471.4670840425[/C][C]-1352.46708404247[/C][/ROW]
[ROW][C]96[/C][C]13713[/C][C]14991.5421999882[/C][C]-1278.54219998819[/C][/ROW]
[ROW][C]97[/C][C]13210[/C][C]12787.8119087772[/C][C]422.18809122283[/C][/ROW]
[ROW][C]98[/C][C]14251[/C][C]12957.4085355135[/C][C]1293.59146448652[/C][/ROW]
[ROW][C]99[/C][C]20139[/C][C]21148.6492016738[/C][C]-1009.64920167382[/C][/ROW]
[ROW][C]100[/C][C]21725[/C][C]21783.5337733780[/C][C]-58.5337733780252[/C][/ROW]
[ROW][C]101[/C][C]26099[/C][C]23777.4866096851[/C][C]2321.51339031487[/C][/ROW]
[ROW][C]102[/C][C]21084[/C][C]22147.0885534734[/C][C]-1063.08855347341[/C][/ROW]
[ROW][C]103[/C][C]18024[/C][C]15766.5562523142[/C][C]2257.44374768581[/C][/ROW]
[ROW][C]104[/C][C]16722[/C][C]15054.4360832651[/C][C]1667.56391673492[/C][/ROW]
[ROW][C]105[/C][C]14385[/C][C]14267.0812882495[/C][C]117.918711750523[/C][/ROW]
[ROW][C]106[/C][C]21342[/C][C]18051.4833665591[/C][C]3290.51663344086[/C][/ROW]
[ROW][C]107[/C][C]17180[/C][C]18488.4207925968[/C][C]-1308.42079259681[/C][/ROW]
[ROW][C]108[/C][C]14577[/C][C]16051.8193322975[/C][C]-1474.81933229747[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76639&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76639&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
1372377055.55795940171181.442040598286
1493749209.65373173377164.346268266230
151183711732.6882617630104.311738237036
161378413700.480043520883.519956479202
171592615742.3962939177183.603706082293
181382113555.7523335736265.247666426436
19111439946.74386504421196.25613495580
2079758858.93553571608-883.93553571608
2176107566.7097672439843.2902327560214
221001510152.0549428651-137.054942865141
23127599971.902526544162787.09747345584
2488169441.05644068983-625.05644068983
25106778197.965706392052479.03429360795
261094710663.6571207825283.342879217487
271520013180.67493942082019.32506057923
281701015407.40980615611602.59019384390
292090017708.28283331143191.71716668865
301620515978.8265410794226.173458920628
311214312783.1523910586-640.152391058584
32899710534.6613258750-1537.66132587503
3355689568.03863235537-4000.03863235537
341147411523.4405678943-49.4405678942767
351225612647.2557624707-391.255762470704
361058310179.5213810568403.478618943216
371086210447.1648486553414.835151344701
381096511663.7979604003-698.797960400292
391440514811.0778627426-406.07786274265
402037916520.29878986503858.70121013496
412012819830.747511393297.252488606988
421781616396.42805091771419.57194908227
431226812981.9255246590-713.925524658989
44864210327.0324213861-1685.03242138608
4579628254.59799501542-292.597995015418
461393212459.94454124961472.05545875042
471593613644.49375674192291.50624325811
481262811899.2292618824728.77073811762
491226712221.235000673145.7649993269042
501247012901.2627604665-431.262760466518
511894416218.83201699172725.16798300832
522125920242.71682711281016.2831728872
532201521599.6599758524415.340024147561
541858118680.8012396306-99.801239630564
551517514122.15750977771052.8424902223
561030611287.0075962935-981.007596293519
57107929930.0345236007861.965476399306
581475215077.387399979-325.387399978985
591375416381.5175654954-2627.51756549536
601173813275.0480767129-1537.04807671289
611218112985.5733340186-804.573334018613
621296513338.3625063755-373.362506375493
631999018053.57126989691936.42873010306
642312521215.60259488171909.39740511827
652354122429.95397390041111.04602609963
662124719379.71330417001867.28669582996
671518915599.9880366453-410.988036645305
681476711668.76056472623098.23943527378
691089511686.2773256260-791.277325625988
701713016086.11911149381043.88088850617
711769716567.25670330681129.74329669315
721661114462.16099989862148.83900010144
731267415009.2180471533-2335.21804715328
741276015349.3411978374-2589.34119783743
752024920783.6984438491-534.698443849062
762213523598.9294861054-1463.92948610542
772067724000.6414043071-3323.6414043071
781993320673.7362766254-740.736276625386
791538815529.5294040313-141.529404031309
801511313177.62276241091935.37723758906
811340111318.58572385432082.41427614568
821613516918.8166038724-783.81660387242
831756217183.8308753920378.169124608034
841472015420.6858304150-700.68583041495
851222513596.2037807742-1371.20378077415
861160813951.4636916296-2343.46369162962
872098520319.4872646026665.512735397373
881969222885.9391831898-3193.9391831898
892408122225.96615446741855.03384553261
902211420745.20294313051368.79705686955
911422016154.0401457494-1934.0401457494
921343414469.5752900437-1035.57529004371
931359812264.28381123511333.71618876487
941718716495.3749721818691.625027818169
951611917471.4670840425-1352.46708404247
961371314991.5421999882-1278.54219998819
971321012787.8119087772422.18809122283
981425112957.40853551351293.59146448652
992013921148.6492016738-1009.64920167382
1002172521783.5337733780-58.5337733780252
1012609923777.48660968512321.51339031487
1022108422147.0885534734-1063.08855347341
1031802415766.55625231422257.44374768581
1041672215054.43608326511667.56391673492
1051438514267.0812882495117.918711750523
1062134218051.48336655913290.51663344086
1071718018488.4207925968-1308.42079259681
1081457716051.8193322975-1474.81933229747







