Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 17 Aug 2011 19:31:07 -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/Aug/17/t1313624178g5muxgwgceust98.htm/, Retrieved Wed, 15 May 2024 04:10:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123990, Retrieved Wed, 15 May 2024 04:10:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGuy Hendrickx
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [reeksAstap32] [2011-08-17 23:31:07] [f94d9a6f82d80010722d76d48bd1e82c] [Current]
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Dataseries X:
5740
5639
5538
5336
7380
7279
5740
4718
4819
4819
4920
5133
4516
3898
3392
3392
5336
5538
3999
2258
3179
3179
3898
4313
4212
3179
3696
3493
5234
4819
3179
1954
3078
3392
3696
4100
3280
2572
2876
2977
5639
5639
4100
3898
4516
4212
5032
6054
6257
4819
4414
3999
6773
6976
6459
6976
6874
6054
6976
7998
8413
7178
6358
6976
9638
10458
10256
10660
10559
9537
11278
11693
12300
10458
9739
10559
12513
14254
13839
13839
14042
13333
15176
15176
14862
13120
13434
13637
14973
16714
15479
16097
15580
15277
17636
17119
16400
15378
16400
16917
17534
18354
17534
18040
17423
17322
19883
20096
19276
17838
19063
19579
20197
21118
20197
20916
20602
19478
21837
21837




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123990&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123990&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123990&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.141124056690015
beta0.189208072976742
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.141124056690015 \tabularnewline
beta & 0.189208072976742 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123990&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]0.141124056690015[/C][/ROW]
[ROW][C]beta[/C][C]0.189208072976742[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123990&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123990&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
alpha0.141124056690015
beta0.189208072976742
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3553855380
453365437-101
573805319.049587381792060.95041261821
672795561.233495375821717.76650462418
757405800.85337431722-60.8533743172229
847185787.84230534431-1069.84230534431
948195603.87189842823-784.871898428235
1048195439.16017042537-620.160170425365
1149205281.13383011576-361.133830115759
1251335150.01941052885-17.0194105288519
1345165067.01336471942-551.013364719422
1438984893.93487122431-995.93487122431
1533924631.47398530513-1239.47398530513
1633924301.54767177599-909.547671775994
1753363993.895328160081342.10467183992
1855384039.841922574881498.15807742512
1939994147.81494020349-148.814940203491
2022584019.3868159453-1761.3868159453
2131793616.35378934331-437.353789343308
2231793388.49553650381-209.495536503814
2338983187.1996544726710.800345527398
2443133134.759317023671178.24068297633
2542123179.747216069771032.25278393023
2631793231.69572912665-52.6957291266476
2736963129.12483533113566.875164668868
2834933129.12689287893363.87310712107
2952343110.19654741692123.8034525831
3048193396.344109801641422.65589019836
3131793621.53037228208-442.530372282076
3219543571.67762063734-1617.67762063734
3330783312.78840030748-234.788400307481
3433923242.78884125643149.211158743567
3536963230.9650658784465.0349341216
3641003276.12889771507823.871102284928
3732803393.93199560084-113.93199560084
3825723376.34632534397-804.34632534397
3928763239.84908066617-363.849080666166
4029773155.80116480019-178.801164800189
4156393093.09364662692545.9063533731
4256393482.888216517522156.11178348248
4341003875.24548437225224.754515627754
4438984001.04313222612-103.043132226121
4545164077.82920801872438.17079198128
4642124242.6935419256-30.6935419256006
4750324340.57026584448691.429734155521
4860544558.818381868861495.18161813114
4962574930.419281036491326.58071896351
5048195313.64864474321-494.648644743213
5144145426.65071794786-1012.65071794786
5239995439.51062931371-1440.51062931371
5367735353.52497198881419.4750280112
5469765709.054646358211266.94535364179
