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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 computationWed, 13 Aug 2014 16:11:05 +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/2014/Aug/13/t1407942678dq00m6gyfpgaegk.htm/, Retrieved Thu, 16 May 2024 04:29:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235535, Retrieved Thu, 16 May 2024 04:29:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-08-13 15:11:05] [b3e3d38149b35cb70244b37a39776b3a] [Current]
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Dataseries X:
1020
970
1030
970
1070
1650
1010
980
1050
1010
1040
1120
1090
1060
990
950
1540
870
1070
1050
1020
960
1100
1190
1040
1090
1050
850
1100
850
1040
990
1040
1100
1030
1290
1040
1170
1040
860
1090
870
1080
1000
980
1080
1040
1280
1140
1220
1080
790
1020
830
1150
1030
900
1140
1010
1270
1090
1090
980
850
1010
810
1070
1040
880
1110
1010
1230
490
1040
1010
860
1010
800
1130
1040
940
1070
1030
1320
1040
1070
1070
770
1010
810
1150
1030
890
1010
1120
1250
990
1020
1110
830
1030
870
1260
980
940
970
1100
1320




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235535&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235535&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235535&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.181729312706756
beta0.161595572835216
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.181729312706756 \tabularnewline
beta & 0.161595572835216 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235535&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]0.181729312706756[/C][/ROW]
[ROW][C]beta[/C][C]0.161595572835216[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235535&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235535&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
alpha0.181729312706756
beta0.161595572835216
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31030920110
4970893.22055616040176.779443839599
51070862.658718719802207.341281280198
61650861.912713596011788.087286403989
71010989.84876623162920.1512337683705
8980978.8201020962991.17989790370098
91050964.37843978474485.6215602152558
101010967.79672132462742.2032786753734
111040964.56399741584375.4360025841572
121120969.58593644779150.41406355221
131090992.6507444861297.3492555138801
1410601008.9309431776251.0690568223844
159901018.30040040845-28.3004004084495
169501012.41501270559-62.4150127055852
171540998.4970799748541.5029200252
188701110.23086610982-240.230866109823
1910701072.84593223301-2.84593223301135
2010501078.51722373397-28.5172237339652
2110201078.6858336777-58.6858336776957
229601071.64851639333-111.648516393333
2311001051.7075840094148.2924159905854
2411901062.25079393467127.749206065334
2510401090.98519823742-50.9851982374248
2610901085.741057495634.25894250437
2710501090.66146736598-40.6614673659824
288501086.22443084638-236.224430846375
2911001039.3107506364160.689249363591
308501048.13722955397-198.13722955397
3110401004.1087232021435.8912767978589
329901003.6640631129-13.6640631128951
331040993.81247736907746.1875226309231
341100996.194052088648103.805947911352
3510301012.0950168217817.9049831782244
3612901012.91106769011277.088932309891
3710401068.96561385441-28.965613854414
3811701068.55045458024101.44954541976
3910401094.81478610275-54.8147861027455
408601091.07158128789-231.071581287895
4110901048.5115514197741.488448580229
428701056.70204529848-186.702045298479
4310801017.9408234940262.0591765059776
4410001026.20927782011-26.209277820107
459801017.66708785675-37.6670878567461
4610801005.9365216747574.0634783252474
4710401016.6856709159623.3143290840418
