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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 23 Dec 2016 08:49:37 +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/Dec/23/t1482479409i43obqvsgkac074.htm/, Retrieved Tue, 07 May 2024 13:22:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302758, Retrieved Tue, 07 May 2024 13:22:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-23 07:49:37] [36884fbde1107444791dd71ee0072a5a] [Current]
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Dataseries X:
8160
6540
6660
8260
6340
6940
6320
8540
8360
8940
8760
8820
8040
8780
7780
6600
6400
7120
6800
8100
9620
9120
7880
7740
7400
7820
6260
5860
5600
5820
6720
6940
7940
7680
8040
8060
6900
5460
6180
5460
5240
5440
5280
7120
6160
7320
7460
5320
6480
5600
6540
4920
5560
6260
5580
6380
6020
6280
6100
5020
5100
5480
5980
5920
5360
4800
4980
5880
5880
7080
7760
4620
5280
5280
5360
4680
5040
5760
6120
5140
5520
5700
4540
4880
5080
5220
4980
5000
4780
5820
5480
4880
5460
5580
5660
5280
5440
4760
4460
5220
4640
4980
4800
5540
5920
5780
6020
5620




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302758&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302758&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302758&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.140337798742308
beta0.0726051565403305
gamma0.340632845397915

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.140337798742308 \tabularnewline
beta & 0.0726051565403305 \tabularnewline
gamma & 0.340632845397915 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302758&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]0.140337798742308[/C][/ROW]
[ROW][C]beta[/C][C]0.0726051565403305[/C][/ROW]
[ROW][C]gamma[/C][C]0.340632845397915[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302758&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302758&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
alpha0.140337798742308
beta0.0726051565403305
gamma0.340632845397915







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1380407977.105824521762.8941754783009
1487808734.0776282037345.9223717962723
1577807725.2530370471254.7469629528759
1666006522.7293755367177.27062446329
1764006371.1853997042228.8146002957847
1871207180.22335622501-60.223356225013
1968006511.70580662961288.294193370392
2081008773.92047855731-673.920478557309
2196208359.700864925571260.29913507443
2291209182.50743460131-62.5074346013062
2378809092.12884367833-1212.12884367833
2477408986.23820119693-1246.23820119693
2574008024.24695641638-624.246956416383
2678208653.54158795499-833.541587954986
2762607523.69271172931-1263.69271172931
2858606172.89935323368-312.899353233681
2956005928.84396813034-328.843968130335
3058206557.33048925427-737.330489254266
3167205904.14902803078815.850971969225
3269407724.11423882894-784.114238828935
3379407773.56775632059166.43224367941
3476807956.74115143072-276.741151430715
3580407485.17737462568554.822625374315
3680607554.82887914286505.171120857139
3769007046.32822052773-146.328220527733
3854607587.24527400605-2127.24527400605
3961806241.79714582508-61.7971458250759
4054605408.6988796388551.3011203611513
4152405211.375379550428.6246204495965
4254405694.08582602013-254.085826020129
4352805554.10682362842-274.106823628425
4471206572.40200987386547.597990126142
4561607024.80390656247-864.80390656247
4673206899.48747765669420.512522343313
4774606766.49597600979693.504023990209
4853206821.80050450312-1501.80050450312
4964805918.12946438223561.870535617774
5056005928.56652190335-328.566521903353
5165405477.58835981221062.4116401878
5249204908.3184391170211.6815608829829
