Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 07 Aug 2012 11:21:28 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/07/t134435290757aopkux6bknzpc.htm/, Retrieved Fri, 03 May 2024 05:01:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169078, Retrieved Fri, 03 May 2024 05:01:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBuytaert Madelaine
Estimated Impact136
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [tijdreeks 2 stap 6] [2012-08-07 09:28:35] [5005f81c99651a78c406841ef0f05757]
- RMP   [Mean versus Median] [Tijdreeks 2 stap 12] [2012-08-07 11:30:32] [5005f81c99651a78c406841ef0f05757]
- RMP     [(Partial) Autocorrelation Function] [Tijdreeks 2 stap 17] [2012-08-07 12:37:22] [5005f81c99651a78c406841ef0f05757]
- RMP         [Exponential Smoothing] [Tijdreeks 2 stap 27] [2012-08-07 15:21:28] [d5bad77c67fde5063ee1c54428b9a54e] [Current]
Feedback Forum

Post a new message
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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169078&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169078&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169078&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.18172931270663
beta0.161595572835499
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.18172931270663 \tabularnewline
beta & 0.161595572835499 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169078&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]0.18172931270663[/C][/ROW]
[ROW][C]beta[/C][C]0.161595572835499[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169078&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169078&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
alpha0.18172931270663
beta0.161595572835499
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31030920110
4970893.22055616039176.7794438396095
51070862.65871871979207.34128128021
61650861.912713595987788.087286404013
71010989.84876623154920.1512337684509
8980978.8201020962721.17989790372826
91050964.37843978476485.6215602152364
101010967.79672132467642.2032786753243
111040964.56399741592175.4360025840786
121120969.585936447888150.414063552112
131090992.65074448622797.3492555137725
1410601008.9309431777451.0690568222632
159901018.30040040859-28.3004004085857
169501012.41501270574-62.4150127057389
171540998.497079974966541.502920025034
188701110.23086610993-240.230866109935
1910701072.84593223317-2.84593223316665
2010501078.51722373412-28.5172237341214
2110201078.68583367785-58.6858336778503
229601071.64851639348-111.648516393484
2311001051.7075840095648.2924159904389
2411901062.25079393479127.749206065214
2510401090.98519823751-50.9851982375133
2610901085.741057495714.2589425042886
2710501090.66146736605-40.6614673660488
288501086.22443084643-236.224430846432
2911001039.3107506364760.6892493635271
308501048.137229554-198.137229554003
3110401004.1087232021735.8912767978267
329901003.6640631129-13.664063112898
331040993.81247736906146.1875226309387
341100996.194052088612103.805947911388
3510301012.0950168217217.9049831782803
3612901012.91106769005277.08893230995
3710401068.96561385433-28.9656138543294
3811701068.55045458018101.449545419825
3910401094.81478610269-54.8147861026855
408601091.07158128786-231.071581287859
4110901048.5115514197741.4884485802297
428701056.70204529847-186.702045298474
4310801017.9408234940462.0591765059627
4410001026.20927782011-26.2092778201081
459801017.66708785675-37.6670878567463
4610801005.9365216747574.0634783252477
4710401016.6856709159523.3143290840543
4812801018.89687594296261.103124057042
4911401071.9889999313168.0110000686921
5012201091.98788033576128.012119664242