4812801018.89687594297261.103124057027
4911401071.9889999313568.0110000686534
5012201091.98788033579128.012119664212
5110801126.65001038557-46.6500103855706
527901128.20095694663-338.200956946628
5310201066.83672043027-46.8367204302676
548301057.04646867549-227.046468675494
5511501007.83922850759142.160771492412
5610301029.902552301350.0974476986480113
579001026.15166761393-126.15166761393
581140995.752965799959144.247034200041
5910101018.72968673476-8.72968673476237
6012701013.64969163816256.350308361843
6110901064.2706522579425.7293477420649
6210901073.7366090198116.263390980185
639801081.95992531481-101.959925314809
648501065.70437790939-215.704377909394
6510101022.44361382517-12.4436138251673
668101015.75586141657-205.755861416566
671070967.895246256409102.104753743591
681040978.98040390911661.0195960908839
69880984.391125366393-104.391125366393
701110956.676252207904153.323747792096
711010980.29833102702229.7016689729783
721230982.326893015027247.673106984973
734901031.24058466129-541.24058466129
741040920.89110923181119.10889076819
751010934.04431950988375.9556804901174
76860941.585890608863-81.5858906088629
771010918.10163578002391.8983642199765
78800928.843302663728-128.843302663728
791130895.686041657092234.313958342908
801040935.406116661925104.593883338075
81940954.62382380574-14.6238238057399
821070951.746726217551118.253273782449
831030976.4899950334253.5100049665803
841320991.038923820115328.961076179885
8510401065.30587203603-25.305872036035
8610701074.4489824905-4.44898249050357
8710701087.251749425-17.2517494250039
887701097.22125219531-327.221252195307
8910101041.25081749999-31.2508174999891
908101038.14915458901-228.149154589014
911150992.565315290362157.434684709638
9210301021.676691757948.3233082420636
938901023.93458796316-133.934587963162
941010996.40684397648513.5931560235149
951120996.088400997481123.911599002519
9612501019.45692169465230.543078305346
979901068.97378627944-78.9737862794409
9810201059.92316806267-39.9231680626674
9911101056.7967820564953.2032179435139
1008301072.15659058133-242.156590581332
10110301026.729535682743.2704643172583
1028701025.99981337927-155.999813379267
1031260991.744820683319268.255179316681
1049801042.46715282463-62.4671528246345
1059401031.25309168648-91.2530916864766
1069701012.12798384047-42.1279838404689
10711001000.6931902227299.3068097772804
10813201017.87755300442302.122446995583

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1030 & 920 & 110 \tabularnewline
4 & 970 & 893.220556160401 & 76.779443839599 \tabularnewline
5 & 1070 & 862.658718719802 & 207.341281280198 \tabularnewline
6 & 1650 & 861.912713596011 & 788.087286403989 \tabularnewline
7 & 1010 & 989.848766231629 & 20.1512337683705 \tabularnewline
8 & 980 & 978.820102096299 & 1.17989790370098 \tabularnewline
9 & 1050 & 964.378439784744 & 85.6215602152558 \tabularnewline
10 & 1010 & 967.796721324627 & 42.2032786753734 \tabularnewline
11 & 1040 & 964.563997415843 & 75.4360025841572 \tabularnewline
12 & 1120 & 969.58593644779 & 150.41406355221 \tabularnewline
13 & 1090 & 992.65074448612 & 97.3492555138801 \tabularnewline
14 & 1060 & 1008.93094317762 & 51.0690568223844 \tabularnewline
15 & 990 & 1018.30040040845 & -28.3004004084495 \tabularnewline
16 & 950 & 1012.41501270559 & -62.4150127055852 \tabularnewline
17 & 1540 & 998.4970799748 & 541.5029200252 \tabularnewline
18 & 870 & 1110.23086610982 & -240.230866109823 \tabularnewline
19 & 1070 & 1072.84593223301 & -2.84593223301135 \tabularnewline
20 & 1050 & 1078.51722373397 & -28.5172237339652 \tabularnewline
21 & 1020 & 1078.6858336777 & -58.6858336776957 \tabularnewline
22 & 960 & 1071.64851639333 & -111.648516393333 \tabularnewline