5355604716.75985515382843.24014484618
5462605208.613130827571051.38686917243
5555805271.82273305864308.177266941365
5663806617.63409125493-237.634091254933
5760206570.3443335062-550.344333506201
5862806888.07413364453-608.074133644534
5961006713.06484919678-613.064849196784
6050205977.29919920329-957.299199203289
6151005766.85788043112-666.85788043112
6254805365.6277596954114.372240304605
6359805377.18009495418602.81990504582
6459204514.567359716591405.43264028341
6553604766.84966825038593.150331749619
6648005267.36196184977-467.361961849773
6749804918.3490983466461.6509016533564
6858805958.73671639514-78.736716395143
6958805841.5740515874738.4259484125314
7070806191.53098502751888.46901497249
7177606240.32106016771519.6789398323
7246205728.45891129151-1108.45891129151
7352805609.55421024016-329.554210240164
7452805517.85128210235-237.851282102351
7553605654.09805907613-294.098059076135
7646804905.85819294136-225.858192941363
7750404697.47588682172342.524113178277
7857604842.12134925695917.878650743053
7961204856.646487934491263.35351206551
8051406072.5748123109-932.574812310901
8155205890.60884462704-370.608844627041
8257006443.30230780923-743.302307809226
8345406430.37143073062-1890.37143073062
8448804793.5498360074686.450163992542
8550805029.5876165780950.412383421909
8652205005.01378954497214.986210455032
8749805167.1837903085-187.183790308498
8850004493.57816122686506.421838773136
8947804553.83729571643226.162704283568
9058204828.46237244011991.537627559893
9154804942.27649674996537.723503250041
9248805370.70683637684-490.706836376844
9354605401.659631792158.3403682078961
9455805873.01096038111-293.010960381105
9556605578.920836693581.0791633065
9652804819.53080624438460.469193755624
9754405124.28414577612315.715854223878
9847605212.97866884898-452.978668848983
9944605184.22358921592-724.223589215923
10052204650.0217367454569.9782632546
10146404650.39394726826-10.3939472682587
10249805120.23425411497-140.234254114966
10348004944.89454988723-144.894549887225
10455404964.99918064721575.000819352788
10559205304.56989413823615.430105861767
10657805758.8095492520321.1904507479658
10760205631.51211222223388.487887777775
10856205031.04583751204588.954162487961

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8040 & 7977.1058245217 & 62.8941754783009 \tabularnewline
14 & 8780 & 8734.07762820373 & 45.9223717962723 \tabularnewline
15 & 7780 & 7725.25303704712 & 54.7469629528759 \tabularnewline
16 & 6600 & 6522.72937553671 & 77.27062446329 \tabularnewline
17 & 6400 & 6371.18539970422 & 28.8146002957847 \tabularnewline
18 & 7120 & 7180.22335622501 & -60.223356225013 \tabularnewline
19 & 6800 & 6511.70580662961 & 288.294193370392 \tabularnewline
20 & 8100 & 8773.92047855731 & -673.920478557309 \tabularnewline
21 & 9620 & 8359.70086492557 & 1260.29913507443 \tabularnewline
22 & 9120 & 9182.50743460131 & -62.5074346013062 \tabularnewline
23 & 7880 & 9092.12884367833 & -1212.12884367833 \tabularnewline
24 & 7740 & 8986.23820119693 & -1246.23820119693 \tabularnewline
25 & 7400 & 8024.24695641638 & -624.246956416383 \tabularnewline
26 & 7820 & 8653.54158795499 & -833.541587954986 \tabularnewline
27 & 6260 & 7523.69271172931 & -1263.69271172931 \tabularnewline
28 & 5860 & 6172.89935323368 & -312.899353233681 \tabularnewline
29 & 5600 & 5928.84396813034 & -328.843968130335 \tabularnewline
30 & 5820 & 6557.33048925427 & -737.330489254266 \tabularnewline
31 & 6720 & 5904.14902803078 & 815.850971969225 \tabularnewline
32 & 6940 & 7724.11423882894 & -784.114238828935 \tabularnewline
33 & 7940 & 7773.56775632059 & 166.43224367941 \tabularnewline
