Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 10 Aug 2010 16:28:31 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/10/t1281457743ih78f2ct9lageef.htm/, Retrieved Fri, 01 Nov 2024 00:13:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78588, Retrieved Fri, 01 Nov 2024 00:13:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPlatini Olivier
Estimated Impact189
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A - Sta...] [2010-08-10 16:28:31] [49dea061148f13f4e9d1975b9f021cec] [Current]
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Dataseries X:
94
93
92
90
110
109
94
84
85
85
86
88
93
94
90
91
104
103
88
79
82
88
93
89
94
96
94
92
113
122
107
98
103
110
113
110
123
124
118
117
139
146
134
121
123
122
127
122
139
136
127
123
140
146
138
120
122
115
115
102
119
114
108
102
121
109
102
95
98
92
94
90
113
111
103
90
108
99
95
91
85
72
90
90
114
115
104
93
101
90
79
75
71
61
84
87
107
99
93
74
87
71
67
61
63
52
80
84
102
93
87
72
83
72
66
64
64
47
77
79




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78588&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78588&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78588&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.842738612560252
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.842738612560252 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78588&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]0.842738612560252[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78588&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78588&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
alpha0.842738612560252
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
29394-1
39293.1572613874397-1.15726138743975
49092.1819925314192-2.18199253141921
511090.343143172874219.6568568271258
6109106.9087354226622.09126457733829
794108.671124831064-14.6711248310642
88496.3072014462349-12.3072014462349
98585.9354475749354-0.93544757493538
108585.1471097835115-0.147109783511482
118685.0231346886610.976865311339026
128885.8463768057972.15362319420294
139387.66131822845725.33868177154278
149492.16043149750791.83956850249211
159093.7107069050076-3.71070690500763
169190.58355091626380.416449083736239
1710490.934508639293613.0654913607064
18103101.9453027010331.05469729896672
1988102.834136839436-14.8341368394355
207990.3328369408407-11.3328369408407
218280.7822176609451.21778233905496
228881.80848985976066.1915101402394
239387.02631452499875.97368547500132
248992.0605699340726-3.06056993407262
259489.48130947418864.51869052581137
269693.28938445852.71061554149995
279495.573724839128-1.57372483912798
289294.2474861516497-2.24748615164967
2911392.3534427904620.6465572095400
30122109.75309376737412.2469062326264
31107120.074034534013-13.0740345340127
3298109.056040810254-11.0560408102540
3310399.7386883174113.26131168258898
34110102.4871215999237.5128784000774
35113108.8185143191384.18148568086228
36110112.342413760268-2.34241376026816
37123110.36837123789812.6316287621023
38124121.0135325352482.98646746475202
39118123.530343982949-5.53034398294943
40117118.869709567778-1.86970956777768
41139117.29403312073821.7059668792619
42146135.58648953284610.4135104671540
43134144.362356895817-10.3623568958170
44121135.629598622582-14.6295986225820
45123123.300670977074-0.300670977073878
46122123.047283935018-1.04728393501750
47127122.1646973246644.83530267533578
48122126.239593592586-4.23959359258556
49139122.66672437055116.3332756294493
50136136.431406413077-0.431406413076957
51127136.067843571071-9.06784357107088
52123128.426021661073-5.42602166107321
53140123.85330369469816.1466963053015
54146137.460748136468.53925186353996
55138144.657105404242-6.65710540424226
56120139.046905632204-19.0469056322038
57122122.995342806154-0.995342806154326
58115122.156528990674-7.156528990674
59115116.125445678326-1.12544567832617
60102115.176989148862-13.1769891488617
