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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 24 Nov 2015 15:11:07 +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/2015/Nov/24/t1448377940hh7ifxdpcee7t9o.htm/, Retrieved Tue, 14 May 2024 11:29:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284037, Retrieved Tue, 14 May 2024 11:29:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-24 15:11:07] [7e1e09e1787c74b32ad6066a9a323b17] [Current]
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Dataseries X:
92,44
94,36
93,42
92,97
94,83
91,47
88,42
86,36
86,01
87,87
89,81
88,41
86,33
89,64
89,53
88,3
99,49
98,81
90,97
92,58
92,98
95
92,47
88,65
84,81
88,6
89,31
92,34
91,53
96,95
95,44
89,59
89,86
91,66
92,7
90,54
86,17
89,15
89,73
91,07
93,36
96,27
95
94,72
97,16
100,92
98,66
95,87
94,6
98,41
98,05
99,82
106,96
107,45
100,25
99,28
101,38
101
97,43
95,38
95,17
94,13
96,43
105,38
98,39
99,8
94,43
90,16
85,49
90,57
88,22
89,66




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284037&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284037&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284037&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.896533443677752
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.896533443677752 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284037&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]0.896533443677752[/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=284037&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284037&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
alpha0.896533443677752
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
294.3692.441.92
393.4294.1613442118613-0.741344211861275
492.9793.4967043326507-0.526704332650709
594.8393.02449628349941.80550371650062
691.4794.6431907480267-3.17319074802666
788.4291.7983191192519-3.37831911925194
886.3688.7695430454266-2.40954304542662
986.0186.6093071212205-0.599307121220519
1087.8786.07200824401211.79799175598791
1189.8187.68396798471212.12603201528786
1288.4189.5900267887473-1.18002678874731
1386.3388.5320933081997-2.20209330819968
1489.6486.55784301129973.08215698870032
1589.5389.32109983033460.20890016966537
1688.389.5083858188296-1.2083858188296
1799.4988.425027519382911.0649724806171
1898.8198.34514540163010.464854598369897
1990.9798.7619030955161-7.79190309551612
2092.5891.77620138048970.803798619510275
2192.9892.49683372486270.483166275137307
229592.93000844938052.06999155061951
2392.4794.7858251026412-2.31582510264124
2488.6592.7096104484149-4.0596104484149
2584.8189.0700339131073-4.26003391310732
2688.685.25077103880523.34922896119478
2789.3188.25346681305041.05653318694958
2892.3489.20068414950623.13931585049384
2991.5392.0151857997415-0.485185799741544
3096.9591.58020050387575.36979949612429
3195.4496.3944053379951-0.95440533799507
3289.5995.5387490336579-5.9487490336579
3389.8690.2054965769379-0.34549657693789
3491.6689.89574734103691.7642526589631
3592.791.47745885289471.22254114710528
