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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 07 Aug 2012 10:24:34 -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/t13443494979bfm0m5dm69nn02.htm/, Retrieved Fri, 03 May 2024 12:00:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169076, Retrieved Fri, 03 May 2024 12:00:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBuytaert Madelaine
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [tijdreeks 1 stap 20] [2012-08-07 09:08:28] [5005f81c99651a78c406841ef0f05757]
- RMPD    [Exponential Smoothing] [Tijdreeks 1 stap 32] [2012-08-07 14:24:34] [d5bad77c67fde5063ee1c54428b9a54e] [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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169076&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169076&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169076&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0166349237186978
beta0.123094203000456
gamma0.628042420767867

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0166349237186978 \tabularnewline
beta & 0.123094203000456 \tabularnewline
gamma & 0.628042420767867 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169076&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]0.0166349237186978[/C][/ROW]
[ROW][C]beta[/C][C]0.123094203000456[/C][/ROW]
[ROW][C]gamma[/C][C]0.628042420767867[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169076&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169076&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
alpha0.0166349237186978
beta0.123094203000456
gamma0.628042420767867







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310901139.33978145826-49.3397814582597
1410601099.1202329441-39.1202329441032
159901021.9761689801-31.9761689801027
16950980.912412177852-30.9124121778516
1715401584.78086237977-44.7808623797705
18870888.123048498275-18.1230484982752
1910701020.122407120949.877592879098
201050982.12752174179367.8724782582066
2110201049.03382963241-29.0338296324119
229601008.51971277041-48.5197127704114
2311001017.4923650743682.5076349256367
2411901107.6396220818982.3603779181115
2510401077.74852741599-37.7485274159894
2610901044.9051519217745.0948480782304
271050975.61175700266374.3882429973368
28850938.285071995565-88.285071995565
2911001517.78257167018-417.782571670176
30850851.013972285135-1.01397228513451
3110401019.9143788811220.0856211188807
32990993.005970403139-3.00597040313949
331040998.22112732178641.7788726782143
341100948.119497876101151.880502123899
3510301038.87898710833-8.87898710833406
3612901124.68801826614165.311981733855
3710401025.007636060314.9923639396998
3811701043.85635363253126.14364636747
391040995.61617093235944.3838290676407
40860861.069942000246-1.06994200024587
4110901228.85251018998-138.852510189981
42870833.23325766904736.7667423309529
4310801013.1758521524166.8241478475911
441000974.50672863753525.4932713624646
459801008.38517018296-28.3851701829564
4610801025.5458169686154.4541830313856
4710401016.3159033826123.6840966173927
4812801207.8496148057372.1503851942668
4911401017.64832530586122.351674694141
5012201106.4366610516113.563338948405
5110801009.6619073118370.3380926881675
52790850.254327888861-60.2543278888612
5310201128.92874316945-108.928743169449
54830846.289954914574-16.2899549145735
