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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 computationSat, 23 Apr 2016 16:48:04 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/23/t1461426502vf3mnkek62vn0w9.htm/, Retrieved Mon, 13 May 2024 11:21:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294608, Retrieved Mon, 13 May 2024 11:21:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-23 15:48:04] [3e335ee00fe90bc89d5a716289abc4a1] [Current]
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Dataseries X:
7612
7381
6978
6819
6688
6454
6679
6921
7807
7898
7832
7384
7620
7281
6929
6587
6071
5928
5964
6374
7160
7213
6890
6525
6739
6580
6391
6254
6114
5978
6315
6427
7132
7292
7708
7525
7450
7526
7263
7070
6893
6781
7188
7015
8273
8470
8230
8137
8122
8367
8141
7750
7504
7330
7608
7647
8942
8865
8320
8207
8105
8290
8162
8051
7699
7440
7656
7549
9086
8942
8764
8500
8239
8443
8349
8288
7970
7496
7745
7543
9036
9075
8859
8605
8419
8495
8284
7582
7691
7046
7442
7596
8597
8436
7881
7477
7508
7361
7299
6914
6768
6746
7052
7139
7714
7750
7622
7424
7444
7208
7128
7022
6688
6199
6400
6474
7182
7330
7410
7442
7753
7762
7814
7838
7298
7155
7076
7450
8216
8246
8335
8171
8485
8435
8369
8210
7888
8061
8139
7837
8943
8523
8104
7969
7921
7930
7706
7552
7379
6946
7128
7393
8092
8004
7903
7710
7867
7860
7723
7477
7126
7161
7162
7406
7944
8084
8088
7972
8184
7914
7845
7610
7278
6883
7123
7182
7912
7893
7671
7403
7663
7589
7450
7069
6670
6285
6506
6539
7291
7391
7126
6752
6835
6664
6562
6174
5741
5398
5203
5673
6379
6418
6272
6059




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294608&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294608&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294608&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0355839451433407
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0355839451433407 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294608&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0355839451433407[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294608&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294608&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
alpha1
beta0.0355839451433407
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
369787150-172
468196740.8795614353578.1204385646543
566886584.6593948358103.340605164196
664546457.33666126105-3.33666126104617
766796223.21792968977455.782070310229
869216464.43645387701456.563546122991
978076722.68278605671084.3172139433
1078987647.26707031564250.732929684364
1178327747.1891371311584.810862868846
1273847684.20704222304-300.207042223039
1376207225.52449130093394.475508699071
1472817475.56148616287-194.561486162868
1569297129.63822091224-200.638220912242
1665876770.49872146564-183.498721465644
1760716421.96911302714-350.969113027137
1859285893.4802473621734.5197526378279
1959645751.7085963464212.291403653601
2063745795.26276200841578.737237991589
2171606225.85651613751934.143483862487
2272137045.09702662328167.902973376716
2368907104.07167681733-214.071676817325
2465256773.45416201271-248.454162012715
2567396399.61318274102339.386817258981
2665806625.68990462874-45.6899046287363
2763916465.06407756882-74.0640775688225
2862546273.42858549552-19.4285854955215
2961146135.73723977504-21.737239775036
3059785994.96374302731-16.9637430273133
3163155858.360106126456.639893873996
3264276211.60915505988215.390844940123
3371326331.2736110706800.726388929395
3472927064.76661496909227.233385030907
3577087232.85247527677475.147524723231
3675257665.76009873151-140.760098731515
3774507477.75129909988-27.7512990998803
3875267401.76379839505124.236201604946
3972637482.18461257778-219.184612577781
4070707211.38515934755-141.385159347549
4168937013.35411759324-120.354117593243
4267816832.07144327503-51.0714432750301
4371886718.25411983914469.745880160859
4470157141.96953147009-126.969531470095
4582736964.451454627391308.54854537261
4684708269.01477428333200.985225716675
4782308473.16662152985-243.166621529848
4881378224.51379380864-87.5137938086391
4981228128.39970777047-6.3997077704671
5083678113.17198092023253.82801907977
5181418367.20418322701-226.204183227006
5277508133.15494597986-383.154945979863
5375047728.52078140072-224.520781400715
5473307474.53144623181-144.531446231813
5576087295.38844717761312.611552822388
5676477584.5123995244262.4876004755815
5789427625.735954871881316.26404512812
5888658967.57382244787-102.573822447872
5983208886.92384117674-566.923841176744
6082078321.75045431186-114.750454311858
6181058204.66718044045-99.6671804404523
6282908099.12062895907190.879371040933
6381628290.91287002718-128.912870027183
6480518158.32564153187-107.325641531866
6576998043.50657179112-344.506571791121
6674407679.24766883899-239.247668838986
6776567411.73429291535244.265707084653
6875497636.42623043665-87.4262304366466
6990867526.31526024871559.6847397513
7089429118.81499646892-176.814996468916
7187648968.52322133405-204.523221334046
7285008783.24547824556-283.245478245555
7382398509.16648668557-270.166486685566
7484438238.55289724378204.447102756221
7583498449.82793173297-100.827931732971
7682888352.24007614127-64.2400761412682
7779708288.95416079585-318.954160795853
7874967959.60451343485-463.604513434853
7977457469.10763586058275.892364139418
8075437727.92497461159-184.924974611587
8190367519.344614459371516.65538554063
8290759066.31319649988.68680350019713
8388599105.62230723903-246.622307239026
8486058880.84651258711-275.846512587108
8584198617.03080541523-198.030805415226
8684958423.9840880986471.0159119013606
8782848502.51111441204-218.511114412042
8875828283.73562690359-701.735626903594
8976917556.76510485073134.234895149271
9070467670.54171199604-624.541711996042
9174427003.31805397665438.681946023353
9275967414.92808827932181.071911720685
9385977575.371341252981021.62865874702
9484368612.7249194027-176.724919402703
9578818445.43634956522-564.436349565216
9674777870.35147746538-393.35147746538
9775087452.354480069255.6455199308002
9873617485.33456719789-124.33456719789
9972997333.9102527793-34.9102527792993
10069147270.66800825946-356.66800825946
10167686872.97635341917-104.976353419172
10267466723.2408806177622.7591193822445
10370526702.05073987336349.949260126636
10471397020.50331514866118.496684851337
10577147111.71989468208602.280105317919
10677507708.1513969106441.8486030893609
10776227745.6405353073-123.640535307296
10874247613.24091728143-189.240917281428