61119104.07223159582814.9277684041715
62114116.652438429381-2.65243842938075
63108114.417126147503-6.41712614750293
64102109.009166161332-7.00916616133219
65121103.10227119532717.8977288046732
66109118.185378336157-9.18537833615675
67102110.444505341303-8.44450534130301
6895103.327994626216-8.32799462621568
699896.30967198950941.69032801049056
709297.734176671842-5.73417667184198
719492.90176457923851.09823542076150
729093.8272899739956-3.82728997399558
7311390.601884931444822.3981150685552
74111109.4776413482841.52235865171613
75103110.760591766250-7.76059176625023
7690104.220441428514-14.220441428514
7710892.236326349053815.7636736509462
7899105.520982810505-6.5209828105048
7995100.025498804251-5.02549880425073
809195.7903169145333-4.79031691453326
818591.7533318842556-6.75333188425559
827286.0620383419591-14.0620383419591
839074.211415659887415.7885843401126
849087.51706532096442.48293467903558
8511489.609530247452624.3904697525474
86115110.1643208864074.83567911359282
87104114.239534393383-10.2395343933830
8893105.610283385440-12.6102833854404
8910194.98311066120286.01688933879723
9090100.053775634509-10.0537756345093
917991.5810707052909-12.5810707052909
927580.9785166345916-5.97851663459161
937175.9401898207875-4.9401898207875
946171.7769011054328-10.7769011054328
958462.694790420141321.3052095798587
968780.64951318177686.35048681822319
9710786.001313632048420.9986863679516
9899103.697717447364-4.6977174473638
999399.7387695635723-6.73876956357233
1007494.0597482512041-20.0597482512041
1018777.15462384167649.84537615832357
1027185.4517024854758-14.4517024854758
1036773.2726947837324-6.27269478373239
1046167.9864526846758-6.98645268467583
1056362.09869924247430.901300757525725
1065262.858260192371-10.858260192371
1078053.707585063034126.2924149369659
1088475.86521834787128.13478165212882
10910282.720712950866819.2792870491332
1109398.9681125698041-5.96811256980415
1118793.938553663124-6.938553663124
1127288.091166575888-16.0911665758880
1138374.53051918124838.46948081875175
1147281.6680776955488-9.66807769554877
1156673.5204153122773-7.5204153122773
1166467.1826709461319-3.18267094613185
1176464.5005112487529-0.500511248752872
1184764.078711093408-17.0787110934081
1197749.68582180223227.314178197768
1207972.70453443984256.29546556015751

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 93 & 94 & -1 \tabularnewline
3 & 92 & 93.1572613874397 & -1.15726138743975 \tabularnewline
4 & 90 & 92.1819925314192 & -2.18199253141921 \tabularnewline
5 & 110 & 90.3431431728742 & 19.6568568271258 \tabularnewline
6 & 109 & 106.908735422662 & 2.09126457733829 \tabularnewline
7 & 94 & 108.671124831064 & -14.6711248310642 \tabularnewline
8 & 84 & 96.3072014462349 & -12.3072014462349 \tabularnewline
9 & 85 & 85.9354475749354 & -0.93544757493538 \tabularnewline
10 & 85 & 85.1471097835115 & -0.147109783511482 \tabularnewline
11 & 86 & 85.023134688661 & 0.976865311339026 \tabularnewline
12 & 88 & 85.846376805797 & 2.15362319420294 \tabularnewline
13 & 93 & 87.6613182284572 & 5.33868177154278 \tabularnewline
14 & 94 & 92.1604314975079 & 1.83956850249211 \tabularnewline
15 & 90 & 93.7107069050076 & -3.71070690500763 \tabularnewline
16 & 91 & 90.5835509162638 & 0.416449083736239 \tabularnewline
17 & 104 & 90.9345086392936 & 13.0654913607064 \tabularnewline
18 & 103 & 101.945302701033 & 1.05469729896672 \tabularnewline
19 & 88 & 102.834136839436 & -14.8341368394355 \tabularnewline
20 & 79 & 90.3328369408407 & -11.3328369408407 \tabularnewline
21 & 82 & 80.782217660945 & 1.21778233905496 \tabularnewline
22 & 88 & 81.8084898597606 & 6.1915101402394 \tabularnewline
23 & 93 & 87.0263145249987 & 5.97368547500132 \tabularnewline
24 & 89 & 92.0605699340726 & -3.06056993407262 \tabularnewline
25 & 94 & 89.4813094741886 & 4.51869052581137 \tabularnewline
26 & 96 & 93.2893844585 & 2.71061554149995 \tabularnewline
27 & 94 & 95.573724839128 & -1.57372483912798 \tabularnewline