5110801126.65001038554-46.6500103855446
527901128.20095694663-338.200956946627
5310201066.83672043031-46.8367204303129
548301057.04646867554-227.046468675538
5511501007.83922850764142.160771492355
5610301029.902552301380.097447698624137
579001026.15166761394-126.151667613944
581140995.752965799976144.247034200024
5910101018.72968673475-8.7296867347527
6012701013.64969163814256.350308361856
6110901064.2706522578925.7293477421051
6210901073.7366090197816.2633909802166
639801081.95992531479-101.959925314787
648501065.70437790939-215.704377909392
6510101022.44361382519-12.4436138251897
668101015.75586141658-205.755861416581
671070967.895246256436102.104753743564
681040978.98040390911761.0195960908832
69880984.391125366379-104.391125366379
701110956.676252207896153.323747792104
711010980.29833102699129.7016689730092
721230982.326893014995247.673106985005
734901031.24058466124-541.240584661238
741040920.891109231826119.108890768174
751010934.04431950987475.9556804901256
76860941.585890608843-81.5858906088425
771010918.10163578001191.8983642199888
78800928.843302663704-128.843302663704
791130895.686041657082234.313958342918
801040935.406116661889104.593883338111
81940954.623823805703-14.6238238057032
821070951.746726217529118.253273782471
831030976.48999503339853.5100049666021
841320991.038923820104328.961076179896
8510401065.30587203601-25.3058720360077
8610701074.44898249051-4.44898249050789
8710701087.25174942503-17.2517494250314
887701097.22125219535-327.221252195354
8910101041.25081750008-31.2508175000792
908101038.1491545891-228.149154589099
911150992.565315290457157.434684709543
9210301021.676691757998.32330824200631
938901023.93458796321-133.934587963205
941010996.4068439765313.59315602347
951120996.088400997508123.911599002492
9612501019.45692169465230.543078305345
979901068.97378627941-78.9737862794141
9810201059.92316806266-39.9231680626558
9911101056.7967820564853.2032179435191
1008301072.15659058132-242.156590581322
10110301026.729535682763.27046431724216
1028701025.99981337927-155.999813379274
1031260991.744820683332268.255179316668
1049801042.46715282461-62.4671528246074
1059401031.25309168646-91.2530916864578
1069701012.12798384046-42.1279838404579
10711001000.6931902227199.3068097772922
10813201017.87755300439302.12244699561

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1030 & 920 & 110 \tabularnewline
4 & 970 & 893.220556160391 & 76.7794438396095 \tabularnewline
5 & 1070 & 862.65871871979 & 207.34128128021 \tabularnewline
6 & 1650 & 861.912713595987 & 788.087286404013 \tabularnewline
7 & 1010 & 989.848766231549 & 20.1512337684509 \tabularnewline
8 & 980 & 978.820102096272 & 1.17989790372826 \tabularnewline
9 & 1050 & 964.378439784764 & 85.6215602152364 \tabularnewline
10 & 1010 & 967.796721324676 & 42.2032786753243 \tabularnewline
11 & 1040 & 964.563997415921 & 75.4360025840786 \tabularnewline
12 & 1120 & 969.585936447888 & 150.414063552112 \tabularnewline
13 & 1090 & 992.650744486227 & 97.3492555137725 \tabularnewline
14 & 1060 & 1008.93094317774 & 51.0690568222632 \tabularnewline
15 & 990 & 1018.30040040859 & -28.3004004085857 \tabularnewline
16 & 950 & 1012.41501270574 & -62.4150127057389 \tabularnewline
17 & 1540 & 998.497079974966 & 541.502920025034 \tabularnewline
18 & 870 & 1110.23086610993 & -240.230866109935 \tabularnewline
19 & 1070 & 1072.84593223317 & -2.84593223316665 \tabularnewline
20 & 1050 & 1078.51722373412 & -28.5172237341214 \tabularnewline
21 & 1020 & 1078.68583367785 & -58.6858336778503 \tabularnewline
22 & 960 & 1071.64851639348 & -111.648516393484 \tabularnewline
23 & 1100 & 1051.70758400956 & 48.2924159904389 \tabularnewline