34 & 7680 & 7956.74115143072 & -276.741151430715 \tabularnewline
35 & 8040 & 7485.17737462568 & 554.822625374315 \tabularnewline
36 & 8060 & 7554.82887914286 & 505.171120857139 \tabularnewline
37 & 6900 & 7046.32822052773 & -146.328220527733 \tabularnewline
38 & 5460 & 7587.24527400605 & -2127.24527400605 \tabularnewline
39 & 6180 & 6241.79714582508 & -61.7971458250759 \tabularnewline
40 & 5460 & 5408.69887963885 & 51.3011203611513 \tabularnewline
41 & 5240 & 5211.3753795504 & 28.6246204495965 \tabularnewline
42 & 5440 & 5694.08582602013 & -254.085826020129 \tabularnewline
43 & 5280 & 5554.10682362842 & -274.106823628425 \tabularnewline
44 & 7120 & 6572.40200987386 & 547.597990126142 \tabularnewline
45 & 6160 & 7024.80390656247 & -864.80390656247 \tabularnewline
46 & 7320 & 6899.48747765669 & 420.512522343313 \tabularnewline
47 & 7460 & 6766.49597600979 & 693.504023990209 \tabularnewline
48 & 5320 & 6821.80050450312 & -1501.80050450312 \tabularnewline
49 & 6480 & 5918.12946438223 & 561.870535617774 \tabularnewline
50 & 5600 & 5928.56652190335 & -328.566521903353 \tabularnewline
51 & 6540 & 5477.5883598122 & 1062.4116401878 \tabularnewline
52 & 4920 & 4908.31843911702 & 11.6815608829829 \tabularnewline
53 & 5560 & 4716.75985515382 & 843.24014484618 \tabularnewline
54 & 6260 & 5208.61313082757 & 1051.38686917243 \tabularnewline
55 & 5580 & 5271.82273305864 & 308.177266941365 \tabularnewline
56 & 6380 & 6617.63409125493 & -237.634091254933 \tabularnewline
57 & 6020 & 6570.3443335062 & -550.344333506201 \tabularnewline
58 & 6280 & 6888.07413364453 & -608.074133644534 \tabularnewline
59 & 6100 & 6713.06484919678 & -613.064849196784 \tabularnewline
60 & 5020 & 5977.29919920329 & -957.299199203289 \tabularnewline
61 & 5100 & 5766.85788043112 & -666.85788043112 \tabularnewline
62 & 5480 & 5365.6277596954 & 114.372240304605 \tabularnewline
63 & 5980 & 5377.18009495418 & 602.81990504582 \tabularnewline
64 & 5920 & 4514.56735971659 & 1405.43264028341 \tabularnewline
65 & 5360 & 4766.84966825038 & 593.150331749619 \tabularnewline
66 & 4800 & 5267.36196184977 & -467.361961849773 \tabularnewline
67 & 4980 & 4918.34909834664 & 61.6509016533564 \tabularnewline
68 & 5880 & 5958.73671639514 & -78.736716395143 \tabularnewline
69 & 5880 & 5841.57405158747 & 38.4259484125314 \tabularnewline
70 & 7080 & 6191.53098502751 & 888.46901497249 \tabularnewline
71 & 7760 & 6240.3210601677 & 1519.6789398323 \tabularnewline
72 & 4620 & 5728.45891129151 & -1108.45891129151 \tabularnewline
73 & 5280 & 5609.55421024016 & -329.554210240164 \tabularnewline
74 & 5280 & 5517.85128210235 & -237.851282102351 \tabularnewline
75 & 5360 & 5654.09805907613 & -294.098059076135 \tabularnewline
76 & 4680 & 4905.85819294136 & -225.858192941363 \tabularnewline
77 & 5040 & 4697.47588682172 & 342.524113178277 \tabularnewline
78 & 5760 & 4842.12134925695 & 917.878650743053 \tabularnewline
79 & 6120 & 4856.64648793449 & 1263.35351206551 \tabularnewline
80 & 5140 & 6072.5748123109 & -932.574812310901 \tabularnewline
81 & 5520 & 5890.60884462704 & -370.608844627041 \tabularnewline
82 & 5700 & 6443.30230780923 & -743.302307809226 \tabularnewline
83 & 4540 & 6430.37143073062 & -1890.37143073062 \tabularnewline
84 & 4880 & 4793.54983600746 & 86.450163992542 \tabularnewline
85 & 5080 & 5029.58761657809 & 50.412383421909 \tabularnewline
86 & 5220 & 5005.01378954497 & 214.986210455032 \tabularnewline
87 & 4980 & 5167.1837903085 & -187.183790308498 \tabularnewline
88 & 5000 & 4493.57816122686 & 506.421838773136 \tabularnewline
89 & 4780 & 4553.83729571643 & 226.162704283568 \tabularnewline
90 & 5820 & 4828.46237244011 & 991.537627559893 \tabularnewline