5564596076.88844946341382.111550536593
5669766330.05398711135645.946012888649
5768746637.70084261518236.299157384819
5860546893.8462874567-839.846287456701
5969766975.69630485070.303695149304986
6079987176.11980522852821.880194771483
6184137514.43320358921898.566796410787
6271787887.5622868712-709.562286871198
6363588014.79907229234-1656.79907229234
6469767964.11842451874-988.11842451874
6596387981.420151152791656.57984884721
66104588416.186108572462041.81389142754
67102568959.837985108531296.16201489147
68106609432.87031685911227.1296831409
69105599928.92711055738630.072889442617
70953710357.5489145494-820.548914549436
711127810559.5429429568718.457057043237
721169310997.9118417627695.088158237299
731230011451.5429392711848.457060728861
741045811949.4734183912-1491.4734183912
75973912077.3583748688-2338.35837486878
761055912023.2890877905-1464.28908779046
771251312053.4728341292459.527165870761
781425412367.42354195921886.57645804078
791383912933.1402426712905.859757328784
801383913384.642319982454.357680018005
811404213784.5587653538257.441234646209
821333314163.5597102698-830.559710269752
831517614366.8400999008809.159900099223
841517614823.1304073544352.869592645622
851486215224.4494326977-362.449432697678
861312015515.1416791744-2395.14167917437
871343415455.0175298288-2021.01752982876
881363715393.7264704052-1756.72647040521
891497315322.8254595645-349.825459564487
901671415441.13105349461272.86894650537
911547915822.4257705819-343.425770581942
921609715966.4523304315130.547669568505
931558016180.8538040938-600.85380409382
941527716275.9930501183-998.993050118286
951763616288.27034718451347.72965281546
961711916667.7134942373451.286505762728
971640016932.6971146871-532.697114687093
981537817044.5929973234-1666.59299732338
991640016951.9678422145-551.967842214497
1001691717001.9045697835-84.9045697834517
1011753417115.4880553289418.511944671063
1021835417311.29074837021042.70925162976
1031753417623.0249227187-89.0249227186687
1041804017772.6670526439267.332947356106
1051742317979.7381246129-556.73812461293
1061732218055.6470278268-733.647027826792
1071988318087.00012481111795.99987518894
1082009618523.30370363691572.69629636314
1091927618970.0876145234305.912385476586
1101783819246.2662555996-1408.26625559958
1111906319242.9297938187-179.929793818745
1121957919408.1367051898170.863294810202
1132019719627.4113196606569.588680339428
1142111819918.16472722841199.83527277156
1152019720329.8988651005-132.898865100469
1162091620550.003514593365.996485406973
1172060220850.287068726-248.287068725997
1181947821057.2507214043-1579.25072140434
1192183721034.2145301142802.785469885766
1202183721368.7767750649468.223224935067

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5538 & 5538 & 0 \tabularnewline
4 & 5336 & 5437 & -101 \tabularnewline
5 & 7380 & 5319.04958738179 & 2060.95041261821 \tabularnewline
6 & 7279 & 5561.23349537582 & 1717.76650462418 \tabularnewline
7 & 5740 & 5800.85337431722 & -60.8533743172229 \tabularnewline
8 & 4718 & 5787.84230534431 & -1069.84230534431 \tabularnewline
9 & 4819 & 5603.87189842823 & -784.871898428235 \tabularnewline
10 & 4819 & 5439.16017042537 & -620.160170425365 \tabularnewline
11 & 4920 & 5281.13383011576 & -361.133830115759 \tabularnewline
12 & 5133 & 5150.01941052885 & -17.0194105288519 \tabularnewline
13 & 4516 & 5067.01336471942 & -551.013364719422 \tabularnewline
14 & 3898 & 4893.93487122431 & -995.93487122431 \tabularnewline
15 & 3392 & 4631.47398530513 & -1239.47398530513 \tabularnewline
16 & 3392 & 4301.54767177599 & -909.547671775994 \tabularnewline
17 & 5336 & 3993.89532816008 & 1342.10467183992 \tabularnewline
18 & 5538 & 4039.84192257488 & 1498.15807742512 \tabularnewline
19 & 3999 & 4147.81494020349 & -148.814940203491 \tabularnewline
20 & 2258 & 4019.3868159453 & -1761.3868159453 \tabularnewline
21 & 3179 & 3616.35378934331 & -437.353789343308 \tabularnewline
22 & 3179 & 3388.49553650381 & -209.495536503814 \tabularnewline
23 & 3898 & 3187.1996544726 & 710.800345527398 \tabularnewline
