Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Aug 2010 13:46:38 +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/16/t1281966373o4r9nju7is3c5pd.htm/, Retrieved Thu, 16 May 2024 09:26:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78995, Retrieved Thu, 16 May 2024 09:26:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-08-16 13:46:38] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
244
243
242
240
260
259
244
234
235
235
236
238
240
233
233
233
247
251
233
226
233
233
227
225
223
212
206
202
223
221
212
205
204
200
195
193
196
180
174
164
192
189
181
167
166
164
167
164
161
141
134
111
147
144
142
140
143
137
140
130
129
112
101
74
104
103
100
98
99
91
92
94
93
76
64
32
62
69
69
68
68
59
66
73
70
57
48
22
64
74
67
61
61
52
54
69
69
53
50
22
69
78
74
63
67
59
60
80
77
58
54
32
78
86
84
78
72
64
62
72




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78995&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78995&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78995&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.644806046017667
beta8.40256683676266e-19
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.644806046017667 \tabularnewline
beta & 8.40256683676266e-19 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78995&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]0.644806046017667[/C][/ROW]
[ROW][C]beta[/C][C]8.40256683676266e-19[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78995&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78995&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
alpha0.644806046017667
beta8.40256683676266e-19
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32422420
4240241-1
5260239.35519395398220.6448060460177
6259251.6670897113177.3329102886834
7244255.395394600365-11.3953946003648
8234247.047575265292-13.0475752652925
9235237.634419848361-2.63441984836135
10235234.9357300023890.0642699976110066
11236233.9771716854262.0228283145739
12238234.2815036127193.71849638728094
13240235.6792125653334.32078743466732
14233237.465282426763-4.46528242676334
15233233.58604132081-0.586041320809898
16233232.2081583339360.7918416660645
17247231.71874262770315.2812573722974
18251240.57218977211210.4278102278880
19233246.296104853779-13.2961048537790
20226236.722696055577-10.7226960555775
21233228.8086368093314.19136319066868
22233230.5112531357302.48874686426961
23227231.116012160819-4.11601216081894
24225227.461982634041-2.46198263404065
25223224.874481346421-1.87448134642074
26212222.665804441101-10.6658044411013
27206214.788429251837-8.7884292518371
28202208.121596935254-6.12159693525402
29223203.17435422011919.825645779881
30221214.9580504851916.04194951480909
31212217.853936062073-5.85393606207333
32205213.079282696248-8.07928269624759
33204206.869712366221-2.86971236622122
34200204.01930448215-4.01930448215012
35195200.427632651274-5.42763265127383
36193195.927862302170-2.92786230216956
37196193.0399589878232.96004101217659
38180193.948611328935-13.9486113289351
39174183.954462410487-9.95446241048722
40164176.535764863349-12.5357648633495
41192167.45262788800624.5473721119941
42189182.2809218396656.71907816033485
43181185.613424061114-4.61342406111433
44167181.638660333664-14.6386603336644
45166171.199563644919-5.19956364491861
46164166.846853570021-2.84685357002144
47167164.0111851759452.98881482405537
48164164.938391044923-0.938391044922753
49161163.333310825628-2.33331082562773
50141160.828777898024-19.8287778980245
51134147.043062024237-13.0430620242368
52111137.632816772425-26.6328167724255
53147119.45981549508527.5401845049152
54144136.2178929722967.7821070277038
55142140.2358426345161.76415736548381
56140140.373381969907-0.373381969906745
57143139.1326230182373.8673769817631
58137140.626331078307-3.62633107830729
59140137.2880508741532.71194912584701
60130138.036732066991-8.03673206699148
