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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 Jan 2009 07:02:58 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jan/16/t12321146323uk9364byokr6yj.htm/, Retrieved Sun, 05 May 2024 02:59:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36919, Retrieved Sun, 05 May 2024 02:59:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact207
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10_eigen r...] [2009-01-16 14:02:58] [49ed6f8c7db7571d0c4403fef2ba00f0] [Current]
- RM D    [Exponential Smoothing] [] [2010-01-15 14:54:39] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
9.733
9.259
9.864
9.215
10.103
9.380
9.896
10.117
9.451
9.700
9.081
9.084
9.743
8.587
9.731
9.563
9.998
9.437
10.038
9.918
9.252
9.737
9.035
9.133
9.487
8.700
9.627
8.947
9.283
8.829
9.947
9.628
9.318
9.605
8.640
9.214
9.567
8.547
9.185
9.470
9.123
9.278
10.170
9.434
9.655
9.429
8.739
9.552
9.687
9.019
9.672
9.206
9.069
9.788
10.312
10.105
9.863
9.656
9.295
9.946
9.701
9.049
10.190
9.706
9.765
9.893
9.994
10.433
10.073
10.112
9.266
9.820
10.097
9.115
10.411
9.678
10.408
10.153
10.368
10.581
10.597
10.680
9.738
9.556




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36919&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36919&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36919&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.104257118442592
beta0.130348248958748
gamma0.727179362160777

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.104257118442592 \tabularnewline
beta & 0.130348248958748 \tabularnewline
gamma & 0.727179362160777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36919&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]0.104257118442592[/C][/ROW]
[ROW][C]beta[/C][C]0.130348248958748[/C][/ROW]
[ROW][C]gamma[/C][C]0.727179362160777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36919&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36919&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
alpha0.104257118442592
beta0.130348248958748
gamma0.727179362160777







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139.7439.74921180555556-0.00621180555555689
148.5878.5914210517089-0.0044210517089045
159.7319.74796524911992-0.0169652491199201
169.5639.58113773811941-0.0181377381194121
179.99810.0105664997792-0.0125664997792239
189.4379.44390532731992-0.00690532731992022
1910.0389.836157197501520.201842802498481
209.91810.1042072026046-0.186207202604637
219.2529.4482280595629-0.196228059562895
229.7379.661037483947060.0759625160529449
239.0359.034090357043780.00090964295621987
249.1339.033455795665350.0995442043346504
259.4879.68611954460467-0.199119544604669
268.78.505818749955550.194181250044446
279.6279.67403227138516-0.0470322713851612
288.9479.50203221803877-0.555032218038768
299.2839.87054444746039-0.58754444746039
308.8299.23124105346515-0.402241053465149
319.9479.696491061292450.250508938707553
329.6289.69575706142734-0.0677570614273417
339.3189.026114333252370.291885666747625
349.6059.454256425658830.150743574341170
358.648.7743828634714-0.134382863471398
369.2148.810215657085870.403784342914131
379.5679.290519203430950.276480796569048
388.5478.41290900379630.134090996203700