28 & 92 & 94.2474861516497 & -2.24748615164967 \tabularnewline
29 & 113 & 92.35344279046 & 20.6465572095400 \tabularnewline
30 & 122 & 109.753093767374 & 12.2469062326264 \tabularnewline
31 & 107 & 120.074034534013 & -13.0740345340127 \tabularnewline
32 & 98 & 109.056040810254 & -11.0560408102540 \tabularnewline
33 & 103 & 99.738688317411 & 3.26131168258898 \tabularnewline
34 & 110 & 102.487121599923 & 7.5128784000774 \tabularnewline
35 & 113 & 108.818514319138 & 4.18148568086228 \tabularnewline
36 & 110 & 112.342413760268 & -2.34241376026816 \tabularnewline
37 & 123 & 110.368371237898 & 12.6316287621023 \tabularnewline
38 & 124 & 121.013532535248 & 2.98646746475202 \tabularnewline
39 & 118 & 123.530343982949 & -5.53034398294943 \tabularnewline
40 & 117 & 118.869709567778 & -1.86970956777768 \tabularnewline
41 & 139 & 117.294033120738 & 21.7059668792619 \tabularnewline
42 & 146 & 135.586489532846 & 10.4135104671540 \tabularnewline
43 & 134 & 144.362356895817 & -10.3623568958170 \tabularnewline
44 & 121 & 135.629598622582 & -14.6295986225820 \tabularnewline
45 & 123 & 123.300670977074 & -0.300670977073878 \tabularnewline
46 & 122 & 123.047283935018 & -1.04728393501750 \tabularnewline
47 & 127 & 122.164697324664 & 4.83530267533578 \tabularnewline
48 & 122 & 126.239593592586 & -4.23959359258556 \tabularnewline
49 & 139 & 122.666724370551 & 16.3332756294493 \tabularnewline
50 & 136 & 136.431406413077 & -0.431406413076957 \tabularnewline
51 & 127 & 136.067843571071 & -9.06784357107088 \tabularnewline
52 & 123 & 128.426021661073 & -5.42602166107321 \tabularnewline
53 & 140 & 123.853303694698 & 16.1466963053015 \tabularnewline
54 & 146 & 137.46074813646 & 8.53925186353996 \tabularnewline
55 & 138 & 144.657105404242 & -6.65710540424226 \tabularnewline
56 & 120 & 139.046905632204 & -19.0469056322038 \tabularnewline
57 & 122 & 122.995342806154 & -0.995342806154326 \tabularnewline
58 & 115 & 122.156528990674 & -7.156528990674 \tabularnewline
59 & 115 & 116.125445678326 & -1.12544567832617 \tabularnewline
60 & 102 & 115.176989148862 & -13.1769891488617 \tabularnewline
61 & 119 & 104.072231595828 & 14.9277684041715 \tabularnewline
62 & 114 & 116.652438429381 & -2.65243842938075 \tabularnewline
63 & 108 & 114.417126147503 & -6.41712614750293 \tabularnewline
64 & 102 & 109.009166161332 & -7.00916616133219 \tabularnewline
65 & 121 & 103.102271195327 & 17.8977288046732 \tabularnewline
66 & 109 & 118.185378336157 & -9.18537833615675 \tabularnewline
67 & 102 & 110.444505341303 & -8.44450534130301 \tabularnewline
68 & 95 & 103.327994626216 & -8.32799462621568 \tabularnewline
69 & 98 & 96.3096719895094 & 1.69032801049056 \tabularnewline
70 & 92 & 97.734176671842 & -5.73417667184198 \tabularnewline
71 & 94 & 92.9017645792385 & 1.09823542076150 \tabularnewline
72 & 90 & 93.8272899739956 & -3.82728997399558 \tabularnewline
73 & 113 & 90.6018849314448 & 22.3981150685552 \tabularnewline
74 & 111 & 109.477641348284 & 1.52235865171613 \tabularnewline
75 & 103 & 110.760591766250 & -7.76059176625023 \tabularnewline
76 & 90 & 104.220441428514 & -14.220441428514 \tabularnewline
77 & 108 & 92.2363263490538 & 15.7636736509462 \tabularnewline
78 & 99 & 105.520982810505 & -6.5209828105048 \tabularnewline
79 & 95 & 100.025498804251 & -5.02549880425073 \tabularnewline
80 & 91 & 95.7903169145333 & -4.79031691453326 \tabularnewline
81 & 85 & 91.7533318842556 & -6.75333188425559 \tabularnewline
82 & 72 & 86.0620383419591 & -14.0620383419591 \tabularnewline
83 & 90 & 74.2114156598874 & 15.7885843401126 \tabularnewline
84 & 90 & 87.5170653209644 & 2.48293467903558 \tabularnewline
85 & 114 & 89.6095302474526 & 24.3904697525474 \tabularnewline
86 & 115 & 110.164320886407 & 4.83567911359282 \tabularnewline
87 & 104 & 114.239534393383 & -10.2395343933830 \tabularnewline
88 & 93 & 105.610283385440 & -12.6102833854404 \tabularnewline
89 & 101 & 94.9831106612028 & 6.01688933879723 \tabularnewline