3690.5492.5735078775468-2.03350787754677
3786.1790.7504000573439-4.58040005734394
3889.1586.64391822051162.5060817794884
3989.7388.89070434841440.839295651585587
4091.0789.64316096919421.42683903080578
4193.3690.92236987905632.43763012094365
4296.2793.10778680579863.16221319420143
439595.9428166904392-0.942816690439201
4494.7295.0975499962029-0.377549996202873
4597.1694.75906379794662.4009362020534
46100.9296.91158339922414.00841660077589
4798.66100.505262938013-1.84526293801279
4895.8798.8509230017053-2.98092300170525
4994.696.1784258376482-1.57842583764823
5098.4194.76331428583153.64668571416848
5198.0598.03268998716540.0173100128345567
5299.8298.04820899258211.77179100741787
53106.9699.63667888593977.32332111406025
54107.45106.2022811834861.24771881651384
55100.25107.320902830797-7.07090283079685
5699.28100.981601965992-1.7016019659918
57101.3899.45605889565231.92394110434766
58101101.180936439366-0.18093643936632
5997.43101.018720870294-3.58872087029442
6095.3897.8013125900512-2.42131259005116
6195.1795.6305248754723-0.460524875472288
6294.1395.2176489229659-1.08764892296585
6396.4394.24253528854692.18746471145313
64105.3896.20367055922959.17632944077049
6598.39104.430556793085-6.04055679308502
6699.899.01499560964950.785004390350522
6794.4399.7187782990326-5.28877829903257
6890.1694.9772116777527-4.81721167775274
6985.4990.6584203033724-5.1684203033724
7090.5786.02475865041594.54524134958406
7188.2290.099719529905-1.87971952990503
7289.6688.41448810661091.24551189338905

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 94.36 & 92.44 & 1.92 \tabularnewline
3 & 93.42 & 94.1613442118613 & -0.741344211861275 \tabularnewline
4 & 92.97 & 93.4967043326507 & -0.526704332650709 \tabularnewline
5 & 94.83 & 93.0244962834994 & 1.80550371650062 \tabularnewline
6 & 91.47 & 94.6431907480267 & -3.17319074802666 \tabularnewline
7 & 88.42 & 91.7983191192519 & -3.37831911925194 \tabularnewline
8 & 86.36 & 88.7695430454266 & -2.40954304542662 \tabularnewline
9 & 86.01 & 86.6093071212205 & -0.599307121220519 \tabularnewline
10 & 87.87 & 86.0720082440121 & 1.79799175598791 \tabularnewline
11 & 89.81 & 87.6839679847121 & 2.12603201528786 \tabularnewline
12 & 88.41 & 89.5900267887473 & -1.18002678874731 \tabularnewline
13 & 86.33 & 88.5320933081997 & -2.20209330819968 \tabularnewline
14 & 89.64 & 86.5578430112997 & 3.08215698870032 \tabularnewline
15 & 89.53 & 89.3210998303346 & 0.20890016966537 \tabularnewline
16 & 88.3 & 89.5083858188296 & -1.2083858188296 \tabularnewline
17 & 99.49 & 88.4250275193829 & 11.0649724806171 \tabularnewline
18 & 98.81 & 98.3451454016301 & 0.464854598369897 \tabularnewline
19 & 90.97 & 98.7619030955161 & -7.79190309551612 \tabularnewline
20 & 92.58 & 91.7762013804897 & 0.803798619510275 \tabularnewline
21 & 92.98 & 92.4968337248627 & 0.483166275137307 \tabularnewline
22 & 95 & 92.9300084493805 & 2.06999155061951 \tabularnewline
23 & 92.47 & 94.7858251026412 & -2.31582510264124 \tabularnewline
24 & 88.65 & 92.7096104484149 & -4.0596104484149 \tabularnewline