399.1859.41384606663035-0.228846066630352
409.478.885632671552750.584367328447248
419.1239.36087799802199-0.237877998021986
429.2788.892601911801140.38539808819886
4310.179.889723501809530.280276498190473
449.4349.70976556226683-0.275765562266832
459.6559.274848786195530.380151213804471
469.4299.64361094053915-0.214610940539155
478.7398.75831278021701-0.0193127802170068
489.5529.176637703159040.375362296840962
499.6879.590622207411520.0963777925884752
509.0198.61860492541160.400395074588394
519.6729.431638092996050.240361907003951
529.2069.50915549927118-0.303155499271181
539.0699.37133980919556-0.302339809195562
549.7889.31649977824350.471500221756504
5510.31210.26947160212730.0425283978726494
5610.1059.71465512642050.390344873579497
579.8639.797594224601530.0654057753984656
589.6569.76302433612392-0.107024336123915
599.2959.034505547351990.260494452648013
609.9469.76123486620590.184765133794105
619.7019.99319182517576-0.292191825175763
629.0499.19297379127453-0.143973791274528
6310.199.85189863562260.338101364377390
649.7069.593791841416150.112208158583853
659.7659.513671144512010.251328855487987
669.89310.0419911671626-0.148991167162610
679.99410.6638057580476-0.669805758047628
6810.43310.2645496397060.168450360294006
6910.07310.1129555016226-0.0399555016226181
7010.1129.953909093226280.158090906773724
719.2669.49484565780211-0.228845657802111
729.8210.1170063570882-0.297006357088240
7310.0979.9772906954930.119709304507003
749.1159.31138696973763-0.196386969737627
7510.41110.27296885957280.138031140427190
769.6789.83825957816496-0.160259578164959
7710.4089.808043224090130.59995677590987
7810.15310.10438579135290.0486142086471233
7910.36810.4026771225169-0.0346771225168734
8010.58110.619395981753-0.0383959817529966
8110.59710.31142419731460.285575802685445
8210.6810.32067726806670.359322731933254
839.7389.63865102753110.0993489724689116
849.55610.2631854517764-0.707185451776443

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9.743 & 9.74921180555556 & -0.00621180555555689 \tabularnewline
14 & 8.587 & 8.5914210517089 & -0.0044210517089045 \tabularnewline
15 & 9.731 & 9.74796524911992 & -0.0169652491199201 \tabularnewline
16 & 9.563 & 9.58113773811941 & -0.0181377381194121 \tabularnewline
17 & 9.998 & 10.0105664997792 & -0.0125664997792239 \tabularnewline
18 & 9.437 & 9.44390532731992 & -0.00690532731992022 \tabularnewline
19 & 10.038 & 9.83615719750152 & 0.201842802498481 \tabularnewline
20 & 9.918 & 10.1042072026046 & -0.186207202604637 \tabularnewline
21 & 9.252 & 9.4482280595629 & -0.196228059562895 \tabularnewline
22 & 9.737 & 9.66103748394706 & 0.0759625160529449 \tabularnewline
23 & 9.035 & 9.03409035704378 & 0.00090964295621987 \tabularnewline
24 & 9.133 & 9.03345579566535 & 0.0995442043346504 \tabularnewline
25 & 9.487 & 9.68611954460467 & -0.199119544604669 \tabularnewline
26 & 8.7 & 8.50581874995555 & 0.194181250044446 \tabularnewline
27 & 9.627 & 9.67403227138516 & -0.0470322713851612 \tabularnewline
28 & 8.947 & 9.50203221803877 & -0.555032218038768 \tabularnewline
29 & 9.283 & 9.87054444746039 & -0.58754444746039 \tabularnewline
30 & 8.829 & 9.23124105346515 & -0.402241053465149 \tabularnewline
31 & 9.947 & 9.69649106129245 & 0.250508938707553 \tabularnewline