61129131.854598639971-2.8545986399713
62112129.013936177964-17.013936177964
63101117.043247263854-16.0432472638541
6474105.698464430365-31.6984644303646
6510484.259102916189519.7408970838105
6610395.9881527096437.01184729035695
6710099.50943423621780.4905657637822
689898.8257540066738-0.825754006673833
699997.29330283064721.70669716935276
709197.3937914841671-6.39379148416714
719292.2710360781999-0.271036078199899
729491.09627037628772.90372962371231
739391.9686127936581.03138720634200
747691.6336575000926-15.6336575000926
756480.5529806226635-16.5529806226635
763268.8795186375568-36.8795186375568
776244.099382045839017.9006179541610
786954.641808730134414.3581912698656
796962.90005727082186.09994272917818
806865.83333722295742.16666277704259
816866.23041448127591.7695855187241
825966.3714539226945-7.37145392269451
836660.61829586540045.38170413459955
847363.08845122926859.91154877073149
857068.47947780203511.52052219796485
865768.459919708387-11.4599197083870
874860.070494193542-12.0704941935420
882251.287366559125-29.287366559125
896431.402695529865632.5973044701344
907451.42163453608722.5783654639130
916764.98030109641462.01969890358544
926165.2826151605817-4.2826151605817
936161.5211590122717-0.521159012271696
945260.1851125302223-8.18511253022231
955453.90730248340.0926975165999977
966952.967074402554516.0329255974455
976962.30520176313886.69479823686123
985365.6220481431353-12.6220481431353
995056.4832751873156-6.4832751873156
1002251.3028201485382-29.3028201485382
1016931.408184551392537.5918154486075
1027854.647614433434923.3523855665651
1037468.70537383569185.29462616430823
1046371.119380797841-8.11938079784105
1056764.88395496947342.11604503052661
1065965.2483935988026-6.24839359880259
1076060.2193916283966-0.219391628396593
1088059.077926579960820.9220734200392
1097771.56860601642765.43139398357241
1105874.070801695339-16.0708016953391
1115462.7082515978335-8.70825159783347
1123256.0931183173074-24.0931183173074
1137839.557729958888638.4422700411114
1148663.34553810404122.6544618959589
1158476.95327210383227.04672789616777
1167880.4970448559226-2.49704485592257
1177277.8869352356464-5.88693523564638
1186473.0910038031871-9.09100380318715
1196266.2290695865225-4.22906958652247
1207262.50213994810339.49786005189665

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 242 & 242 & 0 \tabularnewline
4 & 240 & 241 & -1 \tabularnewline
5 & 260 & 239.355193953982 & 20.6448060460177 \tabularnewline
6 & 259 & 251.667089711317 & 7.3329102886834 \tabularnewline
7 & 244 & 255.395394600365 & -11.3953946003648 \tabularnewline
8 & 234 & 247.047575265292 & -13.0475752652925 \tabularnewline
9 & 235 & 237.634419848361 & -2.63441984836135 \tabularnewline
10 & 235 & 234.935730002389 & 0.0642699976110066 \tabularnewline
11 & 236 & 233.977171685426 & 2.0228283145739 \tabularnewline
12 & 238 & 234.281503612719 & 3.71849638728094 \tabularnewline
13 & 240 & 235.679212565333 & 4.32078743466732 \tabularnewline
14 & 233 & 237.465282426763 & -4.46528242676334 \tabularnewline
15 & 233 & 233.58604132081 & -0.586041320809898 \tabularnewline
16 & 233 & 232.208158333936 & 0.7918416660645 \tabularnewline
17 & 247 & 231.718742627703 & 15.2812573722974 \tabularnewline
18 & 251 & 240.572189772112 & 10.4278102278880 \tabularnewline
19 & 233 & 246.296104853779 & -13.2961048537790 \tabularnewline
20 & 226 & 236.722696055577 & -10.7226960555775 \tabularnewline
21 & 233 & 228.808636809331 & 4.19136319066868 \tabularnewline
22 & 233 & 230.511253135730 & 2.48874686426961 \tabularnewline
23 & 227 & 231.116012160819 & -4.11601216081894 \tabularnewline
24 & 225 & 227.461982634041 & -2.46198263404065 \tabularnewline
25 & 223 & 224.874481346421 & -1.87448134642074 \tabularnewline
26 & 212 & 222.665804441101 & -10.6658044411013 \tabularnewline
27 & 206 & 214.788429251837 & -8.7884292518371 \tabularnewline
28 & 202 & 208.121596935254 & -6.12159693525402 \tabularnewline