24 & 1190 & 1062.25079393479 & 127.749206065214 \tabularnewline
25 & 1040 & 1090.98519823751 & -50.9851982375133 \tabularnewline
26 & 1090 & 1085.74105749571 & 4.2589425042886 \tabularnewline
27 & 1050 & 1090.66146736605 & -40.6614673660488 \tabularnewline
28 & 850 & 1086.22443084643 & -236.224430846432 \tabularnewline
29 & 1100 & 1039.31075063647 & 60.6892493635271 \tabularnewline
30 & 850 & 1048.137229554 & -198.137229554003 \tabularnewline
31 & 1040 & 1004.10872320217 & 35.8912767978267 \tabularnewline
32 & 990 & 1003.6640631129 & -13.664063112898 \tabularnewline
33 & 1040 & 993.812477369061 & 46.1875226309387 \tabularnewline
34 & 1100 & 996.194052088612 & 103.805947911388 \tabularnewline
35 & 1030 & 1012.09501682172 & 17.9049831782803 \tabularnewline
36 & 1290 & 1012.91106769005 & 277.08893230995 \tabularnewline
37 & 1040 & 1068.96561385433 & -28.9656138543294 \tabularnewline
38 & 1170 & 1068.55045458018 & 101.449545419825 \tabularnewline
39 & 1040 & 1094.81478610269 & -54.8147861026855 \tabularnewline
40 & 860 & 1091.07158128786 & -231.071581287859 \tabularnewline
41 & 1090 & 1048.51155141977 & 41.4884485802297 \tabularnewline
42 & 870 & 1056.70204529847 & -186.702045298474 \tabularnewline
43 & 1080 & 1017.94082349404 & 62.0591765059627 \tabularnewline
44 & 1000 & 1026.20927782011 & -26.2092778201081 \tabularnewline
45 & 980 & 1017.66708785675 & -37.6670878567463 \tabularnewline
46 & 1080 & 1005.93652167475 & 74.0634783252477 \tabularnewline
47 & 1040 & 1016.68567091595 & 23.3143290840543 \tabularnewline
48 & 1280 & 1018.89687594296 & 261.103124057042 \tabularnewline
49 & 1140 & 1071.98899993131 & 68.0110000686921 \tabularnewline
50 & 1220 & 1091.98788033576 & 128.012119664242 \tabularnewline
51 & 1080 & 1126.65001038554 & -46.6500103855446 \tabularnewline
52 & 790 & 1128.20095694663 & -338.200956946627 \tabularnewline
53 & 1020 & 1066.83672043031 & -46.8367204303129 \tabularnewline
54 & 830 & 1057.04646867554 & -227.046468675538 \tabularnewline
55 & 1150 & 1007.83922850764 & 142.160771492355 \tabularnewline
56 & 1030 & 1029.90255230138 & 0.097447698624137 \tabularnewline
57 & 900 & 1026.15166761394 & -126.151667613944 \tabularnewline
58 & 1140 & 995.752965799976 & 144.247034200024 \tabularnewline
59 & 1010 & 1018.72968673475 & -8.7296867347527 \tabularnewline
60 & 1270 & 1013.64969163814 & 256.350308361856 \tabularnewline
61 & 1090 & 1064.27065225789 & 25.7293477421051 \tabularnewline
62 & 1090 & 1073.73660901978 & 16.2633909802166 \tabularnewline
63 & 980 & 1081.95992531479 & -101.959925314787 \tabularnewline
64 & 850 & 1065.70437790939 & -215.704377909392 \tabularnewline
65 & 1010 & 1022.44361382519 & -12.4436138251897 \tabularnewline
66 & 810 & 1015.75586141658 & -205.755861416581 \tabularnewline
67 & 1070 & 967.895246256436 & 102.104753743564 \tabularnewline
68 & 1040 & 978.980403909117 & 61.0195960908832 \tabularnewline
69 & 880 & 984.391125366379 & -104.391125366379 \tabularnewline
70 & 1110 & 956.676252207896 & 153.323747792104 \tabularnewline
71 & 1010 & 980.298331026991 & 29.7016689730092 \tabularnewline
72 & 1230 & 982.326893014995 & 247.673106985005 \tabularnewline
73 & 490 & 1031.24058466124 & -541.240584661238 \tabularnewline
74 & 1040 & 920.891109231826 & 119.108890768174 \tabularnewline
75 & 1010 & 934.044319509874 & 75.9556804901256 \tabularnewline
76 & 860 & 941.585890608843 & -81.5858906088425 \tabularnewline
77 & 1010 & 918.101635780011 & 91.8983642199888 \tabularnewline
78 & 800 & 928.843302663704 & -128.843302663704 \tabularnewline
79 & 1130 & 895.686041657082 & 234.313958342918 \tabularnewline