32 & 9.628 & 9.69575706142734 & -0.0677570614273417 \tabularnewline
33 & 9.318 & 9.02611433325237 & 0.291885666747625 \tabularnewline
34 & 9.605 & 9.45425642565883 & 0.150743574341170 \tabularnewline
35 & 8.64 & 8.7743828634714 & -0.134382863471398 \tabularnewline
36 & 9.214 & 8.81021565708587 & 0.403784342914131 \tabularnewline
37 & 9.567 & 9.29051920343095 & 0.276480796569048 \tabularnewline
38 & 8.547 & 8.4129090037963 & 0.134090996203700 \tabularnewline
39 & 9.185 & 9.41384606663035 & -0.228846066630352 \tabularnewline
40 & 9.47 & 8.88563267155275 & 0.584367328447248 \tabularnewline
41 & 9.123 & 9.36087799802199 & -0.237877998021986 \tabularnewline
42 & 9.278 & 8.89260191180114 & 0.38539808819886 \tabularnewline
43 & 10.17 & 9.88972350180953 & 0.280276498190473 \tabularnewline
44 & 9.434 & 9.70976556226683 & -0.275765562266832 \tabularnewline
45 & 9.655 & 9.27484878619553 & 0.380151213804471 \tabularnewline
46 & 9.429 & 9.64361094053915 & -0.214610940539155 \tabularnewline
47 & 8.739 & 8.75831278021701 & -0.0193127802170068 \tabularnewline
48 & 9.552 & 9.17663770315904 & 0.375362296840962 \tabularnewline
49 & 9.687 & 9.59062220741152 & 0.0963777925884752 \tabularnewline
50 & 9.019 & 8.6186049254116 & 0.400395074588394 \tabularnewline
51 & 9.672 & 9.43163809299605 & 0.240361907003951 \tabularnewline
52 & 9.206 & 9.50915549927118 & -0.303155499271181 \tabularnewline
53 & 9.069 & 9.37133980919556 & -0.302339809195562 \tabularnewline
54 & 9.788 & 9.3164997782435 & 0.471500221756504 \tabularnewline
55 & 10.312 & 10.2694716021273 & 0.0425283978726494 \tabularnewline
56 & 10.105 & 9.7146551264205 & 0.390344873579497 \tabularnewline
57 & 9.863 & 9.79759422460153 & 0.0654057753984656 \tabularnewline
58 & 9.656 & 9.76302433612392 & -0.107024336123915 \tabularnewline
59 & 9.295 & 9.03450554735199 & 0.260494452648013 \tabularnewline
60 & 9.946 & 9.7612348662059 & 0.184765133794105 \tabularnewline
61 & 9.701 & 9.99319182517576 & -0.292191825175763 \tabularnewline
62 & 9.049 & 9.19297379127453 & -0.143973791274528 \tabularnewline
63 & 10.19 & 9.8518986356226 & 0.338101364377390 \tabularnewline
64 & 9.706 & 9.59379184141615 & 0.112208158583853 \tabularnewline
65 & 9.765 & 9.51367114451201 & 0.251328855487987 \tabularnewline
66 & 9.893 & 10.0419911671626 & -0.148991167162610 \tabularnewline
67 & 9.994 & 10.6638057580476 & -0.669805758047628 \tabularnewline
68 & 10.433 & 10.264549639706 & 0.168450360294006 \tabularnewline
69 & 10.073 & 10.1129555016226 & -0.0399555016226181 \tabularnewline
70 & 10.112 & 9.95390909322628 & 0.158090906773724 \tabularnewline
71 & 9.266 & 9.49484565780211 & -0.228845657802111 \tabularnewline
72 & 9.82 & 10.1170063570882 & -0.297006357088240 \tabularnewline
73 & 10.097 & 9.977290695493 & 0.119709304507003 \tabularnewline
74 & 9.115 & 9.31138696973763 & -0.196386969737627 \tabularnewline
75 & 10.411 & 10.2729688595728 & 0.138031140427190 \tabularnewline
76 & 9.678 & 9.83825957816496 & -0.160259578164959 \tabularnewline
77 & 10.408 & 9.80804322409013 & 0.59995677590987 \tabularnewline
78 & 10.153 & 10.1043857913529 & 0.0486142086471233 \tabularnewline
79 & 10.368 & 10.4026771225169 & -0.0346771225168734 \tabularnewline
80 & 10.581 & 10.619395981753 & -0.0383959817529966 \tabularnewline