5511501042.06859804744107.931401952564
561030979.94724234362550.0527576563746
57900981.675492937545-81.6754929375447
5811401049.0413905372490.9586094627571
5910101022.38604374788-12.3860437478813
6012701242.0246637172927.9753362827096
6110901083.96362661346.0363733865961
6210901164.80810325277-74.8081032527709
639801039.70929545324-59.7092954532422
64850800.76785570523849.2321442947616
6510101047.86325095837-37.8632509583651
66810826.36507773941-16.3650777394101
6710701095.64425376423-25.6442537642347
681040996.74655805021443.2534419497861
69880917.910710637561-37.9107106375609
7011101090.0734090527219.9265909472808
711010999.53866811981710.4613318801833
7212301240.67713781432-10.6771378143212
734901070.79104080212-580.791040802116
7410401089.62279147764-49.6227914776355
751010975.83389694545934.1661030545414
76860809.08990062862850.9100993713716
771010996.13897940729313.8610205927067
78800793.4956869872416.50431301275887
7911301049.1140105271680.8859894728396
801040995.21070067873844.789299321262
81940869.12723386676170.8727661332388
8210701072.72158677696-2.72158677696189
831030978.00810611054151.9918938894593
8413201199.97900277459120.020997225408
851040690.287875122444349.712124877556
8610701051.3875221147218.6124778852836
871070992.84653274121677.1534672587836
88770839.428166367651-69.4281663676512
8910101002.809434269967.19056573003945
90810797.36383736959612.6361626304036
9111501100.9502035930549.049796406945
9210301025.914988779624.08501122038069
93890916.487632697008-26.4876326970078
9410101074.91294656428-64.9129465642786
9511201014.12406065895105.875939341054
9612501282.01149457536-32.0114945753601
97990909.35811615811480.6418838418856
9810201061.61675187578-41.6167518757782
9911101038.4397216908271.5602783091813
100830795.00445545035334.9955445496465
10110301007.9541952468222.0458047531815
102870806.31943314603563.6805668539653
10312601134.73084243834125.269157561662
1049801033.53376609989-53.5337660998869
105940904.31779442365435.6822055763458
1069701041.59856668242-71.5985666824229
10711001087.1841026725512.8158973274517
10813201270.1055675278949.8944324721056

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1090 & 1139.33978145826 & -49.3397814582597 \tabularnewline
14 & 1060 & 1099.1202329441 & -39.1202329441032 \tabularnewline
15 & 990 & 1021.9761689801 & -31.9761689801027 \tabularnewline
16 & 950 & 980.912412177852 & -30.9124121778516 \tabularnewline
17 & 1540 & 1584.78086237977 & -44.7808623797705 \tabularnewline
18 & 870 & 888.123048498275 & -18.1230484982752 \tabularnewline
19 & 1070 & 1020.1224071209 & 49.877592879098 \tabularnewline
20 & 1050 & 982.127521741793 & 67.8724782582066 \tabularnewline
21 & 1020 & 1049.03382963241 & -29.0338296324119 \tabularnewline
22 & 960 & 1008.51971277041 & -48.5197127704114 \tabularnewline
23 & 1100 & 1017.49236507436 & 82.5076349256367 \tabularnewline
24 & 1190 & 1107.63962208189 & 82.3603779181115 \tabularnewline
25 & 1040 & 1077.74852741599 & -37.7485274159894 \tabularnewline
26 & 1090 & 1044.90515192177 & 45.0948480782304 \tabularnewline
27 & 1050 & 975.611757002663 & 74.3882429973368 \tabularnewline
28 & 850 & 938.285071995565 & -88.285071995565 \tabularnewline
29 & 1100 & 1517.78257167018 & -417.782571670176 \tabularnewline
30 & 850 & 851.013972285135 & -1.01397228513451 \tabularnewline
31 & 1040 & 1019.91437888112 & 20.0856211188807 \tabularnewline