23 & 1100 & 1051.70758400941 & 48.2924159905854 \tabularnewline
24 & 1190 & 1062.25079393467 & 127.749206065334 \tabularnewline
25 & 1040 & 1090.98519823742 & -50.9851982374248 \tabularnewline
26 & 1090 & 1085.74105749563 & 4.25894250437 \tabularnewline
27 & 1050 & 1090.66146736598 & -40.6614673659824 \tabularnewline
28 & 850 & 1086.22443084638 & -236.224430846375 \tabularnewline
29 & 1100 & 1039.31075063641 & 60.689249363591 \tabularnewline
30 & 850 & 1048.13722955397 & -198.13722955397 \tabularnewline
31 & 1040 & 1004.10872320214 & 35.8912767978589 \tabularnewline
32 & 990 & 1003.6640631129 & -13.6640631128951 \tabularnewline
33 & 1040 & 993.812477369077 & 46.1875226309231 \tabularnewline
34 & 1100 & 996.194052088648 & 103.805947911352 \tabularnewline
35 & 1030 & 1012.09501682178 & 17.9049831782244 \tabularnewline
36 & 1290 & 1012.91106769011 & 277.088932309891 \tabularnewline
37 & 1040 & 1068.96561385441 & -28.965613854414 \tabularnewline
38 & 1170 & 1068.55045458024 & 101.44954541976 \tabularnewline
39 & 1040 & 1094.81478610275 & -54.8147861027455 \tabularnewline
40 & 860 & 1091.07158128789 & -231.071581287895 \tabularnewline
41 & 1090 & 1048.51155141977 & 41.488448580229 \tabularnewline
42 & 870 & 1056.70204529848 & -186.702045298479 \tabularnewline
43 & 1080 & 1017.94082349402 & 62.0591765059776 \tabularnewline
44 & 1000 & 1026.20927782011 & -26.209277820107 \tabularnewline
45 & 980 & 1017.66708785675 & -37.6670878567461 \tabularnewline
46 & 1080 & 1005.93652167475 & 74.0634783252474 \tabularnewline
47 & 1040 & 1016.68567091596 & 23.3143290840418 \tabularnewline
48 & 1280 & 1018.89687594297 & 261.103124057027 \tabularnewline
49 & 1140 & 1071.98899993135 & 68.0110000686534 \tabularnewline
50 & 1220 & 1091.98788033579 & 128.012119664212 \tabularnewline
51 & 1080 & 1126.65001038557 & -46.6500103855706 \tabularnewline
52 & 790 & 1128.20095694663 & -338.200956946628 \tabularnewline
53 & 1020 & 1066.83672043027 & -46.8367204302676 \tabularnewline
54 & 830 & 1057.04646867549 & -227.046468675494 \tabularnewline
55 & 1150 & 1007.83922850759 & 142.160771492412 \tabularnewline
56 & 1030 & 1029.90255230135 & 0.0974476986480113 \tabularnewline
57 & 900 & 1026.15166761393 & -126.15166761393 \tabularnewline
58 & 1140 & 995.752965799959 & 144.247034200041 \tabularnewline
59 & 1010 & 1018.72968673476 & -8.72968673476237 \tabularnewline
60 & 1270 & 1013.64969163816 & 256.350308361843 \tabularnewline
61 & 1090 & 1064.27065225794 & 25.7293477420649 \tabularnewline
62 & 1090 & 1073.73660901981 & 16.263390980185 \tabularnewline
63 & 980 & 1081.95992531481 & -101.959925314809 \tabularnewline
64 & 850 & 1065.70437790939 & -215.704377909394 \tabularnewline
65 & 1010 & 1022.44361382517 & -12.4436138251673 \tabularnewline
66 & 810 & 1015.75586141657 & -205.755861416566 \tabularnewline
67 & 1070 & 967.895246256409 & 102.104753743591 \tabularnewline
68 & 1040 & 978.980403909116 & 61.0195960908839 \tabularnewline
69 & 880 & 984.391125366393 & -104.391125366393 \tabularnewline
70 & 1110 & 956.676252207904 & 153.323747792096 \tabularnewline
71 & 1010 & 980.298331027022 & 29.7016689729783 \tabularnewline
72 & 1230 & 982.326893015027 & 247.673106984973 \tabularnewline
73 & 490 & 1031.24058466129 & -541.24058466129 \tabularnewline
74 & 1040 & 920.89110923181 & 119.10889076819 \tabularnewline
75 & 1010 & 934.044319509883 & 75.9556804901174 \tabularnewline
76 & 860 & 941.585890608863 & -81.5858906088629 \tabularnewline
77 & 1010 & 918.101635780023 & 91.8983642199765 \tabularnewline
78 & 800 & 928.843302663728 & -128.843302663728 \tabularnewline