10974447408.5069788620135.4930211379897
11072087429.76996057916-221.769960579156
11171287185.87851046747-57.8785104674662
11270227103.81896472601-81.8189647260142
11366886994.90752317352-306.907523173519
11461996649.98654270483-450.986542704833
11564006144.93866230884255.061337691161
11664746355.01475095743118.985249042571
11771826433.24871553223748.751284467773
11873307167.89224016473162.107759835266
11974107321.6606737980288.3393262019781
12074427404.8041355355937.1958644644074
12177537438.12771113625314.872288863747
12277627760.332109390341.6678906096613
12378147769.391459518344.6085404817022
12478387822.9788073757215.0211926242764
12572987847.51332067005-549.513320670053
12671557287.95946881179-132.959468811795
12770767140.22824636731-64.2282463673082
12874507058.94275197192391.057248028079
12982167446.85811163366769.141888366342
13082468240.227214396735.77278560326886
13183358270.4326328829664.5673671170371
13281718361.73019453251-190.730194532505
13384858190.94326175308294.056738246918
13484358515.40696059589-80.4069605958903
13583698462.5457637209-93.5457637209038
13682108393.21703639627-183.217036396267
13778888227.69745142382-339.697451423815
13880617893.60967594702167.390324052982
13981398072.5660840556566.4339159443543
14078378152.93006487627-315.930064876267
14189437839.688026778581103.31197322142
14285238984.94821950968-461.948219509681
14381048548.51027940758-444.510279407583
14479698113.69285000949-144.692850009493
14579217973.54410757212-52.5441075721219
14679307923.674380930676.32561906933097
14777067932.89947141263-226.89947141263
14875527700.82549306883-148.82549306883
14973797541.52969488754-162.529694887538
15069467362.7462471405-416.746247140496
15171286914.91677154356213.083228456444
15273937104.49911345592288.500886544084
15380927379.76511317651712.234886823494
15480048104.10924031841-100.109240318407
15579038012.54695860257-109.546958602575
15677107907.64884563704-197.648845637041
15778677707.61571995625159.384280043752
15878607870.28724143404-10.2872414340354
15977237862.92118079917-139.921180799171
16074777720.94223317722-243.942233177221
16171267466.2618061337-340.261806133699
16271617103.1539486898657.8460513101363
16371627140.2123394064421.787660593558
16474067141.98763032581264.012369674195
16579447395.38223200546548.617767994545
16680847952.90421656644131.095783433565
16780888097.56912173266-9.56912173265846
16879728101.22861462985-129.228614629853
16981847980.63015069591203.369849304086
17079148199.86685225736-285.866852257361
17178457919.69458186834-74.6945818683353
17276107848.03665396463-238.036653964627
17372787604.56637072785-326.566370727846
17468837260.94585090621-377.945850906207
17571236852.49704648041270.502953519594
17671827102.1226087395679.8773912604402
17779127163.96496144836748.035038551636
17878937920.58299922548-27.5829992254821
17976717900.60148729415-229.601487294154
18074037670.43136056545-267.43136056545
18176637392.91509770148270.08490229852
18275897662.52578404891-73.5257840489148
18374507585.9094465827-135.909446582697
18470697442.07325229104-373.073252291037
18566707047.79783414706-377.797834147064
18662856635.3542967415-350.354296741502
18765066237.88730866552268.112691334481
18865396468.427815966270.572184033801
18972916503.9390526915787.060947308497
19073917283.94578626499107.054213735006
19171267387.7551975339-261.755197533905
19267527113.44091494387-361.440914943873
19368356726.57942125395108.420578746048
19466646813.43745318046-149.437453180461
19565626637.11987904413-75.1198790441267
19661746532.44681738905-358.446817389046
19757416131.69186550227-390.691865502269
19853985684.78950759229-286.789507592287
19952035331.58440548644-128.584405486437
20056735132.00886505532540.991134944681
20163795621.25946392422757.740536075776
20264186354.2228615928363.7771384071702
20362726395.49230378731-123.49230378731
20460596245.09796042372-186.097960423717

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 6978 & 7150 & -172 \tabularnewline
4 & 6819 & 6740.87956143535 & 78.1204385646543 \tabularnewline
5 & 6688 & 6584.6593948358 & 103.340605164196 \tabularnewline
6 & 6454 & 6457.33666126105 & -3.33666126104617 \tabularnewline
7 & 6679 & 6223.21792968977 & 455.782070310229 \tabularnewline
8 & 6921 & 6464.43645387701 & 456.563546122991 \tabularnewline
9 & 7807 & 6722.6827860567 & 1084.3172139433 \tabularnewline
10 & 7898 & 7647.26707031564 & 250.732929684364 \tabularnewline
11 & 7832 & 7747.18913713115 & 84.810862868846 \tabularnewline
12 & 7384 & 7684.20704222304 & -300.207042223039 \tabularnewline
13 & 7620 & 7225.52449130093 & 394.475508699071 \tabularnewline
14 & 7281 & 7475.56148616287 & -194.561486162868 \tabularnewline
15 & 6929 & 7129.63822091224 & -200.638220912242 \tabularnewline
16 & 6587 & 6770.49872146564 & -183.498721465644 \tabularnewline
17 & 6071 & 6421.96911302714 & -350.969113027137 \tabularnewline
18 & 5928 & 5893.48024736217 & 34.5197526378279 \tabularnewline
19 & 5964 & 5751.7085963464 & 212.291403653601 \tabularnewline
20 & 6374 & 5795.26276200841 & 578.737237991589 \tabularnewline
21 & 7160 & 6225.85651613751 & 934.143483862487 \tabularnewline
22 & 7213 & 7045.09702662328 & 167.902973376716 \tabularnewline
23 & 6890 & 7104.07167681733 & -214.071676817325 \tabularnewline
24 & 6525 & 6773.45416201271 & -248.454162012715 \tabularnewline
25 & 6739 & 6399.61318274102 & 339.386817258981 \tabularnewline
26 & 6580 & 6625.68990462874 & -45.6899046287363 \tabularnewline
27 & 6391 & 6465.06407756882 & -74.0640775688225 \tabularnewline
28 & 6254 & 6273.42858549552 & -19.4285854955215 \tabularnewline
29 & 6114 & 6135.73723977504 & -21.737239775036 \tabularnewline
30 & 5978 & 5994.96374302731 & -16.9637430273133 \tabularnewline
31 & 6315 & 5858.360106126 & 456.639893873996 \tabularnewline
32 & 6427 & 6211.60915505988 & 215.390844940123 \tabularnewline
33 & 7132 & 6331.2736110706 & 800.726388929395 \tabularnewline
34 & 7292 & 7064.76661496909 & 227.233385030907 \tabularnewline
35 & 7708 & 7232.85247527677 & 475.147524723231 \tabularnewline
36 & 7525 & 7665.76009873151 & -140.760098731515 \tabularnewline
37 & 7450 & 7477.75129909988 & -27.7512990998803 \tabularnewline
38 & 7526 & 7401.76379839505 & 124.236201604946 \tabularnewline
39 & 7263 & 7482.18461257778 & -219.184612577781 \tabularnewline
40 & 7070 & 7211.38515934755 & -141.385159347549 \tabularnewline
41 & 6893 & 7013.35411759324 & -120.354117593243 \tabularnewline