32 & 990 & 993.005970403139 & -3.00597040313949 \tabularnewline
33 & 1040 & 998.221127321786 & 41.7788726782143 \tabularnewline
34 & 1100 & 948.119497876101 & 151.880502123899 \tabularnewline
35 & 1030 & 1038.87898710833 & -8.87898710833406 \tabularnewline
36 & 1290 & 1124.68801826614 & 165.311981733855 \tabularnewline
37 & 1040 & 1025.0076360603 & 14.9923639396998 \tabularnewline
38 & 1170 & 1043.85635363253 & 126.14364636747 \tabularnewline
39 & 1040 & 995.616170932359 & 44.3838290676407 \tabularnewline
40 & 860 & 861.069942000246 & -1.06994200024587 \tabularnewline
41 & 1090 & 1228.85251018998 & -138.852510189981 \tabularnewline
42 & 870 & 833.233257669047 & 36.7667423309529 \tabularnewline
43 & 1080 & 1013.17585215241 & 66.8241478475911 \tabularnewline
44 & 1000 & 974.506728637535 & 25.4932713624646 \tabularnewline
45 & 980 & 1008.38517018296 & -28.3851701829564 \tabularnewline
46 & 1080 & 1025.54581696861 & 54.4541830313856 \tabularnewline
47 & 1040 & 1016.31590338261 & 23.6840966173927 \tabularnewline
48 & 1280 & 1207.84961480573 & 72.1503851942668 \tabularnewline
49 & 1140 & 1017.64832530586 & 122.351674694141 \tabularnewline
50 & 1220 & 1106.4366610516 & 113.563338948405 \tabularnewline
51 & 1080 & 1009.66190731183 & 70.3380926881675 \tabularnewline
52 & 790 & 850.254327888861 & -60.2543278888612 \tabularnewline
53 & 1020 & 1128.92874316945 & -108.928743169449 \tabularnewline
54 & 830 & 846.289954914574 & -16.2899549145735 \tabularnewline
55 & 1150 & 1042.06859804744 & 107.931401952564 \tabularnewline
56 & 1030 & 979.947242343625 & 50.0527576563746 \tabularnewline
57 & 900 & 981.675492937545 & -81.6754929375447 \tabularnewline
58 & 1140 & 1049.04139053724 & 90.9586094627571 \tabularnewline
59 & 1010 & 1022.38604374788 & -12.3860437478813 \tabularnewline
60 & 1270 & 1242.02466371729 & 27.9753362827096 \tabularnewline
61 & 1090 & 1083.9636266134 & 6.0363733865961 \tabularnewline
62 & 1090 & 1164.80810325277 & -74.8081032527709 \tabularnewline
63 & 980 & 1039.70929545324 & -59.7092954532422 \tabularnewline
64 & 850 & 800.767855705238 & 49.2321442947616 \tabularnewline
65 & 1010 & 1047.86325095837 & -37.8632509583651 \tabularnewline
66 & 810 & 826.36507773941 & -16.3650777394101 \tabularnewline
67 & 1070 & 1095.64425376423 & -25.6442537642347 \tabularnewline
68 & 1040 & 996.746558050214 & 43.2534419497861 \tabularnewline
69 & 880 & 917.910710637561 & -37.9107106375609 \tabularnewline
70 & 1110 & 1090.07340905272 & 19.9265909472808 \tabularnewline
71 & 1010 & 999.538668119817 & 10.4613318801833 \tabularnewline
72 & 1230 & 1240.67713781432 & -10.6771378143212 \tabularnewline
73 & 490 & 1070.79104080212 & -580.791040802116 \tabularnewline
74 & 1040 & 1089.62279147764 & -49.6227914776355 \tabularnewline
75 & 1010 & 975.833896945459 & 34.1661030545414 \tabularnewline
76 & 860 & 809.089900628628 & 50.9100993713716 \tabularnewline
77 & 1010 & 996.138979407293 & 13.8610205927067 \tabularnewline
78 & 800 & 793.495686987241 & 6.50431301275887 \tabularnewline
79 & 1130 & 1049.11401052716 & 80.8859894728396 \tabularnewline
80 & 1040 & 995.210700678738 & 44.789299321262 \tabularnewline
81 & 940 & 869.127233866761 & 70.8727661332388 \tabularnewline
82 & 1070 & 1072.72158677696 & -2.72158677696189 \tabularnewline
83 & 1030 & 978.008106110541 & 51.9918938894593 \tabularnewline