81 & 10.597 & 10.3114241973146 & 0.285575802685445 \tabularnewline
82 & 10.68 & 10.3206772680667 & 0.359322731933254 \tabularnewline
83 & 9.738 & 9.6386510275311 & 0.0993489724689116 \tabularnewline
84 & 9.556 & 10.2631854517764 & -0.707185451776443 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36919&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]9.743[/C][C]9.74921180555556[/C][C]-0.00621180555555689[/C][/ROW]
[ROW][C]14[/C][C]8.587[/C][C]8.5914210517089[/C][C]-0.0044210517089045[/C][/ROW]
[ROW][C]15[/C][C]9.731[/C][C]9.74796524911992[/C][C]-0.0169652491199201[/C][/ROW]
[ROW][C]16[/C][C]9.563[/C][C]9.58113773811941[/C][C]-0.0181377381194121[/C][/ROW]
[ROW][C]17[/C][C]9.998[/C][C]10.0105664997792[/C][C]-0.0125664997792239[/C][/ROW]
[ROW][C]18[/C][C]9.437[/C][C]9.44390532731992[/C][C]-0.00690532731992022[/C][/ROW]
[ROW][C]19[/C][C]10.038[/C][C]9.83615719750152[/C][C]0.201842802498481[/C][/ROW]
[ROW][C]20[/C][C]9.918[/C][C]10.1042072026046[/C][C]-0.186207202604637[/C][/ROW]
[ROW][C]21[/C][C]9.252[/C][C]9.4482280595629[/C][C]-0.196228059562895[/C][/ROW]
[ROW][C]22[/C][C]9.737[/C][C]9.66103748394706[/C][C]0.0759625160529449[/C][/ROW]
[ROW][C]23[/C][C]9.035[/C][C]9.03409035704378[/C][C]0.00090964295621987[/C][/ROW]
[ROW][C]24[/C][C]9.133[/C][C]9.03345579566535[/C][C]0.0995442043346504[/C][/ROW]
[ROW][C]25[/C][C]9.487[/C][C]9.68611954460467[/C][C]-0.199119544604669[/C][/ROW]
[ROW][C]26[/C][C]8.7[/C][C]8.50581874995555[/C][C]0.194181250044446[/C][/ROW]
[ROW][C]27[/C][C]9.627[/C][C]9.67403227138516[/C][C]-0.0470322713851612[/C][/ROW]
[ROW][C]28[/C][C]8.947[/C][C]9.50203221803877[/C][C]-0.555032218038768[/C][/ROW]
[ROW][C]29[/C][C]9.283[/C][C]9.87054444746039[/C][C]-0.58754444746039[/C][/ROW]
[ROW][C]30[/C][C]8.829[/C][C]9.23124105346515[/C][C]-0.402241053465149[/C][/ROW]
[ROW][C]31[/C][C]9.947[/C][C]9.69649106129245[/C][C]0.250508938707553[/C][/ROW]
[ROW][C]32[/C][C]9.628[/C][C]9.69575706142734[/C][C]-0.0677570614273417[/C][/ROW]
[ROW][C]33[/C][C]9.318[/C][C]9.02611433325237[/C][C]0.291885666747625[/C][/ROW]
[ROW][C]34[/C][C]9.605[/C][C]9.45425642565883[/C][C]0.150743574341170[/C][/ROW]
[ROW][C]35[/C][C]8.64[/C][C]8.7743828634714[/C][C]-0.134382863471398[/C][/ROW]
[ROW][C]36[/C][C]9.214[/C][C]8.81021565708587[/C][C]0.403784342914131[/C][/ROW]
[ROW][C]37[/C][C]9.567[/C][C]9.29051920343095[/C][C]0.276480796569048[/C][/ROW]
[ROW][C]38[/C][C]8.547[/C][C]8.4129090037963[/C][C]0.134090996203700[/C][/ROW]
[ROW][C]39[/C][C]9.185[/C][C]9.41384606663035[/C][C]-0.228846066630352[/C][/ROW]
[ROW][C]40[/C][C]9.47[/C][C]8.88563267155275[/C][C]0.584367328447248[/C][/ROW]
[ROW][C]41[/C][C]9.123[/C][C]9.36087799802199[/C][C]-0.237877998021986[/C][/ROW]
[ROW][C]42[/C][C]9.278[/C][C]8.89260191180114[/C][C]0.38539808819886[/C][/ROW]
[ROW][C]43[/C][C]10.17[/C][C]9.88972350180953[/C][C]0.280276498190473[/C][/ROW]
[ROW][C]44[/C][C]9.434[/C][C]9.70976556226683[/C][C]-0.275765562266832[/C][/ROW]
[ROW][C]45[/C][C]9.655[/C][C]9.27484878619553[/C][C]0.380151213804471[/C][/ROW]
[ROW][C]46[/C][C]9.429[/C][C]9.64361094053915[/C][C]-0.214610940539155[/C][/ROW]
[ROW][C]47[/C][C]8.739[/C][C]8.75831278021701[/C][C]-0.0193127802170068[/C][/ROW]
[ROW][C]48[/C][C]9.552[/C][C]9.17663770315904[/C][C]0.375362296840962[/C][/ROW]