42 & 6781 & 6832.07144327503 & -51.0714432750301 \tabularnewline
43 & 7188 & 6718.25411983914 & 469.745880160859 \tabularnewline
44 & 7015 & 7141.96953147009 & -126.969531470095 \tabularnewline
45 & 8273 & 6964.45145462739 & 1308.54854537261 \tabularnewline
46 & 8470 & 8269.01477428333 & 200.985225716675 \tabularnewline
47 & 8230 & 8473.16662152985 & -243.166621529848 \tabularnewline
48 & 8137 & 8224.51379380864 & -87.5137938086391 \tabularnewline
49 & 8122 & 8128.39970777047 & -6.3997077704671 \tabularnewline
50 & 8367 & 8113.17198092023 & 253.82801907977 \tabularnewline
51 & 8141 & 8367.20418322701 & -226.204183227006 \tabularnewline
52 & 7750 & 8133.15494597986 & -383.154945979863 \tabularnewline
53 & 7504 & 7728.52078140072 & -224.520781400715 \tabularnewline
54 & 7330 & 7474.53144623181 & -144.531446231813 \tabularnewline
55 & 7608 & 7295.38844717761 & 312.611552822388 \tabularnewline
56 & 7647 & 7584.51239952442 & 62.4876004755815 \tabularnewline
57 & 8942 & 7625.73595487188 & 1316.26404512812 \tabularnewline
58 & 8865 & 8967.57382244787 & -102.573822447872 \tabularnewline
59 & 8320 & 8886.92384117674 & -566.923841176744 \tabularnewline
60 & 8207 & 8321.75045431186 & -114.750454311858 \tabularnewline
61 & 8105 & 8204.66718044045 & -99.6671804404523 \tabularnewline
62 & 8290 & 8099.12062895907 & 190.879371040933 \tabularnewline
63 & 8162 & 8290.91287002718 & -128.912870027183 \tabularnewline
64 & 8051 & 8158.32564153187 & -107.325641531866 \tabularnewline
65 & 7699 & 8043.50657179112 & -344.506571791121 \tabularnewline
66 & 7440 & 7679.24766883899 & -239.247668838986 \tabularnewline
67 & 7656 & 7411.73429291535 & 244.265707084653 \tabularnewline
68 & 7549 & 7636.42623043665 & -87.4262304366466 \tabularnewline
69 & 9086 & 7526.3152602487 & 1559.6847397513 \tabularnewline
70 & 8942 & 9118.81499646892 & -176.814996468916 \tabularnewline
71 & 8764 & 8968.52322133405 & -204.523221334046 \tabularnewline
72 & 8500 & 8783.24547824556 & -283.245478245555 \tabularnewline
73 & 8239 & 8509.16648668557 & -270.166486685566 \tabularnewline
74 & 8443 & 8238.55289724378 & 204.447102756221 \tabularnewline
75 & 8349 & 8449.82793173297 & -100.827931732971 \tabularnewline
76 & 8288 & 8352.24007614127 & -64.2400761412682 \tabularnewline
77 & 7970 & 8288.95416079585 & -318.954160795853 \tabularnewline
78 & 7496 & 7959.60451343485 & -463.604513434853 \tabularnewline
79 & 7745 & 7469.10763586058 & 275.892364139418 \tabularnewline
80 & 7543 & 7727.92497461159 & -184.924974611587 \tabularnewline
81 & 9036 & 7519.34461445937 & 1516.65538554063 \tabularnewline
82 & 9075 & 9066.3131964998 & 8.68680350019713 \tabularnewline
83 & 8859 & 9105.62230723903 & -246.622307239026 \tabularnewline
84 & 8605 & 8880.84651258711 & -275.846512587108 \tabularnewline
85 & 8419 & 8617.03080541523 & -198.030805415226 \tabularnewline
86 & 8495 & 8423.98408809864 & 71.0159119013606 \tabularnewline
87 & 8284 & 8502.51111441204 & -218.511114412042 \tabularnewline
88 & 7582 & 8283.73562690359 & -701.735626903594 \tabularnewline
89 & 7691 & 7556.76510485073 & 134.234895149271 \tabularnewline
90 & 7046 & 7670.54171199604 & -624.541711996042 \tabularnewline
91 & 7442 & 7003.31805397665 & 438.681946023353 \tabularnewline
92 & 7596 & 7414.92808827932 & 181.071911720685 \tabularnewline
93 & 8597 & 7575.37134125298 & 1021.62865874702 \tabularnewline
94 & 8436 & 8612.7249194027 & -176.724919402703 \tabularnewline
95 & 7881 & 8445.43634956522 & -564.436349565216 \tabularnewline
96 & 7477 & 7870.35147746538 & -393.35147746538 \tabularnewline
97 & 7508 & 7452.3544800692 & 55.6455199308002 \tabularnewline
98 & 7361 & 7485.33456719789 & -124.33456719789 \tabularnewline
99 & 7299 & 7333.9102527793 & -34.9102527792993 \tabularnewline
100 & 6914 & 7270.66800825946 & -356.66800825946 \tabularnewline
101 & 6768 & 6872.97635341917 & -104.976353419172 \tabularnewline
102 & 6746 & 6723.24088061776 & 22.7591193822445 \tabularnewline
103 & 7052 & 6702.05073987336 & 349.949260126636 \tabularnewline
104 & 7139 & 7020.50331514866 & 118.496684851337 \tabularnewline
105 & 7714 & 7111.71989468208 & 602.280105317919 \tabularnewline
106 & 7750 & 7708.15139691064 & 41.8486030893609 \tabularnewline
107 & 7622 & 7745.6405353073 & -123.640535307296 \tabularnewline
108 & 7424 & 7613.24091728143 & -189.240917281428 \tabularnewline
109 & 7444 & 7408.50697886201 & 35.4930211379897 \tabularnewline
110 & 7208 & 7429.76996057916 & -221.769960579156 \tabularnewline
111 & 7128 & 7185.87851046747 & -57.8785104674662 \tabularnewline
112 & 7022 & 7103.81896472601 & -81.8189647260142 \tabularnewline
113 & 6688 & 6994.90752317352 & -306.907523173519 \tabularnewline
114 & 6199 & 6649.98654270483 & -450.986542704833 \tabularnewline
115 & 6400 & 6144.93866230884 & 255.061337691161 \tabularnewline
116 & 6474 & 6355.01475095743 & 118.985249042571 \tabularnewline
117 & 7182 & 6433.24871553223 & 748.751284467773 \tabularnewline
118 & 7330 & 7167.89224016473 & 162.107759835266 \tabularnewline
119 & 7410 & 7321.66067379802 & 88.3393262019781 \tabularnewline
120 & 7442 & 7404.80413553559 & 37.1958644644074 \tabularnewline
121 & 7753 & 7438.12771113625 & 314.872288863747 \tabularnewline
122 & 7762 & 7760.33210939034 & 1.6678906096613 \tabularnewline
123 & 7814 & 7769.3914595183 & 44.6085404817022 \tabularnewline
124 & 7838 & 7822.97880737572 & 15.0211926242764 \tabularnewline
125 & 7298 & 7847.51332067005 & -549.513320670053 \tabularnewline
126 & 7155 & 7287.95946881179 & -132.959468811795 \tabularnewline
127 & 7076 & 7140.22824636731 & -64.2282463673082 \tabularnewline
128 & 7450 & 7058.94275197192 & 391.057248028079 \tabularnewline
129 & 8216 & 7446.85811163366 & 769.141888366342 \tabularnewline
130 & 8246 & 8240.22721439673 & 5.77278560326886 \tabularnewline
131 & 8335 & 8270.43263288296 & 64.5673671170371 \tabularnewline
132 & 8171 & 8361.73019453251 & -190.730194532505 \tabularnewline
133 & 8485 & 8190.94326175308 & 294.056738246918 \tabularnewline
134 & 8435 & 8515.40696059589 & -80.4069605958903 \tabularnewline
135 & 8369 & 8462.5457637209 & -93.5457637209038 \tabularnewline
136 & 8210 & 8393.21703639627 & -183.217036396267 \tabularnewline
137 & 7888 & 8227.69745142382 & -339.697451423815 \tabularnewline
138 & 8061 & 7893.60967594702 & 167.390324052982 \tabularnewline
139 & 8139 & 8072.56608405565 & 66.4339159443543 \tabularnewline
140 & 7837 & 8152.93006487627 & -315.930064876267 \tabularnewline