91 & 5480 & 4942.27649674996 & 537.723503250041 \tabularnewline
92 & 4880 & 5370.70683637684 & -490.706836376844 \tabularnewline
93 & 5460 & 5401.6596317921 & 58.3403682078961 \tabularnewline
94 & 5580 & 5873.01096038111 & -293.010960381105 \tabularnewline
95 & 5660 & 5578.9208366935 & 81.0791633065 \tabularnewline
96 & 5280 & 4819.53080624438 & 460.469193755624 \tabularnewline
97 & 5440 & 5124.28414577612 & 315.715854223878 \tabularnewline
98 & 4760 & 5212.97866884898 & -452.978668848983 \tabularnewline
99 & 4460 & 5184.22358921592 & -724.223589215923 \tabularnewline
100 & 5220 & 4650.0217367454 & 569.9782632546 \tabularnewline
101 & 4640 & 4650.39394726826 & -10.3939472682587 \tabularnewline
102 & 4980 & 5120.23425411497 & -140.234254114966 \tabularnewline
103 & 4800 & 4944.89454988723 & -144.894549887225 \tabularnewline
104 & 5540 & 4964.99918064721 & 575.000819352788 \tabularnewline
105 & 5920 & 5304.56989413823 & 615.430105861767 \tabularnewline
106 & 5780 & 5758.80954925203 & 21.1904507479658 \tabularnewline
107 & 6020 & 5631.51211222223 & 388.487887777775 \tabularnewline
108 & 5620 & 5031.04583751204 & 588.954162487961 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302758&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]8040[/C][C]7977.1058245217[/C][C]62.8941754783009[/C][/ROW]
[ROW][C]14[/C][C]8780[/C][C]8734.07762820373[/C][C]45.9223717962723[/C][/ROW]
[ROW][C]15[/C][C]7780[/C][C]7725.25303704712[/C][C]54.7469629528759[/C][/ROW]
[ROW][C]16[/C][C]6600[/C][C]6522.72937553671[/C][C]77.27062446329[/C][/ROW]
[ROW][C]17[/C][C]6400[/C][C]6371.18539970422[/C][C]28.8146002957847[/C][/ROW]
[ROW][C]18[/C][C]7120[/C][C]7180.22335622501[/C][C]-60.223356225013[/C][/ROW]
[ROW][C]19[/C][C]6800[/C][C]6511.70580662961[/C][C]288.294193370392[/C][/ROW]
[ROW][C]20[/C][C]8100[/C][C]8773.92047855731[/C][C]-673.920478557309[/C][/ROW]
[ROW][C]21[/C][C]9620[/C][C]8359.70086492557[/C][C]1260.29913507443[/C][/ROW]
[ROW][C]22[/C][C]9120[/C][C]9182.50743460131[/C][C]-62.5074346013062[/C][/ROW]
[ROW][C]23[/C][C]7880[/C][C]9092.12884367833[/C][C]-1212.12884367833[/C][/ROW]
[ROW][C]24[/C][C]7740[/C][C]8986.23820119693[/C][C]-1246.23820119693[/C][/ROW]
[ROW][C]25[/C][C]7400[/C][C]8024.24695641638[/C][C]-624.246956416383[/C][/ROW]
[ROW][C]26[/C][C]7820[/C][C]8653.54158795499[/C][C]-833.541587954986[/C][/ROW]
[ROW][C]27[/C][C]6260[/C][C]7523.69271172931[/C][C]-1263.69271172931[/C][/ROW]
[ROW][C]28[/C][C]5860[/C][C]6172.89935323368[/C][C]-312.899353233681[/C][/ROW]
[ROW][C]29[/C][C]5600[/C][C]5928.84396813034[/C][C]-328.843968130335[/C][/ROW]
[ROW][C]30[/C][C]5820[/C][C]6557.33048925427[/C][C]-737.330489254266[/C][/ROW]
[ROW][C]31[/C][C]6720[/C][C]5904.14902803078[/C][C]815.850971969225[/C][/ROW]
[ROW][C]32[/C][C]6940[/C][C]7724.11423882894[/C][C]-784.114238828935[/C][/ROW]
[ROW][C]33[/C][C]7940[/C][C]7773.56775632059[/C][C]166.43224367941[/C][/ROW]
[ROW][C]34[/C][C]7680[/C][C]7956.74115143072[/C][C]-276.741151430715[/C][/ROW]
[ROW][C]35[/C][C]8040[/C][C]7485.17737462568[/C][C]554.822625374315[/C][/ROW]
[ROW][C]36[/C][C]8060[/C][C]7554.82887914286[/C][C]505.171120857139[/C][/ROW]
[ROW][C]37[/C][C]6900[/C][C]7046.32822052773[/C][C]-146.328220527733[/C][/ROW]
[ROW][C]38[/C][C]5460[/C][C]7587.24527400605[/C][C]-2127.24527400605[/C][/ROW]
[ROW][C]39[/C][C]6180[/C][C]6241.79714582508[/C][C]-61.7971458250759[/C][/ROW]
[ROW][C]40[/C][C]5460[/C][C]5408.69887963885[/C][C]51.3011203611513[/C][/ROW]
[ROW][C]41[/C][C]5240[/C][C]5211.3753795504[/C][C]28.6246204495965[/C][/ROW]
[ROW][C]42[/C][C]5440[/C][C]5694.08582602013[/C][C]-254.085826020129[/C][/ROW]