90 & 90 & 100.053775634509 & -10.0537756345093 \tabularnewline
91 & 79 & 91.5810707052909 & -12.5810707052909 \tabularnewline
92 & 75 & 80.9785166345916 & -5.97851663459161 \tabularnewline
93 & 71 & 75.9401898207875 & -4.9401898207875 \tabularnewline
94 & 61 & 71.7769011054328 & -10.7769011054328 \tabularnewline
95 & 84 & 62.6947904201413 & 21.3052095798587 \tabularnewline
96 & 87 & 80.6495131817768 & 6.35048681822319 \tabularnewline
97 & 107 & 86.0013136320484 & 20.9986863679516 \tabularnewline
98 & 99 & 103.697717447364 & -4.6977174473638 \tabularnewline
99 & 93 & 99.7387695635723 & -6.73876956357233 \tabularnewline
100 & 74 & 94.0597482512041 & -20.0597482512041 \tabularnewline
101 & 87 & 77.1546238416764 & 9.84537615832357 \tabularnewline
102 & 71 & 85.4517024854758 & -14.4517024854758 \tabularnewline
103 & 67 & 73.2726947837324 & -6.27269478373239 \tabularnewline
104 & 61 & 67.9864526846758 & -6.98645268467583 \tabularnewline
105 & 63 & 62.0986992424743 & 0.901300757525725 \tabularnewline
106 & 52 & 62.858260192371 & -10.858260192371 \tabularnewline
107 & 80 & 53.7075850630341 & 26.2924149369659 \tabularnewline
108 & 84 & 75.8652183478712 & 8.13478165212882 \tabularnewline
109 & 102 & 82.7207129508668 & 19.2792870491332 \tabularnewline
110 & 93 & 98.9681125698041 & -5.96811256980415 \tabularnewline
111 & 87 & 93.938553663124 & -6.938553663124 \tabularnewline
112 & 72 & 88.091166575888 & -16.0911665758880 \tabularnewline
113 & 83 & 74.5305191812483 & 8.46948081875175 \tabularnewline
114 & 72 & 81.6680776955488 & -9.66807769554877 \tabularnewline
115 & 66 & 73.5204153122773 & -7.5204153122773 \tabularnewline
116 & 64 & 67.1826709461319 & -3.18267094613185 \tabularnewline
117 & 64 & 64.5005112487529 & -0.500511248752872 \tabularnewline
118 & 47 & 64.078711093408 & -17.0787110934081 \tabularnewline
119 & 77 & 49.685821802232 & 27.314178197768 \tabularnewline
120 & 79 & 72.7045344398425 & 6.29546556015751 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78588&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]2[/C][C]93[/C][C]94[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]92[/C][C]93.1572613874397[/C][C]-1.15726138743975[/C][/ROW]
[ROW][C]4[/C][C]90[/C][C]92.1819925314192[/C][C]-2.18199253141921[/C][/ROW]
[ROW][C]5[/C][C]110[/C][C]90.3431431728742[/C][C]19.6568568271258[/C][/ROW]
[ROW][C]6[/C][C]109[/C][C]106.908735422662[/C][C]2.09126457733829[/C][/ROW]
[ROW][C]7[/C][C]94[/C][C]108.671124831064[/C][C]-14.6711248310642[/C][/ROW]
[ROW][C]8[/C][C]84[/C][C]96.3072014462349[/C][C]-12.3072014462349[/C][/ROW]
[ROW][C]9[/C][C]85[/C][C]85.9354475749354[/C][C]-0.93544757493538[/C][/ROW]
[ROW][C]10[/C][C]85[/C][C]85.1471097835115[/C][C]-0.147109783511482[/C][/ROW]
[ROW][C]11[/C][C]86[/C][C]85.023134688661[/C][C]0.976865311339026[/C][/ROW]
[ROW][C]12[/C][C]88[/C][C]85.846376805797[/C][C]2.15362319420294[/C][/ROW]
[ROW][C]13[/C][C]93[/C][C]87.6613182284572[/C][C]5.33868177154278[/C][/ROW]
[ROW][C]14[/C][C]94[/C][C]92.1604314975079[/C][C]1.83956850249211[/C][/ROW]
[ROW][C]15[/C][C]90[/C][C]93.7107069050076[/C][C]-3.71070690500763[/C][/ROW]
[ROW][C]16[/C][C]91[/C][C]90.5835509162638[/C][C]0.416449083736239[/C][/ROW]
[ROW][C]17[/C][C]104[/C][C]90.9345086392936[/C][C]13.0654913607064[/C][/ROW]
[ROW][C]18[/C][C]103[/C][C]101.945302701033[/C][C]1.05469729896672[/C][/ROW]
[ROW][C]19[/C][C]88[/C][C]102.834136839436[/C][C]-14.8341368394355[/C][/ROW]
[ROW][C]20[/C][C]79[/C][C]90.3328369408407[/C][C]-11.3328369408407[/C][/ROW]
[ROW][C]21[/C][C]82[/C][C]80.782217660945[/C][C]1.21778233905496[/C][/ROW]
[ROW][C]22[/C][C]88[/C][C]81.8084898597606[/C][C]6.1915101402394[/C][/ROW]
[ROW][C]23[/C][C]93[/C][C]87.0263145249987[/C][C]5.97368547500132[/C][/ROW]
[ROW][C]24[/C][C]89[/C][C]92.0605699340726[/C][C]-3.06056993407262[/C][/ROW]
[ROW][C]25[/C][C]94[/C][C]89.4813094741886[/C][C]4.51869052581137[/C][/ROW]