141 & 8943 & 7839.68802677858 & 1103.31197322142 \tabularnewline
142 & 8523 & 8984.94821950968 & -461.948219509681 \tabularnewline
143 & 8104 & 8548.51027940758 & -444.510279407583 \tabularnewline
144 & 7969 & 8113.69285000949 & -144.692850009493 \tabularnewline
145 & 7921 & 7973.54410757212 & -52.5441075721219 \tabularnewline
146 & 7930 & 7923.67438093067 & 6.32561906933097 \tabularnewline
147 & 7706 & 7932.89947141263 & -226.89947141263 \tabularnewline
148 & 7552 & 7700.82549306883 & -148.82549306883 \tabularnewline
149 & 7379 & 7541.52969488754 & -162.529694887538 \tabularnewline
150 & 6946 & 7362.7462471405 & -416.746247140496 \tabularnewline
151 & 7128 & 6914.91677154356 & 213.083228456444 \tabularnewline
152 & 7393 & 7104.49911345592 & 288.500886544084 \tabularnewline
153 & 8092 & 7379.76511317651 & 712.234886823494 \tabularnewline
154 & 8004 & 8104.10924031841 & -100.109240318407 \tabularnewline
155 & 7903 & 8012.54695860257 & -109.546958602575 \tabularnewline
156 & 7710 & 7907.64884563704 & -197.648845637041 \tabularnewline
157 & 7867 & 7707.61571995625 & 159.384280043752 \tabularnewline
158 & 7860 & 7870.28724143404 & -10.2872414340354 \tabularnewline
159 & 7723 & 7862.92118079917 & -139.921180799171 \tabularnewline
160 & 7477 & 7720.94223317722 & -243.942233177221 \tabularnewline
161 & 7126 & 7466.2618061337 & -340.261806133699 \tabularnewline
162 & 7161 & 7103.15394868986 & 57.8460513101363 \tabularnewline
163 & 7162 & 7140.21233940644 & 21.787660593558 \tabularnewline
164 & 7406 & 7141.98763032581 & 264.012369674195 \tabularnewline
165 & 7944 & 7395.38223200546 & 548.617767994545 \tabularnewline
166 & 8084 & 7952.90421656644 & 131.095783433565 \tabularnewline
167 & 8088 & 8097.56912173266 & -9.56912173265846 \tabularnewline
168 & 7972 & 8101.22861462985 & -129.228614629853 \tabularnewline
169 & 8184 & 7980.63015069591 & 203.369849304086 \tabularnewline
170 & 7914 & 8199.86685225736 & -285.866852257361 \tabularnewline
171 & 7845 & 7919.69458186834 & -74.6945818683353 \tabularnewline
172 & 7610 & 7848.03665396463 & -238.036653964627 \tabularnewline
173 & 7278 & 7604.56637072785 & -326.566370727846 \tabularnewline
174 & 6883 & 7260.94585090621 & -377.945850906207 \tabularnewline
175 & 7123 & 6852.49704648041 & 270.502953519594 \tabularnewline
176 & 7182 & 7102.12260873956 & 79.8773912604402 \tabularnewline
177 & 7912 & 7163.96496144836 & 748.035038551636 \tabularnewline
178 & 7893 & 7920.58299922548 & -27.5829992254821 \tabularnewline
179 & 7671 & 7900.60148729415 & -229.601487294154 \tabularnewline
180 & 7403 & 7670.43136056545 & -267.43136056545 \tabularnewline
181 & 7663 & 7392.91509770148 & 270.08490229852 \tabularnewline
182 & 7589 & 7662.52578404891 & -73.5257840489148 \tabularnewline
183 & 7450 & 7585.9094465827 & -135.909446582697 \tabularnewline
184 & 7069 & 7442.07325229104 & -373.073252291037 \tabularnewline
185 & 6670 & 7047.79783414706 & -377.797834147064 \tabularnewline
186 & 6285 & 6635.3542967415 & -350.354296741502 \tabularnewline
187 & 6506 & 6237.88730866552 & 268.112691334481 \tabularnewline
188 & 6539 & 6468.4278159662 & 70.572184033801 \tabularnewline
189 & 7291 & 6503.9390526915 & 787.060947308497 \tabularnewline
190 & 7391 & 7283.94578626499 & 107.054213735006 \tabularnewline
191 & 7126 & 7387.7551975339 & -261.755197533905 \tabularnewline
192 & 6752 & 7113.44091494387 & -361.440914943873 \tabularnewline
193 & 6835 & 6726.57942125395 & 108.420578746048 \tabularnewline
194 & 6664 & 6813.43745318046 & -149.437453180461 \tabularnewline
195 & 6562 & 6637.11987904413 & -75.1198790441267 \tabularnewline
196 & 6174 & 6532.44681738905 & -358.446817389046 \tabularnewline
197 & 5741 & 6131.69186550227 & -390.691865502269 \tabularnewline
198 & 5398 & 5684.78950759229 & -286.789507592287 \tabularnewline
199 & 5203 & 5331.58440548644 & -128.584405486437 \tabularnewline
200 & 5673 & 5132.00886505532 & 540.991134944681 \tabularnewline
201 & 6379 & 5621.25946392422 & 757.740536075776 \tabularnewline
202 & 6418 & 6354.22286159283 & 63.7771384071702 \tabularnewline
203 & 6272 & 6395.49230378731 & -123.49230378731 \tabularnewline
204 & 6059 & 6245.09796042372 & -186.097960423717 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294608&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]6978[/C][C]7150[/C][C]-172[/C][/ROW]
[ROW][C]4[/C][C]6819[/C][C]6740.87956143535[/C][C]78.1204385646543[/C][/ROW]
[ROW][C]5[/C][C]6688[/C][C]6584.6593948358[/C][C]103.340605164196[/C][/ROW]
[ROW][C]6[/C][C]6454[/C][C]6457.33666126105[/C][C]-3.33666126104617[/C][/ROW]
[ROW][C]7[/C][C]6679[/C][C]6223.21792968977[/C][C]455.782070310229[/C][/ROW]
[ROW][C]8[/C][C]6921[/C][C]6464.43645387701[/C][C]456.563546122991[/C][/ROW]
[ROW][C]9[/C][C]7807[/C][C]6722.6827860567[/C][C]1084.3172139433[/C][/ROW]
[ROW][C]10[/C][C]7898[/C][C]7647.26707031564[/C][C]250.732929684364[/C][/ROW]
[ROW][C]11[/C][C]7832[/C][C]7747.18913713115[/C][C]84.810862868846[/C][/ROW]
[ROW][C]12[/C][C]7384[/C][C]7684.20704222304[/C][C]-300.207042223039[/C][/ROW]
[ROW][C]13[/C][C]7620[/C][C]7225.52449130093[/C][C]394.475508699071[/C][/ROW]
[ROW][C]14[/C][C]7281[/C][C]7475.56148616287[/C][C]-194.561486162868[/C][/ROW]
[ROW][C]15[/C][C]6929[/C][C]7129.63822091224[/C][C]-200.638220912242[/C][/ROW]
[ROW][C]16[/C][C]6587[/C][C]6770.49872146564[/C][C]-183.498721465644[/C][/ROW]
[ROW][C]17[/C][C]6071[/C][C]6421.96911302714[/C][C]-350.969113027137[/C][/ROW]
[ROW][C]18[/C][C]5928[/C][C]5893.48024736217[/C][C]34.5197526378279[/C][/ROW]
[ROW][C]19[/C][C]5964[/C][C]5751.7085963464[/C][C]212.291403653601[/C][/ROW]
[ROW][C]20[/C][C]6374[/C][C]5795.26276200841[/C][C]578.737237991589[/C][/ROW]
[ROW][C]21[/C][C]7160[/C][C]6225.85651613751[/C][C]934.143483862487[/C][/ROW]
[ROW][C]22[/C][C]7213[/C][C]7045.09702662328[/C][C]167.902973376716[/C][/ROW]
[ROW][C]23[/C][C]6890[/C][C]7104.07167681733[/C][C]-214.071676817325[/C][/ROW]
[ROW][C]24[/C][C]6525[/C][C]6773.45416201271[/C][C]-248.454162012715[/C][/ROW]
[ROW][C]25[/C][C]6739[/C][C]6399.61318274102[/C][C]339.386817258981[/C][/ROW]
[ROW][C]26[/C][C]6580[/C][C]6625.68990462874[/C][C]-45.6899046287363[/C][/ROW]
[ROW][C]27[/C][C]6391[/C][C]6465.06407756882[/C][C]-74.0640775688225[/C][/ROW]
[ROW][C]28[/C][C]6254[/C][C]6273.42858549552[/C][C]-19.4285854955215[/C][/ROW]
[ROW][C]29[/C][C]6114[/C][C]6135.73723977504[/C][C]-21.737239775036[/C][/ROW]
[ROW][C]30[/C][C]5978[/C][C]5994.96374302731[/C][C]-16.9637430273133[/C][/ROW]