[ROW][C]43[/C][C]5280[/C][C]5554.10682362842[/C][C]-274.106823628425[/C][/ROW]
[ROW][C]44[/C][C]7120[/C][C]6572.40200987386[/C][C]547.597990126142[/C][/ROW]
[ROW][C]45[/C][C]6160[/C][C]7024.80390656247[/C][C]-864.80390656247[/C][/ROW]
[ROW][C]46[/C][C]7320[/C][C]6899.48747765669[/C][C]420.512522343313[/C][/ROW]
[ROW][C]47[/C][C]7460[/C][C]6766.49597600979[/C][C]693.504023990209[/C][/ROW]
[ROW][C]48[/C][C]5320[/C][C]6821.80050450312[/C][C]-1501.80050450312[/C][/ROW]
[ROW][C]49[/C][C]6480[/C][C]5918.12946438223[/C][C]561.870535617774[/C][/ROW]
[ROW][C]50[/C][C]5600[/C][C]5928.56652190335[/C][C]-328.566521903353[/C][/ROW]
[ROW][C]51[/C][C]6540[/C][C]5477.5883598122[/C][C]1062.4116401878[/C][/ROW]
[ROW][C]52[/C][C]4920[/C][C]4908.31843911702[/C][C]11.6815608829829[/C][/ROW]
[ROW][C]53[/C][C]5560[/C][C]4716.75985515382[/C][C]843.24014484618[/C][/ROW]
[ROW][C]54[/C][C]6260[/C][C]5208.61313082757[/C][C]1051.38686917243[/C][/ROW]
[ROW][C]55[/C][C]5580[/C][C]5271.82273305864[/C][C]308.177266941365[/C][/ROW]
[ROW][C]56[/C][C]6380[/C][C]6617.63409125493[/C][C]-237.634091254933[/C][/ROW]
[ROW][C]57[/C][C]6020[/C][C]6570.3443335062[/C][C]-550.344333506201[/C][/ROW]
[ROW][C]58[/C][C]6280[/C][C]6888.07413364453[/C][C]-608.074133644534[/C][/ROW]
[ROW][C]59[/C][C]6100[/C][C]6713.06484919678[/C][C]-613.064849196784[/C][/ROW]
[ROW][C]60[/C][C]5020[/C][C]5977.29919920329[/C][C]-957.299199203289[/C][/ROW]
[ROW][C]61[/C][C]5100[/C][C]5766.85788043112[/C][C]-666.85788043112[/C][/ROW]
[ROW][C]62[/C][C]5480[/C][C]5365.6277596954[/C][C]114.372240304605[/C][/ROW]
[ROW][C]63[/C][C]5980[/C][C]5377.18009495418[/C][C]602.81990504582[/C][/ROW]
[ROW][C]64[/C][C]5920[/C][C]4514.56735971659[/C][C]1405.43264028341[/C][/ROW]
[ROW][C]65[/C][C]5360[/C][C]4766.84966825038[/C][C]593.150331749619[/C][/ROW]
[ROW][C]66[/C][C]4800[/C][C]5267.36196184977[/C][C]-467.361961849773[/C][/ROW]
[ROW][C]67[/C][C]4980[/C][C]4918.34909834664[/C][C]61.6509016533564[/C][/ROW]
[ROW][C]68[/C][C]5880[/C][C]5958.73671639514[/C][C]-78.736716395143[/C][/ROW]
[ROW][C]69[/C][C]5880[/C][C]5841.57405158747[/C][C]38.4259484125314[/C][/ROW]
[ROW][C]70[/C][C]7080[/C][C]6191.53098502751[/C][C]888.46901497249[/C][/ROW]
[ROW][C]71[/C][C]7760[/C][C]6240.3210601677[/C][C]1519.6789398323[/C][/ROW]
[ROW][C]72[/C][C]4620[/C][C]5728.45891129151[/C][C]-1108.45891129151[/C][/ROW]
[ROW][C]73[/C][C]5280[/C][C]5609.55421024016[/C][C]-329.554210240164[/C][/ROW]
[ROW][C]74[/C][C]5280[/C][C]5517.85128210235[/C][C]-237.851282102351[/C][/ROW]
[ROW][C]75[/C][C]5360[/C][C]5654.09805907613[/C][C]-294.098059076135[/C][/ROW]
[ROW][C]76[/C][C]4680[/C][C]4905.85819294136[/C][C]-225.858192941363[/C][/ROW]
[ROW][C]77[/C][C]5040[/C][C]4697.47588682172[/C][C]342.524113178277[/C][/ROW]
[ROW][C]78[/C][C]5760[/C][C]4842.12134925695[/C][C]917.878650743053[/C][/ROW]
[ROW][C]79[/C][C]6120[/C][C]4856.64648793449[/C][C]1263.35351206551[/C][/ROW]
[ROW][C]80[/C][C]5140[/C][C]6072.5748123109[/C][C]-932.574812310901[/C][/ROW]
[ROW][C]81[/C][C]5520[/C][C]5890.60884462704[/C][C]-370.608844627041[/C][/ROW]
[ROW][C]82[/C][C]5700[/C][C]6443.30230780923[/C][C]-743.302307809226[/C][/ROW]
[ROW][C]83[/C][C]4540[/C][C]6430.37143073062[/C][C]-1890.37143073062[/C][/ROW]
[ROW][C]84[/C][C]4880[/C][C]4793.54983600746[/C][C]86.450163992542[/C][/ROW]
[ROW][C]85[/C][C]5080[/C][C]5029.58761657809[/C][C]50.412383421909[/C][/ROW]
[ROW][C]86[/C][C]5220[/C][C]5005.01378954497[/C][C]214.986210455032[/C][/ROW]
[ROW][C]87[/C][C]4980[/C][C]5167.1837903085[/C][C]-187.183790308498[/C][/ROW]
[ROW][C]88[/C][C]5000[/C][C]4493.57816122686[/C][C]506.421838773136[/C][/ROW]