25 & 84.81 & 89.0700339131073 & -4.26003391310732 \tabularnewline
26 & 88.6 & 85.2507710388052 & 3.34922896119478 \tabularnewline
27 & 89.31 & 88.2534668130504 & 1.05653318694958 \tabularnewline
28 & 92.34 & 89.2006841495062 & 3.13931585049384 \tabularnewline
29 & 91.53 & 92.0151857997415 & -0.485185799741544 \tabularnewline
30 & 96.95 & 91.5802005038757 & 5.36979949612429 \tabularnewline
31 & 95.44 & 96.3944053379951 & -0.95440533799507 \tabularnewline
32 & 89.59 & 95.5387490336579 & -5.9487490336579 \tabularnewline
33 & 89.86 & 90.2054965769379 & -0.34549657693789 \tabularnewline
34 & 91.66 & 89.8957473410369 & 1.7642526589631 \tabularnewline
35 & 92.7 & 91.4774588528947 & 1.22254114710528 \tabularnewline
36 & 90.54 & 92.5735078775468 & -2.03350787754677 \tabularnewline
37 & 86.17 & 90.7504000573439 & -4.58040005734394 \tabularnewline
38 & 89.15 & 86.6439182205116 & 2.5060817794884 \tabularnewline
39 & 89.73 & 88.8907043484144 & 0.839295651585587 \tabularnewline
40 & 91.07 & 89.6431609691942 & 1.42683903080578 \tabularnewline
41 & 93.36 & 90.9223698790563 & 2.43763012094365 \tabularnewline
42 & 96.27 & 93.1077868057986 & 3.16221319420143 \tabularnewline
43 & 95 & 95.9428166904392 & -0.942816690439201 \tabularnewline
44 & 94.72 & 95.0975499962029 & -0.377549996202873 \tabularnewline
45 & 97.16 & 94.7590637979466 & 2.4009362020534 \tabularnewline
46 & 100.92 & 96.9115833992241 & 4.00841660077589 \tabularnewline
47 & 98.66 & 100.505262938013 & -1.84526293801279 \tabularnewline
48 & 95.87 & 98.8509230017053 & -2.98092300170525 \tabularnewline
49 & 94.6 & 96.1784258376482 & -1.57842583764823 \tabularnewline
50 & 98.41 & 94.7633142858315 & 3.64668571416848 \tabularnewline
51 & 98.05 & 98.0326899871654 & 0.0173100128345567 \tabularnewline
52 & 99.82 & 98.0482089925821 & 1.77179100741787 \tabularnewline
53 & 106.96 & 99.6366788859397 & 7.32332111406025 \tabularnewline
54 & 107.45 & 106.202281183486 & 1.24771881651384 \tabularnewline
55 & 100.25 & 107.320902830797 & -7.07090283079685 \tabularnewline
56 & 99.28 & 100.981601965992 & -1.7016019659918 \tabularnewline
57 & 101.38 & 99.4560588956523 & 1.92394110434766 \tabularnewline
58 & 101 & 101.180936439366 & -0.18093643936632 \tabularnewline
59 & 97.43 & 101.018720870294 & -3.58872087029442 \tabularnewline
60 & 95.38 & 97.8013125900512 & -2.42131259005116 \tabularnewline
61 & 95.17 & 95.6305248754723 & -0.460524875472288 \tabularnewline
62 & 94.13 & 95.2176489229659 & -1.08764892296585 \tabularnewline
63 & 96.43 & 94.2425352885469 & 2.18746471145313 \tabularnewline
64 & 105.38 & 96.2036705592295 & 9.17632944077049 \tabularnewline
65 & 98.39 & 104.430556793085 & -6.04055679308502 \tabularnewline
66 & 99.8 & 99.0149956096495 & 0.785004390350522 \tabularnewline
67 & 94.43 & 99.7187782990326 & -5.28877829903257 \tabularnewline
68 & 90.16 & 94.9772116777527 & -4.81721167775274 \tabularnewline
69 & 85.49 & 90.6584203033724 & -5.1684203033724 \tabularnewline