29 & 223 & 203.174354220119 & 19.825645779881 \tabularnewline
30 & 221 & 214.958050485191 & 6.04194951480909 \tabularnewline
31 & 212 & 217.853936062073 & -5.85393606207333 \tabularnewline
32 & 205 & 213.079282696248 & -8.07928269624759 \tabularnewline
33 & 204 & 206.869712366221 & -2.86971236622122 \tabularnewline
34 & 200 & 204.01930448215 & -4.01930448215012 \tabularnewline
35 & 195 & 200.427632651274 & -5.42763265127383 \tabularnewline
36 & 193 & 195.927862302170 & -2.92786230216956 \tabularnewline
37 & 196 & 193.039958987823 & 2.96004101217659 \tabularnewline
38 & 180 & 193.948611328935 & -13.9486113289351 \tabularnewline
39 & 174 & 183.954462410487 & -9.95446241048722 \tabularnewline
40 & 164 & 176.535764863349 & -12.5357648633495 \tabularnewline
41 & 192 & 167.452627888006 & 24.5473721119941 \tabularnewline
42 & 189 & 182.280921839665 & 6.71907816033485 \tabularnewline
43 & 181 & 185.613424061114 & -4.61342406111433 \tabularnewline
44 & 167 & 181.638660333664 & -14.6386603336644 \tabularnewline
45 & 166 & 171.199563644919 & -5.19956364491861 \tabularnewline
46 & 164 & 166.846853570021 & -2.84685357002144 \tabularnewline
47 & 167 & 164.011185175945 & 2.98881482405537 \tabularnewline
48 & 164 & 164.938391044923 & -0.938391044922753 \tabularnewline
49 & 161 & 163.333310825628 & -2.33331082562773 \tabularnewline
50 & 141 & 160.828777898024 & -19.8287778980245 \tabularnewline
51 & 134 & 147.043062024237 & -13.0430620242368 \tabularnewline
52 & 111 & 137.632816772425 & -26.6328167724255 \tabularnewline
53 & 147 & 119.459815495085 & 27.5401845049152 \tabularnewline
54 & 144 & 136.217892972296 & 7.7821070277038 \tabularnewline
55 & 142 & 140.235842634516 & 1.76415736548381 \tabularnewline
56 & 140 & 140.373381969907 & -0.373381969906745 \tabularnewline
57 & 143 & 139.132623018237 & 3.8673769817631 \tabularnewline
58 & 137 & 140.626331078307 & -3.62633107830729 \tabularnewline
59 & 140 & 137.288050874153 & 2.71194912584701 \tabularnewline
60 & 130 & 138.036732066991 & -8.03673206699148 \tabularnewline
61 & 129 & 131.854598639971 & -2.8545986399713 \tabularnewline
62 & 112 & 129.013936177964 & -17.013936177964 \tabularnewline
63 & 101 & 117.043247263854 & -16.0432472638541 \tabularnewline
64 & 74 & 105.698464430365 & -31.6984644303646 \tabularnewline
65 & 104 & 84.2591029161895 & 19.7408970838105 \tabularnewline
66 & 103 & 95.988152709643 & 7.01184729035695 \tabularnewline
67 & 100 & 99.5094342362178 & 0.4905657637822 \tabularnewline
68 & 98 & 98.8257540066738 & -0.825754006673833 \tabularnewline
69 & 99 & 97.2933028306472 & 1.70669716935276 \tabularnewline
70 & 91 & 97.3937914841671 & -6.39379148416714 \tabularnewline
71 & 92 & 92.2710360781999 & -0.271036078199899 \tabularnewline
72 & 94 & 91.0962703762877 & 2.90372962371231 \tabularnewline
73 & 93 & 91.968612793658 & 1.03138720634200 \tabularnewline
74 & 76 & 91.6336575000926 & -15.6336575000926 \tabularnewline
75 & 64 & 80.5529806226635 & -16.5529806226635 \tabularnewline
76 & 32 & 68.8795186375568 & -36.8795186375568 \tabularnewline
77 & 62 & 44.0993820458390 & 17.9006179541610 \tabularnewline
78 & 69 & 54.6418087301344 & 14.3581912698656 \tabularnewline
79 & 69 & 62.9000572708218 & 6.09994272917818 \tabularnewline
80 & 68 & 65.8333372229574 & 2.16666277704259 \tabularnewline
81 & 68 & 66.2304144812759 & 1.7695855187241 \tabularnewline
82 & 59 & 66.3714539226945 & -7.37145392269451 \tabularnewline
83 & 66 & 60.6182958654004 & 5.38170413459955 \tabularnewline
84 & 73 & 63.0884512292685 & 9.91154877073149 \tabularnewline
85 & 70 & 68.4794778020351 & 1.52052219796485 \tabularnewline
86 & 57 & 68.459919708387 & -11.4599197083870 \tabularnewline
87 & 48 & 60.070494193542 & -12.0704941935420 \tabularnewline
88 & 22 & 51.287366559125 & -29.287366559125 \tabularnewline
89 & 64 & 31.4026955298656 & 32.5973044701344 \tabularnewline