24 & 4313 & 3134.75931702367 & 1178.24068297633 \tabularnewline
25 & 4212 & 3179.74721606977 & 1032.25278393023 \tabularnewline
26 & 3179 & 3231.69572912665 & -52.6957291266476 \tabularnewline
27 & 3696 & 3129.12483533113 & 566.875164668868 \tabularnewline
28 & 3493 & 3129.12689287893 & 363.87310712107 \tabularnewline
29 & 5234 & 3110.1965474169 & 2123.8034525831 \tabularnewline
30 & 4819 & 3396.34410980164 & 1422.65589019836 \tabularnewline
31 & 3179 & 3621.53037228208 & -442.530372282076 \tabularnewline
32 & 1954 & 3571.67762063734 & -1617.67762063734 \tabularnewline
33 & 3078 & 3312.78840030748 & -234.788400307481 \tabularnewline
34 & 3392 & 3242.78884125643 & 149.211158743567 \tabularnewline
35 & 3696 & 3230.9650658784 & 465.0349341216 \tabularnewline
36 & 4100 & 3276.12889771507 & 823.871102284928 \tabularnewline
37 & 3280 & 3393.93199560084 & -113.93199560084 \tabularnewline
38 & 2572 & 3376.34632534397 & -804.34632534397 \tabularnewline
39 & 2876 & 3239.84908066617 & -363.849080666166 \tabularnewline
40 & 2977 & 3155.80116480019 & -178.801164800189 \tabularnewline
41 & 5639 & 3093.0936466269 & 2545.9063533731 \tabularnewline
42 & 5639 & 3482.88821651752 & 2156.11178348248 \tabularnewline
43 & 4100 & 3875.24548437225 & 224.754515627754 \tabularnewline
44 & 3898 & 4001.04313222612 & -103.043132226121 \tabularnewline
45 & 4516 & 4077.82920801872 & 438.17079198128 \tabularnewline
46 & 4212 & 4242.6935419256 & -30.6935419256006 \tabularnewline
47 & 5032 & 4340.57026584448 & 691.429734155521 \tabularnewline
48 & 6054 & 4558.81838186886 & 1495.18161813114 \tabularnewline
49 & 6257 & 4930.41928103649 & 1326.58071896351 \tabularnewline
50 & 4819 & 5313.64864474321 & -494.648644743213 \tabularnewline
51 & 4414 & 5426.65071794786 & -1012.65071794786 \tabularnewline
52 & 3999 & 5439.51062931371 & -1440.51062931371 \tabularnewline
53 & 6773 & 5353.5249719888 & 1419.4750280112 \tabularnewline
54 & 6976 & 5709.05464635821 & 1266.94535364179 \tabularnewline
55 & 6459 & 6076.88844946341 & 382.111550536593 \tabularnewline
56 & 6976 & 6330.05398711135 & 645.946012888649 \tabularnewline
57 & 6874 & 6637.70084261518 & 236.299157384819 \tabularnewline
58 & 6054 & 6893.8462874567 & -839.846287456701 \tabularnewline
59 & 6976 & 6975.6963048507 & 0.303695149304986 \tabularnewline
60 & 7998 & 7176.11980522852 & 821.880194771483 \tabularnewline
61 & 8413 & 7514.43320358921 & 898.566796410787 \tabularnewline
62 & 7178 & 7887.5622868712 & -709.562286871198 \tabularnewline
63 & 6358 & 8014.79907229234 & -1656.79907229234 \tabularnewline
64 & 6976 & 7964.11842451874 & -988.11842451874 \tabularnewline
65 & 9638 & 7981.42015115279 & 1656.57984884721 \tabularnewline
66 & 10458 & 8416.18610857246 & 2041.81389142754 \tabularnewline
67 & 10256 & 8959.83798510853 & 1296.16201489147 \tabularnewline
68 & 10660 & 9432.8703168591 & 1227.1296831409 \tabularnewline
69 & 10559 & 9928.92711055738 & 630.072889442617 \tabularnewline
70 & 9537 & 10357.5489145494 & -820.548914549436 \tabularnewline
71 & 11278 & 10559.5429429568 & 718.457057043237 \tabularnewline
72 & 11693 & 10997.9118417627 & 695.088158237299 \tabularnewline
73 & 12300 & 11451.5429392711 & 848.457060728861 \tabularnewline
74 & 10458 & 11949.4734183912 & -1491.4734183912 \tabularnewline
75 & 9739 & 12077.3583748688 & -2338.35837486878 \tabularnewline
76 & 10559 & 12023.2890877905 & -1464.28908779046 \tabularnewline
77 & 12513 & 12053.4728341292 & 459.527165870761 \tabularnewline
78 & 14254 & 12367.4235419592 & 1886.57645804078 \tabularnewline
79 & 13839 & 12933.1402426712 & 905.859757328784 \tabularnewline
80 & 13839 & 13384.642319982 & 454.357680018005 \tabularnewline
81 & 14042 & 13784.5587653538 & 257.441234646209 \tabularnewline
82 & 13333 & 14163.5597102698 & -830.559710269752 \tabularnewline
83 & 15176 & 14366.8400999008 & 809.159900099223 \tabularnewline
84 & 15176 & 14823.1304073544 & 352.869592645622 \tabularnewline
85 & 14862 & 15224.4494326977 & -362.449432697678 \tabularnewline