79 & 1130 & 895.686041657092 & 234.313958342908 \tabularnewline
80 & 1040 & 935.406116661925 & 104.593883338075 \tabularnewline
81 & 940 & 954.62382380574 & -14.6238238057399 \tabularnewline
82 & 1070 & 951.746726217551 & 118.253273782449 \tabularnewline
83 & 1030 & 976.48999503342 & 53.5100049665803 \tabularnewline
84 & 1320 & 991.038923820115 & 328.961076179885 \tabularnewline
85 & 1040 & 1065.30587203603 & -25.305872036035 \tabularnewline
86 & 1070 & 1074.4489824905 & -4.44898249050357 \tabularnewline
87 & 1070 & 1087.251749425 & -17.2517494250039 \tabularnewline
88 & 770 & 1097.22125219531 & -327.221252195307 \tabularnewline
89 & 1010 & 1041.25081749999 & -31.2508174999891 \tabularnewline
90 & 810 & 1038.14915458901 & -228.149154589014 \tabularnewline
91 & 1150 & 992.565315290362 & 157.434684709638 \tabularnewline
92 & 1030 & 1021.67669175794 & 8.3233082420636 \tabularnewline
93 & 890 & 1023.93458796316 & -133.934587963162 \tabularnewline
94 & 1010 & 996.406843976485 & 13.5931560235149 \tabularnewline
95 & 1120 & 996.088400997481 & 123.911599002519 \tabularnewline
96 & 1250 & 1019.45692169465 & 230.543078305346 \tabularnewline
97 & 990 & 1068.97378627944 & -78.9737862794409 \tabularnewline
98 & 1020 & 1059.92316806267 & -39.9231680626674 \tabularnewline
99 & 1110 & 1056.79678205649 & 53.2032179435139 \tabularnewline
100 & 830 & 1072.15659058133 & -242.156590581332 \tabularnewline
101 & 1030 & 1026.72953568274 & 3.2704643172583 \tabularnewline
102 & 870 & 1025.99981337927 & -155.999813379267 \tabularnewline
103 & 1260 & 991.744820683319 & 268.255179316681 \tabularnewline
104 & 980 & 1042.46715282463 & -62.4671528246345 \tabularnewline
105 & 940 & 1031.25309168648 & -91.2530916864766 \tabularnewline
106 & 970 & 1012.12798384047 & -42.1279838404689 \tabularnewline
107 & 1100 & 1000.69319022272 & 99.3068097772804 \tabularnewline
108 & 1320 & 1017.87755300442 & 302.122446995583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235535&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]1030[/C][C]920[/C][C]110[/C][/ROW]
[ROW][C]4[/C][C]970[/C][C]893.220556160401[/C][C]76.779443839599[/C][/ROW]
[ROW][C]5[/C][C]1070[/C][C]862.658718719802[/C][C]207.341281280198[/C][/ROW]
[ROW][C]6[/C][C]1650[/C][C]861.912713596011[/C][C]788.087286403989[/C][/ROW]
[ROW][C]7[/C][C]1010[/C][C]989.848766231629[/C][C]20.1512337683705[/C][/ROW]
[ROW][C]8[/C][C]980[/C][C]978.820102096299[/C][C]1.17989790370098[/C][/ROW]
[ROW][C]9[/C][C]1050[/C][C]964.378439784744[/C][C]85.6215602152558[/C][/ROW]
[ROW][C]10[/C][C]1010[/C][C]967.796721324627[/C][C]42.2032786753734[/C][/ROW]
[ROW][C]11[/C][C]1040[/C][C]964.563997415843[/C][C]75.4360025841572[/C][/ROW]
[ROW][C]12[/C][C]1120[/C][C]969.58593644779[/C][C]150.41406355221[/C][/ROW]
[ROW][C]13[/C][C]1090[/C][C]992.65074448612[/C][C]97.3492555138801[/C][/ROW]
[ROW][C]14[/C][C]1060[/C][C]1008.93094317762[/C][C]51.0690568223844[/C][/ROW]
[ROW][C]15[/C][C]990[/C][C]1018.30040040845[/C][C]-28.3004004084495[/C][/ROW]
[ROW][C]16[/C][C]950[/C][C]1012.41501270559[/C][C]-62.4150127055852[/C][/ROW]
[ROW][C]17[/C][C]1540[/C][C]998.4970799748[/C][C]541.5029200252[/C][/ROW]
[ROW][C]18[/C][C]870[/C][C]1110.23086610982[/C][C]-240.230866109823[/C][/ROW]
[ROW][C]19[/C][C]1070[/C][C]1072.84593223301[/C][C]-2.84593223301135[/C][/ROW]
[ROW][C]20[/C][C]1050[/C][C]1078.51722373397[/C][C]-28.5172237339652[/C][/ROW]
[ROW][C]21[/C][C]1020[/C][C]1078.6858336777[/C][C]-58.6858336776957[/C][/ROW]
[ROW][C]22[/C][C]960[/C][C]1071.64851639333[/C][C]-111.648516393333[/C][/ROW]
[ROW][C]23[/C][C]1100[/C][C]1051.70758400941[/C][C]48.2924159905854[/C][/ROW]