80 & 1040 & 935.406116661889 & 104.593883338111 \tabularnewline
81 & 940 & 954.623823805703 & -14.6238238057032 \tabularnewline
82 & 1070 & 951.746726217529 & 118.253273782471 \tabularnewline
83 & 1030 & 976.489995033398 & 53.5100049666021 \tabularnewline
84 & 1320 & 991.038923820104 & 328.961076179896 \tabularnewline
85 & 1040 & 1065.30587203601 & -25.3058720360077 \tabularnewline
86 & 1070 & 1074.44898249051 & -4.44898249050789 \tabularnewline
87 & 1070 & 1087.25174942503 & -17.2517494250314 \tabularnewline
88 & 770 & 1097.22125219535 & -327.221252195354 \tabularnewline
89 & 1010 & 1041.25081750008 & -31.2508175000792 \tabularnewline
90 & 810 & 1038.1491545891 & -228.149154589099 \tabularnewline
91 & 1150 & 992.565315290457 & 157.434684709543 \tabularnewline
92 & 1030 & 1021.67669175799 & 8.32330824200631 \tabularnewline
93 & 890 & 1023.93458796321 & -133.934587963205 \tabularnewline
94 & 1010 & 996.40684397653 & 13.59315602347 \tabularnewline
95 & 1120 & 996.088400997508 & 123.911599002492 \tabularnewline
96 & 1250 & 1019.45692169465 & 230.543078305345 \tabularnewline
97 & 990 & 1068.97378627941 & -78.9737862794141 \tabularnewline
98 & 1020 & 1059.92316806266 & -39.9231680626558 \tabularnewline
99 & 1110 & 1056.79678205648 & 53.2032179435191 \tabularnewline
100 & 830 & 1072.15659058132 & -242.156590581322 \tabularnewline
101 & 1030 & 1026.72953568276 & 3.27046431724216 \tabularnewline
102 & 870 & 1025.99981337927 & -155.999813379274 \tabularnewline
103 & 1260 & 991.744820683332 & 268.255179316668 \tabularnewline
104 & 980 & 1042.46715282461 & -62.4671528246074 \tabularnewline
105 & 940 & 1031.25309168646 & -91.2530916864578 \tabularnewline
106 & 970 & 1012.12798384046 & -42.1279838404579 \tabularnewline
107 & 1100 & 1000.69319022271 & 99.3068097772922 \tabularnewline
108 & 1320 & 1017.87755300439 & 302.12244699561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169078&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]893.220556160391[/C][C]76.7794438396095[/C][/ROW]
[ROW][C]5[/C][C]1070[/C][C]862.65871871979[/C][C]207.34128128021[/C][/ROW]
[ROW][C]6[/C][C]1650[/C][C]861.912713595987[/C][C]788.087286404013[/C][/ROW]
[ROW][C]7[/C][C]1010[/C][C]989.848766231549[/C][C]20.1512337684509[/C][/ROW]
[ROW][C]8[/C][C]980[/C][C]978.820102096272[/C][C]1.17989790372826[/C][/ROW]
[ROW][C]9[/C][C]1050[/C][C]964.378439784764[/C][C]85.6215602152364[/C][/ROW]
[ROW][C]10[/C][C]1010[/C][C]967.796721324676[/C][C]42.2032786753243[/C][/ROW]
[ROW][C]11[/C][C]1040[/C][C]964.563997415921[/C][C]75.4360025840786[/C][/ROW]
[ROW][C]12[/C][C]1120[/C][C]969.585936447888[/C][C]150.414063552112[/C][/ROW]
[ROW][C]13[/C][C]1090[/C][C]992.650744486227[/C][C]97.3492555137725[/C][/ROW]
[ROW][C]14[/C][C]1060[/C][C]1008.93094317774[/C][C]51.0690568222632[/C][/ROW]
[ROW][C]15[/C][C]990[/C][C]1018.30040040859[/C][C]-28.3004004085857[/C][/ROW]
[ROW][C]16[/C][C]950[/C][C]1012.41501270574[/C][C]-62.4150127057389[/C][/ROW]
[ROW][C]17[/C][C]1540[/C][C]998.497079974966[/C][C]541.502920025034[/C][/ROW]
[ROW][C]18[/C][C]870[/C][C]1110.23086610993[/C][C]-240.230866109935[/C][/ROW]
[ROW][C]19[/C][C]1070[/C][C]1072.84593223317[/C][C]-2.84593223316665[/C][/ROW]
[ROW][C]20[/C][C]1050[/C][C]1078.51722373412[/C][C]-28.5172237341214[/C][/ROW]
[ROW][C]21[/C][C]1020[/C][C]1078.68583367785[/C][C]-58.6858336778503[/C][/ROW]
[ROW][C]22[/C][C]960[/C][C]1071.64851639348[/C][C]-111.648516393484[/C][/ROW]
[ROW][C]23[/C][C]1100[/C][C]1051.70758400956[/C][C]48.2924159904389[/C][/ROW]
[ROW][C]24[/C][C]1190[/C][C]1062.25079393479[/C][C]127.749206065214[/C][/ROW]
[ROW][C]25[/C][C]1040[/C][C]1090.98519823751[/C][C]-50.9851982375133[/C][/ROW]
