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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 17 Aug 2011 13:22:32 -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/2011/Aug/17/t1313601803iye9rsp8juwtlk6.htm/, Retrieved Wed, 15 May 2024 10:20:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123974, Retrieved Wed, 15 May 2024 10:20:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Vlaenderen Lynn
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeksB- stap27] [2011-08-17 17:22:32] [d08a5fa9e4c562ec79e796d78c067f4f] [Current]
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Dataseries X:
960
1160
1040
1030
1080
1020
1000
1060
1000
980
980
1080
980
1290
1030
1000
1130
1030
900
1040
1080
1010
890
1080
950
1310
1060
1070
1150
1060
950
1090
1080
1040
900
1000
1020
1250
1060
1050
1180
1100
1020
1090
1020
960
860
1070
1040
1310
1040
1010
1130
1030
930
1070
990
970
850
1130
1060
1380
1000
970
1080
940
960
1070
1010
1020
750
1140
1040
1420
900
900
1090
950
930
1080
1000
1010
770
1100
1100
1390
930
940
1100
1030
920
1080
1000
1070
830
1100
1170
1330
980
910
1030
970
960
1100
960
1080
730
1140




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123974&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123974&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123974&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0228941545111917
beta0
gamma0.854812717118728

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0228941545111917 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.854812717118728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123974&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]0.0228941545111917[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.854812717118728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123974&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123974&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
alpha0.0228941545111917
beta0
gamma0.854812717118728







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13980972.6255341880347.37446581196571
1412901287.935683364092.06431663591184
1510301025.624261164434.37573883557252
161000991.2824236884148.71757631158641
1711301124.123322243775.8766777562289
1810301028.149180828651.85081917134835
199001003.33287078505-103.33287078505
2010401054.85846909153-14.8584690915288
211080989.65961402066490.3403859793356
221010973.5358644588636.4641355411401
23890973.67866369504-83.6786636950395
2410801069.4042284554310.5957715445679
25950979.69759398348-29.6975939834799
2613101289.7237474070420.2762525929616
2710601029.7598701459630.2401298540447
281070999.63666323401770.3633367659835
2911501131.516050134918.4839498651022
3010601032.4679733554727.5320266445276
31950920.38572440193129.6142755980688
3210901048.8526159144641.147384085544
3310801072.802522489787.19747751021669
3410401009.7755520831630.2244479168377
35900909.427126631974-9.42712663197449
3610001085.59463278426-85.5946327842587
371020960.03106886746259.968931132538
3812501313.85034225531-63.8503422553051
3910601060.28271151336-0.282711513357071
4010501062.9733177123-12.9733177123046
4111801149.6129134157530.3870865842539
4211001058.3946871813641.6053128186404
431020948.37381704315871.6261829568417
4410901087.4354780512.56452194900498
4510201082.14565768485-62.1456576848507
469601036.76423921869-76.7642392186904
47860900.84771787133-40.8477178713297