[ROW][C]49[/C][C]9.687[/C][C]9.59062220741152[/C][C]0.0963777925884752[/C][/ROW]
[ROW][C]50[/C][C]9.019[/C][C]8.6186049254116[/C][C]0.400395074588394[/C][/ROW]
[ROW][C]51[/C][C]9.672[/C][C]9.43163809299605[/C][C]0.240361907003951[/C][/ROW]
[ROW][C]52[/C][C]9.206[/C][C]9.50915549927118[/C][C]-0.303155499271181[/C][/ROW]
[ROW][C]53[/C][C]9.069[/C][C]9.37133980919556[/C][C]-0.302339809195562[/C][/ROW]
[ROW][C]54[/C][C]9.788[/C][C]9.3164997782435[/C][C]0.471500221756504[/C][/ROW]
[ROW][C]55[/C][C]10.312[/C][C]10.2694716021273[/C][C]0.0425283978726494[/C][/ROW]
[ROW][C]56[/C][C]10.105[/C][C]9.7146551264205[/C][C]0.390344873579497[/C][/ROW]
[ROW][C]57[/C][C]9.863[/C][C]9.79759422460153[/C][C]0.0654057753984656[/C][/ROW]
[ROW][C]58[/C][C]9.656[/C][C]9.76302433612392[/C][C]-0.107024336123915[/C][/ROW]
[ROW][C]59[/C][C]9.295[/C][C]9.03450554735199[/C][C]0.260494452648013[/C][/ROW]
[ROW][C]60[/C][C]9.946[/C][C]9.7612348662059[/C][C]0.184765133794105[/C][/ROW]
[ROW][C]61[/C][C]9.701[/C][C]9.99319182517576[/C][C]-0.292191825175763[/C][/ROW]
[ROW][C]62[/C][C]9.049[/C][C]9.19297379127453[/C][C]-0.143973791274528[/C][/ROW]
[ROW][C]63[/C][C]10.19[/C][C]9.8518986356226[/C][C]0.338101364377390[/C][/ROW]
[ROW][C]64[/C][C]9.706[/C][C]9.59379184141615[/C][C]0.112208158583853[/C][/ROW]
[ROW][C]65[/C][C]9.765[/C][C]9.51367114451201[/C][C]0.251328855487987[/C][/ROW]
[ROW][C]66[/C][C]9.893[/C][C]10.0419911671626[/C][C]-0.148991167162610[/C][/ROW]
[ROW][C]67[/C][C]9.994[/C][C]10.6638057580476[/C][C]-0.669805758047628[/C][/ROW]
[ROW][C]68[/C][C]10.433[/C][C]10.264549639706[/C][C]0.168450360294006[/C][/ROW]
[ROW][C]69[/C][C]10.073[/C][C]10.1129555016226[/C][C]-0.0399555016226181[/C][/ROW]
[ROW][C]70[/C][C]10.112[/C][C]9.95390909322628[/C][C]0.158090906773724[/C][/ROW]
[ROW][C]71[/C][C]9.266[/C][C]9.49484565780211[/C][C]-0.228845657802111[/C][/ROW]
[ROW][C]72[/C][C]9.82[/C][C]10.1170063570882[/C][C]-0.297006357088240[/C][/ROW]
[ROW][C]73[/C][C]10.097[/C][C]9.977290695493[/C][C]0.119709304507003[/C][/ROW]
[ROW][C]74[/C][C]9.115[/C][C]9.31138696973763[/C][C]-0.196386969737627[/C][/ROW]
[ROW][C]75[/C][C]10.411[/C][C]10.2729688595728[/C][C]0.138031140427190[/C][/ROW]
[ROW][C]76[/C][C]9.678[/C][C]9.83825957816496[/C][C]-0.160259578164959[/C][/ROW]
[ROW][C]77[/C][C]10.408[/C][C]9.80804322409013[/C][C]0.59995677590987[/C][/ROW]
[ROW][C]78[/C][C]10.153[/C][C]10.1043857913529[/C][C]0.0486142086471233[/C][/ROW]
[ROW][C]79[/C][C]10.368[/C][C]10.4026771225169[/C][C]-0.0346771225168734[/C][/ROW]
[ROW][C]80[/C][C]10.581[/C][C]10.619395981753[/C][C]-0.0383959817529966[/C][/ROW]
[ROW][C]81[/C][C]10.597[/C][C]10.3114241973146[/C][C]0.285575802685445[/C][/ROW]
[ROW][C]82[/C][C]10.68[/C][C]10.3206772680667[/C][C]0.359322731933254[/C][/ROW]
[ROW][C]83[/C][C]9.738[/C][C]9.6386510275311[/C][C]0.0993489724689116[/C][/ROW]
[ROW][C]84[/C][C]9.556[/C][C]10.2631854517764[/C][C]-0.707185451776443[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36919&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36919&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
139.7439.74921180555556-0.00621180555555689
148.5878.5914210517089-0.0044210517089045
159.7319.74796524911992-0.0169652491199201
169.5639.58113773811941-0.0181377381194121