90 & 74 & 51.421634536087 & 22.5783654639130 \tabularnewline
91 & 67 & 64.9803010964146 & 2.01969890358544 \tabularnewline
92 & 61 & 65.2826151605817 & -4.2826151605817 \tabularnewline
93 & 61 & 61.5211590122717 & -0.521159012271696 \tabularnewline
94 & 52 & 60.1851125302223 & -8.18511253022231 \tabularnewline
95 & 54 & 53.9073024834 & 0.0926975165999977 \tabularnewline
96 & 69 & 52.9670744025545 & 16.0329255974455 \tabularnewline
97 & 69 & 62.3052017631388 & 6.69479823686123 \tabularnewline
98 & 53 & 65.6220481431353 & -12.6220481431353 \tabularnewline
99 & 50 & 56.4832751873156 & -6.4832751873156 \tabularnewline
100 & 22 & 51.3028201485382 & -29.3028201485382 \tabularnewline
101 & 69 & 31.4081845513925 & 37.5918154486075 \tabularnewline
102 & 78 & 54.6476144334349 & 23.3523855665651 \tabularnewline
103 & 74 & 68.7053738356918 & 5.29462616430823 \tabularnewline
104 & 63 & 71.119380797841 & -8.11938079784105 \tabularnewline
105 & 67 & 64.8839549694734 & 2.11604503052661 \tabularnewline
106 & 59 & 65.2483935988026 & -6.24839359880259 \tabularnewline
107 & 60 & 60.2193916283966 & -0.219391628396593 \tabularnewline
108 & 80 & 59.0779265799608 & 20.9220734200392 \tabularnewline
109 & 77 & 71.5686060164276 & 5.43139398357241 \tabularnewline
110 & 58 & 74.070801695339 & -16.0708016953391 \tabularnewline
111 & 54 & 62.7082515978335 & -8.70825159783347 \tabularnewline
112 & 32 & 56.0931183173074 & -24.0931183173074 \tabularnewline
113 & 78 & 39.5577299588886 & 38.4422700411114 \tabularnewline
114 & 86 & 63.345538104041 & 22.6544618959589 \tabularnewline
115 & 84 & 76.9532721038322 & 7.04672789616777 \tabularnewline
116 & 78 & 80.4970448559226 & -2.49704485592257 \tabularnewline
117 & 72 & 77.8869352356464 & -5.88693523564638 \tabularnewline
118 & 64 & 73.0910038031871 & -9.09100380318715 \tabularnewline
119 & 62 & 66.2290695865225 & -4.22906958652247 \tabularnewline
120 & 72 & 62.5021399481033 & 9.49786005189665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78995&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]242[/C][C]242[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]240[/C][C]241[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]260[/C][C]239.355193953982[/C][C]20.6448060460177[/C][/ROW]
[ROW][C]6[/C][C]259[/C][C]251.667089711317[/C][C]7.3329102886834[/C][/ROW]
[ROW][C]7[/C][C]244[/C][C]255.395394600365[/C][C]-11.3953946003648[/C][/ROW]
[ROW][C]8[/C][C]234[/C][C]247.047575265292[/C][C]-13.0475752652925[/C][/ROW]
[ROW][C]9[/C][C]235[/C][C]237.634419848361[/C][C]-2.63441984836135[/C][/ROW]
[ROW][C]10[/C][C]235[/C][C]234.935730002389[/C][C]0.0642699976110066[/C][/ROW]
[ROW][C]11[/C][C]236[/C][C]233.977171685426[/C][C]2.0228283145739[/C][/ROW]
[ROW][C]12[/C][C]238[/C][C]234.281503612719[/C][C]3.71849638728094[/C][/ROW]
[ROW][C]13[/C][C]240[/C][C]235.679212565333[/C][C]4.32078743466732[/C][/ROW]
[ROW][C]14[/C][C]233[/C][C]237.465282426763[/C][C]-4.46528242676334[/C][/ROW]
[ROW][C]15[/C][C]233[/C][C]233.58604132081[/C][C]-0.586041320809898[/C][/ROW]
[ROW][C]16[/C][C]233[/C][C]232.208158333936[/C][C]0.7918416660645[/C][/ROW]
[ROW][C]17[/C][C]247[/C][C]231.718742627703[/C][C]15.2812573722974[/C][/ROW]
[ROW][C]18[/C][C]251[/C][C]240.572189772112[/C][C]10.4278102278880[/C][/ROW]
[ROW][C]19[/C][C]233[/C][C]246.296104853779[/C][C]-13.2961048537790[/C][/ROW]
[ROW][C]20[/C][C]226[/C][C]236.722696055577[/C][C]-10.7226960555775[/C][/ROW]
[ROW][C]21[/C][C]233[/C][C]228.808636809331[/C][C]4.19136319066868[/C][/ROW]
[ROW][C]22[/C][C]233[/C][C]230.511253135730[/C][C]2.48874686426961[/C][/ROW]
[ROW][C]23[/C][C]227[/C][C]231.116012160819[/C][C]-4.11601216081894[/C][/ROW]
[ROW][C]24[/C][C]225[/C][C]227.461982634041[/C][C]-2.46198263404065[/C][/ROW]
[ROW][C]25[/C][C]223[/C][C]224.874481346421[/C][C]-1.87448134642074[/C][/ROW]
[ROW][C]26[/C][C]212[/C][C]222.665804441101[/C][C]-10.6658044411013[/C][/ROW]