4810701012.6775376902957.3224623097146
4910401011.9668152579128.0331847420878
5013101261.6358269471448.3641730528616
5110401063.73163964834-23.7316396483427
5210101055.28566878112-45.285668781122
5311301177.40195312909-47.4019531290933
5410301093.77275195604-63.7727519560385
559301006.4140468281-76.4140468281046
5610701084.40321736092-14.4032173609214
579901024.67624256209-34.6762425620932
58970967.7136525039122.28634749608807
59850863.605932681263-13.6059326812633
6011301058.0553371239471.9446628760559
6110601033.2157281129226.7842718870793
6213801299.8374525572280.1625474427756
6310001042.44377512054-42.443775120541
649701015.56656449656-45.5665644965644
6510801135.90880733941-55.9088073394114
669401038.41126194833-98.4112619483292
67960939.70099065434620.2990093456541
6810701071.69840523681-1.69840523680978
691010995.32940406356314.6705959364366
701020970.36929437688749.6307056231135
71750854.071575735572-104.071575735572
7211401117.9053393085522.0946606914545
7310401054.20457865281-14.2045786528126
7414201364.471702484355.5282975157033
759001004.10803301952-104.108033019515
76900973.210784933563-73.2107849335629
7710901084.281855926855.71814407315401
78950952.695350925229-2.69535092522881
79930955.328278578563-25.3282785785627
8010801067.9079193726912.0920806273109
8110001005.52672522016-5.52672522015826
8210101009.30438445140.695615548602177
83770763.5076601449576.49233985504281
8411001135.25209415373-35.2520941537282
8511001039.9197605160360.080239483972
8613901410.13143446287-20.1314344628749
87930914.70055116663815.2994488333625
88940912.34373123771327.6562687622873
8911001091.648864341998.35113565800611
901030953.09533083768776.9046691623131
91920938.646650513516-18.6466505135162
9210801082.63433600781-2.63433600780513
9310001005.2000175069-5.20001750689823
9410701014.1823199113355.8176800886749
95830774.48923918458455.5107608154156
9611001112.48918296165-12.4891829616497
9711701097.303603865272.6963961347985
9813301400.80791475904-70.8079147590397
99980933.81021592985846.189784070142
100910942.481545311532-32.4815453115318
10110301104.28540631956-74.2854063195641
1029701021.09880394767-51.0988039476667
103960923.91106895030936.088931049691
10411001082.5260449478517.4739550521465
1059601003.40912253301-43.4091225330087
10610801062.4812342316417.5187657683607
107730821.654980220916-91.6549802209161
10811401099.4892455604740.5107544395257

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 980 & 972.625534188034 & 7.37446581196571 \tabularnewline
14 & 1290 & 1287.93568336409 & 2.06431663591184 \tabularnewline
15 & 1030 & 1025.62426116443 & 4.37573883557252 \tabularnewline
16 & 1000 & 991.282423688414 & 8.71757631158641 \tabularnewline
17 & 1130 & 1124.12332224377 & 5.8766777562289 \tabularnewline
18 & 1030 & 1028.14918082865 & 1.85081917134835 \tabularnewline
19 & 900 & 1003.33287078505 & -103.33287078505 \tabularnewline
20 & 1040 & 1054.85846909153 & -14.8584690915288 \tabularnewline
21 & 1080 & 989.659614020664 & 90.3403859793356 \tabularnewline
22 & 1010 & 973.53586445886 & 36.4641355411401 \tabularnewline
23 & 890 & 973.67866369504 & -83.6786636950395 \tabularnewline
24 & 1080 & 1069.40422845543 & 10.5957715445679 \tabularnewline
25 & 950 & 979.69759398348 & -29.6975939834799 \tabularnewline
26 & 1310 & 1289.72374740704 & 20.2762525929616 \tabularnewline
27 & 1060 & 1029.75987014596 & 30.2401298540447 \tabularnewline