[ROW][C]24[/C][C]1190[/C][C]1062.25079393467[/C][C]127.749206065334[/C][/ROW]
[ROW][C]25[/C][C]1040[/C][C]1090.98519823742[/C][C]-50.9851982374248[/C][/ROW]
[ROW][C]26[/C][C]1090[/C][C]1085.74105749563[/C][C]4.25894250437[/C][/ROW]
[ROW][C]27[/C][C]1050[/C][C]1090.66146736598[/C][C]-40.6614673659824[/C][/ROW]
[ROW][C]28[/C][C]850[/C][C]1086.22443084638[/C][C]-236.224430846375[/C][/ROW]
[ROW][C]29[/C][C]1100[/C][C]1039.31075063641[/C][C]60.689249363591[/C][/ROW]
[ROW][C]30[/C][C]850[/C][C]1048.13722955397[/C][C]-198.13722955397[/C][/ROW]
[ROW][C]31[/C][C]1040[/C][C]1004.10872320214[/C][C]35.8912767978589[/C][/ROW]
[ROW][C]32[/C][C]990[/C][C]1003.6640631129[/C][C]-13.6640631128951[/C][/ROW]
[ROW][C]33[/C][C]1040[/C][C]993.812477369077[/C][C]46.1875226309231[/C][/ROW]
[ROW][C]34[/C][C]1100[/C][C]996.194052088648[/C][C]103.805947911352[/C][/ROW]
[ROW][C]35[/C][C]1030[/C][C]1012.09501682178[/C][C]17.9049831782244[/C][/ROW]
[ROW][C]36[/C][C]1290[/C][C]1012.91106769011[/C][C]277.088932309891[/C][/ROW]
[ROW][C]37[/C][C]1040[/C][C]1068.96561385441[/C][C]-28.965613854414[/C][/ROW]
[ROW][C]38[/C][C]1170[/C][C]1068.55045458024[/C][C]101.44954541976[/C][/ROW]
[ROW][C]39[/C][C]1040[/C][C]1094.81478610275[/C][C]-54.8147861027455[/C][/ROW]
[ROW][C]40[/C][C]860[/C][C]1091.07158128789[/C][C]-231.071581287895[/C][/ROW]
[ROW][C]41[/C][C]1090[/C][C]1048.51155141977[/C][C]41.488448580229[/C][/ROW]
[ROW][C]42[/C][C]870[/C][C]1056.70204529848[/C][C]-186.702045298479[/C][/ROW]
[ROW][C]43[/C][C]1080[/C][C]1017.94082349402[/C][C]62.0591765059776[/C][/ROW]
[ROW][C]44[/C][C]1000[/C][C]1026.20927782011[/C][C]-26.209277820107[/C][/ROW]
[ROW][C]45[/C][C]980[/C][C]1017.66708785675[/C][C]-37.6670878567461[/C][/ROW]
[ROW][C]46[/C][C]1080[/C][C]1005.93652167475[/C][C]74.0634783252474[/C][/ROW]
[ROW][C]47[/C][C]1040[/C][C]1016.68567091596[/C][C]23.3143290840418[/C][/ROW]
[ROW][C]48[/C][C]1280[/C][C]1018.89687594297[/C][C]261.103124057027[/C][/ROW]
[ROW][C]49[/C][C]1140[/C][C]1071.98899993135[/C][C]68.0110000686534[/C][/ROW]
[ROW][C]50[/C][C]1220[/C][C]1091.98788033579[/C][C]128.012119664212[/C][/ROW]
[ROW][C]51[/C][C]1080[/C][C]1126.65001038557[/C][C]-46.6500103855706[/C][/ROW]
[ROW][C]52[/C][C]790[/C][C]1128.20095694663[/C][C]-338.200956946628[/C][/ROW]
[ROW][C]53[/C][C]1020[/C][C]1066.83672043027[/C][C]-46.8367204302676[/C][/ROW]
[ROW][C]54[/C][C]830[/C][C]1057.04646867549[/C][C]-227.046468675494[/C][/ROW]
[ROW][C]55[/C][C]1150[/C][C]1007.83922850759[/C][C]142.160771492412[/C][/ROW]
[ROW][C]56[/C][C]1030[/C][C]1029.90255230135[/C][C]0.0974476986480113[/C][/ROW]
[ROW][C]57[/C][C]900[/C][C]1026.15166761393[/C][C]-126.15166761393[/C][/ROW]
[ROW][C]58[/C][C]1140[/C][C]995.752965799959[/C][C]144.247034200041[/C][/ROW]
[ROW][C]59[/C][C]1010[/C][C]1018.72968673476[/C][C]-8.72968673476237[/C][/ROW]
[ROW][C]60[/C][C]1270[/C][C]1013.64969163816[/C][C]256.350308361843[/C][/ROW]
[ROW][C]61[/C][C]1090[/C][C]1064.27065225794[/C][C]25.7293477420649[/C][/ROW]
[ROW][C]62[/C][C]1090[/C][C]1073.73660901981[/C][C]16.263390980185[/C][/ROW]
[ROW][C]63[/C][C]980[/C][C]1081.95992531481[/C][C]-101.959925314809[/C][/ROW]
[ROW][C]64[/C][C]850[/C][C]1065.70437790939[/C][C]-215.704377909394[/C][/ROW]
[ROW][C]65[/C][C]1010[/C][C]1022.44361382517[/C][C]-12.4436138251673[/C][/ROW]
[ROW][C]66[/C][C]810[/C][C]1015.75586141657[/C][C]-205.755861416566[/C][/ROW]
[ROW][C]67[/C][C]1070[/C][C]967.895246256409[/C][C]102.104753743591[/C][/ROW]
[ROW][C]68[/C][C]1040[/C][C]978.980403909116[/C][C]61.0195960908839[/C][/ROW]
[ROW][C]69[/C][C]880[/C][C]984.391125366393[/C][C]-104.391125366393[/C][/ROW]
[ROW][C]70[/C][C]1110[/C][C]956.676252207904[/C][C]153.323747792096[/C][/ROW]