[ROW][C]27[/C][C]206[/C][C]214.788429251837[/C][C]-8.7884292518371[/C][/ROW]
[ROW][C]28[/C][C]202[/C][C]208.121596935254[/C][C]-6.12159693525402[/C][/ROW]
[ROW][C]29[/C][C]223[/C][C]203.174354220119[/C][C]19.825645779881[/C][/ROW]
[ROW][C]30[/C][C]221[/C][C]214.958050485191[/C][C]6.04194951480909[/C][/ROW]
[ROW][C]31[/C][C]212[/C][C]217.853936062073[/C][C]-5.85393606207333[/C][/ROW]
[ROW][C]32[/C][C]205[/C][C]213.079282696248[/C][C]-8.07928269624759[/C][/ROW]
[ROW][C]33[/C][C]204[/C][C]206.869712366221[/C][C]-2.86971236622122[/C][/ROW]
[ROW][C]34[/C][C]200[/C][C]204.01930448215[/C][C]-4.01930448215012[/C][/ROW]
[ROW][C]35[/C][C]195[/C][C]200.427632651274[/C][C]-5.42763265127383[/C][/ROW]
[ROW][C]36[/C][C]193[/C][C]195.927862302170[/C][C]-2.92786230216956[/C][/ROW]
[ROW][C]37[/C][C]196[/C][C]193.039958987823[/C][C]2.96004101217659[/C][/ROW]
[ROW][C]38[/C][C]180[/C][C]193.948611328935[/C][C]-13.9486113289351[/C][/ROW]
[ROW][C]39[/C][C]174[/C][C]183.954462410487[/C][C]-9.95446241048722[/C][/ROW]
[ROW][C]40[/C][C]164[/C][C]176.535764863349[/C][C]-12.5357648633495[/C][/ROW]
[ROW][C]41[/C][C]192[/C][C]167.452627888006[/C][C]24.5473721119941[/C][/ROW]
[ROW][C]42[/C][C]189[/C][C]182.280921839665[/C][C]6.71907816033485[/C][/ROW]
[ROW][C]43[/C][C]181[/C][C]185.613424061114[/C][C]-4.61342406111433[/C][/ROW]
[ROW][C]44[/C][C]167[/C][C]181.638660333664[/C][C]-14.6386603336644[/C][/ROW]
[ROW][C]45[/C][C]166[/C][C]171.199563644919[/C][C]-5.19956364491861[/C][/ROW]
[ROW][C]46[/C][C]164[/C][C]166.846853570021[/C][C]-2.84685357002144[/C][/ROW]
[ROW][C]47[/C][C]167[/C][C]164.011185175945[/C][C]2.98881482405537[/C][/ROW]
[ROW][C]48[/C][C]164[/C][C]164.938391044923[/C][C]-0.938391044922753[/C][/ROW]
[ROW][C]49[/C][C]161[/C][C]163.333310825628[/C][C]-2.33331082562773[/C][/ROW]
[ROW][C]50[/C][C]141[/C][C]160.828777898024[/C][C]-19.8287778980245[/C][/ROW]
[ROW][C]51[/C][C]134[/C][C]147.043062024237[/C][C]-13.0430620242368[/C][/ROW]
[ROW][C]52[/C][C]111[/C][C]137.632816772425[/C][C]-26.6328167724255[/C][/ROW]
[ROW][C]53[/C][C]147[/C][C]119.459815495085[/C][C]27.5401845049152[/C][/ROW]
[ROW][C]54[/C][C]144[/C][C]136.217892972296[/C][C]7.7821070277038[/C][/ROW]
[ROW][C]55[/C][C]142[/C][C]140.235842634516[/C][C]1.76415736548381[/C][/ROW]
[ROW][C]56[/C][C]140[/C][C]140.373381969907[/C][C]-0.373381969906745[/C][/ROW]
[ROW][C]57[/C][C]143[/C][C]139.132623018237[/C][C]3.8673769817631[/C][/ROW]
[ROW][C]58[/C][C]137[/C][C]140.626331078307[/C][C]-3.62633107830729[/C][/ROW]
[ROW][C]59[/C][C]140[/C][C]137.288050874153[/C][C]2.71194912584701[/C][/ROW]
[ROW][C]60[/C][C]130[/C][C]138.036732066991[/C][C]-8.03673206699148[/C][/ROW]
[ROW][C]61[/C][C]129[/C][C]131.854598639971[/C][C]-2.8545986399713[/C][/ROW]
[ROW][C]62[/C][C]112[/C][C]129.013936177964[/C][C]-17.013936177964[/C][/ROW]
[ROW][C]63[/C][C]101[/C][C]117.043247263854[/C][C]-16.0432472638541[/C][/ROW]
[ROW][C]64[/C][C]74[/C][C]105.698464430365[/C][C]-31.6984644303646[/C][/ROW]
[ROW][C]65[/C][C]104[/C][C]84.2591029161895[/C][C]19.7408970838105[/C][/ROW]
[ROW][C]66[/C][C]103[/C][C]95.988152709643[/C][C]7.01184729035695[/C][/ROW]
[ROW][C]67[/C][C]100[/C][C]99.5094342362178[/C][C]0.4905657637822[/C][/ROW]
[ROW][C]68[/C][C]98[/C][C]98.8257540066738[/C][C]-0.825754006673833[/C][/ROW]
[ROW][C]69[/C][C]99[/C][C]97.2933028306472[/C][C]1.70669716935276[/C][/ROW]
[ROW][C]70[/C][C]91[/C][C]97.3937914841671[/C][C]-6.39379148416714[/C][/ROW]
[ROW][C]71[/C][C]92[/C][C]92.2710360781999[/C][C]-0.271036078199899[/C][/ROW]
[ROW][C]72[/C][C]94[/C][C]91.0962703762877[/C][C]2.90372962371231[/C][/ROW]
[ROW][C]73[/C][C]93[/C][C]91.968612793658[/C][C]1.03138720634200[/C][/ROW]
[ROW][C]74[/C][C]76[/C][C]91.6336575000926[/C][C]-15.6336575000926[/C][/ROW]
[ROW][C]75[/C][C]64[/C][C]80.5529806226635[/C][C]-16.5529806226635[/C][/ROW]
[ROW][C]76[/C][C]32[/C][C]68.8795186375568[/C][C]-36.8795186375568[/C][/ROW]