84 & 1320 & 1199.97900277459 & 120.020997225408 \tabularnewline
85 & 1040 & 690.287875122444 & 349.712124877556 \tabularnewline
86 & 1070 & 1051.38752211472 & 18.6124778852836 \tabularnewline
87 & 1070 & 992.846532741216 & 77.1534672587836 \tabularnewline
88 & 770 & 839.428166367651 & -69.4281663676512 \tabularnewline
89 & 1010 & 1002.80943426996 & 7.19056573003945 \tabularnewline
90 & 810 & 797.363837369596 & 12.6361626304036 \tabularnewline
91 & 1150 & 1100.95020359305 & 49.049796406945 \tabularnewline
92 & 1030 & 1025.91498877962 & 4.08501122038069 \tabularnewline
93 & 890 & 916.487632697008 & -26.4876326970078 \tabularnewline
94 & 1010 & 1074.91294656428 & -64.9129465642786 \tabularnewline
95 & 1120 & 1014.12406065895 & 105.875939341054 \tabularnewline
96 & 1250 & 1282.01149457536 & -32.0114945753601 \tabularnewline
97 & 990 & 909.358116158114 & 80.6418838418856 \tabularnewline
98 & 1020 & 1061.61675187578 & -41.6167518757782 \tabularnewline
99 & 1110 & 1038.43972169082 & 71.5602783091813 \tabularnewline
100 & 830 & 795.004455450353 & 34.9955445496465 \tabularnewline
101 & 1030 & 1007.95419524682 & 22.0458047531815 \tabularnewline
102 & 870 & 806.319433146035 & 63.6805668539653 \tabularnewline
103 & 1260 & 1134.73084243834 & 125.269157561662 \tabularnewline
104 & 980 & 1033.53376609989 & -53.5337660998869 \tabularnewline
105 & 940 & 904.317794423654 & 35.6822055763458 \tabularnewline
106 & 970 & 1041.59856668242 & -71.5985666824229 \tabularnewline
107 & 1100 & 1087.18410267255 & 12.8158973274517 \tabularnewline
108 & 1320 & 1270.10556752789 & 49.8944324721056 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169076&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]1090[/C][C]1139.33978145826[/C][C]-49.3397814582597[/C][/ROW]
[ROW][C]14[/C][C]1060[/C][C]1099.1202329441[/C][C]-39.1202329441032[/C][/ROW]
[ROW][C]15[/C][C]990[/C][C]1021.9761689801[/C][C]-31.9761689801027[/C][/ROW]
[ROW][C]16[/C][C]950[/C][C]980.912412177852[/C][C]-30.9124121778516[/C][/ROW]
[ROW][C]17[/C][C]1540[/C][C]1584.78086237977[/C][C]-44.7808623797705[/C][/ROW]
[ROW][C]18[/C][C]870[/C][C]888.123048498275[/C][C]-18.1230484982752[/C][/ROW]
[ROW][C]19[/C][C]1070[/C][C]1020.1224071209[/C][C]49.877592879098[/C][/ROW]
[ROW][C]20[/C][C]1050[/C][C]982.127521741793[/C][C]67.8724782582066[/C][/ROW]
[ROW][C]21[/C][C]1020[/C][C]1049.03382963241[/C][C]-29.0338296324119[/C][/ROW]
[ROW][C]22[/C][C]960[/C][C]1008.51971277041[/C][C]-48.5197127704114[/C][/ROW]
[ROW][C]23[/C][C]1100[/C][C]1017.49236507436[/C][C]82.5076349256367[/C][/ROW]
[ROW][C]24[/C][C]1190[/C][C]1107.63962208189[/C][C]82.3603779181115[/C][/ROW]
[ROW][C]25[/C][C]1040[/C][C]1077.74852741599[/C][C]-37.7485274159894[/C][/ROW]
[ROW][C]26[/C][C]1090[/C][C]1044.90515192177[/C][C]45.0948480782304[/C][/ROW]
[ROW][C]27[/C][C]1050[/C][C]975.611757002663[/C][C]74.3882429973368[/C][/ROW]
[ROW][C]28[/C][C]850[/C][C]938.285071995565[/C][C]-88.285071995565[/C][/ROW]
[ROW][C]29[/C][C]1100[/C][C]1517.78257167018[/C][C]-417.782571670176[/C][/ROW]
[ROW][C]30[/C][C]850[/C][C]851.013972285135[/C][C]-1.01397228513451[/C][/ROW]
[ROW][C]31[/C][C]1040[/C][C]1019.91437888112[/C][C]20.0856211188807[/C][/ROW]
[ROW][C]32[/C][C]990[/C][C]993.005970403139[/C][C]-3.00597040313949[/C][/ROW]
[ROW][C]33[/C][C]1040[/C][C]998.221127321786[/C][C]41.7788726782143[/C][/ROW]