179.99810.0105664997792-0.0125664997792239
189.4379.44390532731992-0.00690532731992022
1910.0389.836157197501520.201842802498481
209.91810.1042072026046-0.186207202604637
219.2529.4482280595629-0.196228059562895
229.7379.661037483947060.0759625160529449
239.0359.034090357043780.00090964295621987
249.1339.033455795665350.0995442043346504
259.4879.68611954460467-0.199119544604669
268.78.505818749955550.194181250044446
279.6279.67403227138516-0.0470322713851612
288.9479.50203221803877-0.555032218038768
299.2839.87054444746039-0.58754444746039
308.8299.23124105346515-0.402241053465149
319.9479.696491061292450.250508938707553
329.6289.69575706142734-0.0677570614273417
339.3189.026114333252370.291885666747625
349.6059.454256425658830.150743574341170
358.648.7743828634714-0.134382863471398
369.2148.810215657085870.403784342914131
379.5679.290519203430950.276480796569048
388.5478.41290900379630.134090996203700
399.1859.41384606663035-0.228846066630352
409.478.885632671552750.584367328447248
419.1239.36087799802199-0.237877998021986
429.2788.892601911801140.38539808819886
4310.179.889723501809530.280276498190473
449.4349.70976556226683-0.275765562266832
459.6559.274848786195530.380151213804471
469.4299.64361094053915-0.214610940539155
478.7398.75831278021701-0.0193127802170068
489.5529.176637703159040.375362296840962
499.6879.590622207411520.0963777925884752
509.0198.61860492541160.400395074588394
519.6729.431638092996050.240361907003951
529.2069.50915549927118-0.303155499271181
539.0699.37133980919556-0.302339809195562
549.7889.31649977824350.471500221756504
5510.31210.26947160212730.0425283978726494
5610.1059.71465512642050.390344873579497
579.8639.797594224601530.0654057753984656
589.6569.76302433612392-0.107024336123915
599.2959.034505547351990.260494452648013
609.9469.76123486620590.184765133794105
619.7019.99319182517576-0.292191825175763
629.0499.19297379127453-0.143973791274528
6310.199.85189863562260.338101364377390
649.7069.593791841416150.112208158583853
659.7659.513671144512010.251328855487987
669.89310.0419911671626-0.148991167162610
679.99410.6638057580476-0.669805758047628
6810.43310.2645496397060.168450360294006
6910.07310.1129555016226-0.0399555016226181
7010.1129.953909093226280.158090906773724
719.2669.49484565780211-0.228845657802111
729.8210.1170063570882-0.297006357088240
7310.0979.9772906954930.119709304507003
749.1159.31138696973763-0.196386969737627
7510.41110.27296885957280.138031140427190
769.6789.83825957816496-0.160259578164959
7710.4089.808043224090130.59995677590987
7810.15310.10438579135290.0486142086471233
7910.36810.4026771225169-0.0346771225168734
8010.58110.619395981753-0.0383959817529966
8110.59710.31142419731460.285575802685445
8210.6810.32067726806670.359322731933254
839.7389.63865102753110.0993489724689116
849.55610.2631854517764-0.707185451776443







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8510.35912042222389.8103701484197610.9078706960277
869.480195467494978.9276478434434610.0327430915465
8710.688103043116310.130867889214311.2453381970183
8810.05085331993199.4879638925834510.6137427472804
8910.54084857950429.9712692842366511.1104278747719
9010.41568699787959.8383219140740410.9930520816850
9110.654167451868410.067869463346911.2404654403899