[ROW][C]71[/C][C]1010[/C][C]980.298331027022[/C][C]29.7016689729783[/C][/ROW]
[ROW][C]72[/C][C]1230[/C][C]982.326893015027[/C][C]247.673106984973[/C][/ROW]
[ROW][C]73[/C][C]490[/C][C]1031.24058466129[/C][C]-541.24058466129[/C][/ROW]
[ROW][C]74[/C][C]1040[/C][C]920.89110923181[/C][C]119.10889076819[/C][/ROW]
[ROW][C]75[/C][C]1010[/C][C]934.044319509883[/C][C]75.9556804901174[/C][/ROW]
[ROW][C]76[/C][C]860[/C][C]941.585890608863[/C][C]-81.5858906088629[/C][/ROW]
[ROW][C]77[/C][C]1010[/C][C]918.101635780023[/C][C]91.8983642199765[/C][/ROW]
[ROW][C]78[/C][C]800[/C][C]928.843302663728[/C][C]-128.843302663728[/C][/ROW]
[ROW][C]79[/C][C]1130[/C][C]895.686041657092[/C][C]234.313958342908[/C][/ROW]
[ROW][C]80[/C][C]1040[/C][C]935.406116661925[/C][C]104.593883338075[/C][/ROW]
[ROW][C]81[/C][C]940[/C][C]954.62382380574[/C][C]-14.6238238057399[/C][/ROW]
[ROW][C]82[/C][C]1070[/C][C]951.746726217551[/C][C]118.253273782449[/C][/ROW]
[ROW][C]83[/C][C]1030[/C][C]976.48999503342[/C][C]53.5100049665803[/C][/ROW]
[ROW][C]84[/C][C]1320[/C][C]991.038923820115[/C][C]328.961076179885[/C][/ROW]
[ROW][C]85[/C][C]1040[/C][C]1065.30587203603[/C][C]-25.305872036035[/C][/ROW]
[ROW][C]86[/C][C]1070[/C][C]1074.4489824905[/C][C]-4.44898249050357[/C][/ROW]
[ROW][C]87[/C][C]1070[/C][C]1087.251749425[/C][C]-17.2517494250039[/C][/ROW]
[ROW][C]88[/C][C]770[/C][C]1097.22125219531[/C][C]-327.221252195307[/C][/ROW]
[ROW][C]89[/C][C]1010[/C][C]1041.25081749999[/C][C]-31.2508174999891[/C][/ROW]
[ROW][C]90[/C][C]810[/C][C]1038.14915458901[/C][C]-228.149154589014[/C][/ROW]
[ROW][C]91[/C][C]1150[/C][C]992.565315290362[/C][C]157.434684709638[/C][/ROW]
[ROW][C]92[/C][C]1030[/C][C]1021.67669175794[/C][C]8.3233082420636[/C][/ROW]
[ROW][C]93[/C][C]890[/C][C]1023.93458796316[/C][C]-133.934587963162[/C][/ROW]
[ROW][C]94[/C][C]1010[/C][C]996.406843976485[/C][C]13.5931560235149[/C][/ROW]
[ROW][C]95[/C][C]1120[/C][C]996.088400997481[/C][C]123.911599002519[/C][/ROW]
[ROW][C]96[/C][C]1250[/C][C]1019.45692169465[/C][C]230.543078305346[/C][/ROW]
[ROW][C]97[/C][C]990[/C][C]1068.97378627944[/C][C]-78.9737862794409[/C][/ROW]
[ROW][C]98[/C][C]1020[/C][C]1059.92316806267[/C][C]-39.9231680626674[/C][/ROW]
[ROW][C]99[/C][C]1110[/C][C]1056.79678205649[/C][C]53.2032179435139[/C][/ROW]
[ROW][C]100[/C][C]830[/C][C]1072.15659058133[/C][C]-242.156590581332[/C][/ROW]
[ROW][C]101[/C][C]1030[/C][C]1026.72953568274[/C][C]3.2704643172583[/C][/ROW]
[ROW][C]102[/C][C]870[/C][C]1025.99981337927[/C][C]-155.999813379267[/C][/ROW]
[ROW][C]103[/C][C]1260[/C][C]991.744820683319[/C][C]268.255179316681[/C][/ROW]
[ROW][C]104[/C][C]980[/C][C]1042.46715282463[/C][C]-62.4671528246345[/C][/ROW]
[ROW][C]105[/C][C]940[/C][C]1031.25309168648[/C][C]-91.2530916864766[/C][/ROW]
[ROW][C]106[/C][C]970[/C][C]1012.12798384047[/C][C]-42.1279838404689[/C][/ROW]
[ROW][C]107[/C][C]1100[/C][C]1000.69319022272[/C][C]99.3068097772804[/C][/ROW]
[ROW][C]108[/C][C]1320[/C][C]1017.87755300442[/C][C]302.122446995583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235535&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235535&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
31030920110
4970893.22055616040176.779443839599
51070862.658718719802207.341281280198
61650861.912713596011788.087286403989
71010989.84876623162920.1512337683705
8980978.8201020962991.17989790370098
91050964.37843978474485.6215602152558
101010967.79672132462742.2032786753734
111040964.56399741584375.4360025841572
121120969.58593644779150.41406355221
131090992.6507444861297.3492555138801
1410601008.9309431776251.0690568223844
159901018.30040040845-28.3004004084495
169501012.41501270559-62.4150127055852