[ROW][C]77[/C][C]62[/C][C]44.0993820458390[/C][C]17.9006179541610[/C][/ROW]
[ROW][C]78[/C][C]69[/C][C]54.6418087301344[/C][C]14.3581912698656[/C][/ROW]
[ROW][C]79[/C][C]69[/C][C]62.9000572708218[/C][C]6.09994272917818[/C][/ROW]
[ROW][C]80[/C][C]68[/C][C]65.8333372229574[/C][C]2.16666277704259[/C][/ROW]
[ROW][C]81[/C][C]68[/C][C]66.2304144812759[/C][C]1.7695855187241[/C][/ROW]
[ROW][C]82[/C][C]59[/C][C]66.3714539226945[/C][C]-7.37145392269451[/C][/ROW]
[ROW][C]83[/C][C]66[/C][C]60.6182958654004[/C][C]5.38170413459955[/C][/ROW]
[ROW][C]84[/C][C]73[/C][C]63.0884512292685[/C][C]9.91154877073149[/C][/ROW]
[ROW][C]85[/C][C]70[/C][C]68.4794778020351[/C][C]1.52052219796485[/C][/ROW]
[ROW][C]86[/C][C]57[/C][C]68.459919708387[/C][C]-11.4599197083870[/C][/ROW]
[ROW][C]87[/C][C]48[/C][C]60.070494193542[/C][C]-12.0704941935420[/C][/ROW]
[ROW][C]88[/C][C]22[/C][C]51.287366559125[/C][C]-29.287366559125[/C][/ROW]
[ROW][C]89[/C][C]64[/C][C]31.4026955298656[/C][C]32.5973044701344[/C][/ROW]
[ROW][C]90[/C][C]74[/C][C]51.421634536087[/C][C]22.5783654639130[/C][/ROW]
[ROW][C]91[/C][C]67[/C][C]64.9803010964146[/C][C]2.01969890358544[/C][/ROW]
[ROW][C]92[/C][C]61[/C][C]65.2826151605817[/C][C]-4.2826151605817[/C][/ROW]
[ROW][C]93[/C][C]61[/C][C]61.5211590122717[/C][C]-0.521159012271696[/C][/ROW]
[ROW][C]94[/C][C]52[/C][C]60.1851125302223[/C][C]-8.18511253022231[/C][/ROW]
[ROW][C]95[/C][C]54[/C][C]53.9073024834[/C][C]0.0926975165999977[/C][/ROW]
[ROW][C]96[/C][C]69[/C][C]52.9670744025545[/C][C]16.0329255974455[/C][/ROW]
[ROW][C]97[/C][C]69[/C][C]62.3052017631388[/C][C]6.69479823686123[/C][/ROW]
[ROW][C]98[/C][C]53[/C][C]65.6220481431353[/C][C]-12.6220481431353[/C][/ROW]
[ROW][C]99[/C][C]50[/C][C]56.4832751873156[/C][C]-6.4832751873156[/C][/ROW]
[ROW][C]100[/C][C]22[/C][C]51.3028201485382[/C][C]-29.3028201485382[/C][/ROW]
[ROW][C]101[/C][C]69[/C][C]31.4081845513925[/C][C]37.5918154486075[/C][/ROW]
[ROW][C]102[/C][C]78[/C][C]54.6476144334349[/C][C]23.3523855665651[/C][/ROW]
[ROW][C]103[/C][C]74[/C][C]68.7053738356918[/C][C]5.29462616430823[/C][/ROW]
[ROW][C]104[/C][C]63[/C][C]71.119380797841[/C][C]-8.11938079784105[/C][/ROW]
[ROW][C]105[/C][C]67[/C][C]64.8839549694734[/C][C]2.11604503052661[/C][/ROW]
[ROW][C]106[/C][C]59[/C][C]65.2483935988026[/C][C]-6.24839359880259[/C][/ROW]
[ROW][C]107[/C][C]60[/C][C]60.2193916283966[/C][C]-0.219391628396593[/C][/ROW]
[ROW][C]108[/C][C]80[/C][C]59.0779265799608[/C][C]20.9220734200392[/C][/ROW]
[ROW][C]109[/C][C]77[/C][C]71.5686060164276[/C][C]5.43139398357241[/C][/ROW]
[ROW][C]110[/C][C]58[/C][C]74.070801695339[/C][C]-16.0708016953391[/C][/ROW]
[ROW][C]111[/C][C]54[/C][C]62.7082515978335[/C][C]-8.70825159783347[/C][/ROW]
[ROW][C]112[/C][C]32[/C][C]56.0931183173074[/C][C]-24.0931183173074[/C][/ROW]
[ROW][C]113[/C][C]78[/C][C]39.5577299588886[/C][C]38.4422700411114[/C][/ROW]
[ROW][C]114[/C][C]86[/C][C]63.345538104041[/C][C]22.6544618959589[/C][/ROW]
[ROW][C]115[/C][C]84[/C][C]76.9532721038322[/C][C]7.04672789616777[/C][/ROW]
[ROW][C]116[/C][C]78[/C][C]80.4970448559226[/C][C]-2.49704485592257[/C][/ROW]
[ROW][C]117[/C][C]72[/C][C]77.8869352356464[/C][C]-5.88693523564638[/C][/ROW]
[ROW][C]118[/C][C]64[/C][C]73.0910038031871[/C][C]-9.09100380318715[/C][/ROW]
[ROW][C]119[/C][C]62[/C][C]66.2290695865225[/C][C]-4.22906958652247[/C][/ROW]
[ROW][C]120[/C][C]72[/C][C]62.5021399481033[/C][C]9.49786005189665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78995&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78995&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
32422420
4240241-1
5260239.35519395398220.6448060460177
6259251.6670897113177.3329102886834
7244255.395394600365-11.3953946003648
8234247.047575265292-13.0475752652925
9235237.634419848361-2.63441984836135
10235234.9357300023890.0642699976110066
11236233.9771716854262.0228283145739
12238234.2815036127193.71849638728094