[ROW][C]26[/C][C]96[/C][C]93.2893844585[/C][C]2.71061554149995[/C][/ROW]
[ROW][C]27[/C][C]94[/C][C]95.573724839128[/C][C]-1.57372483912798[/C][/ROW]
[ROW][C]28[/C][C]92[/C][C]94.2474861516497[/C][C]-2.24748615164967[/C][/ROW]
[ROW][C]29[/C][C]113[/C][C]92.35344279046[/C][C]20.6465572095400[/C][/ROW]
[ROW][C]30[/C][C]122[/C][C]109.753093767374[/C][C]12.2469062326264[/C][/ROW]
[ROW][C]31[/C][C]107[/C][C]120.074034534013[/C][C]-13.0740345340127[/C][/ROW]
[ROW][C]32[/C][C]98[/C][C]109.056040810254[/C][C]-11.0560408102540[/C][/ROW]
[ROW][C]33[/C][C]103[/C][C]99.738688317411[/C][C]3.26131168258898[/C][/ROW]
[ROW][C]34[/C][C]110[/C][C]102.487121599923[/C][C]7.5128784000774[/C][/ROW]
[ROW][C]35[/C][C]113[/C][C]108.818514319138[/C][C]4.18148568086228[/C][/ROW]
[ROW][C]36[/C][C]110[/C][C]112.342413760268[/C][C]-2.34241376026816[/C][/ROW]
[ROW][C]37[/C][C]123[/C][C]110.368371237898[/C][C]12.6316287621023[/C][/ROW]
[ROW][C]38[/C][C]124[/C][C]121.013532535248[/C][C]2.98646746475202[/C][/ROW]
[ROW][C]39[/C][C]118[/C][C]123.530343982949[/C][C]-5.53034398294943[/C][/ROW]
[ROW][C]40[/C][C]117[/C][C]118.869709567778[/C][C]-1.86970956777768[/C][/ROW]
[ROW][C]41[/C][C]139[/C][C]117.294033120738[/C][C]21.7059668792619[/C][/ROW]
[ROW][C]42[/C][C]146[/C][C]135.586489532846[/C][C]10.4135104671540[/C][/ROW]
[ROW][C]43[/C][C]134[/C][C]144.362356895817[/C][C]-10.3623568958170[/C][/ROW]
[ROW][C]44[/C][C]121[/C][C]135.629598622582[/C][C]-14.6295986225820[/C][/ROW]
[ROW][C]45[/C][C]123[/C][C]123.300670977074[/C][C]-0.300670977073878[/C][/ROW]
[ROW][C]46[/C][C]122[/C][C]123.047283935018[/C][C]-1.04728393501750[/C][/ROW]
[ROW][C]47[/C][C]127[/C][C]122.164697324664[/C][C]4.83530267533578[/C][/ROW]
[ROW][C]48[/C][C]122[/C][C]126.239593592586[/C][C]-4.23959359258556[/C][/ROW]
[ROW][C]49[/C][C]139[/C][C]122.666724370551[/C][C]16.3332756294493[/C][/ROW]
[ROW][C]50[/C][C]136[/C][C]136.431406413077[/C][C]-0.431406413076957[/C][/ROW]
[ROW][C]51[/C][C]127[/C][C]136.067843571071[/C][C]-9.06784357107088[/C][/ROW]
[ROW][C]52[/C][C]123[/C][C]128.426021661073[/C][C]-5.42602166107321[/C][/ROW]
[ROW][C]53[/C][C]140[/C][C]123.853303694698[/C][C]16.1466963053015[/C][/ROW]
[ROW][C]54[/C][C]146[/C][C]137.46074813646[/C][C]8.53925186353996[/C][/ROW]
[ROW][C]55[/C][C]138[/C][C]144.657105404242[/C][C]-6.65710540424226[/C][/ROW]
[ROW][C]56[/C][C]120[/C][C]139.046905632204[/C][C]-19.0469056322038[/C][/ROW]
[ROW][C]57[/C][C]122[/C][C]122.995342806154[/C][C]-0.995342806154326[/C][/ROW]
[ROW][C]58[/C][C]115[/C][C]122.156528990674[/C][C]-7.156528990674[/C][/ROW]
[ROW][C]59[/C][C]115[/C][C]116.125445678326[/C][C]-1.12544567832617[/C][/ROW]
[ROW][C]60[/C][C]102[/C][C]115.176989148862[/C][C]-13.1769891488617[/C][/ROW]
[ROW][C]61[/C][C]119[/C][C]104.072231595828[/C][C]14.9277684041715[/C][/ROW]
[ROW][C]62[/C][C]114[/C][C]116.652438429381[/C][C]-2.65243842938075[/C][/ROW]
[ROW][C]63[/C][C]108[/C][C]114.417126147503[/C][C]-6.41712614750293[/C][/ROW]
[ROW][C]64[/C][C]102[/C][C]109.009166161332[/C][C]-7.00916616133219[/C][/ROW]
[ROW][C]65[/C][C]121[/C][C]103.102271195327[/C][C]17.8977288046732[/C][/ROW]
[ROW][C]66[/C][C]109[/C][C]118.185378336157[/C][C]-9.18537833615675[/C][/ROW]
[ROW][C]67[/C][C]102[/C][C]110.444505341303[/C][C]-8.44450534130301[/C][/ROW]
[ROW][C]68[/C][C]95[/C][C]103.327994626216[/C][C]-8.32799462621568[/C][/ROW]
[ROW][C]69[/C][C]98[/C][C]96.3096719895094[/C][C]1.69032801049056[/C][/ROW]
[ROW][C]70[/C][C]92[/C][C]97.734176671842[/C][C]-5.73417667184198[/C][/ROW]
[ROW][C]71[/C][C]94[/C][C]92.9017645792385[/C][C]1.09823542076150[/C][/ROW]
[ROW][C]72[/C][C]90[/C][C]93.8272899739956[/C][C]-3.82728997399558[/C][/ROW]
[ROW][C]73[/C][C]113[/C][C]90.6018849314448[/C][C]22.3981150685552[/C][/ROW]
[ROW][C]74[/C][C]111[/C][C]109.477641348284[/C][C]1.52235865171613[/C][/ROW]
[ROW][C]75[/C][C]103[/C][C]110.760591766250[/C][C]-7.76059176625023[/C][/ROW]
[ROW][C]76[/C][C]90[/C][C]104.220441428514[/C][C]-14.220441428514[/C][/ROW]