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10914574.803886102111514.767477410817634.8402947933
11015074.574242279411985.5977883718163.5506961888
11122077.359451167818959.416812077125195.3020902585
11223273.694115139020126.758372240726420.6298580374
11326328.03816307323152.081648182329503.9946779637
11422891.057899418819686.05222264526096.0635761926
11518122.009443838314887.925520249721356.0933674269
11616842.118863196413578.926938359820105.3107880330
11715144.001815640911851.671490093218436.3321411887
11820309.892076721716988.392329427023631.3918240164
11918268.072776419714917.371987264321618.773565575
12015936.582020623112556.647991994819316.5160492515

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 14574.8038861021 & 11514.7674774108 & 17634.8402947933 \tabularnewline
110 & 15074.5742422794 & 11985.59778837 & 18163.5506961888 \tabularnewline
111 & 22077.3594511678 & 18959.4168120771 & 25195.3020902585 \tabularnewline
112 & 23273.6941151390 & 20126.7583722407 & 26420.6298580374 \tabularnewline
113 & 26328.038163073 & 23152.0816481823 & 29503.9946779637 \tabularnewline
114 & 22891.0578994188 & 19686.052222645 & 26096.0635761926 \tabularnewline
115 & 18122.0094438383 & 14887.9255202497 & 21356.0933674269 \tabularnewline
116 & 16842.1188631964 & 13578.9269383598 & 20105.3107880330 \tabularnewline
117 & 15144.0018156409 & 11851.6714900932 & 18436.3321411887 \tabularnewline
118 & 20309.8920767217 & 16988.3923294270 & 23631.3918240164 \tabularnewline
119 & 18268.0727764197 & 14917.3719872643 & 21618.773565575 \tabularnewline
120 & 15936.5820206231 & 12556.6479919948 & 19316.5160492515 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76639&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]14574.8038861021[/C][C]11514.7674774108[/C][C]17634.8402947933[/C][/ROW]
[ROW][C]110[/C][C]15074.5742422794[/C][C]11985.59778837[/C][C]18163.5506961888[/C][/ROW]
[ROW][C]111[/C][C]22077.3594511678[/C][C]18959.4168120771[/C][C]25195.3020902585[/C][/ROW]
[ROW][C]112[/C][C]23273.6941151390[/C][C]20126.7583722407[/C][C]26420.6298580374[/C][/ROW]
[ROW][C]113[/C][C]26328.038163073[/C][C]23152.0816481823[/C][C]29503.9946779637[/C][/ROW]
[ROW][C]114[/C][C]22891.0578994188[/C][C]19686.052222645[/C][C]26096.0635761926[/C][/ROW]
[ROW][C]115[/C][C]18122.0094438383[/C][C]14887.9255202497[/C][C]21356.0933674269[/C][/ROW]
[ROW][C]116[/C][C]16842.1188631964[/C][C]13578.9269383598[/C][C]20105.3107880330[/C][/ROW]
[ROW][C]117[/C][C]15144.0018156409[/C][C]11851.6714900932[/C][C]18436.3321411887[/C][/ROW]
[ROW][C]118[/C][C]20309.8920767217[/C][C]16988.3923294270[/C][C]23631.3918240164[/C][/ROW]
[ROW][C]119[/C][C]18268.0727764197[/C][C]14917.3719872643[/C][C]21618.773565575[/C][/ROW]
[ROW][C]120[/C][C]15936.5820206231[/C][C]12556.6479919948[/C][C]19316.5160492515[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76639&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76639&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
10914574.803886102111514.767477410817634.8402947933
11015074.574242279411985.5977883718163.5506961888
11122077.359451167818959.416812077125195.3020902585
11223273.694115139020126.758372240726420.6298580374
11326328.03816307323152.081648182329503.9946779637
11422891.057899418819686.05222264526096.0635761926
11518122.009443838314887.925520249721356.0933674269
11616842.118863196413578.926938359820105.3107880330
11715144.001815640911851.671490093218436.3321411887
11820309.892076721716988.392329427023631.3918240164
11918268.072776419714917.371987264321618.773565575
12015936.582020623112556.647991994819316.5160492515



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')