171540998.4970799748541.5029200252
188701110.23086610982-240.230866109823
1910701072.84593223301-2.84593223301135
2010501078.51722373397-28.5172237339652
2110201078.6858336777-58.6858336776957
229601071.64851639333-111.648516393333
2311001051.7075840094148.2924159905854
2411901062.25079393467127.749206065334
2510401090.98519823742-50.9851982374248
2610901085.741057495634.25894250437
2710501090.66146736598-40.6614673659824
288501086.22443084638-236.224430846375
2911001039.3107506364160.689249363591
308501048.13722955397-198.13722955397
3110401004.1087232021435.8912767978589
329901003.6640631129-13.6640631128951
331040993.81247736907746.1875226309231
341100996.194052088648103.805947911352
3510301012.0950168217817.9049831782244
3612901012.91106769011277.088932309891
3710401068.96561385441-28.965613854414
3811701068.55045458024101.44954541976
3910401094.81478610275-54.8147861027455
408601091.07158128789-231.071581287895
4110901048.5115514197741.488448580229
428701056.70204529848-186.702045298479
4310801017.9408234940262.0591765059776
4410001026.20927782011-26.209277820107
459801017.66708785675-37.6670878567461
4610801005.9365216747574.0634783252474
4710401016.6856709159623.3143290840418
4812801018.89687594297261.103124057027
4911401071.9889999313568.0110000686534
5012201091.98788033579128.012119664212
5110801126.65001038557-46.6500103855706
527901128.20095694663-338.200956946628
5310201066.83672043027-46.8367204302676
548301057.04646867549-227.046468675494
5511501007.83922850759142.160771492412
5610301029.902552301350.0974476986480113
579001026.15166761393-126.15166761393
581140995.752965799959144.247034200041
5910101018.72968673476-8.72968673476237
6012701013.64969163816256.350308361843
6110901064.2706522579425.7293477420649
6210901073.7366090198116.263390980185
639801081.95992531481-101.959925314809
648501065.70437790939-215.704377909394
6510101022.44361382517-12.4436138251673
668101015.75586141657-205.755861416566
671070967.895246256409102.104753743591
681040978.98040390911661.0195960908839
69880984.391125366393-104.391125366393
701110956.676252207904153.323747792096
711010980.29833102702229.7016689729783
721230982.326893015027247.673106984973
734901031.24058466129-541.24058466129
741040920.89110923181119.10889076819
751010934.04431950988375.9556804901174
76860941.585890608863-81.5858906088629
771010918.10163578002391.8983642199765
78800928.843302663728-128.843302663728
791130895.686041657092234.313958342908
801040935.406116661925104.593883338075
81940954.62382380574-14.6238238057399
821070951.746726217551118.253273782449
831030976.4899950334253.5100049665803
841320991.038923820115328.961076179885
8510401065.30587203603-25.305872036035
8610701074.4489824905-4.44898249050357
8710701087.251749425-17.2517494250039
887701097.22125219531-327.221252195307
8910101041.25081749999-31.2508174999891
908101038.14915458901-228.149154589014
911150992.565315290362157.434684709638
9210301021.676691757948.3233082420636
938901023.93458796316-133.934587963162
941010996.40684397648513.5931560235149
951120996.088400997481123.911599002519
9612501019.45692169465230.543078305346
979901068.97378627944-78.9737862794409
9810201059.92316806267-39.9231680626674
9911101056.7967820564953.2032179435139
1008301072.15659058133-242.156590581332
10110301026.729535682743.2704643172583
1028701025.99981337927-155.999813379267
1031260991.744820683319268.255179316681
1049801042.46715282463-62.4671528246345
1059401031.25309168648-91.2530916864766
1069701012.12798384047-42.1279838404689
10711001000.6931902227299.3068097772804
10813201017.87755300442302.122446995583