[ROW][C]77[/C][C]108[/C][C]92.2363263490538[/C][C]15.7636736509462[/C][/ROW]
[ROW][C]78[/C][C]99[/C][C]105.520982810505[/C][C]-6.5209828105048[/C][/ROW]
[ROW][C]79[/C][C]95[/C][C]100.025498804251[/C][C]-5.02549880425073[/C][/ROW]
[ROW][C]80[/C][C]91[/C][C]95.7903169145333[/C][C]-4.79031691453326[/C][/ROW]
[ROW][C]81[/C][C]85[/C][C]91.7533318842556[/C][C]-6.75333188425559[/C][/ROW]
[ROW][C]82[/C][C]72[/C][C]86.0620383419591[/C][C]-14.0620383419591[/C][/ROW]
[ROW][C]83[/C][C]90[/C][C]74.2114156598874[/C][C]15.7885843401126[/C][/ROW]
[ROW][C]84[/C][C]90[/C][C]87.5170653209644[/C][C]2.48293467903558[/C][/ROW]
[ROW][C]85[/C][C]114[/C][C]89.6095302474526[/C][C]24.3904697525474[/C][/ROW]
[ROW][C]86[/C][C]115[/C][C]110.164320886407[/C][C]4.83567911359282[/C][/ROW]
[ROW][C]87[/C][C]104[/C][C]114.239534393383[/C][C]-10.2395343933830[/C][/ROW]
[ROW][C]88[/C][C]93[/C][C]105.610283385440[/C][C]-12.6102833854404[/C][/ROW]
[ROW][C]89[/C][C]101[/C][C]94.9831106612028[/C][C]6.01688933879723[/C][/ROW]
[ROW][C]90[/C][C]90[/C][C]100.053775634509[/C][C]-10.0537756345093[/C][/ROW]
[ROW][C]91[/C][C]79[/C][C]91.5810707052909[/C][C]-12.5810707052909[/C][/ROW]
[ROW][C]92[/C][C]75[/C][C]80.9785166345916[/C][C]-5.97851663459161[/C][/ROW]
[ROW][C]93[/C][C]71[/C][C]75.9401898207875[/C][C]-4.9401898207875[/C][/ROW]
[ROW][C]94[/C][C]61[/C][C]71.7769011054328[/C][C]-10.7769011054328[/C][/ROW]
[ROW][C]95[/C][C]84[/C][C]62.6947904201413[/C][C]21.3052095798587[/C][/ROW]
[ROW][C]96[/C][C]87[/C][C]80.6495131817768[/C][C]6.35048681822319[/C][/ROW]
[ROW][C]97[/C][C]107[/C][C]86.0013136320484[/C][C]20.9986863679516[/C][/ROW]
[ROW][C]98[/C][C]99[/C][C]103.697717447364[/C][C]-4.6977174473638[/C][/ROW]
[ROW][C]99[/C][C]93[/C][C]99.7387695635723[/C][C]-6.73876956357233[/C][/ROW]
[ROW][C]100[/C][C]74[/C][C]94.0597482512041[/C][C]-20.0597482512041[/C][/ROW]
[ROW][C]101[/C][C]87[/C][C]77.1546238416764[/C][C]9.84537615832357[/C][/ROW]
[ROW][C]102[/C][C]71[/C][C]85.4517024854758[/C][C]-14.4517024854758[/C][/ROW]
[ROW][C]103[/C][C]67[/C][C]73.2726947837324[/C][C]-6.27269478373239[/C][/ROW]
[ROW][C]104[/C][C]61[/C][C]67.9864526846758[/C][C]-6.98645268467583[/C][/ROW]
[ROW][C]105[/C][C]63[/C][C]62.0986992424743[/C][C]0.901300757525725[/C][/ROW]
[ROW][C]106[/C][C]52[/C][C]62.858260192371[/C][C]-10.858260192371[/C][/ROW]
[ROW][C]107[/C][C]80[/C][C]53.7075850630341[/C][C]26.2924149369659[/C][/ROW]
[ROW][C]108[/C][C]84[/C][C]75.8652183478712[/C][C]8.13478165212882[/C][/ROW]
[ROW][C]109[/C][C]102[/C][C]82.7207129508668[/C][C]19.2792870491332[/C][/ROW]
[ROW][C]110[/C][C]93[/C][C]98.9681125698041[/C][C]-5.96811256980415[/C][/ROW]
[ROW][C]111[/C][C]87[/C][C]93.938553663124[/C][C]-6.938553663124[/C][/ROW]
[ROW][C]112[/C][C]72[/C][C]88.091166575888[/C][C]-16.0911665758880[/C][/ROW]
[ROW][C]113[/C][C]83[/C][C]74.5305191812483[/C][C]8.46948081875175[/C][/ROW]
[ROW][C]114[/C][C]72[/C][C]81.6680776955488[/C][C]-9.66807769554877[/C][/ROW]
[ROW][C]115[/C][C]66[/C][C]73.5204153122773[/C][C]-7.5204153122773[/C][/ROW]
[ROW][C]116[/C][C]64[/C][C]67.1826709461319[/C][C]-3.18267094613185[/C][/ROW]
[ROW][C]117[/C][C]64[/C][C]64.5005112487529[/C][C]-0.500511248752872[/C][/ROW]
[ROW][C]118[/C][C]47[/C][C]64.078711093408[/C][C]-17.0787110934081[/C][/ROW]
[ROW][C]119[/C][C]77[/C][C]49.685821802232[/C][C]27.314178197768[/C][/ROW]
[ROW][C]120[/C][C]79[/C][C]72.7045344398425[/C][C]6.29546556015751[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78588&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78588&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
29394-1
39293.1572613874397-1.15726138743975
49092.1819925314192-2.18199253141921
511090.343143172874219.6568568271258
6109106.9087354226622.09126457733829
794108.671124831064-14.6711248310642
88496.3072014462349-12.3072014462349
98585.9354475749354-0.93544757493538
108585.1471097835115-0.147109783511482
118685.0231346886610.976865311339026