28 & 1070 & 999.636663234017 & 70.3633367659835 \tabularnewline
29 & 1150 & 1131.5160501349 & 18.4839498651022 \tabularnewline
30 & 1060 & 1032.46797335547 & 27.5320266445276 \tabularnewline
31 & 950 & 920.385724401931 & 29.6142755980688 \tabularnewline
32 & 1090 & 1048.85261591446 & 41.147384085544 \tabularnewline
33 & 1080 & 1072.80252248978 & 7.19747751021669 \tabularnewline
34 & 1040 & 1009.77555208316 & 30.2244479168377 \tabularnewline
35 & 900 & 909.427126631974 & -9.42712663197449 \tabularnewline
36 & 1000 & 1085.59463278426 & -85.5946327842587 \tabularnewline
37 & 1020 & 960.031068867462 & 59.968931132538 \tabularnewline
38 & 1250 & 1313.85034225531 & -63.8503422553051 \tabularnewline
39 & 1060 & 1060.28271151336 & -0.282711513357071 \tabularnewline
40 & 1050 & 1062.9733177123 & -12.9733177123046 \tabularnewline
41 & 1180 & 1149.61291341575 & 30.3870865842539 \tabularnewline
42 & 1100 & 1058.39468718136 & 41.6053128186404 \tabularnewline
43 & 1020 & 948.373817043158 & 71.6261829568417 \tabularnewline
44 & 1090 & 1087.435478051 & 2.56452194900498 \tabularnewline
45 & 1020 & 1082.14565768485 & -62.1456576848507 \tabularnewline
46 & 960 & 1036.76423921869 & -76.7642392186904 \tabularnewline
47 & 860 & 900.84771787133 & -40.8477178713297 \tabularnewline
48 & 1070 & 1012.67753769029 & 57.3224623097146 \tabularnewline
49 & 1040 & 1011.96681525791 & 28.0331847420878 \tabularnewline
50 & 1310 & 1261.63582694714 & 48.3641730528616 \tabularnewline
51 & 1040 & 1063.73163964834 & -23.7316396483427 \tabularnewline
52 & 1010 & 1055.28566878112 & -45.285668781122 \tabularnewline
53 & 1130 & 1177.40195312909 & -47.4019531290933 \tabularnewline
54 & 1030 & 1093.77275195604 & -63.7727519560385 \tabularnewline
55 & 930 & 1006.4140468281 & -76.4140468281046 \tabularnewline
56 & 1070 & 1084.40321736092 & -14.4032173609214 \tabularnewline
57 & 990 & 1024.67624256209 & -34.6762425620932 \tabularnewline
58 & 970 & 967.713652503912 & 2.28634749608807 \tabularnewline
59 & 850 & 863.605932681263 & -13.6059326812633 \tabularnewline
60 & 1130 & 1058.05533712394 & 71.9446628760559 \tabularnewline
61 & 1060 & 1033.21572811292 & 26.7842718870793 \tabularnewline
62 & 1380 & 1299.83745255722 & 80.1625474427756 \tabularnewline
63 & 1000 & 1042.44377512054 & -42.443775120541 \tabularnewline
64 & 970 & 1015.56656449656 & -45.5665644965644 \tabularnewline
65 & 1080 & 1135.90880733941 & -55.9088073394114 \tabularnewline
66 & 940 & 1038.41126194833 & -98.4112619483292 \tabularnewline
67 & 960 & 939.700990654346 & 20.2990093456541 \tabularnewline
68 & 1070 & 1071.69840523681 & -1.69840523680978 \tabularnewline
69 & 1010 & 995.329404063563 & 14.6705959364366 \tabularnewline
70 & 1020 & 970.369294376887 & 49.6307056231135 \tabularnewline
71 & 750 & 854.071575735572 & -104.071575735572 \tabularnewline
72 & 1140 & 1117.90533930855 & 22.0946606914545 \tabularnewline
73 & 1040 & 1054.20457865281 & -14.2045786528126 \tabularnewline
74 & 1420 & 1364.4717024843 & 55.5282975157033 \tabularnewline
75 & 900 & 1004.10803301952 & -104.108033019515 \tabularnewline
76 & 900 & 973.210784933563 & -73.2107849335629 \tabularnewline
77 & 1090 & 1084.28185592685 & 5.71814407315401 \tabularnewline
78 & 950 & 952.695350925229 & -2.69535092522881 \tabularnewline
79 & 930 & 955.328278578563 & -25.3282785785627 \tabularnewline
80 & 1080 & 1067.90791937269 & 12.0920806273109 \tabularnewline