[ROW][C]89[/C][C]4780[/C][C]4553.83729571643[/C][C]226.162704283568[/C][/ROW]
[ROW][C]90[/C][C]5820[/C][C]4828.46237244011[/C][C]991.537627559893[/C][/ROW]
[ROW][C]91[/C][C]5480[/C][C]4942.27649674996[/C][C]537.723503250041[/C][/ROW]
[ROW][C]92[/C][C]4880[/C][C]5370.70683637684[/C][C]-490.706836376844[/C][/ROW]
[ROW][C]93[/C][C]5460[/C][C]5401.6596317921[/C][C]58.3403682078961[/C][/ROW]
[ROW][C]94[/C][C]5580[/C][C]5873.01096038111[/C][C]-293.010960381105[/C][/ROW]
[ROW][C]95[/C][C]5660[/C][C]5578.9208366935[/C][C]81.0791633065[/C][/ROW]
[ROW][C]96[/C][C]5280[/C][C]4819.53080624438[/C][C]460.469193755624[/C][/ROW]
[ROW][C]97[/C][C]5440[/C][C]5124.28414577612[/C][C]315.715854223878[/C][/ROW]
[ROW][C]98[/C][C]4760[/C][C]5212.97866884898[/C][C]-452.978668848983[/C][/ROW]
[ROW][C]99[/C][C]4460[/C][C]5184.22358921592[/C][C]-724.223589215923[/C][/ROW]
[ROW][C]100[/C][C]5220[/C][C]4650.0217367454[/C][C]569.9782632546[/C][/ROW]
[ROW][C]101[/C][C]4640[/C][C]4650.39394726826[/C][C]-10.3939472682587[/C][/ROW]
[ROW][C]102[/C][C]4980[/C][C]5120.23425411497[/C][C]-140.234254114966[/C][/ROW]
[ROW][C]103[/C][C]4800[/C][C]4944.89454988723[/C][C]-144.894549887225[/C][/ROW]
[ROW][C]104[/C][C]5540[/C][C]4964.99918064721[/C][C]575.000819352788[/C][/ROW]
[ROW][C]105[/C][C]5920[/C][C]5304.56989413823[/C][C]615.430105861767[/C][/ROW]
[ROW][C]106[/C][C]5780[/C][C]5758.80954925203[/C][C]21.1904507479658[/C][/ROW]
[ROW][C]107[/C][C]6020[/C][C]5631.51211222223[/C][C]388.487887777775[/C][/ROW]
[ROW][C]108[/C][C]5620[/C][C]5031.04583751204[/C][C]588.954162487961[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302758&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302758&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
1380407977.105824521762.8941754783009
1487808734.0776282037345.9223717962723
1577807725.2530370471254.7469629528759
1666006522.7293755367177.27062446329
1764006371.1853997042228.8146002957847
1871207180.22335622501-60.223356225013
1968006511.70580662961288.294193370392
2081008773.92047855731-673.920478557309
2196208359.700864925571260.29913507443
2291209182.50743460131-62.5074346013062
2378809092.12884367833-1212.12884367833
2477408986.23820119693-1246.23820119693
2574008024.24695641638-624.246956416383
2678208653.54158795499-833.541587954986
2762607523.69271172931-1263.69271172931
2858606172.89935323368-312.899353233681
2956005928.84396813034-328.843968130335
3058206557.33048925427-737.330489254266
3167205904.14902803078815.850971969225
3269407724.11423882894-784.114238828935
3379407773.56775632059166.43224367941
3476807956.74115143072-276.741151430715
3580407485.17737462568554.822625374315
3680607554.82887914286505.171120857139
3769007046.32822052773-146.328220527733
3854607587.24527400605-2127.24527400605
3961806241.79714582508-61.7971458250759
4054605408.6988796388551.3011203611513
4152405211.375379550428.6246204495965
4254405694.08582602013-254.085826020129
4352805554.10682362842-274.106823628425
4471206572.40200987386547.597990126142
4561607024.80390656247-864.80390656247
4673206899.48747765669420.512522343313
4774606766.49597600979693.504023990209
4853206821.80050450312-1501.80050450312
4964805918.12946438223561.870535617774
5056005928.56652190335-328.566521903353
5165405477.58835981221062.4116401878
5249204908.3184391170211.6815608829829
5355604716.75985515382843.24014484618
5462605208.613130827571051.38686917243
5555805271.82273305864308.177266941365
5663806617.63409125493-237.634091254933
5760206570.3443335062-550.344333506201
5862806888.07413364453-608.074133644534
5961006713.06484919678-613.064849196784
6050205977.29919920329-957.299199203289
6151005766.85788043112-666.85788043112