[ROW][C]31[/C][C]6315[/C][C]5858.360106126[/C][C]456.639893873996[/C][/ROW]
[ROW][C]32[/C][C]6427[/C][C]6211.60915505988[/C][C]215.390844940123[/C][/ROW]
[ROW][C]33[/C][C]7132[/C][C]6331.2736110706[/C][C]800.726388929395[/C][/ROW]
[ROW][C]34[/C][C]7292[/C][C]7064.76661496909[/C][C]227.233385030907[/C][/ROW]
[ROW][C]35[/C][C]7708[/C][C]7232.85247527677[/C][C]475.147524723231[/C][/ROW]
[ROW][C]36[/C][C]7525[/C][C]7665.76009873151[/C][C]-140.760098731515[/C][/ROW]
[ROW][C]37[/C][C]7450[/C][C]7477.75129909988[/C][C]-27.7512990998803[/C][/ROW]
[ROW][C]38[/C][C]7526[/C][C]7401.76379839505[/C][C]124.236201604946[/C][/ROW]
[ROW][C]39[/C][C]7263[/C][C]7482.18461257778[/C][C]-219.184612577781[/C][/ROW]
[ROW][C]40[/C][C]7070[/C][C]7211.38515934755[/C][C]-141.385159347549[/C][/ROW]
[ROW][C]41[/C][C]6893[/C][C]7013.35411759324[/C][C]-120.354117593243[/C][/ROW]
[ROW][C]42[/C][C]6781[/C][C]6832.07144327503[/C][C]-51.0714432750301[/C][/ROW]
[ROW][C]43[/C][C]7188[/C][C]6718.25411983914[/C][C]469.745880160859[/C][/ROW]
[ROW][C]44[/C][C]7015[/C][C]7141.96953147009[/C][C]-126.969531470095[/C][/ROW]
[ROW][C]45[/C][C]8273[/C][C]6964.45145462739[/C][C]1308.54854537261[/C][/ROW]
[ROW][C]46[/C][C]8470[/C][C]8269.01477428333[/C][C]200.985225716675[/C][/ROW]
[ROW][C]47[/C][C]8230[/C][C]8473.16662152985[/C][C]-243.166621529848[/C][/ROW]
[ROW][C]48[/C][C]8137[/C][C]8224.51379380864[/C][C]-87.5137938086391[/C][/ROW]
[ROW][C]49[/C][C]8122[/C][C]8128.39970777047[/C][C]-6.3997077704671[/C][/ROW]
[ROW][C]50[/C][C]8367[/C][C]8113.17198092023[/C][C]253.82801907977[/C][/ROW]
[ROW][C]51[/C][C]8141[/C][C]8367.20418322701[/C][C]-226.204183227006[/C][/ROW]
[ROW][C]52[/C][C]7750[/C][C]8133.15494597986[/C][C]-383.154945979863[/C][/ROW]
[ROW][C]53[/C][C]7504[/C][C]7728.52078140072[/C][C]-224.520781400715[/C][/ROW]
[ROW][C]54[/C][C]7330[/C][C]7474.53144623181[/C][C]-144.531446231813[/C][/ROW]
[ROW][C]55[/C][C]7608[/C][C]7295.38844717761[/C][C]312.611552822388[/C][/ROW]
[ROW][C]56[/C][C]7647[/C][C]7584.51239952442[/C][C]62.4876004755815[/C][/ROW]
[ROW][C]57[/C][C]8942[/C][C]7625.73595487188[/C][C]1316.26404512812[/C][/ROW]
[ROW][C]58[/C][C]8865[/C][C]8967.57382244787[/C][C]-102.573822447872[/C][/ROW]
[ROW][C]59[/C][C]8320[/C][C]8886.92384117674[/C][C]-566.923841176744[/C][/ROW]
[ROW][C]60[/C][C]8207[/C][C]8321.75045431186[/C][C]-114.750454311858[/C][/ROW]
[ROW][C]61[/C][C]8105[/C][C]8204.66718044045[/C][C]-99.6671804404523[/C][/ROW]
[ROW][C]62[/C][C]8290[/C][C]8099.12062895907[/C][C]190.879371040933[/C][/ROW]
[ROW][C]63[/C][C]8162[/C][C]8290.91287002718[/C][C]-128.912870027183[/C][/ROW]
[ROW][C]64[/C][C]8051[/C][C]8158.32564153187[/C][C]-107.325641531866[/C][/ROW]
[ROW][C]65[/C][C]7699[/C][C]8043.50657179112[/C][C]-344.506571791121[/C][/ROW]
[ROW][C]66[/C][C]7440[/C][C]7679.24766883899[/C][C]-239.247668838986[/C][/ROW]
[ROW][C]67[/C][C]7656[/C][C]7411.73429291535[/C][C]244.265707084653[/C][/ROW]
[ROW][C]68[/C][C]7549[/C][C]7636.42623043665[/C][C]-87.4262304366466[/C][/ROW]
[ROW][C]69[/C][C]9086[/C][C]7526.3152602487[/C][C]1559.6847397513[/C][/ROW]
[ROW][C]70[/C][C]8942[/C][C]9118.81499646892[/C][C]-176.814996468916[/C][/ROW]
[ROW][C]71[/C][C]8764[/C][C]8968.52322133405[/C][C]-204.523221334046[/C][/ROW]
[ROW][C]72[/C][C]8500[/C][C]8783.24547824556[/C][C]-283.245478245555[/C][/ROW]
[ROW][C]73[/C][C]8239[/C][C]8509.16648668557[/C][C]-270.166486685566[/C][/ROW]
[ROW][C]74[/C][C]8443[/C][C]8238.55289724378[/C][C]204.447102756221[/C][/ROW]
[ROW][C]75[/C][C]8349[/C][C]8449.82793173297[/C][C]-100.827931732971[/C][/ROW]
[ROW][C]76[/C][C]8288[/C][C]8352.24007614127[/C][C]-64.2400761412682[/C][/ROW]
[ROW][C]77[/C][C]7970[/C][C]8288.95416079585[/C][C]-318.954160795853[/C][/ROW]
[ROW][C]78[/C][C]7496[/C][C]7959.60451343485[/C][C]-463.604513434853[/C][/ROW]
[ROW][C]79[/C][C]7745[/C][C]7469.10763586058[/C][C]275.892364139418[/C][/ROW]
[ROW][C]80[/C][C]7543[/C][C]7727.92497461159[/C][C]-184.924974611587[/C][/ROW]
[ROW][C]81[/C][C]9036[/C][C]7519.34461445937[/C][C]1516.65538554063[/C][/ROW]
[ROW][C]82[/C][C]9075[/C][C]9066.3131964998[/C][C]8.68680350019713[/C][/ROW]
[ROW][C]83[/C][C]8859[/C][C]9105.62230723903[/C][C]-246.622307239026[/C][/ROW]
[ROW][C]84[/C][C]8605[/C][C]8880.84651258711[/C][C]-275.846512587108[/C][/ROW]
[ROW][C]85[/C][C]8419[/C][C]8617.03080541523[/C][C]-198.030805415226[/C][/ROW]
[ROW][C]86[/C][C]8495[/C][C]8423.98408809864[/C][C]71.0159119013606[/C][/ROW]
[ROW][C]87[/C][C]8284[/C][C]8502.51111441204[/C][C]-218.511114412042[/C][/ROW]
[ROW][C]88[/C][C]7582[/C][C]8283.73562690359[/C][C]-701.735626903594[/C][/ROW]
[ROW][C]89[/C][C]7691[/C][C]7556.76510485073[/C][C]134.234895149271[/C][/ROW]
[ROW][C]90[/C][C]7046[/C][C]7670.54171199604[/C][C]-624.541711996042[/C][/ROW]
[ROW][C]91[/C][C]7442[/C][C]7003.31805397665[/C][C]438.681946023353[/C][/ROW]
[ROW][C]92[/C][C]7596[/C][C]7414.92808827932[/C][C]181.071911720685[/C][/ROW]
[ROW][C]93[/C][C]8597[/C][C]7575.37134125298[/C][C]1021.62865874702[/C][/ROW]
[ROW][C]94[/C][C]8436[/C][C]8612.7249194027[/C][C]-176.724919402703[/C][/ROW]
[ROW][C]95[/C][C]7881[/C][C]8445.43634956522[/C][C]-564.436349565216[/C][/ROW]
[ROW][C]96[/C][C]7477[/C][C]7870.35147746538[/C][C]-393.35147746538[/C][/ROW]
[ROW][C]97[/C][C]7508[/C][C]7452.3544800692[/C][C]55.6455199308002[/C][/ROW]
[ROW][C]98[/C][C]7361[/C][C]7485.33456719789[/C][C]-124.33456719789[/C][/ROW]
[ROW][C]99[/C][C]7299[/C][C]7333.9102527793[/C][C]-34.9102527792993[/C][/ROW]
[ROW][C]100[/C][C]6914[/C][C]7270.66800825946[/C][C]-356.66800825946[/C][/ROW]
[ROW][C]101[/C][C]6768[/C][C]6872.97635341917[/C][C]-104.976353419172[/C][/ROW]
[ROW][C]102[/C][C]6746[/C][C]6723.24088061776[/C][C]22.7591193822445[/C][/ROW]
[ROW][C]103[/C][C]7052[/C][C]6702.05073987336[/C][C]349.949260126636[/C][/ROW]
[ROW][C]104[/C][C]7139[/C][C]7020.50331514866[/C][C]118.496684851337[/C][/ROW]
[ROW][C]105[/C][C]7714[/C][C]7111.71989468208[/C][C]602.280105317919[/C][/ROW]
[ROW][C]106[/C][C]7750[/C][C]7708.15139691064[/C][C]41.8486030893609[/C][/ROW]
[ROW][C]107[/C][C]7622[/C][C]7745.6405353073[/C][C]-123.640535307296[/C][/ROW]
[ROW][C]108[/C][C]7424[/C][C]7613.24091728143[/C][C]-189.240917281428[/C][/ROW]
[ROW][C]109[/C][C]7444[/C][C]7408.50697886201[/C][C]35.4930211379897[/C][/ROW]
[ROW][C]110[/C][C]7208[/C][C]7429.76996057916[/C][C]-221.769960579156[/C][/ROW]
[ROW][C]111[/C][C]7128[/C][C]7185.87851046747[/C][C]-57.8785104674662[/C][/ROW]