[ROW][C]26[/C][C]1090[/C][C]1085.74105749571[/C][C]4.2589425042886[/C][/ROW]
[ROW][C]27[/C][C]1050[/C][C]1090.66146736605[/C][C]-40.6614673660488[/C][/ROW]
[ROW][C]28[/C][C]850[/C][C]1086.22443084643[/C][C]-236.224430846432[/C][/ROW]
[ROW][C]29[/C][C]1100[/C][C]1039.31075063647[/C][C]60.6892493635271[/C][/ROW]
[ROW][C]30[/C][C]850[/C][C]1048.137229554[/C][C]-198.137229554003[/C][/ROW]
[ROW][C]31[/C][C]1040[/C][C]1004.10872320217[/C][C]35.8912767978267[/C][/ROW]
[ROW][C]32[/C][C]990[/C][C]1003.6640631129[/C][C]-13.664063112898[/C][/ROW]
[ROW][C]33[/C][C]1040[/C][C]993.812477369061[/C][C]46.1875226309387[/C][/ROW]
[ROW][C]34[/C][C]1100[/C][C]996.194052088612[/C][C]103.805947911388[/C][/ROW]
[ROW][C]35[/C][C]1030[/C][C]1012.09501682172[/C][C]17.9049831782803[/C][/ROW]
[ROW][C]36[/C][C]1290[/C][C]1012.91106769005[/C][C]277.08893230995[/C][/ROW]
[ROW][C]37[/C][C]1040[/C][C]1068.96561385433[/C][C]-28.9656138543294[/C][/ROW]
[ROW][C]38[/C][C]1170[/C][C]1068.55045458018[/C][C]101.449545419825[/C][/ROW]
[ROW][C]39[/C][C]1040[/C][C]1094.81478610269[/C][C]-54.8147861026855[/C][/ROW]
[ROW][C]40[/C][C]860[/C][C]1091.07158128786[/C][C]-231.071581287859[/C][/ROW]
[ROW][C]41[/C][C]1090[/C][C]1048.51155141977[/C][C]41.4884485802297[/C][/ROW]
[ROW][C]42[/C][C]870[/C][C]1056.70204529847[/C][C]-186.702045298474[/C][/ROW]
[ROW][C]43[/C][C]1080[/C][C]1017.94082349404[/C][C]62.0591765059627[/C][/ROW]
[ROW][C]44[/C][C]1000[/C][C]1026.20927782011[/C][C]-26.2092778201081[/C][/ROW]
[ROW][C]45[/C][C]980[/C][C]1017.66708785675[/C][C]-37.6670878567463[/C][/ROW]
[ROW][C]46[/C][C]1080[/C][C]1005.93652167475[/C][C]74.0634783252477[/C][/ROW]
[ROW][C]47[/C][C]1040[/C][C]1016.68567091595[/C][C]23.3143290840543[/C][/ROW]
[ROW][C]48[/C][C]1280[/C][C]1018.89687594296[/C][C]261.103124057042[/C][/ROW]
[ROW][C]49[/C][C]1140[/C][C]1071.98899993131[/C][C]68.0110000686921[/C][/ROW]
[ROW][C]50[/C][C]1220[/C][C]1091.98788033576[/C][C]128.012119664242[/C][/ROW]
[ROW][C]51[/C][C]1080[/C][C]1126.65001038554[/C][C]-46.6500103855446[/C][/ROW]
[ROW][C]52[/C][C]790[/C][C]1128.20095694663[/C][C]-338.200956946627[/C][/ROW]
[ROW][C]53[/C][C]1020[/C][C]1066.83672043031[/C][C]-46.8367204303129[/C][/ROW]
[ROW][C]54[/C][C]830[/C][C]1057.04646867554[/C][C]-227.046468675538[/C][/ROW]
[ROW][C]55[/C][C]1150[/C][C]1007.83922850764[/C][C]142.160771492355[/C][/ROW]
[ROW][C]56[/C][C]1030[/C][C]1029.90255230138[/C][C]0.097447698624137[/C][/ROW]
[ROW][C]57[/C][C]900[/C][C]1026.15166761394[/C][C]-126.151667613944[/C][/ROW]
[ROW][C]58[/C][C]1140[/C][C]995.752965799976[/C][C]144.247034200024[/C][/ROW]
[ROW][C]59[/C][C]1010[/C][C]1018.72968673475[/C][C]-8.7296867347527[/C][/ROW]
[ROW][C]60[/C][C]1270[/C][C]1013.64969163814[/C][C]256.350308361856[/C][/ROW]
[ROW][C]61[/C][C]1090[/C][C]1064.27065225789[/C][C]25.7293477421051[/C][/ROW]
[ROW][C]62[/C][C]1090[/C][C]1073.73660901978[/C][C]16.2633909802166[/C][/ROW]
[ROW][C]63[/C][C]980[/C][C]1081.95992531479[/C][C]-101.959925314787[/C][/ROW]
[ROW][C]64[/C][C]850[/C][C]1065.70437790939[/C][C]-215.704377909392[/C][/ROW]
[ROW][C]65[/C][C]1010[/C][C]1022.44361382519[/C][C]-12.4436138251897[/C][/ROW]
[ROW][C]66[/C][C]810[/C][C]1015.75586141658[/C][C]-205.755861416581[/C][/ROW]
[ROW][C]67[/C][C]1070[/C][C]967.895246256436[/C][C]102.104753743564[/C][/ROW]
[ROW][C]68[/C][C]1040[/C][C]978.980403909117[/C][C]61.0195960908832[/C][/ROW]
[ROW][C]69[/C][C]880[/C][C]984.391125366379[/C][C]-104.391125366379[/C][/ROW]
[ROW][C]70[/C][C]1110[/C][C]956.676252207896[/C][C]153.323747792104[/C][/ROW]
[ROW][C]71[/C][C]1010[/C][C]980.298331026991[/C][C]29.7016689730092[/C][/ROW]