86 & 13120 & 15515.1416791744 & -2395.14167917437 \tabularnewline
87 & 13434 & 15455.0175298288 & -2021.01752982876 \tabularnewline
88 & 13637 & 15393.7264704052 & -1756.72647040521 \tabularnewline
89 & 14973 & 15322.8254595645 & -349.825459564487 \tabularnewline
90 & 16714 & 15441.1310534946 & 1272.86894650537 \tabularnewline
91 & 15479 & 15822.4257705819 & -343.425770581942 \tabularnewline
92 & 16097 & 15966.4523304315 & 130.547669568505 \tabularnewline
93 & 15580 & 16180.8538040938 & -600.85380409382 \tabularnewline
94 & 15277 & 16275.9930501183 & -998.993050118286 \tabularnewline
95 & 17636 & 16288.2703471845 & 1347.72965281546 \tabularnewline
96 & 17119 & 16667.7134942373 & 451.286505762728 \tabularnewline
97 & 16400 & 16932.6971146871 & -532.697114687093 \tabularnewline
98 & 15378 & 17044.5929973234 & -1666.59299732338 \tabularnewline
99 & 16400 & 16951.9678422145 & -551.967842214497 \tabularnewline
100 & 16917 & 17001.9045697835 & -84.9045697834517 \tabularnewline
101 & 17534 & 17115.4880553289 & 418.511944671063 \tabularnewline
102 & 18354 & 17311.2907483702 & 1042.70925162976 \tabularnewline
103 & 17534 & 17623.0249227187 & -89.0249227186687 \tabularnewline
104 & 18040 & 17772.6670526439 & 267.332947356106 \tabularnewline
105 & 17423 & 17979.7381246129 & -556.73812461293 \tabularnewline
106 & 17322 & 18055.6470278268 & -733.647027826792 \tabularnewline
107 & 19883 & 18087.0001248111 & 1795.99987518894 \tabularnewline
108 & 20096 & 18523.3037036369 & 1572.69629636314 \tabularnewline
109 & 19276 & 18970.0876145234 & 305.912385476586 \tabularnewline
110 & 17838 & 19246.2662555996 & -1408.26625559958 \tabularnewline
111 & 19063 & 19242.9297938187 & -179.929793818745 \tabularnewline
112 & 19579 & 19408.1367051898 & 170.863294810202 \tabularnewline
113 & 20197 & 19627.4113196606 & 569.588680339428 \tabularnewline
114 & 21118 & 19918.1647272284 & 1199.83527277156 \tabularnewline
115 & 20197 & 20329.8988651005 & -132.898865100469 \tabularnewline
116 & 20916 & 20550.003514593 & 365.996485406973 \tabularnewline
117 & 20602 & 20850.287068726 & -248.287068725997 \tabularnewline
118 & 19478 & 21057.2507214043 & -1579.25072140434 \tabularnewline
119 & 21837 & 21034.2145301142 & 802.785469885766 \tabularnewline
120 & 21837 & 21368.7767750649 & 468.223224935067 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123990&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]3[/C][C]5538[/C][C]5538[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]5336[/C][C]5437[/C][C]-101[/C][/ROW]
[ROW][C]5[/C][C]7380[/C][C]5319.04958738179[/C][C]2060.95041261821[/C][/ROW]
[ROW][C]6[/C][C]7279[/C][C]5561.23349537582[/C][C]1717.76650462418[/C][/ROW]
[ROW][C]7[/C][C]5740[/C][C]5800.85337431722[/C][C]-60.8533743172229[/C][/ROW]
[ROW][C]8[/C][C]4718[/C][C]5787.84230534431[/C][C]-1069.84230534431[/C][/ROW]
[ROW][C]9[/C][C]4819[/C][C]5603.87189842823[/C][C]-784.871898428235[/C][/ROW]
[ROW][C]10[/C][C]4819[/C][C]5439.16017042537[/C][C]-620.160170425365[/C][/ROW]
[ROW][C]11[/C][C]4920[/C][C]5281.13383011576[/C][C]-361.133830115759[/C][/ROW]
[ROW][C]12[/C][C]5133[/C][C]5150.01941052885[/C][C]-17.0194105288519[/C][/ROW]
[ROW][C]13[/C][C]4516[/C][C]5067.01336471942[/C][C]-551.013364719422[/C][/ROW]
[ROW][C]14[/C][C]3898[/C][C]4893.93487122431[/C][C]-995.93487122431[/C][/ROW]
[ROW][C]15[/C][C]3392[/C][C]4631.47398530513[/C][C]-1239.47398530513[/C][/ROW]
[ROW][C]16[/C][C]3392[/C][C]4301.54767177599[/C][C]-909.547671775994[/C][/ROW]
[ROW][C]17[/C][C]5336[/C][C]3993.89532816008[/C][C]1342.10467183992[/C][/ROW]
[ROW][C]18[/C][C]5538[/C][C]4039.84192257488[/C][C]1498.15807742512[/C][/ROW]
[ROW][C]19[/C][C]3999[/C][C]4147.81494020349[/C][C]-148.814940203491[/C][/ROW]
[ROW][C]20[/C][C]2258[/C][C]4019.3868159453[/C][C]-1761.3868159453[/C][/ROW]
[ROW][C]21[/C][C]3179[/C][C]3616.35378934331[/C][C]-437.353789343308[/C][/ROW]
[ROW][C]22[/C][C]3179[/C][C]3388.49553650381[/C][C]-209.495536503814[/C][/ROW]
[ROW][C]23[/C][C]3898[/C][C]3187.1996544726[/C][C]710.800345527398[/C][/ROW]