[ROW][C]112[/C][C]7022[/C][C]7103.81896472601[/C][C]-81.8189647260142[/C][/ROW]
[ROW][C]113[/C][C]6688[/C][C]6994.90752317352[/C][C]-306.907523173519[/C][/ROW]
[ROW][C]114[/C][C]6199[/C][C]6649.98654270483[/C][C]-450.986542704833[/C][/ROW]
[ROW][C]115[/C][C]6400[/C][C]6144.93866230884[/C][C]255.061337691161[/C][/ROW]
[ROW][C]116[/C][C]6474[/C][C]6355.01475095743[/C][C]118.985249042571[/C][/ROW]
[ROW][C]117[/C][C]7182[/C][C]6433.24871553223[/C][C]748.751284467773[/C][/ROW]
[ROW][C]118[/C][C]7330[/C][C]7167.89224016473[/C][C]162.107759835266[/C][/ROW]
[ROW][C]119[/C][C]7410[/C][C]7321.66067379802[/C][C]88.3393262019781[/C][/ROW]
[ROW][C]120[/C][C]7442[/C][C]7404.80413553559[/C][C]37.1958644644074[/C][/ROW]
[ROW][C]121[/C][C]7753[/C][C]7438.12771113625[/C][C]314.872288863747[/C][/ROW]
[ROW][C]122[/C][C]7762[/C][C]7760.33210939034[/C][C]1.6678906096613[/C][/ROW]
[ROW][C]123[/C][C]7814[/C][C]7769.3914595183[/C][C]44.6085404817022[/C][/ROW]
[ROW][C]124[/C][C]7838[/C][C]7822.97880737572[/C][C]15.0211926242764[/C][/ROW]
[ROW][C]125[/C][C]7298[/C][C]7847.51332067005[/C][C]-549.513320670053[/C][/ROW]
[ROW][C]126[/C][C]7155[/C][C]7287.95946881179[/C][C]-132.959468811795[/C][/ROW]
[ROW][C]127[/C][C]7076[/C][C]7140.22824636731[/C][C]-64.2282463673082[/C][/ROW]
[ROW][C]128[/C][C]7450[/C][C]7058.94275197192[/C][C]391.057248028079[/C][/ROW]
[ROW][C]129[/C][C]8216[/C][C]7446.85811163366[/C][C]769.141888366342[/C][/ROW]
[ROW][C]130[/C][C]8246[/C][C]8240.22721439673[/C][C]5.77278560326886[/C][/ROW]
[ROW][C]131[/C][C]8335[/C][C]8270.43263288296[/C][C]64.5673671170371[/C][/ROW]
[ROW][C]132[/C][C]8171[/C][C]8361.73019453251[/C][C]-190.730194532505[/C][/ROW]
[ROW][C]133[/C][C]8485[/C][C]8190.94326175308[/C][C]294.056738246918[/C][/ROW]
[ROW][C]134[/C][C]8435[/C][C]8515.40696059589[/C][C]-80.4069605958903[/C][/ROW]
[ROW][C]135[/C][C]8369[/C][C]8462.5457637209[/C][C]-93.5457637209038[/C][/ROW]
[ROW][C]136[/C][C]8210[/C][C]8393.21703639627[/C][C]-183.217036396267[/C][/ROW]
[ROW][C]137[/C][C]7888[/C][C]8227.69745142382[/C][C]-339.697451423815[/C][/ROW]
[ROW][C]138[/C][C]8061[/C][C]7893.60967594702[/C][C]167.390324052982[/C][/ROW]
[ROW][C]139[/C][C]8139[/C][C]8072.56608405565[/C][C]66.4339159443543[/C][/ROW]
[ROW][C]140[/C][C]7837[/C][C]8152.93006487627[/C][C]-315.930064876267[/C][/ROW]
[ROW][C]141[/C][C]8943[/C][C]7839.68802677858[/C][C]1103.31197322142[/C][/ROW]
[ROW][C]142[/C][C]8523[/C][C]8984.94821950968[/C][C]-461.948219509681[/C][/ROW]
[ROW][C]143[/C][C]8104[/C][C]8548.51027940758[/C][C]-444.510279407583[/C][/ROW]
[ROW][C]144[/C][C]7969[/C][C]8113.69285000949[/C][C]-144.692850009493[/C][/ROW]
[ROW][C]145[/C][C]7921[/C][C]7973.54410757212[/C][C]-52.5441075721219[/C][/ROW]
[ROW][C]146[/C][C]7930[/C][C]7923.67438093067[/C][C]6.32561906933097[/C][/ROW]
[ROW][C]147[/C][C]7706[/C][C]7932.89947141263[/C][C]-226.89947141263[/C][/ROW]
[ROW][C]148[/C][C]7552[/C][C]7700.82549306883[/C][C]-148.82549306883[/C][/ROW]
[ROW][C]149[/C][C]7379[/C][C]7541.52969488754[/C][C]-162.529694887538[/C][/ROW]
[ROW][C]150[/C][C]6946[/C][C]7362.7462471405[/C][C]-416.746247140496[/C][/ROW]
[ROW][C]151[/C][C]7128[/C][C]6914.91677154356[/C][C]213.083228456444[/C][/ROW]
[ROW][C]152[/C][C]7393[/C][C]7104.49911345592[/C][C]288.500886544084[/C][/ROW]
[ROW][C]153[/C][C]8092[/C][C]7379.76511317651[/C][C]712.234886823494[/C][/ROW]
[ROW][C]154[/C][C]8004[/C][C]8104.10924031841[/C][C]-100.109240318407[/C][/ROW]
[ROW][C]155[/C][C]7903[/C][C]8012.54695860257[/C][C]-109.546958602575[/C][/ROW]
[ROW][C]156[/C][C]7710[/C][C]7907.64884563704[/C][C]-197.648845637041[/C][/ROW]
[ROW][C]157[/C][C]7867[/C][C]7707.61571995625[/C][C]159.384280043752[/C][/ROW]
[ROW][C]158[/C][C]7860[/C][C]7870.28724143404[/C][C]-10.2872414340354[/C][/ROW]
[ROW][C]159[/C][C]7723[/C][C]7862.92118079917[/C][C]-139.921180799171[/C][/ROW]
[ROW][C]160[/C][C]7477[/C][C]7720.94223317722[/C][C]-243.942233177221[/C][/ROW]
[ROW][C]161[/C][C]7126[/C][C]7466.2618061337[/C][C]-340.261806133699[/C][/ROW]
[ROW][C]162[/C][C]7161[/C][C]7103.15394868986[/C][C]57.8460513101363[/C][/ROW]
[ROW][C]163[/C][C]7162[/C][C]7140.21233940644[/C][C]21.787660593558[/C][/ROW]
[ROW][C]164[/C][C]7406[/C][C]7141.98763032581[/C][C]264.012369674195[/C][/ROW]
[ROW][C]165[/C][C]7944[/C][C]7395.38223200546[/C][C]548.617767994545[/C][/ROW]
[ROW][C]166[/C][C]8084[/C][C]7952.90421656644[/C][C]131.095783433565[/C][/ROW]
[ROW][C]167[/C][C]8088[/C][C]8097.56912173266[/C][C]-9.56912173265846[/C][/ROW]
[ROW][C]168[/C][C]7972[/C][C]8101.22861462985[/C][C]-129.228614629853[/C][/ROW]
[ROW][C]169[/C][C]8184[/C][C]7980.63015069591[/C][C]203.369849304086[/C][/ROW]
[ROW][C]170[/C][C]7914[/C][C]8199.86685225736[/C][C]-285.866852257361[/C][/ROW]
[ROW][C]171[/C][C]7845[/C][C]7919.69458186834[/C][C]-74.6945818683353[/C][/ROW]
[ROW][C]172[/C][C]7610[/C][C]7848.03665396463[/C][C]-238.036653964627[/C][/ROW]
[ROW][C]173[/C][C]7278[/C][C]7604.56637072785[/C][C]-326.566370727846[/C][/ROW]
[ROW][C]174[/C][C]6883[/C][C]7260.94585090621[/C][C]-377.945850906207[/C][/ROW]
[ROW][C]175[/C][C]7123[/C][C]6852.49704648041[/C][C]270.502953519594[/C][/ROW]
[ROW][C]176[/C][C]7182[/C][C]7102.12260873956[/C][C]79.8773912604402[/C][/ROW]
[ROW][C]177[/C][C]7912[/C][C]7163.96496144836[/C][C]748.035038551636[/C][/ROW]
[ROW][C]178[/C][C]7893[/C][C]7920.58299922548[/C][C]-27.5829992254821[/C][/ROW]
[ROW][C]179[/C][C]7671[/C][C]7900.60148729415[/C][C]-229.601487294154[/C][/ROW]
[ROW][C]180[/C][C]7403[/C][C]7670.43136056545[/C][C]-267.43136056545[/C][/ROW]
[ROW][C]181[/C][C]7663[/C][C]7392.91509770148[/C][C]270.08490229852[/C][/ROW]
[ROW][C]182[/C][C]7589[/C][C]7662.52578404891[/C][C]-73.5257840489148[/C][/ROW]
[ROW][C]183[/C][C]7450[/C][C]7585.9094465827[/C][C]-135.909446582697[/C][/ROW]
[ROW][C]184[/C][C]7069[/C][C]7442.07325229104[/C][C]-373.073252291037[/C][/ROW]
[ROW][C]185[/C][C]6670[/C][C]7047.79783414706[/C][C]-377.797834147064[/C][/ROW]
[ROW][C]186[/C][C]6285[/C][C]6635.3542967415[/C][C]-350.354296741502[/C][/ROW]
[ROW][C]187[/C][C]6506[/C][C]6237.88730866552[/C][C]268.112691334481[/C][/ROW]
[ROW][C]188[/C][C]6539[/C][C]6468.4278159662[/C][C]70.572184033801[/C][/ROW]
[ROW][C]189[/C][C]7291[/C][C]6503.9390526915[/C][C]787.060947308497[/C][/ROW]
[ROW][C]190[/C][C]7391[/C][C]7283.94578626499[/C][C]107.054213735006[/C][/ROW]
[ROW][C]191[/C][C]7126[/C][C]7387.7551975339[/C][C]-261.755197533905[/C][/ROW]
[ROW][C]192[/C][C]6752[/C][C]7113.44091494387[/C][C]-361.440914943873[/C][/ROW]