[ROW][C]72[/C][C]1230[/C][C]982.326893014995[/C][C]247.673106985005[/C][/ROW]
[ROW][C]73[/C][C]490[/C][C]1031.24058466124[/C][C]-541.240584661238[/C][/ROW]
[ROW][C]74[/C][C]1040[/C][C]920.891109231826[/C][C]119.108890768174[/C][/ROW]
[ROW][C]75[/C][C]1010[/C][C]934.044319509874[/C][C]75.9556804901256[/C][/ROW]
[ROW][C]76[/C][C]860[/C][C]941.585890608843[/C][C]-81.5858906088425[/C][/ROW]
[ROW][C]77[/C][C]1010[/C][C]918.101635780011[/C][C]91.8983642199888[/C][/ROW]
[ROW][C]78[/C][C]800[/C][C]928.843302663704[/C][C]-128.843302663704[/C][/ROW]
[ROW][C]79[/C][C]1130[/C][C]895.686041657082[/C][C]234.313958342918[/C][/ROW]
[ROW][C]80[/C][C]1040[/C][C]935.406116661889[/C][C]104.593883338111[/C][/ROW]
[ROW][C]81[/C][C]940[/C][C]954.623823805703[/C][C]-14.6238238057032[/C][/ROW]
[ROW][C]82[/C][C]1070[/C][C]951.746726217529[/C][C]118.253273782471[/C][/ROW]
[ROW][C]83[/C][C]1030[/C][C]976.489995033398[/C][C]53.5100049666021[/C][/ROW]
[ROW][C]84[/C][C]1320[/C][C]991.038923820104[/C][C]328.961076179896[/C][/ROW]
[ROW][C]85[/C][C]1040[/C][C]1065.30587203601[/C][C]-25.3058720360077[/C][/ROW]
[ROW][C]86[/C][C]1070[/C][C]1074.44898249051[/C][C]-4.44898249050789[/C][/ROW]
[ROW][C]87[/C][C]1070[/C][C]1087.25174942503[/C][C]-17.2517494250314[/C][/ROW]
[ROW][C]88[/C][C]770[/C][C]1097.22125219535[/C][C]-327.221252195354[/C][/ROW]
[ROW][C]89[/C][C]1010[/C][C]1041.25081750008[/C][C]-31.2508175000792[/C][/ROW]
[ROW][C]90[/C][C]810[/C][C]1038.1491545891[/C][C]-228.149154589099[/C][/ROW]
[ROW][C]91[/C][C]1150[/C][C]992.565315290457[/C][C]157.434684709543[/C][/ROW]
[ROW][C]92[/C][C]1030[/C][C]1021.67669175799[/C][C]8.32330824200631[/C][/ROW]
[ROW][C]93[/C][C]890[/C][C]1023.93458796321[/C][C]-133.934587963205[/C][/ROW]
[ROW][C]94[/C][C]1010[/C][C]996.40684397653[/C][C]13.59315602347[/C][/ROW]
[ROW][C]95[/C][C]1120[/C][C]996.088400997508[/C][C]123.911599002492[/C][/ROW]
[ROW][C]96[/C][C]1250[/C][C]1019.45692169465[/C][C]230.543078305345[/C][/ROW]
[ROW][C]97[/C][C]990[/C][C]1068.97378627941[/C][C]-78.9737862794141[/C][/ROW]
[ROW][C]98[/C][C]1020[/C][C]1059.92316806266[/C][C]-39.9231680626558[/C][/ROW]
[ROW][C]99[/C][C]1110[/C][C]1056.79678205648[/C][C]53.2032179435191[/C][/ROW]
[ROW][C]100[/C][C]830[/C][C]1072.15659058132[/C][C]-242.156590581322[/C][/ROW]
[ROW][C]101[/C][C]1030[/C][C]1026.72953568276[/C][C]3.27046431724216[/C][/ROW]
[ROW][C]102[/C][C]870[/C][C]1025.99981337927[/C][C]-155.999813379274[/C][/ROW]
[ROW][C]103[/C][C]1260[/C][C]991.744820683332[/C][C]268.255179316668[/C][/ROW]
[ROW][C]104[/C][C]980[/C][C]1042.46715282461[/C][C]-62.4671528246074[/C][/ROW]
[ROW][C]105[/C][C]940[/C][C]1031.25309168646[/C][C]-91.2530916864578[/C][/ROW]
[ROW][C]106[/C][C]970[/C][C]1012.12798384046[/C][C]-42.1279838404579[/C][/ROW]
[ROW][C]107[/C][C]1100[/C][C]1000.69319022271[/C][C]99.3068097772922[/C][/ROW]
[ROW][C]108[/C][C]1320[/C][C]1017.87755300439[/C][C]302.12244699561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169078&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169078&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
4970893.22055616039176.7794438396095
51070862.65871871979207.34128128021
61650861.912713595987788.087286404013
71010989.84876623154920.1512337684509
8980978.8201020962721.17989790372826
91050964.37843978476485.6215602152364
101010967.79672132467642.2032786753243
111040964.56399741592175.4360025840786
121120969.585936447888150.414063552112
131090992.65074448622797.3492555137725
1410601008.9309431777451.0690568222632
159901018.30040040859-28.3004004085857
169501012.41501270574-62.4150127057389
171540998.497079974966541.502920025034
188701110.23086610993-240.230866109935