6254805365.6277596954114.372240304605
6359805377.18009495418602.81990504582
6459204514.567359716591405.43264028341
6553604766.84966825038593.150331749619
6648005267.36196184977-467.361961849773
6749804918.3490983466461.6509016533564
6858805958.73671639514-78.736716395143
6958805841.5740515874738.4259484125314
7070806191.53098502751888.46901497249
7177606240.32106016771519.6789398323
7246205728.45891129151-1108.45891129151
7352805609.55421024016-329.554210240164
7452805517.85128210235-237.851282102351
7553605654.09805907613-294.098059076135
7646804905.85819294136-225.858192941363
7750404697.47588682172342.524113178277
7857604842.12134925695917.878650743053
7961204856.646487934491263.35351206551
8051406072.5748123109-932.574812310901
8155205890.60884462704-370.608844627041
8257006443.30230780923-743.302307809226
8345406430.37143073062-1890.37143073062
8448804793.5498360074686.450163992542
8550805029.5876165780950.412383421909
8652205005.01378954497214.986210455032
8749805167.1837903085-187.183790308498
8850004493.57816122686506.421838773136
8947804553.83729571643226.162704283568
9058204828.46237244011991.537627559893
9154804942.27649674996537.723503250041
9248805370.70683637684-490.706836376844
9354605401.659631792158.3403682078961
9455805873.01096038111-293.010960381105
9556605578.920836693581.0791633065
9652804819.53080624438460.469193755624
9754405124.28414577612315.715854223878
9847605212.97866884898-452.978668848983
9944605184.22358921592-724.223589215923
10052204650.0217367454569.9782632546
10146404650.39394726826-10.3939472682587
10249805120.23425411497-140.234254114966
10348004944.89454988723-144.894549887225
10455404964.99918064721575.000819352788
10559205304.56989413823615.430105861767
10657805758.8095492520321.1904507479658
10760205631.51211222223388.487887777775
10856205031.04583751204588.954162487961







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1095331.169264959794747.506100332095914.83242958749
1105159.370084717954543.649341141085775.09082829483
1115126.712086898794475.263506828675778.16066696892
1125092.458035848784403.433924798045781.48214689951
1134850.651291575794132.886961889715568.41562126186
1145322.467549576924531.086161931636113.84893722221
1155177.704875013814351.684810563466003.72493946416
1165464.800450480964564.174625888976365.42627507295
1175763.354784984064779.327382422046747.38218754609
1185975.281639849534911.061464240137039.50181545893
1195961.747317538434842.676121163497080.81851391337
1205352.17074663944428.861079207966275.48041407085
1215397.671499161934087.344983141096707.99801518278
1225223.662423226673890.334855121476556.98999133186
1235190.531192763373813.798930160436567.2634553663
1245155.785042239483734.944913339796576.62517113918
1254910.908878147873483.232599459526338.58515683622
1265388.517933362613815.745267108416961.29059961682

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 5331.16926495979 & 4747.50610033209 & 5914.83242958749 \tabularnewline
110 & 5159.37008471795 & 4543.64934114108 & 5775.09082829483 \tabularnewline
111 & 5126.71208689879 & 4475.26350682867 & 5778.16066696892 \tabularnewline
112 & 5092.45803584878 & 4403.43392479804 & 5781.48214689951 \tabularnewline
113 & 4850.65129157579 & 4132.88696188971 & 5568.41562126186 \tabularnewline
114 & 5322.46754957692 & 4531.08616193163 & 6113.84893722221 \tabularnewline
115 & 5177.70487501381 & 4351.68481056346 & 6003.72493946416 \tabularnewline
116 & 5464.80045048096 & 4564.17462588897 & 6365.42627507295 \tabularnewline
117 & 5763.35478498406 & 4779.32738242204 & 6747.38218754609 \tabularnewline