[ROW][C]24[/C][C]4313[/C][C]3134.75931702367[/C][C]1178.24068297633[/C][/ROW]
[ROW][C]25[/C][C]4212[/C][C]3179.74721606977[/C][C]1032.25278393023[/C][/ROW]
[ROW][C]26[/C][C]3179[/C][C]3231.69572912665[/C][C]-52.6957291266476[/C][/ROW]
[ROW][C]27[/C][C]3696[/C][C]3129.12483533113[/C][C]566.875164668868[/C][/ROW]
[ROW][C]28[/C][C]3493[/C][C]3129.12689287893[/C][C]363.87310712107[/C][/ROW]
[ROW][C]29[/C][C]5234[/C][C]3110.1965474169[/C][C]2123.8034525831[/C][/ROW]
[ROW][C]30[/C][C]4819[/C][C]3396.34410980164[/C][C]1422.65589019836[/C][/ROW]
[ROW][C]31[/C][C]3179[/C][C]3621.53037228208[/C][C]-442.530372282076[/C][/ROW]
[ROW][C]32[/C][C]1954[/C][C]3571.67762063734[/C][C]-1617.67762063734[/C][/ROW]
[ROW][C]33[/C][C]3078[/C][C]3312.78840030748[/C][C]-234.788400307481[/C][/ROW]
[ROW][C]34[/C][C]3392[/C][C]3242.78884125643[/C][C]149.211158743567[/C][/ROW]
[ROW][C]35[/C][C]3696[/C][C]3230.9650658784[/C][C]465.0349341216[/C][/ROW]
[ROW][C]36[/C][C]4100[/C][C]3276.12889771507[/C][C]823.871102284928[/C][/ROW]
[ROW][C]37[/C][C]3280[/C][C]3393.93199560084[/C][C]-113.93199560084[/C][/ROW]
[ROW][C]38[/C][C]2572[/C][C]3376.34632534397[/C][C]-804.34632534397[/C][/ROW]
[ROW][C]39[/C][C]2876[/C][C]3239.84908066617[/C][C]-363.849080666166[/C][/ROW]
[ROW][C]40[/C][C]2977[/C][C]3155.80116480019[/C][C]-178.801164800189[/C][/ROW]
[ROW][C]41[/C][C]5639[/C][C]3093.0936466269[/C][C]2545.9063533731[/C][/ROW]
[ROW][C]42[/C][C]5639[/C][C]3482.88821651752[/C][C]2156.11178348248[/C][/ROW]
[ROW][C]43[/C][C]4100[/C][C]3875.24548437225[/C][C]224.754515627754[/C][/ROW]
[ROW][C]44[/C][C]3898[/C][C]4001.04313222612[/C][C]-103.043132226121[/C][/ROW]
[ROW][C]45[/C][C]4516[/C][C]4077.82920801872[/C][C]438.17079198128[/C][/ROW]
[ROW][C]46[/C][C]4212[/C][C]4242.6935419256[/C][C]-30.6935419256006[/C][/ROW]
[ROW][C]47[/C][C]5032[/C][C]4340.57026584448[/C][C]691.429734155521[/C][/ROW]
[ROW][C]48[/C][C]6054[/C][C]4558.81838186886[/C][C]1495.18161813114[/C][/ROW]
[ROW][C]49[/C][C]6257[/C][C]4930.41928103649[/C][C]1326.58071896351[/C][/ROW]
[ROW][C]50[/C][C]4819[/C][C]5313.64864474321[/C][C]-494.648644743213[/C][/ROW]
[ROW][C]51[/C][C]4414[/C][C]5426.65071794786[/C][C]-1012.65071794786[/C][/ROW]
[ROW][C]52[/C][C]3999[/C][C]5439.51062931371[/C][C]-1440.51062931371[/C][/ROW]
[ROW][C]53[/C][C]6773[/C][C]5353.5249719888[/C][C]1419.4750280112[/C][/ROW]
[ROW][C]54[/C][C]6976[/C][C]5709.05464635821[/C][C]1266.94535364179[/C][/ROW]
[ROW][C]55[/C][C]6459[/C][C]6076.88844946341[/C][C]382.111550536593[/C][/ROW]
[ROW][C]56[/C][C]6976[/C][C]6330.05398711135[/C][C]645.946012888649[/C][/ROW]
[ROW][C]57[/C][C]6874[/C][C]6637.70084261518[/C][C]236.299157384819[/C][/ROW]
[ROW][C]58[/C][C]6054[/C][C]6893.8462874567[/C][C]-839.846287456701[/C][/ROW]
[ROW][C]59[/C][C]6976[/C][C]6975.6963048507[/C][C]0.303695149304986[/C][/ROW]
[ROW][C]60[/C][C]7998[/C][C]7176.11980522852[/C][C]821.880194771483[/C][/ROW]
[ROW][C]61[/C][C]8413[/C][C]7514.43320358921[/C][C]898.566796410787[/C][/ROW]
[ROW][C]62[/C][C]7178[/C][C]7887.5622868712[/C][C]-709.562286871198[/C][/ROW]
[ROW][C]63[/C][C]6358[/C][C]8014.79907229234[/C][C]-1656.79907229234[/C][/ROW]
[ROW][C]64[/C][C]6976[/C][C]7964.11842451874[/C][C]-988.11842451874[/C][/ROW]
[ROW][C]65[/C][C]9638[/C][C]7981.42015115279[/C][C]1656.57984884721[/C][/ROW]
[ROW][C]66[/C][C]10458[/C][C]8416.18610857246[/C][C]2041.81389142754[/C][/ROW]
[ROW][C]67[/C][C]10256[/C][C]8959.83798510853[/C][C]1296.16201489147[/C][/ROW]
[ROW][C]68[/C][C]10660[/C][C]9432.8703168591[/C][C]1227.1296831409[/C][/ROW]
[ROW][C]69[/C][C]10559[/C][C]9928.92711055738[/C][C]630.072889442617[/C][/ROW]
[ROW][C]70[/C][C]9537[/C][C]10357.5489145494[/C][C]-820.548914549436[/C][/ROW]
[ROW][C]71[/C][C]11278[/C][C]10559.5429429568[/C][C]718.457057043237[/C][/ROW]
[ROW][C]72[/C][C]11693[/C][C]10997.9118417627[/C][C]695.088158237299[/C][/ROW]
[ROW][C]73[/C][C]12300[/C][C]11451.5429392711[/C][C]848.457060728861[/C][/ROW]
[ROW][C]74[/C][C]10458[/C][C]11949.4734183912[/C][C]-1491.4734183912[/C][/ROW]
[ROW][C]75[/C][C]9739[/C][C]12077.3583748688[/C][C]-2338.35837486878[/C][/ROW]