13240235.6792125653334.32078743466732
14233237.465282426763-4.46528242676334
15233233.58604132081-0.586041320809898
16233232.2081583339360.7918416660645
17247231.71874262770315.2812573722974
18251240.57218977211210.4278102278880
19233246.296104853779-13.2961048537790
20226236.722696055577-10.7226960555775
21233228.8086368093314.19136319066868
22233230.5112531357302.48874686426961
23227231.116012160819-4.11601216081894
24225227.461982634041-2.46198263404065
25223224.874481346421-1.87448134642074
26212222.665804441101-10.6658044411013
27206214.788429251837-8.7884292518371
28202208.121596935254-6.12159693525402
29223203.17435422011919.825645779881
30221214.9580504851916.04194951480909
31212217.853936062073-5.85393606207333
32205213.079282696248-8.07928269624759
33204206.869712366221-2.86971236622122
34200204.01930448215-4.01930448215012
35195200.427632651274-5.42763265127383
36193195.927862302170-2.92786230216956
37196193.0399589878232.96004101217659
38180193.948611328935-13.9486113289351
39174183.954462410487-9.95446241048722
40164176.535764863349-12.5357648633495
41192167.45262788800624.5473721119941
42189182.2809218396656.71907816033485
43181185.613424061114-4.61342406111433
44167181.638660333664-14.6386603336644
45166171.199563644919-5.19956364491861
46164166.846853570021-2.84685357002144
47167164.0111851759452.98881482405537
48164164.938391044923-0.938391044922753
49161163.333310825628-2.33331082562773
50141160.828777898024-19.8287778980245
51134147.043062024237-13.0430620242368
52111137.632816772425-26.6328167724255
53147119.45981549508527.5401845049152
54144136.2178929722967.7821070277038
55142140.2358426345161.76415736548381
56140140.373381969907-0.373381969906745
57143139.1326230182373.8673769817631
58137140.626331078307-3.62633107830729
59140137.2880508741532.71194912584701
60130138.036732066991-8.03673206699148
61129131.854598639971-2.8545986399713
62112129.013936177964-17.013936177964
63101117.043247263854-16.0432472638541
6474105.698464430365-31.6984644303646
6510484.259102916189519.7408970838105
6610395.9881527096437.01184729035695
6710099.50943423621780.4905657637822
689898.8257540066738-0.825754006673833
699997.29330283064721.70669716935276
709197.3937914841671-6.39379148416714
719292.2710360781999-0.271036078199899
729491.09627037628772.90372962371231
739391.9686127936581.03138720634200
747691.6336575000926-15.6336575000926
756480.5529806226635-16.5529806226635
763268.8795186375568-36.8795186375568
776244.099382045839017.9006179541610
786954.641808730134414.3581912698656
796962.90005727082186.09994272917818
806865.83333722295742.16666277704259
816866.23041448127591.7695855187241
825966.3714539226945-7.37145392269451
836660.61829586540045.38170413459955
847363.08845122926859.91154877073149
857068.47947780203511.52052219796485
865768.459919708387-11.4599197083870
874860.070494193542-12.0704941935420
882251.287366559125-29.287366559125
896431.402695529865632.5973044701344
907451.42163453608722.5783654639130
916764.98030109641462.01969890358544
926165.2826151605817-4.2826151605817
936161.5211590122717-0.521159012271696
945260.1851125302223-8.18511253022231
955453.90730248340.0926975165999977
966952.967074402554516.0329255974455
976962.30520176313886.69479823686123
985365.6220481431353-12.6220481431353
995056.4832751873156-6.4832751873156
1002251.3028201485382-29.3028201485382
1016931.408184551392537.5918154486075
1027854.647614433434923.3523855665651
1037468.70537383569185.29462616430823
1046371.119380797841-8.11938079784105
1056764.88395496947342.11604503052661
1065965.2483935988026-6.24839359880259
1076060.2193916283966-0.219391628396593
1088059.077926579960820.9220734200392
1097771.56860601642765.43139398357241
1105874.070801695339-16.0708016953391
1115462.7082515978335-8.70825159783347
1123256.0931183173074-24.0931183173074
1137839.557729958888638.4422700411114