1910701072.84593223317-2.84593223316665
2010501078.51722373412-28.5172237341214
2110201078.68583367785-58.6858336778503
229601071.64851639348-111.648516393484
2311001051.7075840095648.2924159904389
2411901062.25079393479127.749206065214
2510401090.98519823751-50.9851982375133
2610901085.741057495714.2589425042886
2710501090.66146736605-40.6614673660488
288501086.22443084643-236.224430846432
2911001039.3107506364760.6892493635271
308501048.137229554-198.137229554003
3110401004.1087232021735.8912767978267
329901003.6640631129-13.664063112898
331040993.81247736906146.1875226309387
341100996.194052088612103.805947911388
3510301012.0950168217217.9049831782803
3612901012.91106769005277.08893230995
3710401068.96561385433-28.9656138543294
3811701068.55045458018101.449545419825
3910401094.81478610269-54.8147861026855
408601091.07158128786-231.071581287859
4110901048.5115514197741.4884485802297
428701056.70204529847-186.702045298474
4310801017.9408234940462.0591765059627
4410001026.20927782011-26.2092778201081
459801017.66708785675-37.6670878567463
4610801005.9365216747574.0634783252477
4710401016.6856709159523.3143290840543
4812801018.89687594296261.103124057042
4911401071.9889999313168.0110000686921
5012201091.98788033576128.012119664242
5110801126.65001038554-46.6500103855446
527901128.20095694663-338.200956946627
5310201066.83672043031-46.8367204303129
548301057.04646867554-227.046468675538
5511501007.83922850764142.160771492355
5610301029.902552301380.097447698624137
579001026.15166761394-126.151667613944
581140995.752965799976144.247034200024
5910101018.72968673475-8.7296867347527
6012701013.64969163814256.350308361856
6110901064.2706522578925.7293477421051
6210901073.7366090197816.2633909802166
639801081.95992531479-101.959925314787
648501065.70437790939-215.704377909392
6510101022.44361382519-12.4436138251897
668101015.75586141658-205.755861416581
671070967.895246256436102.104753743564
681040978.98040390911761.0195960908832
69880984.391125366379-104.391125366379
701110956.676252207896153.323747792104
711010980.29833102699129.7016689730092
721230982.326893014995247.673106985005
734901031.24058466124-541.240584661238
741040920.891109231826119.108890768174
751010934.04431950987475.9556804901256
76860941.585890608843-81.5858906088425
771010918.10163578001191.8983642199888
78800928.843302663704-128.843302663704
791130895.686041657082234.313958342918
801040935.406116661889104.593883338111
81940954.623823805703-14.6238238057032
821070951.746726217529118.253273782471
831030976.48999503339853.5100049666021
841320991.038923820104328.961076179896
8510401065.30587203601-25.3058720360077
8610701074.44898249051-4.44898249050789
8710701087.25174942503-17.2517494250314
887701097.22125219535-327.221252195354
8910101041.25081750008-31.2508175000792
908101038.1491545891-228.149154589099
911150992.565315290457157.434684709543
9210301021.676691757998.32330824200631
938901023.93458796321-133.934587963205
941010996.4068439765313.59315602347
951120996.088400997508123.911599002492
9612501019.45692169465230.543078305345
979901068.97378627941-78.9737862794141
9810201059.92316806266-39.9231680626558
9911101056.7967820564853.2032179435191
1008301072.15659058132-242.156590581322
10110301026.729535682763.27046431724216
1028701025.99981337927-155.999813379274
1031260991.744820683332268.255179316668
1049801042.46715282461-62.4671528246074
1059401031.25309168646-91.2530916864578
1069701012.12798384046-42.1279838404579
10711001000.6931902227199.3068097772922
10813201017.87755300439302.12244699561







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091080.79178702339745.1568281278681416.42674591892