128885.8463768057972.15362319420294
139387.66131822845725.33868177154278
149492.16043149750791.83956850249211
159093.7107069050076-3.71070690500763
169190.58355091626380.416449083736239
1710490.934508639293613.0654913607064
18103101.9453027010331.05469729896672
1988102.834136839436-14.8341368394355
207990.3328369408407-11.3328369408407
218280.7822176609451.21778233905496
228881.80848985976066.1915101402394
239387.02631452499875.97368547500132
248992.0605699340726-3.06056993407262
259489.48130947418864.51869052581137
269693.28938445852.71061554149995
279495.573724839128-1.57372483912798
289294.2474861516497-2.24748615164967
2911392.3534427904620.6465572095400
30122109.75309376737412.2469062326264
31107120.074034534013-13.0740345340127
3298109.056040810254-11.0560408102540
3310399.7386883174113.26131168258898
34110102.4871215999237.5128784000774
35113108.8185143191384.18148568086228
36110112.342413760268-2.34241376026816
37123110.36837123789812.6316287621023
38124121.0135325352482.98646746475202
39118123.530343982949-5.53034398294943
40117118.869709567778-1.86970956777768
41139117.29403312073821.7059668792619
42146135.58648953284610.4135104671540
43134144.362356895817-10.3623568958170
44121135.629598622582-14.6295986225820
45123123.300670977074-0.300670977073878
46122123.047283935018-1.04728393501750
47127122.1646973246644.83530267533578
48122126.239593592586-4.23959359258556
49139122.66672437055116.3332756294493
50136136.431406413077-0.431406413076957
51127136.067843571071-9.06784357107088
52123128.426021661073-5.42602166107321
53140123.85330369469816.1466963053015
54146137.460748136468.53925186353996
55138144.657105404242-6.65710540424226
56120139.046905632204-19.0469056322038
57122122.995342806154-0.995342806154326
58115122.156528990674-7.156528990674
59115116.125445678326-1.12544567832617
60102115.176989148862-13.1769891488617
61119104.07223159582814.9277684041715
62114116.652438429381-2.65243842938075
63108114.417126147503-6.41712614750293
64102109.009166161332-7.00916616133219
65121103.10227119532717.8977288046732
66109118.185378336157-9.18537833615675
67102110.444505341303-8.44450534130301
6895103.327994626216-8.32799462621568
699896.30967198950941.69032801049056
709297.734176671842-5.73417667184198
719492.90176457923851.09823542076150
729093.8272899739956-3.82728997399558
7311390.601884931444822.3981150685552
74111109.4776413482841.52235865171613
75103110.760591766250-7.76059176625023
7690104.220441428514-14.220441428514
7710892.236326349053815.7636736509462
7899105.520982810505-6.5209828105048
7995100.025498804251-5.02549880425073
809195.7903169145333-4.79031691453326
818591.7533318842556-6.75333188425559
827286.0620383419591-14.0620383419591
839074.211415659887415.7885843401126
849087.51706532096442.48293467903558
8511489.609530247452624.3904697525474
86115110.1643208864074.83567911359282
87104114.239534393383-10.2395343933830
8893105.610283385440-12.6102833854404
8910194.98311066120286.01688933879723
9090100.053775634509-10.0537756345093
917991.5810707052909-12.5810707052909
927580.9785166345916-5.97851663459161
937175.9401898207875-4.9401898207875
946171.7769011054328-10.7769011054328
958462.694790420141321.3052095798587
968780.64951318177686.35048681822319
9710786.001313632048420.9986863679516
9899103.697717447364-4.6977174473638
999399.7387695635723-6.73876956357233
1007494.0597482512041-20.0597482512041
1018777.15462384167649.84537615832357
1027185.4517024854758-14.4517024854758
1036773.2726947837324-6.27269478373239
1046167.9864526846758-6.98645268467583
1056362.09869924247430.901300757525725
1065262.858260192371-10.858260192371
1078053.707585063034126.2924149369659
1088475.86521834787128.13478165212882
10910282.720712950866819.2792870491332
1109398.9681125698041-5.96811256980415
1118793.938553663124-6.938553663124
1127288.091166575888-16.0911665758880
1138374.53051918124838.46948081875175
1147281.6680776955488-9.66807769554877