118 & 5975.28163984953 & 4911.06146424013 & 7039.50181545893 \tabularnewline
119 & 5961.74731753843 & 4842.67612116349 & 7080.81851391337 \tabularnewline
120 & 5352.1707466394 & 4428.86107920796 & 6275.48041407085 \tabularnewline
121 & 5397.67149916193 & 4087.34498314109 & 6707.99801518278 \tabularnewline
122 & 5223.66242322667 & 3890.33485512147 & 6556.98999133186 \tabularnewline
123 & 5190.53119276337 & 3813.79893016043 & 6567.2634553663 \tabularnewline
124 & 5155.78504223948 & 3734.94491333979 & 6576.62517113918 \tabularnewline
125 & 4910.90887814787 & 3483.23259945952 & 6338.58515683622 \tabularnewline
126 & 5388.51793336261 & 3815.74526710841 & 6961.29059961682 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302758&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]5331.16926495979[/C][C]4747.50610033209[/C][C]5914.83242958749[/C][/ROW]
[ROW][C]110[/C][C]5159.37008471795[/C][C]4543.64934114108[/C][C]5775.09082829483[/C][/ROW]
[ROW][C]111[/C][C]5126.71208689879[/C][C]4475.26350682867[/C][C]5778.16066696892[/C][/ROW]
[ROW][C]112[/C][C]5092.45803584878[/C][C]4403.43392479804[/C][C]5781.48214689951[/C][/ROW]
[ROW][C]113[/C][C]4850.65129157579[/C][C]4132.88696188971[/C][C]5568.41562126186[/C][/ROW]
[ROW][C]114[/C][C]5322.46754957692[/C][C]4531.08616193163[/C][C]6113.84893722221[/C][/ROW]
[ROW][C]115[/C][C]5177.70487501381[/C][C]4351.68481056346[/C][C]6003.72493946416[/C][/ROW]
[ROW][C]116[/C][C]5464.80045048096[/C][C]4564.17462588897[/C][C]6365.42627507295[/C][/ROW]
[ROW][C]117[/C][C]5763.35478498406[/C][C]4779.32738242204[/C][C]6747.38218754609[/C][/ROW]
[ROW][C]118[/C][C]5975.28163984953[/C][C]4911.06146424013[/C][C]7039.50181545893[/C][/ROW]
[ROW][C]119[/C][C]5961.74731753843[/C][C]4842.67612116349[/C][C]7080.81851391337[/C][/ROW]
[ROW][C]120[/C][C]5352.1707466394[/C][C]4428.86107920796[/C][C]6275.48041407085[/C][/ROW]
[ROW][C]121[/C][C]5397.67149916193[/C][C]4087.34498314109[/C][C]6707.99801518278[/C][/ROW]
[ROW][C]122[/C][C]5223.66242322667[/C][C]3890.33485512147[/C][C]6556.98999133186[/C][/ROW]
[ROW][C]123[/C][C]5190.53119276337[/C][C]3813.79893016043[/C][C]6567.2634553663[/C][/ROW]
[ROW][C]124[/C][C]5155.78504223948[/C][C]3734.94491333979[/C][C]6576.62517113918[/C][/ROW]
[ROW][C]125[/C][C]4910.90887814787[/C][C]3483.23259945952[/C][C]6338.58515683622[/C][/ROW]
[ROW][C]126[/C][C]5388.51793336261[/C][C]3815.74526710841[/C][C]6961.29059961682[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302758&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302758&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
1095331.169264959794747.506100332095914.83242958749
1105159.370084717954543.649341141085775.09082829483
1115126.712086898794475.263506828675778.16066696892
1125092.458035848784403.433924798045781.48214689951
1134850.651291575794132.886961889715568.41562126186
1145322.467549576924531.086161931636113.84893722221
1155177.704875013814351.684810563466003.72493946416
1165464.800450480964564.174625888976365.42627507295
1175763.354784984064779.327382422046747.38218754609
1185975.281639849534911.061464240137039.50181545893
1195961.747317538434842.676121163497080.81851391337
1205352.17074663944428.861079207966275.48041407085
1215397.671499161934087.344983141096707.99801518278
1225223.662423226673890.334855121476556.98999133186
1235190.531192763373813.798930160436567.2634553663
1245155.785042239483734.944913339796576.62517113918
1254910.908878147873483.232599459526338.58515683622
1265388.517933362613815.745267108416961.29059961682



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'multiplicative'
par2 <- 'Triple'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')