[ROW][C]34[/C][C]1100[/C][C]948.119497876101[/C][C]151.880502123899[/C][/ROW]
[ROW][C]35[/C][C]1030[/C][C]1038.87898710833[/C][C]-8.87898710833406[/C][/ROW]
[ROW][C]36[/C][C]1290[/C][C]1124.68801826614[/C][C]165.311981733855[/C][/ROW]
[ROW][C]37[/C][C]1040[/C][C]1025.0076360603[/C][C]14.9923639396998[/C][/ROW]
[ROW][C]38[/C][C]1170[/C][C]1043.85635363253[/C][C]126.14364636747[/C][/ROW]
[ROW][C]39[/C][C]1040[/C][C]995.616170932359[/C][C]44.3838290676407[/C][/ROW]
[ROW][C]40[/C][C]860[/C][C]861.069942000246[/C][C]-1.06994200024587[/C][/ROW]
[ROW][C]41[/C][C]1090[/C][C]1228.85251018998[/C][C]-138.852510189981[/C][/ROW]
[ROW][C]42[/C][C]870[/C][C]833.233257669047[/C][C]36.7667423309529[/C][/ROW]
[ROW][C]43[/C][C]1080[/C][C]1013.17585215241[/C][C]66.8241478475911[/C][/ROW]
[ROW][C]44[/C][C]1000[/C][C]974.506728637535[/C][C]25.4932713624646[/C][/ROW]
[ROW][C]45[/C][C]980[/C][C]1008.38517018296[/C][C]-28.3851701829564[/C][/ROW]
[ROW][C]46[/C][C]1080[/C][C]1025.54581696861[/C][C]54.4541830313856[/C][/ROW]
[ROW][C]47[/C][C]1040[/C][C]1016.31590338261[/C][C]23.6840966173927[/C][/ROW]
[ROW][C]48[/C][C]1280[/C][C]1207.84961480573[/C][C]72.1503851942668[/C][/ROW]
[ROW][C]49[/C][C]1140[/C][C]1017.64832530586[/C][C]122.351674694141[/C][/ROW]
[ROW][C]50[/C][C]1220[/C][C]1106.4366610516[/C][C]113.563338948405[/C][/ROW]
[ROW][C]51[/C][C]1080[/C][C]1009.66190731183[/C][C]70.3380926881675[/C][/ROW]
[ROW][C]52[/C][C]790[/C][C]850.254327888861[/C][C]-60.2543278888612[/C][/ROW]
[ROW][C]53[/C][C]1020[/C][C]1128.92874316945[/C][C]-108.928743169449[/C][/ROW]
[ROW][C]54[/C][C]830[/C][C]846.289954914574[/C][C]-16.2899549145735[/C][/ROW]
[ROW][C]55[/C][C]1150[/C][C]1042.06859804744[/C][C]107.931401952564[/C][/ROW]
[ROW][C]56[/C][C]1030[/C][C]979.947242343625[/C][C]50.0527576563746[/C][/ROW]
[ROW][C]57[/C][C]900[/C][C]981.675492937545[/C][C]-81.6754929375447[/C][/ROW]
[ROW][C]58[/C][C]1140[/C][C]1049.04139053724[/C][C]90.9586094627571[/C][/ROW]
[ROW][C]59[/C][C]1010[/C][C]1022.38604374788[/C][C]-12.3860437478813[/C][/ROW]
[ROW][C]60[/C][C]1270[/C][C]1242.02466371729[/C][C]27.9753362827096[/C][/ROW]
[ROW][C]61[/C][C]1090[/C][C]1083.9636266134[/C][C]6.0363733865961[/C][/ROW]
[ROW][C]62[/C][C]1090[/C][C]1164.80810325277[/C][C]-74.8081032527709[/C][/ROW]
[ROW][C]63[/C][C]980[/C][C]1039.70929545324[/C][C]-59.7092954532422[/C][/ROW]
[ROW][C]64[/C][C]850[/C][C]800.767855705238[/C][C]49.2321442947616[/C][/ROW]
[ROW][C]65[/C][C]1010[/C][C]1047.86325095837[/C][C]-37.8632509583651[/C][/ROW]
[ROW][C]66[/C][C]810[/C][C]826.36507773941[/C][C]-16.3650777394101[/C][/ROW]
[ROW][C]67[/C][C]1070[/C][C]1095.64425376423[/C][C]-25.6442537642347[/C][/ROW]
[ROW][C]68[/C][C]1040[/C][C]996.746558050214[/C][C]43.2534419497861[/C][/ROW]
[ROW][C]69[/C][C]880[/C][C]917.910710637561[/C][C]-37.9107106375609[/C][/ROW]
[ROW][C]70[/C][C]1110[/C][C]1090.07340905272[/C][C]19.9265909472808[/C][/ROW]
[ROW][C]71[/C][C]1010[/C][C]999.538668119817[/C][C]10.4613318801833[/C][/ROW]
[ROW][C]72[/C][C]1230[/C][C]1240.67713781432[/C][C]-10.6771378143212[/C][/ROW]
[ROW][C]73[/C][C]490[/C][C]1070.79104080212[/C][C]-580.791040802116[/C][/ROW]
[ROW][C]74[/C][C]1040[/C][C]1089.62279147764[/C][C]-49.6227914776355[/C][/ROW]
[ROW][C]75[/C][C]1010[/C][C]975.833896945459[/C][C]34.1661030545414[/C][/ROW]
[ROW][C]76[/C][C]860[/C][C]809.089900628628[/C][C]50.9100993713716[/C][/ROW]