81 & 1000 & 1005.52672522016 & -5.52672522015826 \tabularnewline
82 & 1010 & 1009.3043844514 & 0.695615548602177 \tabularnewline
83 & 770 & 763.507660144957 & 6.49233985504281 \tabularnewline
84 & 1100 & 1135.25209415373 & -35.2520941537282 \tabularnewline
85 & 1100 & 1039.91976051603 & 60.080239483972 \tabularnewline
86 & 1390 & 1410.13143446287 & -20.1314344628749 \tabularnewline
87 & 930 & 914.700551166638 & 15.2994488333625 \tabularnewline
88 & 940 & 912.343731237713 & 27.6562687622873 \tabularnewline
89 & 1100 & 1091.64886434199 & 8.35113565800611 \tabularnewline
90 & 1030 & 953.095330837687 & 76.9046691623131 \tabularnewline
91 & 920 & 938.646650513516 & -18.6466505135162 \tabularnewline
92 & 1080 & 1082.63433600781 & -2.63433600780513 \tabularnewline
93 & 1000 & 1005.2000175069 & -5.20001750689823 \tabularnewline
94 & 1070 & 1014.18231991133 & 55.8176800886749 \tabularnewline
95 & 830 & 774.489239184584 & 55.5107608154156 \tabularnewline
96 & 1100 & 1112.48918296165 & -12.4891829616497 \tabularnewline
97 & 1170 & 1097.3036038652 & 72.6963961347985 \tabularnewline
98 & 1330 & 1400.80791475904 & -70.8079147590397 \tabularnewline
99 & 980 & 933.810215929858 & 46.189784070142 \tabularnewline
100 & 910 & 942.481545311532 & -32.4815453115318 \tabularnewline
101 & 1030 & 1104.28540631956 & -74.2854063195641 \tabularnewline
102 & 970 & 1021.09880394767 & -51.0988039476667 \tabularnewline
103 & 960 & 923.911068950309 & 36.088931049691 \tabularnewline
104 & 1100 & 1082.52604494785 & 17.4739550521465 \tabularnewline
105 & 960 & 1003.40912253301 & -43.4091225330087 \tabularnewline
106 & 1080 & 1062.48123423164 & 17.5187657683607 \tabularnewline
107 & 730 & 821.654980220916 & -91.6549802209161 \tabularnewline
108 & 1140 & 1099.48924556047 & 40.5107544395257 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123974&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]980[/C][C]972.625534188034[/C][C]7.37446581196571[/C][/ROW]
[ROW][C]14[/C][C]1290[/C][C]1287.93568336409[/C][C]2.06431663591184[/C][/ROW]
[ROW][C]15[/C][C]1030[/C][C]1025.62426116443[/C][C]4.37573883557252[/C][/ROW]
[ROW][C]16[/C][C]1000[/C][C]991.282423688414[/C][C]8.71757631158641[/C][/ROW]
[ROW][C]17[/C][C]1130[/C][C]1124.12332224377[/C][C]5.8766777562289[/C][/ROW]
[ROW][C]18[/C][C]1030[/C][C]1028.14918082865[/C][C]1.85081917134835[/C][/ROW]
[ROW][C]19[/C][C]900[/C][C]1003.33287078505[/C][C]-103.33287078505[/C][/ROW]
[ROW][C]20[/C][C]1040[/C][C]1054.85846909153[/C][C]-14.8584690915288[/C][/ROW]
[ROW][C]21[/C][C]1080[/C][C]989.659614020664[/C][C]90.3403859793356[/C][/ROW]
[ROW][C]22[/C][C]1010[/C][C]973.53586445886[/C][C]36.4641355411401[/C][/ROW]
[ROW][C]23[/C][C]890[/C][C]973.67866369504[/C][C]-83.6786636950395[/C][/ROW]
[ROW][C]24[/C][C]1080[/C][C]1069.40422845543[/C][C]10.5957715445679[/C][/ROW]
[ROW][C]25[/C][C]950[/C][C]979.69759398348[/C][C]-29.6975939834799[/C][/ROW]
[ROW][C]26[/C][C]1310[/C][C]1289.72374740704[/C][C]20.2762525929616[/C][/ROW]
[ROW][C]27[/C][C]1060[/C][C]1029.75987014596[/C][C]30.2401298540447[/C][/ROW]
[ROW][C]28[/C][C]1070[/C][C]999.636663234017[/C][C]70.3633367659835[/C][/ROW]
[ROW][C]29[/C][C]1150[/C][C]1131.5160501349[/C][C]18.4839498651022[/C][/ROW]
[ROW][C]30[/C][C]1060[/C][C]1032.46797335547[/C][C]27.5320266445276[/C][/ROW]
[ROW][C]31[/C][C]950[/C][C]920.385724401931[/C][C]29.6142755980688[/C][/ROW]