1148663.34553810404122.6544618959589
1158476.95327210383227.04672789616777
1167880.4970448559226-2.49704485592257
1177277.8869352356464-5.88693523564638
1186473.0910038031871-9.09100380318715
1196266.2290695865225-4.22906958652247
1207262.50213994810339.49786005189665







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12167.62641753379641.702315322129993.550519745462
12266.62641753379635.780277936910597.4725571306814
12365.62641753379630.54209652597100.710738541622
12464.62641753379625.7633909773141103.489444090278
12563.62641753379621.3208613303911105.931973737201
12662.62641753379617.1381186182608108.114716449331
12761.62641753379613.1639517403727110.088883327219
12860.6264175337969.362045467727111.890789599865
12959.6264175337965.70553942635055113.547295641241
13058.6264175337962.1739034318747115.078931635717
13157.626417533796-1.24897291906858116.501807986661
13256.626417533796-4.57600769206326117.828842759655

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 67.626417533796 & 41.7023153221299 & 93.550519745462 \tabularnewline
122 & 66.626417533796 & 35.7802779369105 & 97.4725571306814 \tabularnewline
123 & 65.626417533796 & 30.54209652597 & 100.710738541622 \tabularnewline
124 & 64.626417533796 & 25.7633909773141 & 103.489444090278 \tabularnewline
125 & 63.626417533796 & 21.3208613303911 & 105.931973737201 \tabularnewline
126 & 62.626417533796 & 17.1381186182608 & 108.114716449331 \tabularnewline
127 & 61.626417533796 & 13.1639517403727 & 110.088883327219 \tabularnewline
128 & 60.626417533796 & 9.362045467727 & 111.890789599865 \tabularnewline
129 & 59.626417533796 & 5.70553942635055 & 113.547295641241 \tabularnewline
130 & 58.626417533796 & 2.1739034318747 & 115.078931635717 \tabularnewline
131 & 57.626417533796 & -1.24897291906858 & 116.501807986661 \tabularnewline
132 & 56.626417533796 & -4.57600769206326 & 117.828842759655 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78995&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]67.626417533796[/C][C]41.7023153221299[/C][C]93.550519745462[/C][/ROW]
[ROW][C]122[/C][C]66.626417533796[/C][C]35.7802779369105[/C][C]97.4725571306814[/C][/ROW]
[ROW][C]123[/C][C]65.626417533796[/C][C]30.54209652597[/C][C]100.710738541622[/C][/ROW]
[ROW][C]124[/C][C]64.626417533796[/C][C]25.7633909773141[/C][C]103.489444090278[/C][/ROW]
[ROW][C]125[/C][C]63.626417533796[/C][C]21.3208613303911[/C][C]105.931973737201[/C][/ROW]
[ROW][C]126[/C][C]62.626417533796[/C][C]17.1381186182608[/C][C]108.114716449331[/C][/ROW]
[ROW][C]127[/C][C]61.626417533796[/C][C]13.1639517403727[/C][C]110.088883327219[/C][/ROW]
[ROW][C]128[/C][C]60.626417533796[/C][C]9.362045467727[/C][C]111.890789599865[/C][/ROW]
[ROW][C]129[/C][C]59.626417533796[/C][C]5.70553942635055[/C][C]113.547295641241[/C][/ROW]
[ROW][C]130[/C][C]58.626417533796[/C][C]2.1739034318747[/C][C]115.078931635717[/C][/ROW]
[ROW][C]131[/C][C]57.626417533796[/C][C]-1.24897291906858[/C][C]116.501807986661[/C][/ROW]
[ROW][C]132[/C][C]56.626417533796[/C][C]-4.57600769206326[/C][C]117.828842759655[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78995&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78995&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
12167.62641753379641.702315322129993.550519745462
12266.62641753379635.780277936910597.4725571306814
12365.62641753379630.54209652597100.710738541622
12464.62641753379625.7633909773141103.489444090278
12563.62641753379621.3208613303911105.931973737201
12662.62641753379617.1381186182608108.114716449331
12761.62641753379613.1639517403727110.088883327219
12860.6264175337969.362045467727111.890789599865
12959.6264175337965.70553942635055113.547295641241
13058.6264175337962.1739034318747115.078931635717
13157.626417533796-1.24897291906858116.501807986661
13256.626417533796-4.57600769206326117.828842759655



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')