[ROW][C]76[/C][C]10559[/C][C]12023.2890877905[/C][C]-1464.28908779046[/C][/ROW]
[ROW][C]77[/C][C]12513[/C][C]12053.4728341292[/C][C]459.527165870761[/C][/ROW]
[ROW][C]78[/C][C]14254[/C][C]12367.4235419592[/C][C]1886.57645804078[/C][/ROW]
[ROW][C]79[/C][C]13839[/C][C]12933.1402426712[/C][C]905.859757328784[/C][/ROW]
[ROW][C]80[/C][C]13839[/C][C]13384.642319982[/C][C]454.357680018005[/C][/ROW]
[ROW][C]81[/C][C]14042[/C][C]13784.5587653538[/C][C]257.441234646209[/C][/ROW]
[ROW][C]82[/C][C]13333[/C][C]14163.5597102698[/C][C]-830.559710269752[/C][/ROW]
[ROW][C]83[/C][C]15176[/C][C]14366.8400999008[/C][C]809.159900099223[/C][/ROW]
[ROW][C]84[/C][C]15176[/C][C]14823.1304073544[/C][C]352.869592645622[/C][/ROW]
[ROW][C]85[/C][C]14862[/C][C]15224.4494326977[/C][C]-362.449432697678[/C][/ROW]
[ROW][C]86[/C][C]13120[/C][C]15515.1416791744[/C][C]-2395.14167917437[/C][/ROW]
[ROW][C]87[/C][C]13434[/C][C]15455.0175298288[/C][C]-2021.01752982876[/C][/ROW]
[ROW][C]88[/C][C]13637[/C][C]15393.7264704052[/C][C]-1756.72647040521[/C][/ROW]
[ROW][C]89[/C][C]14973[/C][C]15322.8254595645[/C][C]-349.825459564487[/C][/ROW]
[ROW][C]90[/C][C]16714[/C][C]15441.1310534946[/C][C]1272.86894650537[/C][/ROW]
[ROW][C]91[/C][C]15479[/C][C]15822.4257705819[/C][C]-343.425770581942[/C][/ROW]
[ROW][C]92[/C][C]16097[/C][C]15966.4523304315[/C][C]130.547669568505[/C][/ROW]
[ROW][C]93[/C][C]15580[/C][C]16180.8538040938[/C][C]-600.85380409382[/C][/ROW]
[ROW][C]94[/C][C]15277[/C][C]16275.9930501183[/C][C]-998.993050118286[/C][/ROW]
[ROW][C]95[/C][C]17636[/C][C]16288.2703471845[/C][C]1347.72965281546[/C][/ROW]
[ROW][C]96[/C][C]17119[/C][C]16667.7134942373[/C][C]451.286505762728[/C][/ROW]
[ROW][C]97[/C][C]16400[/C][C]16932.6971146871[/C][C]-532.697114687093[/C][/ROW]
[ROW][C]98[/C][C]15378[/C][C]17044.5929973234[/C][C]-1666.59299732338[/C][/ROW]
[ROW][C]99[/C][C]16400[/C][C]16951.9678422145[/C][C]-551.967842214497[/C][/ROW]
[ROW][C]100[/C][C]16917[/C][C]17001.9045697835[/C][C]-84.9045697834517[/C][/ROW]
[ROW][C]101[/C][C]17534[/C][C]17115.4880553289[/C][C]418.511944671063[/C][/ROW]
[ROW][C]102[/C][C]18354[/C][C]17311.2907483702[/C][C]1042.70925162976[/C][/ROW]
[ROW][C]103[/C][C]17534[/C][C]17623.0249227187[/C][C]-89.0249227186687[/C][/ROW]
[ROW][C]104[/C][C]18040[/C][C]17772.6670526439[/C][C]267.332947356106[/C][/ROW]
[ROW][C]105[/C][C]17423[/C][C]17979.7381246129[/C][C]-556.73812461293[/C][/ROW]
[ROW][C]106[/C][C]17322[/C][C]18055.6470278268[/C][C]-733.647027826792[/C][/ROW]
[ROW][C]107[/C][C]19883[/C][C]18087.0001248111[/C][C]1795.99987518894[/C][/ROW]
[ROW][C]108[/C][C]20096[/C][C]18523.3037036369[/C][C]1572.69629636314[/C][/ROW]
[ROW][C]109[/C][C]19276[/C][C]18970.0876145234[/C][C]305.912385476586[/C][/ROW]
[ROW][C]110[/C][C]17838[/C][C]19246.2662555996[/C][C]-1408.26625559958[/C][/ROW]
[ROW][C]111[/C][C]19063[/C][C]19242.9297938187[/C][C]-179.929793818745[/C][/ROW]
[ROW][C]112[/C][C]19579[/C][C]19408.1367051898[/C][C]170.863294810202[/C][/ROW]
[ROW][C]113[/C][C]20197[/C][C]19627.4113196606[/C][C]569.588680339428[/C][/ROW]
[ROW][C]114[/C][C]21118[/C][C]19918.1647272284[/C][C]1199.83527277156[/C][/ROW]
[ROW][C]115[/C][C]20197[/C][C]20329.8988651005[/C][C]-132.898865100469[/C][/ROW]
[ROW][C]116[/C][C]20916[/C][C]20550.003514593[/C][C]365.996485406973[/C][/ROW]
[ROW][C]117[/C][C]20602[/C][C]20850.287068726[/C][C]-248.287068725997[/C][/ROW]
[ROW][C]118[/C][C]19478[/C][C]21057.2507214043[/C][C]-1579.25072140434[/C][/ROW]
[ROW][C]119[/C][C]21837[/C][C]21034.2145301142[/C][C]802.785469885766[/C][/ROW]
[ROW][C]120[/C][C]21837[/C][C]21368.7767750649[/C][C]468.223224935067[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123990&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123990&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
3553855380
453365437-101
573805319.049587381792060.95041261821
672795561.233495375821717.76650462418
757405800.85337431722-60.8533743172229
847185787.84230534431-1069.84230534431
948195603.87189842823-784.871898428235
1048195439.16017042537-620.160170425365