[ROW][C]32[/C][C]1090[/C][C]1048.85261591446[/C][C]41.147384085544[/C][/ROW]
[ROW][C]33[/C][C]1080[/C][C]1072.80252248978[/C][C]7.19747751021669[/C][/ROW]
[ROW][C]34[/C][C]1040[/C][C]1009.77555208316[/C][C]30.2244479168377[/C][/ROW]
[ROW][C]35[/C][C]900[/C][C]909.427126631974[/C][C]-9.42712663197449[/C][/ROW]
[ROW][C]36[/C][C]1000[/C][C]1085.59463278426[/C][C]-85.5946327842587[/C][/ROW]
[ROW][C]37[/C][C]1020[/C][C]960.031068867462[/C][C]59.968931132538[/C][/ROW]
[ROW][C]38[/C][C]1250[/C][C]1313.85034225531[/C][C]-63.8503422553051[/C][/ROW]
[ROW][C]39[/C][C]1060[/C][C]1060.28271151336[/C][C]-0.282711513357071[/C][/ROW]
[ROW][C]40[/C][C]1050[/C][C]1062.9733177123[/C][C]-12.9733177123046[/C][/ROW]
[ROW][C]41[/C][C]1180[/C][C]1149.61291341575[/C][C]30.3870865842539[/C][/ROW]
[ROW][C]42[/C][C]1100[/C][C]1058.39468718136[/C][C]41.6053128186404[/C][/ROW]
[ROW][C]43[/C][C]1020[/C][C]948.373817043158[/C][C]71.6261829568417[/C][/ROW]
[ROW][C]44[/C][C]1090[/C][C]1087.435478051[/C][C]2.56452194900498[/C][/ROW]
[ROW][C]45[/C][C]1020[/C][C]1082.14565768485[/C][C]-62.1456576848507[/C][/ROW]
[ROW][C]46[/C][C]960[/C][C]1036.76423921869[/C][C]-76.7642392186904[/C][/ROW]
[ROW][C]47[/C][C]860[/C][C]900.84771787133[/C][C]-40.8477178713297[/C][/ROW]
[ROW][C]48[/C][C]1070[/C][C]1012.67753769029[/C][C]57.3224623097146[/C][/ROW]
[ROW][C]49[/C][C]1040[/C][C]1011.96681525791[/C][C]28.0331847420878[/C][/ROW]
[ROW][C]50[/C][C]1310[/C][C]1261.63582694714[/C][C]48.3641730528616[/C][/ROW]
[ROW][C]51[/C][C]1040[/C][C]1063.73163964834[/C][C]-23.7316396483427[/C][/ROW]
[ROW][C]52[/C][C]1010[/C][C]1055.28566878112[/C][C]-45.285668781122[/C][/ROW]
[ROW][C]53[/C][C]1130[/C][C]1177.40195312909[/C][C]-47.4019531290933[/C][/ROW]
[ROW][C]54[/C][C]1030[/C][C]1093.77275195604[/C][C]-63.7727519560385[/C][/ROW]
[ROW][C]55[/C][C]930[/C][C]1006.4140468281[/C][C]-76.4140468281046[/C][/ROW]
[ROW][C]56[/C][C]1070[/C][C]1084.40321736092[/C][C]-14.4032173609214[/C][/ROW]
[ROW][C]57[/C][C]990[/C][C]1024.67624256209[/C][C]-34.6762425620932[/C][/ROW]
[ROW][C]58[/C][C]970[/C][C]967.713652503912[/C][C]2.28634749608807[/C][/ROW]
[ROW][C]59[/C][C]850[/C][C]863.605932681263[/C][C]-13.6059326812633[/C][/ROW]
[ROW][C]60[/C][C]1130[/C][C]1058.05533712394[/C][C]71.9446628760559[/C][/ROW]
[ROW][C]61[/C][C]1060[/C][C]1033.21572811292[/C][C]26.7842718870793[/C][/ROW]
[ROW][C]62[/C][C]1380[/C][C]1299.83745255722[/C][C]80.1625474427756[/C][/ROW]
[ROW][C]63[/C][C]1000[/C][C]1042.44377512054[/C][C]-42.443775120541[/C][/ROW]
[ROW][C]64[/C][C]970[/C][C]1015.56656449656[/C][C]-45.5665644965644[/C][/ROW]
[ROW][C]65[/C][C]1080[/C][C]1135.90880733941[/C][C]-55.9088073394114[/C][/ROW]
[ROW][C]66[/C][C]940[/C][C]1038.41126194833[/C][C]-98.4112619483292[/C][/ROW]
[ROW][C]67[/C][C]960[/C][C]939.700990654346[/C][C]20.2990093456541[/C][/ROW]
[ROW][C]68[/C][C]1070[/C][C]1071.69840523681[/C][C]-1.69840523680978[/C][/ROW]
[ROW][C]69[/C][C]1010[/C][C]995.329404063563[/C][C]14.6705959364366[/C][/ROW]
[ROW][C]70[/C][C]1020[/C][C]970.369294376887[/C][C]49.6307056231135[/C][/ROW]
[ROW][C]71[/C][C]750[/C][C]854.071575735572[/C][C]-104.071575735572[/C][/ROW]
[ROW][C]72[/C][C]1140[/C][C]1117.90533930855[/C][C]22.0946606914545[/C][/ROW]
[ROW][C]73[/C][C]1040[/C][C]1054.20457865281[/C][C]-14.2045786528126[/C][/ROW]
[ROW][C]74[/C][C]1420[/C][C]1364.4717024843[/C][C]55.5282975157033[/C][/ROW]
[ROW][C]75[/C][C]900[/C][C]1004.10803301952[/C][C]-104.108033019515[/C][/ROW]