1156673.5204153122773-7.5204153122773
1166467.1826709461319-3.18267094613185
1176464.5005112487529-0.500511248752872
1184764.078711093408-17.0787110934081
1197749.68582180223227.314178197768
1207972.70453443984256.29546556015751







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12178.009966351430557.060690558990898.9592421438702
12278.009966351430550.6135644974357105.406368205425
12378.009966351430545.4177354848047110.602197218056
12478.009966351430540.9432131731266115.076719529734
12578.009966351430536.9534824603425119.066450242518
12678.009966351430533.3185180887367122.701414614124
12778.009966351430529.9577424056556126.062190297205
12878.009966351430526.8171259882238129.202806714637
12978.009966351430523.8583497294807132.161582973380
13078.009966351430521.0530680766078134.966864626253
13178.009966351430518.3796138503228137.640318852538
13278.009966351430515.8209832617849140.198949441076

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 78.0099663514305 & 57.0606905589908 & 98.9592421438702 \tabularnewline
122 & 78.0099663514305 & 50.6135644974357 & 105.406368205425 \tabularnewline
123 & 78.0099663514305 & 45.4177354848047 & 110.602197218056 \tabularnewline
124 & 78.0099663514305 & 40.9432131731266 & 115.076719529734 \tabularnewline
125 & 78.0099663514305 & 36.9534824603425 & 119.066450242518 \tabularnewline
126 & 78.0099663514305 & 33.3185180887367 & 122.701414614124 \tabularnewline
127 & 78.0099663514305 & 29.9577424056556 & 126.062190297205 \tabularnewline
128 & 78.0099663514305 & 26.8171259882238 & 129.202806714637 \tabularnewline
129 & 78.0099663514305 & 23.8583497294807 & 132.161582973380 \tabularnewline
130 & 78.0099663514305 & 21.0530680766078 & 134.966864626253 \tabularnewline
131 & 78.0099663514305 & 18.3796138503228 & 137.640318852538 \tabularnewline
132 & 78.0099663514305 & 15.8209832617849 & 140.198949441076 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78588&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]121[/C][C]78.0099663514305[/C][C]57.0606905589908[/C][C]98.9592421438702[/C][/ROW]
[ROW][C]122[/C][C]78.0099663514305[/C][C]50.6135644974357[/C][C]105.406368205425[/C][/ROW]
[ROW][C]123[/C][C]78.0099663514305[/C][C]45.4177354848047[/C][C]110.602197218056[/C][/ROW]
[ROW][C]124[/C][C]78.0099663514305[/C][C]40.9432131731266[/C][C]115.076719529734[/C][/ROW]
[ROW][C]125[/C][C]78.0099663514305[/C][C]36.9534824603425[/C][C]119.066450242518[/C][/ROW]
[ROW][C]126[/C][C]78.0099663514305[/C][C]33.3185180887367[/C][C]122.701414614124[/C][/ROW]
[ROW][C]127[/C][C]78.0099663514305[/C][C]29.9577424056556[/C][C]126.062190297205[/C][/ROW]
[ROW][C]128[/C][C]78.0099663514305[/C][C]26.8171259882238[/C][C]129.202806714637[/C][/ROW]
[ROW][C]129[/C][C]78.0099663514305[/C][C]23.8583497294807[/C][C]132.161582973380[/C][/ROW]
[ROW][C]130[/C][C]78.0099663514305[/C][C]21.0530680766078[/C][C]134.966864626253[/C][/ROW]
[ROW][C]131[/C][C]78.0099663514305[/C][C]18.3796138503228[/C][C]137.640318852538[/C][/ROW]
[ROW][C]132[/C][C]78.0099663514305[/C][C]15.8209832617849[/C][C]140.198949441076[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78588&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78588&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
12178.009966351430557.060690558990898.9592421438702
12278.009966351430550.6135644974357105.406368205425
12378.009966351430545.4177354848047110.602197218056
12478.009966351430540.9432131731266115.076719529734
12578.009966351430536.9534824603425119.066450242518
12678.009966351430533.3185180887367122.701414614124
12778.009966351430529.9577424056556126.062190297205
12878.009966351430526.8171259882238129.202806714637
12978.009966351430523.8583497294807132.161582973380
13078.009966351430521.0530680766078134.966864626253
13178.009966351430518.3796138503228137.640318852538
13278.009966351430515.8209832617849140.198949441076



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