[ROW][C]193[/C][C]6835[/C][C]6726.57942125395[/C][C]108.420578746048[/C][/ROW]
[ROW][C]194[/C][C]6664[/C][C]6813.43745318046[/C][C]-149.437453180461[/C][/ROW]
[ROW][C]195[/C][C]6562[/C][C]6637.11987904413[/C][C]-75.1198790441267[/C][/ROW]
[ROW][C]196[/C][C]6174[/C][C]6532.44681738905[/C][C]-358.446817389046[/C][/ROW]
[ROW][C]197[/C][C]5741[/C][C]6131.69186550227[/C][C]-390.691865502269[/C][/ROW]
[ROW][C]198[/C][C]5398[/C][C]5684.78950759229[/C][C]-286.789507592287[/C][/ROW]
[ROW][C]199[/C][C]5203[/C][C]5331.58440548644[/C][C]-128.584405486437[/C][/ROW]
[ROW][C]200[/C][C]5673[/C][C]5132.00886505532[/C][C]540.991134944681[/C][/ROW]
[ROW][C]201[/C][C]6379[/C][C]5621.25946392422[/C][C]757.740536075776[/C][/ROW]
[ROW][C]202[/C][C]6418[/C][C]6354.22286159283[/C][C]63.7771384071702[/C][/ROW]
[ROW][C]203[/C][C]6272[/C][C]6395.49230378731[/C][C]-123.49230378731[/C][/ROW]
[ROW][C]204[/C][C]6059[/C][C]6245.09796042372[/C][C]-186.097960423717[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294608&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294608&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
369787150-172
468196740.8795614353578.1204385646543
566886584.6593948358103.340605164196
664546457.33666126105-3.33666126104617
766796223.21792968977455.782070310229
869216464.43645387701456.563546122991
978076722.68278605671084.3172139433
1078987647.26707031564250.732929684364
1178327747.1891371311584.810862868846
1273847684.20704222304-300.207042223039
1376207225.52449130093394.475508699071
1472817475.56148616287-194.561486162868
1569297129.63822091224-200.638220912242
1665876770.49872146564-183.498721465644
1760716421.96911302714-350.969113027137
1859285893.4802473621734.5197526378279
1959645751.7085963464212.291403653601
2063745795.26276200841578.737237991589
2171606225.85651613751934.143483862487
2272137045.09702662328167.902973376716
2368907104.07167681733-214.071676817325
2465256773.45416201271-248.454162012715
2567396399.61318274102339.386817258981
2665806625.68990462874-45.6899046287363
2763916465.06407756882-74.0640775688225
2862546273.42858549552-19.4285854955215
2961146135.73723977504-21.737239775036
3059785994.96374302731-16.9637430273133
3163155858.360106126456.639893873996
3264276211.60915505988215.390844940123
3371326331.2736110706800.726388929395
3472927064.76661496909227.233385030907
3577087232.85247527677475.147524723231
3675257665.76009873151-140.760098731515
3774507477.75129909988-27.7512990998803
3875267401.76379839505124.236201604946
3972637482.18461257778-219.184612577781
4070707211.38515934755-141.385159347549
4168937013.35411759324-120.354117593243
4267816832.07144327503-51.0714432750301
4371886718.25411983914469.745880160859
4470157141.96953147009-126.969531470095
4582736964.451454627391308.54854537261
4684708269.01477428333200.985225716675
4782308473.16662152985-243.166621529848
4881378224.51379380864-87.5137938086391
4981228128.39970777047-6.3997077704671
5083678113.17198092023253.82801907977
5181418367.20418322701-226.204183227006
5277508133.15494597986-383.154945979863
5375047728.52078140072-224.520781400715
5473307474.53144623181-144.531446231813
5576087295.38844717761312.611552822388
5676477584.5123995244262.4876004755815
5789427625.735954871881316.26404512812
5888658967.57382244787-102.573822447872
5983208886.92384117674-566.923841176744
6082078321.75045431186-114.750454311858
6181058204.66718044045-99.6671804404523
6282908099.12062895907190.879371040933
6381628290.91287002718-128.912870027183
6480518158.32564153187-107.325641531866
6576998043.50657179112-344.506571791121
6674407679.24766883899-239.247668838986
6776567411.73429291535244.265707084653
6875497636.42623043665-87.4262304366466
6990867526.31526024871559.6847397513
7089429118.81499646892-176.814996468916
7187648968.52322133405-204.523221334046
7285008783.24547824556-283.245478245555
7382398509.16648668557-270.166486685566
7484438238.55289724378204.447102756221
7583498449.82793173297-100.827931732971
7682888352.24007614127-64.2400761412682
7779708288.95416079585-318.954160795853
7874967959.60451343485-463.604513434853
7977457469.10763586058275.892364139418
8075437727.92497461159-184.924974611587
8190367519.344614459371516.65538554063
8290759066.31319649988.68680350019713
8388599105.62230723903-246.622307239026
8486058880.84651258711-275.846512587108
8584198617.03080541523-198.030805415226
8684958423.9840880986471.0159119013606
8782848502.51111441204-218.511114412042
8875828283.73562690359-701.735626903594
8976917556.76510485073134.234895149271
9070467670.54171199604-624.541711996042
9174427003.31805397665438.681946023353
9275967414.92808827932181.071911720685
9385977575.371341252981021.62865874702
9484368612.7249194027-176.724919402703
9578818445.43634956522-564.436349565216
9674777870.35147746538-393.35147746538
9775087452.354480069255.6455199308002
9873617485.33456719789-124.33456719789
9972997333.9102527793-34.9102527792993
10069147270.66800825946-356.66800825946
10167686872.97635341917-104.976353419172
10267466723.2408806177622.7591193822445
10370526702.05073987336349.949260126636
10471397020.50331514866118.496684851337
10577147111.71989468208602.280105317919
10677507708.1513969106441.8486030893609
10776227745.6405353073-123.640535307296
10874247613.24091728143-189.240917281428
10974447408.5069788620135.4930211379897
11072087429.76996057916-221.769960579156
11171287185.87851046747-57.8785104674662
11270227103.81896472601-81.8189647260142
11366886994.90752317352-306.907523173519
11461996649.98654270483-450.986542704833
11564006144.93866230884255.061337691161
11664746355.01475095743118.985249042571
11771826433.24871553223748.751284467773
11873307167.89224016473162.107759835266
11974107321.6606737980288.3393262019781
12074427404.8041355355937.1958644644074
12177537438.12771113625314.872288863747
12277627760.332109390341.6678906096613
12378147769.391459518344.6085404817022
12478387822.9788073757215.0211926242764
12572987847.51332067005-549.513320670053
12671557287.95946881179-132.959468811795
12770767140.22824636731-64.2282463673082
12874507058.94275197192391.057248028079
12982167446.85811163366769.141888366342
13082468240.227214396735.77278560326886
13183358270.4326328829664.5673671170371
13281718361.73019453251-190.730194532505
13384858190.94326175308294.056738246918
13484358515.40696059589-80.4069605958903
13583698462.5457637209-93.5457637209038
13682108393.21703639627-183.217036396267