[ROW][C]76[/C][C]900[/C][C]973.210784933563[/C][C]-73.2107849335629[/C][/ROW]
[ROW][C]77[/C][C]1090[/C][C]1084.28185592685[/C][C]5.71814407315401[/C][/ROW]
[ROW][C]78[/C][C]950[/C][C]952.695350925229[/C][C]-2.69535092522881[/C][/ROW]
[ROW][C]79[/C][C]930[/C][C]955.328278578563[/C][C]-25.3282785785627[/C][/ROW]
[ROW][C]80[/C][C]1080[/C][C]1067.90791937269[/C][C]12.0920806273109[/C][/ROW]
[ROW][C]81[/C][C]1000[/C][C]1005.52672522016[/C][C]-5.52672522015826[/C][/ROW]
[ROW][C]82[/C][C]1010[/C][C]1009.3043844514[/C][C]0.695615548602177[/C][/ROW]
[ROW][C]83[/C][C]770[/C][C]763.507660144957[/C][C]6.49233985504281[/C][/ROW]
[ROW][C]84[/C][C]1100[/C][C]1135.25209415373[/C][C]-35.2520941537282[/C][/ROW]
[ROW][C]85[/C][C]1100[/C][C]1039.91976051603[/C][C]60.080239483972[/C][/ROW]
[ROW][C]86[/C][C]1390[/C][C]1410.13143446287[/C][C]-20.1314344628749[/C][/ROW]
[ROW][C]87[/C][C]930[/C][C]914.700551166638[/C][C]15.2994488333625[/C][/ROW]
[ROW][C]88[/C][C]940[/C][C]912.343731237713[/C][C]27.6562687622873[/C][/ROW]
[ROW][C]89[/C][C]1100[/C][C]1091.64886434199[/C][C]8.35113565800611[/C][/ROW]
[ROW][C]90[/C][C]1030[/C][C]953.095330837687[/C][C]76.9046691623131[/C][/ROW]
[ROW][C]91[/C][C]920[/C][C]938.646650513516[/C][C]-18.6466505135162[/C][/ROW]
[ROW][C]92[/C][C]1080[/C][C]1082.63433600781[/C][C]-2.63433600780513[/C][/ROW]
[ROW][C]93[/C][C]1000[/C][C]1005.2000175069[/C][C]-5.20001750689823[/C][/ROW]
[ROW][C]94[/C][C]1070[/C][C]1014.18231991133[/C][C]55.8176800886749[/C][/ROW]
[ROW][C]95[/C][C]830[/C][C]774.489239184584[/C][C]55.5107608154156[/C][/ROW]
[ROW][C]96[/C][C]1100[/C][C]1112.48918296165[/C][C]-12.4891829616497[/C][/ROW]
[ROW][C]97[/C][C]1170[/C][C]1097.3036038652[/C][C]72.6963961347985[/C][/ROW]
[ROW][C]98[/C][C]1330[/C][C]1400.80791475904[/C][C]-70.8079147590397[/C][/ROW]
[ROW][C]99[/C][C]980[/C][C]933.810215929858[/C][C]46.189784070142[/C][/ROW]
[ROW][C]100[/C][C]910[/C][C]942.481545311532[/C][C]-32.4815453115318[/C][/ROW]
[ROW][C]101[/C][C]1030[/C][C]1104.28540631956[/C][C]-74.2854063195641[/C][/ROW]
[ROW][C]102[/C][C]970[/C][C]1021.09880394767[/C][C]-51.0988039476667[/C][/ROW]
[ROW][C]103[/C][C]960[/C][C]923.911068950309[/C][C]36.088931049691[/C][/ROW]
[ROW][C]104[/C][C]1100[/C][C]1082.52604494785[/C][C]17.4739550521465[/C][/ROW]
[ROW][C]105[/C][C]960[/C][C]1003.40912253301[/C][C]-43.4091225330087[/C][/ROW]
[ROW][C]106[/C][C]1080[/C][C]1062.48123423164[/C][C]17.5187657683607[/C][/ROW]
[ROW][C]107[/C][C]730[/C][C]821.654980220916[/C][C]-91.6549802209161[/C][/ROW]
[ROW][C]108[/C][C]1140[/C][C]1099.48924556047[/C][C]40.5107544395257[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123974&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123974&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
13980972.6255341880347.37446581196571
1412901287.935683364092.06431663591184
1510301025.624261164434.37573883557252
161000991.2824236884148.71757631158641
1711301124.123322243775.8766777562289
1810301028.149180828651.85081917134835
199001003.33287078505-103.33287078505
2010401054.85846909153-14.8584690915288
211080989.65961402066490.3403859793356
221010973.5358644588636.4641355411401
23890973.67866369504-83.6786636950395
2410801069.4042284554310.5957715445679
25950979.69759398348-29.6975939834799
2613101289.7237474070420.2762525929616
2710601029.7598701459630.2401298540447
281070999.63666323401770.3633367659835