1149205281.13383011576-361.133830115759
1251335150.01941052885-17.0194105288519
1345165067.01336471942-551.013364719422
1438984893.93487122431-995.93487122431
1533924631.47398530513-1239.47398530513
1633924301.54767177599-909.547671775994
1753363993.895328160081342.10467183992
1855384039.841922574881498.15807742512
1939994147.81494020349-148.814940203491
2022584019.3868159453-1761.3868159453
2131793616.35378934331-437.353789343308
2231793388.49553650381-209.495536503814
2338983187.1996544726710.800345527398
2443133134.759317023671178.24068297633
2542123179.747216069771032.25278393023
2631793231.69572912665-52.6957291266476
2736963129.12483533113566.875164668868
2834933129.12689287893363.87310712107
2952343110.19654741692123.8034525831
3048193396.344109801641422.65589019836
3131793621.53037228208-442.530372282076
3219543571.67762063734-1617.67762063734
3330783312.78840030748-234.788400307481
3433923242.78884125643149.211158743567
3536963230.9650658784465.0349341216
3641003276.12889771507823.871102284928
3732803393.93199560084-113.93199560084
3825723376.34632534397-804.34632534397
3928763239.84908066617-363.849080666166
4029773155.80116480019-178.801164800189
4156393093.09364662692545.9063533731
4256393482.888216517522156.11178348248
4341003875.24548437225224.754515627754
4438984001.04313222612-103.043132226121
4545164077.82920801872438.17079198128
4642124242.6935419256-30.6935419256006
4750324340.57026584448691.429734155521
4860544558.818381868861495.18161813114
4962574930.419281036491326.58071896351
5048195313.64864474321-494.648644743213
5144145426.65071794786-1012.65071794786
5239995439.51062931371-1440.51062931371
5367735353.52497198881419.4750280112
5469765709.054646358211266.94535364179
5564596076.88844946341382.111550536593
5669766330.05398711135645.946012888649
5768746637.70084261518236.299157384819
5860546893.8462874567-839.846287456701
5969766975.69630485070.303695149304986
6079987176.11980522852821.880194771483
6184137514.43320358921898.566796410787
6271787887.5622868712-709.562286871198
6363588014.79907229234-1656.79907229234
6469767964.11842451874-988.11842451874
6596387981.420151152791656.57984884721
66104588416.186108572462041.81389142754
67102568959.837985108531296.16201489147
68106609432.87031685911227.1296831409
69105599928.92711055738630.072889442617
70953710357.5489145494-820.548914549436
711127810559.5429429568718.457057043237
721169310997.9118417627695.088158237299
731230011451.5429392711848.457060728861
741045811949.4734183912-1491.4734183912
75973912077.3583748688-2338.35837486878
761055912023.2890877905-1464.28908779046
771251312053.4728341292459.527165870761
781425412367.42354195921886.57645804078
791383912933.1402426712905.859757328784
801383913384.642319982454.357680018005
811404213784.5587653538257.441234646209
821333314163.5597102698-830.559710269752
831517614366.8400999008809.159900099223
841517614823.1304073544352.869592645622
851486215224.4494326977-362.449432697678
861312015515.1416791744-2395.14167917437
871343415455.0175298288-2021.01752982876
881363715393.7264704052-1756.72647040521
891497315322.8254595645-349.825459564487
901671415441.13105349461272.86894650537
911547915822.4257705819-343.425770581942
921609715966.4523304315130.547669568505
931558016180.8538040938-600.85380409382
941527716275.9930501183-998.993050118286
951763616288.27034718451347.72965281546
961711916667.7134942373451.286505762728
971640016932.6971146871-532.697114687093
981537817044.5929973234-1666.59299732338
991640016951.9678422145-551.967842214497
1001691717001.9045697835-84.9045697834517
1011753417115.4880553289418.511944671063
1021835417311.29074837021042.70925162976
1031753417623.0249227187-89.0249227186687
1041804017772.6670526439267.332947356106
1051742317979.7381246129-556.73812461293
1061732218055.6470278268-733.647027826792
1071988318087.00012481111795.99987518894
1082009618523.30370363691572.69629636314
1091927618970.0876145234305.912385476586
1101783819246.2662555996-1408.26625559958
1111906319242.9297938187-179.929793818745