[ROW][C]77[/C][C]1010[/C][C]996.138979407293[/C][C]13.8610205927067[/C][/ROW]
[ROW][C]78[/C][C]800[/C][C]793.495686987241[/C][C]6.50431301275887[/C][/ROW]
[ROW][C]79[/C][C]1130[/C][C]1049.11401052716[/C][C]80.8859894728396[/C][/ROW]
[ROW][C]80[/C][C]1040[/C][C]995.210700678738[/C][C]44.789299321262[/C][/ROW]
[ROW][C]81[/C][C]940[/C][C]869.127233866761[/C][C]70.8727661332388[/C][/ROW]
[ROW][C]82[/C][C]1070[/C][C]1072.72158677696[/C][C]-2.72158677696189[/C][/ROW]
[ROW][C]83[/C][C]1030[/C][C]978.008106110541[/C][C]51.9918938894593[/C][/ROW]
[ROW][C]84[/C][C]1320[/C][C]1199.97900277459[/C][C]120.020997225408[/C][/ROW]
[ROW][C]85[/C][C]1040[/C][C]690.287875122444[/C][C]349.712124877556[/C][/ROW]
[ROW][C]86[/C][C]1070[/C][C]1051.38752211472[/C][C]18.6124778852836[/C][/ROW]
[ROW][C]87[/C][C]1070[/C][C]992.846532741216[/C][C]77.1534672587836[/C][/ROW]
[ROW][C]88[/C][C]770[/C][C]839.428166367651[/C][C]-69.4281663676512[/C][/ROW]
[ROW][C]89[/C][C]1010[/C][C]1002.80943426996[/C][C]7.19056573003945[/C][/ROW]
[ROW][C]90[/C][C]810[/C][C]797.363837369596[/C][C]12.6361626304036[/C][/ROW]
[ROW][C]91[/C][C]1150[/C][C]1100.95020359305[/C][C]49.049796406945[/C][/ROW]
[ROW][C]92[/C][C]1030[/C][C]1025.91498877962[/C][C]4.08501122038069[/C][/ROW]
[ROW][C]93[/C][C]890[/C][C]916.487632697008[/C][C]-26.4876326970078[/C][/ROW]
[ROW][C]94[/C][C]1010[/C][C]1074.91294656428[/C][C]-64.9129465642786[/C][/ROW]
[ROW][C]95[/C][C]1120[/C][C]1014.12406065895[/C][C]105.875939341054[/C][/ROW]
[ROW][C]96[/C][C]1250[/C][C]1282.01149457536[/C][C]-32.0114945753601[/C][/ROW]
[ROW][C]97[/C][C]990[/C][C]909.358116158114[/C][C]80.6418838418856[/C][/ROW]
[ROW][C]98[/C][C]1020[/C][C]1061.61675187578[/C][C]-41.6167518757782[/C][/ROW]
[ROW][C]99[/C][C]1110[/C][C]1038.43972169082[/C][C]71.5602783091813[/C][/ROW]
[ROW][C]100[/C][C]830[/C][C]795.004455450353[/C][C]34.9955445496465[/C][/ROW]
[ROW][C]101[/C][C]1030[/C][C]1007.95419524682[/C][C]22.0458047531815[/C][/ROW]
[ROW][C]102[/C][C]870[/C][C]806.319433146035[/C][C]63.6805668539653[/C][/ROW]
[ROW][C]103[/C][C]1260[/C][C]1134.73084243834[/C][C]125.269157561662[/C][/ROW]
[ROW][C]104[/C][C]980[/C][C]1033.53376609989[/C][C]-53.5337660998869[/C][/ROW]
[ROW][C]105[/C][C]940[/C][C]904.317794423654[/C][C]35.6822055763458[/C][/ROW]
[ROW][C]106[/C][C]970[/C][C]1041.59856668242[/C][C]-71.5985666824229[/C][/ROW]
[ROW][C]107[/C][C]1100[/C][C]1087.18410267255[/C][C]12.8158973274517[/C][/ROW]
[ROW][C]108[/C][C]1320[/C][C]1270.10556752789[/C][C]49.8944324721056[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169076&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169076&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
1310901139.33978145826-49.3397814582597
1410601099.1202329441-39.1202329441032
159901021.9761689801-31.9761689801027
16950980.912412177852-30.9124121778516
1715401584.78086237977-44.7808623797705
18870888.123048498275-18.1230484982752
1910701020.122407120949.877592879098
201050982.12752174179367.8724782582066
2110201049.03382963241-29.0338296324119
229601008.51971277041-48.5197127704114
2311001017.4923650743682.5076349256367
2411901107.6396220818982.3603779181115
2510401077.74852741599-37.7485274159894
2610901044.9051519217745.0948480782304
271050975.61175700266374.3882429973368
28850938.285071995565-88.285071995565
2911001517.78257167018-417.782571670176
30850851.013972285135-1.01397228513451