2911501131.516050134918.4839498651022
3010601032.4679733554727.5320266445276
31950920.38572440193129.6142755980688
3210901048.8526159144641.147384085544
3310801072.802522489787.19747751021669
3410401009.7755520831630.2244479168377
35900909.427126631974-9.42712663197449
3610001085.59463278426-85.5946327842587
371020960.03106886746259.968931132538
3812501313.85034225531-63.8503422553051
3910601060.28271151336-0.282711513357071
4010501062.9733177123-12.9733177123046
4111801149.6129134157530.3870865842539
4211001058.3946871813641.6053128186404
431020948.37381704315871.6261829568417
4410901087.4354780512.56452194900498
4510201082.14565768485-62.1456576848507
469601036.76423921869-76.7642392186904
47860900.84771787133-40.8477178713297
4810701012.6775376902957.3224623097146
4910401011.9668152579128.0331847420878
5013101261.6358269471448.3641730528616
5110401063.73163964834-23.7316396483427
5210101055.28566878112-45.285668781122
5311301177.40195312909-47.4019531290933
5410301093.77275195604-63.7727519560385
559301006.4140468281-76.4140468281046
5610701084.40321736092-14.4032173609214
579901024.67624256209-34.6762425620932
58970967.7136525039122.28634749608807
59850863.605932681263-13.6059326812633
6011301058.0553371239471.9446628760559
6110601033.2157281129226.7842718870793
6213801299.8374525572280.1625474427756
6310001042.44377512054-42.443775120541
649701015.56656449656-45.5665644965644
6510801135.90880733941-55.9088073394114
669401038.41126194833-98.4112619483292
67960939.70099065434620.2990093456541
6810701071.69840523681-1.69840523680978
691010995.32940406356314.6705959364366
701020970.36929437688749.6307056231135
71750854.071575735572-104.071575735572
7211401117.9053393085522.0946606914545
7310401054.20457865281-14.2045786528126
7414201364.471702484355.5282975157033
759001004.10803301952-104.108033019515
76900973.210784933563-73.2107849335629
7710901084.281855926855.71814407315401
78950952.695350925229-2.69535092522881
79930955.328278578563-25.3282785785627
8010801067.9079193726912.0920806273109
8110001005.52672522016-5.52672522015826
8210101009.30438445140.695615548602177
83770763.5076601449576.49233985504281
8411001135.25209415373-35.2520941537282
8511001039.9197605160360.080239483972
8613901410.13143446287-20.1314344628749
87930914.70055116663815.2994488333625
88940912.34373123771327.6562687622873
8911001091.648864341998.35113565800611
901030953.09533083768776.9046691623131
91920938.646650513516-18.6466505135162
9210801082.63433600781-2.63433600780513
9310001005.2000175069-5.20001750689823
9410701014.1823199113355.8176800886749
95830774.48923918458455.5107608154156
9611001112.48918296165-12.4891829616497
9711701097.303603865272.6963961347985
9813301400.80791475904-70.8079147590397
99980933.81021592985846.189784070142
100910942.481545311532-32.4815453115318
10110301104.28540631956-74.2854063195641
1029701021.09880394767-51.0988039476667
103960923.91106895030936.088931049691
10411001082.5260449478517.4739550521465
1059601003.40912253301-43.4091225330087
10610801062.4812342316417.5187657683607
107730821.654980220916-91.6549802209161
10811401099.4892455604740.5107544395257







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091156.6676714981063.576768962481249.75857403352
1101338.646760087851245.531464307911431.76205586779
111970.991599379405877.8519167436251064.13128201518
112912.895814664656819.73175155661006.05987777271