9210.872061182781910.275641471202511.4684808943613
9310.779620236416410.171857875152511.3873825976803
9410.803758984393110.183410370875511.4241075979107
959.906672456372179.2724803398522510.5408645728921
969.985889691793449.3365915880071510.6351877955797

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 10.3591204222238 & 9.81037014841976 & 10.9078706960277 \tabularnewline
86 & 9.48019546749497 & 8.92764784344346 & 10.0327430915465 \tabularnewline
87 & 10.6881030431163 & 10.1308678892143 & 11.2453381970183 \tabularnewline
88 & 10.0508533199319 & 9.48796389258345 & 10.6137427472804 \tabularnewline
89 & 10.5408485795042 & 9.97126928423665 & 11.1104278747719 \tabularnewline
90 & 10.4156869978795 & 9.83832191407404 & 10.9930520816850 \tabularnewline
91 & 10.6541674518684 & 10.0678694633469 & 11.2404654403899 \tabularnewline
92 & 10.8720611827819 & 10.2756414712025 & 11.4684808943613 \tabularnewline
93 & 10.7796202364164 & 10.1718578751525 & 11.3873825976803 \tabularnewline
94 & 10.8037589843931 & 10.1834103708755 & 11.4241075979107 \tabularnewline
95 & 9.90667245637217 & 9.27248033985225 & 10.5408645728921 \tabularnewline
96 & 9.98588969179344 & 9.33659158800715 & 10.6351877955797 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36919&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]85[/C][C]10.3591204222238[/C][C]9.81037014841976[/C][C]10.9078706960277[/C][/ROW]
[ROW][C]86[/C][C]9.48019546749497[/C][C]8.92764784344346[/C][C]10.0327430915465[/C][/ROW]
[ROW][C]87[/C][C]10.6881030431163[/C][C]10.1308678892143[/C][C]11.2453381970183[/C][/ROW]
[ROW][C]88[/C][C]10.0508533199319[/C][C]9.48796389258345[/C][C]10.6137427472804[/C][/ROW]
[ROW][C]89[/C][C]10.5408485795042[/C][C]9.97126928423665[/C][C]11.1104278747719[/C][/ROW]
[ROW][C]90[/C][C]10.4156869978795[/C][C]9.83832191407404[/C][C]10.9930520816850[/C][/ROW]
[ROW][C]91[/C][C]10.6541674518684[/C][C]10.0678694633469[/C][C]11.2404654403899[/C][/ROW]
[ROW][C]92[/C][C]10.8720611827819[/C][C]10.2756414712025[/C][C]11.4684808943613[/C][/ROW]
[ROW][C]93[/C][C]10.7796202364164[/C][C]10.1718578751525[/C][C]11.3873825976803[/C][/ROW]
[ROW][C]94[/C][C]10.8037589843931[/C][C]10.1834103708755[/C][C]11.4241075979107[/C][/ROW]
[ROW][C]95[/C][C]9.90667245637217[/C][C]9.27248033985225[/C][C]10.5408645728921[/C][/ROW]
[ROW][C]96[/C][C]9.98588969179344[/C][C]9.33659158800715[/C][C]10.6351877955797[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36919&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36919&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
8510.35912042222389.8103701484197610.9078706960277
869.480195467494978.9276478434434610.0327430915465
8710.688103043116310.130867889214311.2453381970183
8810.05085331993199.4879638925834510.6137427472804
8910.54084857950429.9712692842366511.1104278747719
9010.41568699787959.8383219140740410.9930520816850
9110.654167451868410.067869463346911.2404654403899
9210.872061182781910.275641471202511.4684808943613
9310.779620236416410.171857875152511.3873825976803
9410.803758984393110.183410370875511.4241075979107
959.906672456372179.2724803398522510.5408645728921
969.985889691793449.3365915880071510.6351877955797



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')