3110401019.9143788811220.0856211188807
32990993.005970403139-3.00597040313949
331040998.22112732178641.7788726782143
341100948.119497876101151.880502123899
3510301038.87898710833-8.87898710833406
3612901124.68801826614165.311981733855
3710401025.007636060314.9923639396998
3811701043.85635363253126.14364636747
391040995.61617093235944.3838290676407
40860861.069942000246-1.06994200024587
4110901228.85251018998-138.852510189981
42870833.23325766904736.7667423309529
4310801013.1758521524166.8241478475911
441000974.50672863753525.4932713624646
459801008.38517018296-28.3851701829564
4610801025.5458169686154.4541830313856
4710401016.3159033826123.6840966173927
4812801207.8496148057372.1503851942668
4911401017.64832530586122.351674694141
5012201106.4366610516113.563338948405
5110801009.6619073118370.3380926881675
52790850.254327888861-60.2543278888612
5310201128.92874316945-108.928743169449
54830846.289954914574-16.2899549145735
5511501042.06859804744107.931401952564
561030979.94724234362550.0527576563746
57900981.675492937545-81.6754929375447
5811401049.0413905372490.9586094627571
5910101022.38604374788-12.3860437478813
6012701242.0246637172927.9753362827096
6110901083.96362661346.0363733865961
6210901164.80810325277-74.8081032527709
639801039.70929545324-59.7092954532422
64850800.76785570523849.2321442947616
6510101047.86325095837-37.8632509583651
66810826.36507773941-16.3650777394101
6710701095.64425376423-25.6442537642347
681040996.74655805021443.2534419497861
69880917.910710637561-37.9107106375609
7011101090.0734090527219.9265909472808
711010999.53866811981710.4613318801833
7212301240.67713781432-10.6771378143212
734901070.79104080212-580.791040802116
7410401089.62279147764-49.6227914776355
751010975.83389694545934.1661030545414
76860809.08990062862850.9100993713716
771010996.13897940729313.8610205927067
78800793.4956869872416.50431301275887
7911301049.1140105271680.8859894728396
801040995.21070067873844.789299321262
81940869.12723386676170.8727661332388
8210701072.72158677696-2.72158677696189
831030978.00810611054151.9918938894593
8413201199.97900277459120.020997225408
851040690.287875122444349.712124877556
8610701051.3875221147218.6124778852836
871070992.84653274121677.1534672587836
88770839.428166367651-69.4281663676512
8910101002.809434269967.19056573003945
90810797.36383736959612.6361626304036
9111501100.9502035930549.049796406945
9210301025.914988779624.08501122038069
93890916.487632697008-26.4876326970078
9410101074.91294656428-64.9129465642786
9511201014.12406065895105.875939341054
9612501282.01149457536-32.0114945753601
97990909.35811615811480.6418838418856
9810201061.61675187578-41.6167518757782
9911101038.4397216908271.5602783091813
100830795.00445545035334.9955445496465
10110301007.9541952468222.0458047531815
102870806.31943314603563.6805668539653
10312601134.73084243834125.269157561662
1049801033.53376609989-53.5337660998869
105940904.31779442365435.6822055763458
1069701041.59856668242-71.5985666824229
10711001087.1841026725512.8158973274517
10813201270.1055675278949.8944324721056







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109966.780531975964839.8841928342281093.6768711177
1101043.20936408844916.2489885512011170.16973962567
1111091.59176954252964.5490051750761218.63453390996
112822.830583133819695.801814818127949.859351449511
1131028.9827299662901.7514697703711156.21399016203