1121957919408.1367051898170.863294810202
1132019719627.4113196606569.588680339428
1142111819918.16472722841199.83527277156
1152019720329.8988651005-132.898865100469
1162091620550.003514593365.996485406973
1172060220850.287068726-248.287068725997
1181947821057.2507214043-1579.25072140434
1192183721034.2145301142802.785469885766
1202183721368.7767750649468.223224935067







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12121668.626646765219604.835935746523732.4173577839
12221902.398957526219809.746192866323995.0517221861
12322136.171268287120005.357041189824266.9854953845
12422369.943579048120190.763301636924549.1238564592
12522603.71588980920365.269692489224842.1620871288
12622837.4882005720528.40030432225146.5760968179
12723071.260511330920679.893363431425462.6276592304
12823305.032822091920819.682806431425790.3828377523
12923538.805132852820947.87015544526129.7401102606
13023772.577443613821064.69109847826480.4637887496
13124006.349754374721170.481024147226842.2184846022
13224240.122065135721265.642850286827214.6012799846

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 21668.6266467652 & 19604.8359357465 & 23732.4173577839 \tabularnewline
122 & 21902.3989575262 & 19809.7461928663 & 23995.0517221861 \tabularnewline
123 & 22136.1712682871 & 20005.3570411898 & 24266.9854953845 \tabularnewline
124 & 22369.9435790481 & 20190.7633016369 & 24549.1238564592 \tabularnewline
125 & 22603.715889809 & 20365.2696924892 & 24842.1620871288 \tabularnewline
126 & 22837.48820057 & 20528.400304322 & 25146.5760968179 \tabularnewline
127 & 23071.2605113309 & 20679.8933634314 & 25462.6276592304 \tabularnewline
128 & 23305.0328220919 & 20819.6828064314 & 25790.3828377523 \tabularnewline
129 & 23538.8051328528 & 20947.870155445 & 26129.7401102606 \tabularnewline
130 & 23772.5774436138 & 21064.691098478 & 26480.4637887496 \tabularnewline
131 & 24006.3497543747 & 21170.4810241472 & 26842.2184846022 \tabularnewline
132 & 24240.1220651357 & 21265.6428502868 & 27214.6012799846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123990&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]21668.6266467652[/C][C]19604.8359357465[/C][C]23732.4173577839[/C][/ROW]
[ROW][C]122[/C][C]21902.3989575262[/C][C]19809.7461928663[/C][C]23995.0517221861[/C][/ROW]
[ROW][C]123[/C][C]22136.1712682871[/C][C]20005.3570411898[/C][C]24266.9854953845[/C][/ROW]
[ROW][C]124[/C][C]22369.9435790481[/C][C]20190.7633016369[/C][C]24549.1238564592[/C][/ROW]
[ROW][C]125[/C][C]22603.715889809[/C][C]20365.2696924892[/C][C]24842.1620871288[/C][/ROW]
[ROW][C]126[/C][C]22837.48820057[/C][C]20528.400304322[/C][C]25146.5760968179[/C][/ROW]
[ROW][C]127[/C][C]23071.2605113309[/C][C]20679.8933634314[/C][C]25462.6276592304[/C][/ROW]
[ROW][C]128[/C][C]23305.0328220919[/C][C]20819.6828064314[/C][C]25790.3828377523[/C][/ROW]
[ROW][C]129[/C][C]23538.8051328528[/C][C]20947.870155445[/C][C]26129.7401102606[/C][/ROW]
[ROW][C]130[/C][C]23772.5774436138[/C][C]21064.691098478[/C][C]26480.4637887496[/C][/ROW]
[ROW][C]131[/C][C]24006.3497543747[/C][C]21170.4810241472[/C][C]26842.2184846022[/C][/ROW]
[ROW][C]132[/C][C]24240.1220651357[/C][C]21265.6428502868[/C][C]27214.6012799846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123990&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123990&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
12121668.626646765219604.835935746523732.4173577839
12221902.398957526219809.746192866323995.0517221861
12322136.171268287120005.357041189824266.9854953845
12422369.943579048120190.763301636924549.1238564592
12522603.71588980920365.269692489224842.1620871288
12622837.4882005720528.40030432225146.5760968179
12723071.260511330920679.893363431425462.6276592304
12823305.032822091920819.682806431425790.3828377523
12923538.805132852820947.87015544526129.7401102606
13023772.577443613821064.69109847826480.4637887496
13124006.349754374721170.481024147226842.2184846022
13224240.122065135721265.642850286827214.6012799846



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