1131040.52695169915947.3385144973761133.71538890093
114978.407486691558885.1946817696071071.62029161351
115955.212517590607861.9753513170351048.44968386418
1161097.453248884761004.191727623131190.71477014639
117967.08414094904873.7982710579271060.37001084015
1181078.03962971489984.7294175478911171.34984188188
119745.625745545158652.29119745091838.960293639407
1201135.948813151911042.589935474071229.30769082975

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1156.667671498 & 1063.57676896248 & 1249.75857403352 \tabularnewline
110 & 1338.64676008785 & 1245.53146430791 & 1431.76205586779 \tabularnewline
111 & 970.991599379405 & 877.851916743625 & 1064.13128201518 \tabularnewline
112 & 912.895814664656 & 819.7317515566 & 1006.05987777271 \tabularnewline
113 & 1040.52695169915 & 947.338514497376 & 1133.71538890093 \tabularnewline
114 & 978.407486691558 & 885.194681769607 & 1071.62029161351 \tabularnewline
115 & 955.212517590607 & 861.975351317035 & 1048.44968386418 \tabularnewline
116 & 1097.45324888476 & 1004.19172762313 & 1190.71477014639 \tabularnewline
117 & 967.08414094904 & 873.798271057927 & 1060.37001084015 \tabularnewline
118 & 1078.03962971489 & 984.729417547891 & 1171.34984188188 \tabularnewline
119 & 745.625745545158 & 652.29119745091 & 838.960293639407 \tabularnewline
120 & 1135.94881315191 & 1042.58993547407 & 1229.30769082975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123974&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]1156.667671498[/C][C]1063.57676896248[/C][C]1249.75857403352[/C][/ROW]
[ROW][C]110[/C][C]1338.64676008785[/C][C]1245.53146430791[/C][C]1431.76205586779[/C][/ROW]
[ROW][C]111[/C][C]970.991599379405[/C][C]877.851916743625[/C][C]1064.13128201518[/C][/ROW]
[ROW][C]112[/C][C]912.895814664656[/C][C]819.7317515566[/C][C]1006.05987777271[/C][/ROW]
[ROW][C]113[/C][C]1040.52695169915[/C][C]947.338514497376[/C][C]1133.71538890093[/C][/ROW]
[ROW][C]114[/C][C]978.407486691558[/C][C]885.194681769607[/C][C]1071.62029161351[/C][/ROW]
[ROW][C]115[/C][C]955.212517590607[/C][C]861.975351317035[/C][C]1048.44968386418[/C][/ROW]
[ROW][C]116[/C][C]1097.45324888476[/C][C]1004.19172762313[/C][C]1190.71477014639[/C][/ROW]
[ROW][C]117[/C][C]967.08414094904[/C][C]873.798271057927[/C][C]1060.37001084015[/C][/ROW]
[ROW][C]118[/C][C]1078.03962971489[/C][C]984.729417547891[/C][C]1171.34984188188[/C][/ROW]
[ROW][C]119[/C][C]745.625745545158[/C][C]652.29119745091[/C][C]838.960293639407[/C][/ROW]
[ROW][C]120[/C][C]1135.94881315191[/C][C]1042.58993547407[/C][C]1229.30769082975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123974&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123974&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
1091156.6676714981063.576768962481249.75857403352
1101338.646760087851245.531464307911431.76205586779
111970.991599379405877.8519167436251064.13128201518
112912.895814664656819.73175155661006.05987777271
1131040.52695169915947.3385144973761133.71538890093
114978.407486691558885.1946817696071071.62029161351
115955.212517590607861.9753513170351048.44968386418
1161097.453248884761004.191727623131190.71477014639
117967.08414094904873.7982710579271060.37001084015
1181078.03962971489984.7294175478911171.34984188188
119745.625745545158652.29119745091838.960293639407
1201135.948813151911042.589935474071229.30769082975



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