114851.70264794753724.494155150062978.911140744998
1151219.301951724391091.536818606391347.06708484239
1161004.59960028165876.9713442592011132.2278563041
117931.030904584312803.3543555915311058.70745357709
1181001.68332341656873.6787846861951129.68786214692
1191101.25060893431972.7485518562351229.75266601238
1201308.05524079038878.2444181790611737.86606340171

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 966.780531975964 & 839.884192834228 & 1093.6768711177 \tabularnewline
110 & 1043.20936408844 & 916.248988551201 & 1170.16973962567 \tabularnewline
111 & 1091.59176954252 & 964.549005175076 & 1218.63453390996 \tabularnewline
112 & 822.830583133819 & 695.801814818127 & 949.859351449511 \tabularnewline
113 & 1028.9827299662 & 901.751469770371 & 1156.21399016203 \tabularnewline
114 & 851.70264794753 & 724.494155150062 & 978.911140744998 \tabularnewline
115 & 1219.30195172439 & 1091.53681860639 & 1347.06708484239 \tabularnewline
116 & 1004.59960028165 & 876.971344259201 & 1132.2278563041 \tabularnewline
117 & 931.030904584312 & 803.354355591531 & 1058.70745357709 \tabularnewline
118 & 1001.68332341656 & 873.678784686195 & 1129.68786214692 \tabularnewline
119 & 1101.25060893431 & 972.748551856235 & 1229.75266601238 \tabularnewline
120 & 1308.05524079038 & 878.244418179061 & 1737.86606340171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169076&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]966.780531975964[/C][C]839.884192834228[/C][C]1093.6768711177[/C][/ROW]
[ROW][C]110[/C][C]1043.20936408844[/C][C]916.248988551201[/C][C]1170.16973962567[/C][/ROW]
[ROW][C]111[/C][C]1091.59176954252[/C][C]964.549005175076[/C][C]1218.63453390996[/C][/ROW]
[ROW][C]112[/C][C]822.830583133819[/C][C]695.801814818127[/C][C]949.859351449511[/C][/ROW]
[ROW][C]113[/C][C]1028.9827299662[/C][C]901.751469770371[/C][C]1156.21399016203[/C][/ROW]
[ROW][C]114[/C][C]851.70264794753[/C][C]724.494155150062[/C][C]978.911140744998[/C][/ROW]
[ROW][C]115[/C][C]1219.30195172439[/C][C]1091.53681860639[/C][C]1347.06708484239[/C][/ROW]
[ROW][C]116[/C][C]1004.59960028165[/C][C]876.971344259201[/C][C]1132.2278563041[/C][/ROW]
[ROW][C]117[/C][C]931.030904584312[/C][C]803.354355591531[/C][C]1058.70745357709[/C][/ROW]
[ROW][C]118[/C][C]1001.68332341656[/C][C]873.678784686195[/C][C]1129.68786214692[/C][/ROW]
[ROW][C]119[/C][C]1101.25060893431[/C][C]972.748551856235[/C][C]1229.75266601238[/C][/ROW]
[ROW][C]120[/C][C]1308.05524079038[/C][C]878.244418179061[/C][C]1737.86606340171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169076&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169076&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
109966.780531975964839.8841928342281093.6768711177
1101043.20936408844916.2489885512011170.16973962567
1111091.59176954252964.5490051750761218.63453390996
112822.830583133819695.801814818127949.859351449511
1131028.9827299662901.7514697703711156.21399016203
114851.70264794753724.494155150062978.911140744998
1151219.301951724391091.536818606391347.06708484239
1161004.59960028165876.9713442592011132.2278563041
117931.030904584312803.3543555915311058.70745357709
1181001.68332341656873.6787846861951129.68786214692
1191101.25060893431972.7485518562351229.75266601238
1201308.05524079038878.2444181790611737.86606340171



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')