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091080.79178702345745.1568281279261416.42674591897
1101088.80151639669745.769861692461431.83317110092
1111096.81124576993744.413114914541449.20937662532
1121104.82097514317740.9716858186081468.67026446774
1131112.83070451641735.3779200924371490.28348894039
1141120.84043388966727.6081358544121514.0727319249
1151128.8501632629717.6765833803551540.02374314544
1161136.85989263614705.6277945718921568.09199070038
1171144.86962200938691.5285040353791598.21073998338
1181152.87935138262675.4600874919191630.29861527332
1191160.88908075586657.5121092222051664.26605228952
1201168.8988101291637.7772277576771700.02039250053

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1080.79178702345 & 745.156828127926 & 1416.42674591897 \tabularnewline
110 & 1088.80151639669 & 745.76986169246 & 1431.83317110092 \tabularnewline
111 & 1096.81124576993 & 744.41311491454 & 1449.20937662532 \tabularnewline
112 & 1104.82097514317 & 740.971685818608 & 1468.67026446774 \tabularnewline
113 & 1112.83070451641 & 735.377920092437 & 1490.28348894039 \tabularnewline
114 & 1120.84043388966 & 727.608135854412 & 1514.0727319249 \tabularnewline
115 & 1128.8501632629 & 717.676583380355 & 1540.02374314544 \tabularnewline
116 & 1136.85989263614 & 705.627794571892 & 1568.09199070038 \tabularnewline
117 & 1144.86962200938 & 691.528504035379 & 1598.21073998338 \tabularnewline
118 & 1152.87935138262 & 675.460087491919 & 1630.29861527332 \tabularnewline
119 & 1160.88908075586 & 657.512109222205 & 1664.26605228952 \tabularnewline
120 & 1168.8988101291 & 637.777227757677 & 1700.02039250053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235535&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]1080.79178702345[/C][C]745.156828127926[/C][C]1416.42674591897[/C][/ROW]
[ROW][C]110[/C][C]1088.80151639669[/C][C]745.76986169246[/C][C]1431.83317110092[/C][/ROW]
[ROW][C]111[/C][C]1096.81124576993[/C][C]744.41311491454[/C][C]1449.20937662532[/C][/ROW]
[ROW][C]112[/C][C]1104.82097514317[/C][C]740.971685818608[/C][C]1468.67026446774[/C][/ROW]
[ROW][C]113[/C][C]1112.83070451641[/C][C]735.377920092437[/C][C]1490.28348894039[/C][/ROW]
[ROW][C]114[/C][C]1120.84043388966[/C][C]727.608135854412[/C][C]1514.0727319249[/C][/ROW]
[ROW][C]115[/C][C]1128.8501632629[/C][C]717.676583380355[/C][C]1540.02374314544[/C][/ROW]
[ROW][C]116[/C][C]1136.85989263614[/C][C]705.627794571892[/C][C]1568.09199070038[/C][/ROW]
[ROW][C]117[/C][C]1144.86962200938[/C][C]691.528504035379[/C][C]1598.21073998338[/C][/ROW]
[ROW][C]118[/C][C]1152.87935138262[/C][C]675.460087491919[/C][C]1630.29861527332[/C][/ROW]
[ROW][C]119[/C][C]1160.88908075586[/C][C]657.512109222205[/C][C]1664.26605228952[/C][/ROW]
[ROW][C]120[/C][C]1168.8988101291[/C][C]637.777227757677[/C][C]1700.02039250053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235535&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235535&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
1091080.79178702345745.1568281279261416.42674591897
1101088.80151639669745.769861692461431.83317110092
1111096.81124576993744.413114914541449.20937662532
1121104.82097514317740.9716858186081468.67026446774
1131112.83070451641735.3779200924371490.28348894039
1141120.84043388966727.6081358544121514.0727319249
1151128.8501632629717.6765833803551540.02374314544
1161136.85989263614705.6277945718921568.09199070038
1171144.86962200938691.5285040353791598.21073998338
1181152.87935138262675.4600874919191630.29861527332
1191160.88908075586657.5121092222051664.26605228952
1201168.8988101291637.7772277576771700.02039250053



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')