1101088.80151639664745.7698616924131431.83317110087
1111096.81124576989744.4131149145031449.20937662527
1121104.82097514313740.9716858185791468.67026446769
1131112.83070451638735.3779200924141490.28348894035
1141120.84043388963727.6081358543911514.07273192487
1151128.85016326288717.6765833803321540.02374314542
1161136.85989263612705.6277945718651568.09199070038
1171144.86962200937691.5285040353441598.21073998339
1181152.87935138262675.4600874918751630.29861527336
1191160.88908075586657.5121092221481664.26605228958
1201168.89881012911637.7772277576051700.02039250061

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1080.79178702339 & 745.156828127868 & 1416.42674591892 \tabularnewline
110 & 1088.80151639664 & 745.769861692413 & 1431.83317110087 \tabularnewline
111 & 1096.81124576989 & 744.413114914503 & 1449.20937662527 \tabularnewline
112 & 1104.82097514313 & 740.971685818579 & 1468.67026446769 \tabularnewline
113 & 1112.83070451638 & 735.377920092414 & 1490.28348894035 \tabularnewline
114 & 1120.84043388963 & 727.608135854391 & 1514.07273192487 \tabularnewline
115 & 1128.85016326288 & 717.676583380332 & 1540.02374314542 \tabularnewline
116 & 1136.85989263612 & 705.627794571865 & 1568.09199070038 \tabularnewline
117 & 1144.86962200937 & 691.528504035344 & 1598.21073998339 \tabularnewline
118 & 1152.87935138262 & 675.460087491875 & 1630.29861527336 \tabularnewline
119 & 1160.88908075586 & 657.512109222148 & 1664.26605228958 \tabularnewline
120 & 1168.89881012911 & 637.777227757605 & 1700.02039250061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169078&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]1080.79178702339[/C][C]745.156828127868[/C][C]1416.42674591892[/C][/ROW]
[ROW][C]110[/C][C]1088.80151639664[/C][C]745.769861692413[/C][C]1431.83317110087[/C][/ROW]
[ROW][C]111[/C][C]1096.81124576989[/C][C]744.413114914503[/C][C]1449.20937662527[/C][/ROW]
[ROW][C]112[/C][C]1104.82097514313[/C][C]740.971685818579[/C][C]1468.67026446769[/C][/ROW]
[ROW][C]113[/C][C]1112.83070451638[/C][C]735.377920092414[/C][C]1490.28348894035[/C][/ROW]
[ROW][C]114[/C][C]1120.84043388963[/C][C]727.608135854391[/C][C]1514.07273192487[/C][/ROW]
[ROW][C]115[/C][C]1128.85016326288[/C][C]717.676583380332[/C][C]1540.02374314542[/C][/ROW]
[ROW][C]116[/C][C]1136.85989263612[/C][C]705.627794571865[/C][C]1568.09199070038[/C][/ROW]
[ROW][C]117[/C][C]1144.86962200937[/C][C]691.528504035344[/C][C]1598.21073998339[/C][/ROW]
[ROW][C]118[/C][C]1152.87935138262[/C][C]675.460087491875[/C][C]1630.29861527336[/C][/ROW]
[ROW][C]119[/C][C]1160.88908075586[/C][C]657.512109222148[/C][C]1664.26605228958[/C][/ROW]
[ROW][C]120[/C][C]1168.89881012911[/C][C]637.777227757605[/C][C]1700.02039250061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169078&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169078&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
1091080.79178702339745.1568281278681416.42674591892
1101088.80151639664745.7698616924131431.83317110087
1111096.81124576989744.4131149145031449.20937662527
1121104.82097514313740.9716858185791468.67026446769
1131112.83070451638735.3779200924141490.28348894035
1141120.84043388963727.6081358543911514.07273192487
1151128.85016326288717.6765833803321540.02374314542
1161136.85989263612705.6277945718651568.09199070038
1171144.86962200937691.5285040353441598.21073998339
1181152.87935138262675.4600874918751630.29861527336
1191160.88908075586657.5121092221481664.26605228958
1201168.89881012911637.7772277576051700.02039250061



Parameters (Session):
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')