13778888227.69745142382-339.697451423815
13880617893.60967594702167.390324052982
13981398072.5660840556566.4339159443543
14078378152.93006487627-315.930064876267
14189437839.688026778581103.31197322142
14285238984.94821950968-461.948219509681
14381048548.51027940758-444.510279407583
14479698113.69285000949-144.692850009493
14579217973.54410757212-52.5441075721219
14679307923.674380930676.32561906933097
14777067932.89947141263-226.89947141263
14875527700.82549306883-148.82549306883
14973797541.52969488754-162.529694887538
15069467362.7462471405-416.746247140496
15171286914.91677154356213.083228456444
15273937104.49911345592288.500886544084
15380927379.76511317651712.234886823494
15480048104.10924031841-100.109240318407
15579038012.54695860257-109.546958602575
15677107907.64884563704-197.648845637041
15778677707.61571995625159.384280043752
15878607870.28724143404-10.2872414340354
15977237862.92118079917-139.921180799171
16074777720.94223317722-243.942233177221
16171267466.2618061337-340.261806133699
16271617103.1539486898657.8460513101363
16371627140.2123394064421.787660593558
16474067141.98763032581264.012369674195
16579447395.38223200546548.617767994545
16680847952.90421656644131.095783433565
16780888097.56912173266-9.56912173265846
16879728101.22861462985-129.228614629853
16981847980.63015069591203.369849304086
17079148199.86685225736-285.866852257361
17178457919.69458186834-74.6945818683353
17276107848.03665396463-238.036653964627
17372787604.56637072785-326.566370727846
17468837260.94585090621-377.945850906207
17571236852.49704648041270.502953519594
17671827102.1226087395679.8773912604402
17779127163.96496144836748.035038551636
17878937920.58299922548-27.5829992254821
17976717900.60148729415-229.601487294154
18074037670.43136056545-267.43136056545
18176637392.91509770148270.08490229852
18275897662.52578404891-73.5257840489148
18374507585.9094465827-135.909446582697
18470697442.07325229104-373.073252291037
18566707047.79783414706-377.797834147064
18662856635.3542967415-350.354296741502
18765066237.88730866552268.112691334481
18865396468.427815966270.572184033801
18972916503.9390526915787.060947308497
19073917283.94578626499107.054213735006
19171267387.7551975339-261.755197533905
19267527113.44091494387-361.440914943873
19368356726.57942125395108.420578746048
19466646813.43745318046-149.437453180461
19565626637.11987904413-75.1198790441267
19661746532.44681738905-358.446817389046
19757416131.69186550227-390.691865502269
19853985684.78950759229-286.789507592287
19952035331.58440548644-128.584405486437
20056735132.00886505532540.991134944681
20163795621.25946392422757.740536075776
20264186354.2228615928363.7771384071702
20362726395.49230378731-123.49230378731
20460596245.09796042372-186.097960423717







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
2056025.475860808715285.981262551516764.97045906592
2065991.951721617424927.378907236587056.52453599827
2075958.427582426144631.486017689367285.36914716291
2085924.903443234854365.861094355867483.94579211384
2095891.379304043564118.185143028077664.57346505905
2105857.855164852273882.261015024287833.44931468027
2115824.331025660993654.478023831577994.1840274904
2125790.80688646973432.529588477668149.08418446174
2135757.282747278413214.845647508068299.71984704876
2145723.758608087123000.306627022518447.21058915174
2155690.234468895842788.085344147518592.38359364417
2165656.710329704552577.553331263028735.86732814608

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
205 & 6025.47586080871 & 5285.98126255151 & 6764.97045906592 \tabularnewline
206 & 5991.95172161742 & 4927.37890723658 & 7056.52453599827 \tabularnewline
207 & 5958.42758242614 & 4631.48601768936 & 7285.36914716291 \tabularnewline
208 & 5924.90344323485 & 4365.86109435586 & 7483.94579211384 \tabularnewline
209 & 5891.37930404356 & 4118.18514302807 & 7664.57346505905 \tabularnewline
210 & 5857.85516485227 & 3882.26101502428 & 7833.44931468027 \tabularnewline
211 & 5824.33102566099 & 3654.47802383157 & 7994.1840274904 \tabularnewline
212 & 5790.8068864697 & 3432.52958847766 & 8149.08418446174 \tabularnewline
213 & 5757.28274727841 & 3214.84564750806 & 8299.71984704876 \tabularnewline
214 & 5723.75860808712 & 3000.30662702251 & 8447.21058915174 \tabularnewline
215 & 5690.23446889584 & 2788.08534414751 & 8592.38359364417 \tabularnewline
216 & 5656.71032970455 & 2577.55333126302 & 8735.86732814608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294608&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]205[/C][C]6025.47586080871[/C][C]5285.98126255151[/C][C]6764.97045906592[/C][/ROW]
[ROW][C]206[/C][C]5991.95172161742[/C][C]4927.37890723658[/C][C]7056.52453599827[/C][/ROW]
[ROW][C]207[/C][C]5958.42758242614[/C][C]4631.48601768936[/C][C]7285.36914716291[/C][/ROW]
[ROW][C]208[/C][C]5924.90344323485[/C][C]4365.86109435586[/C][C]7483.94579211384[/C][/ROW]
[ROW][C]209[/C][C]5891.37930404356[/C][C]4118.18514302807[/C][C]7664.57346505905[/C][/ROW]
[ROW][C]210[/C][C]5857.85516485227[/C][C]3882.26101502428[/C][C]7833.44931468027[/C][/ROW]
[ROW][C]211[/C][C]5824.33102566099[/C][C]3654.47802383157[/C][C]7994.1840274904[/C][/ROW]
[ROW][C]212[/C][C]5790.8068864697[/C][C]3432.52958847766[/C][C]8149.08418446174[/C][/ROW]
[ROW][C]213[/C][C]5757.28274727841[/C][C]3214.84564750806[/C][C]8299.71984704876[/C][/ROW]
[ROW][C]214[/C][C]5723.75860808712[/C][C]3000.30662702251[/C][C]8447.21058915174[/C][/ROW]
[ROW][C]215[/C][C]5690.23446889584[/C][C]2788.08534414751[/C][C]8592.38359364417[/C][/ROW]
[ROW][C]216[/C][C]5656.71032970455[/C][C]2577.55333126302[/C][C]8735.86732814608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294608&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294608&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
2056025.475860808715285.981262551516764.97045906592
2065991.951721617424927.378907236587056.52453599827
2075958.427582426144631.486017689367285.36914716291
2085924.903443234854365.861094355867483.94579211384
2095891.379304043564118.185143028077664.57346505905
2105857.855164852273882.261015024287833.44931468027
2115824.331025660993654.478023831577994.1840274904
2125790.80688646973432.529588477668149.08418446174
2135757.282747278413214.845647508068299.71984704876
2145723.758608087123000.306627022518447.21058915174
2155690.234468895842788.085344147518592.38359364417
2165656.710329704552577.553331263028735.86732814608



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')