70 & 90.57 & 86.0247586504159 & 4.54524134958406 \tabularnewline
71 & 88.22 & 90.099719529905 & -1.87971952990503 \tabularnewline
72 & 89.66 & 88.4144881066109 & 1.24551189338905 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284037&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]94.36[/C][C]92.44[/C][C]1.92[/C][/ROW]
[ROW][C]3[/C][C]93.42[/C][C]94.1613442118613[/C][C]-0.741344211861275[/C][/ROW]
[ROW][C]4[/C][C]92.97[/C][C]93.4967043326507[/C][C]-0.526704332650709[/C][/ROW]
[ROW][C]5[/C][C]94.83[/C][C]93.0244962834994[/C][C]1.80550371650062[/C][/ROW]
[ROW][C]6[/C][C]91.47[/C][C]94.6431907480267[/C][C]-3.17319074802666[/C][/ROW]
[ROW][C]7[/C][C]88.42[/C][C]91.7983191192519[/C][C]-3.37831911925194[/C][/ROW]
[ROW][C]8[/C][C]86.36[/C][C]88.7695430454266[/C][C]-2.40954304542662[/C][/ROW]
[ROW][C]9[/C][C]86.01[/C][C]86.6093071212205[/C][C]-0.599307121220519[/C][/ROW]
[ROW][C]10[/C][C]87.87[/C][C]86.0720082440121[/C][C]1.79799175598791[/C][/ROW]
[ROW][C]11[/C][C]89.81[/C][C]87.6839679847121[/C][C]2.12603201528786[/C][/ROW]
[ROW][C]12[/C][C]88.41[/C][C]89.5900267887473[/C][C]-1.18002678874731[/C][/ROW]
[ROW][C]13[/C][C]86.33[/C][C]88.5320933081997[/C][C]-2.20209330819968[/C][/ROW]
[ROW][C]14[/C][C]89.64[/C][C]86.5578430112997[/C][C]3.08215698870032[/C][/ROW]
[ROW][C]15[/C][C]89.53[/C][C]89.3210998303346[/C][C]0.20890016966537[/C][/ROW]
[ROW][C]16[/C][C]88.3[/C][C]89.5083858188296[/C][C]-1.2083858188296[/C][/ROW]
[ROW][C]17[/C][C]99.49[/C][C]88.4250275193829[/C][C]11.0649724806171[/C][/ROW]
[ROW][C]18[/C][C]98.81[/C][C]98.3451454016301[/C][C]0.464854598369897[/C][/ROW]
[ROW][C]19[/C][C]90.97[/C][C]98.7619030955161[/C][C]-7.79190309551612[/C][/ROW]
[ROW][C]20[/C][C]92.58[/C][C]91.7762013804897[/C][C]0.803798619510275[/C][/ROW]
[ROW][C]21[/C][C]92.98[/C][C]92.4968337248627[/C][C]0.483166275137307[/C][/ROW]
[ROW][C]22[/C][C]95[/C][C]92.9300084493805[/C][C]2.06999155061951[/C][/ROW]
[ROW][C]23[/C][C]92.47[/C][C]94.7858251026412[/C][C]-2.31582510264124[/C][/ROW]
[ROW][C]24[/C][C]88.65[/C][C]92.7096104484149[/C][C]-4.0596104484149[/C][/ROW]
[ROW][C]25[/C][C]84.81[/C][C]89.0700339131073[/C][C]-4.26003391310732[/C][/ROW]
[ROW][C]26[/C][C]88.6[/C][C]85.2507710388052[/C][C]3.34922896119478[/C][/ROW]
[ROW][C]27[/C][C]89.31[/C][C]88.2534668130504[/C][C]1.05653318694958[/C][/ROW]
[ROW][C]28[/C][C]92.34[/C][C]89.2006841495062[/C][C]3.13931585049384[/C][/ROW]
[ROW][C]29[/C][C]91.53[/C][C]92.0151857997415[/C][C]-0.485185799741544[/C][/ROW]
[ROW][C]30[/C][C]96.95[/C][C]91.5802005038757[/C][C]5.36979949612429[/C][/ROW]
[ROW][C]31[/C][C]95.44[/C][C]96.3944053379951[/C][C]-0.95440533799507[/C][/ROW]
[ROW][C]32[/C][C]89.59[/C][C]95.5387490336579[/C][C]-5.9487490336579[/C][/ROW]
[ROW][C]33[/C][C]89.86[/C][C]90.2054965769379[/C][C]-0.34549657693789[/C][/ROW]
[ROW][C]34[/C][C]91.66[/C][C]89.8957473410369[/C][C]1.7642526589631[/C][/ROW]
[ROW][C]35[/C][C]92.7[/C][C]91.4774588528947[/C][C]1.22254114710528[/C][/ROW]
[ROW][C]36[/C][C]90.54[/C][C]92.5735078775468[/C][C]-2.03350787754677[/C][/ROW]
[ROW][C]37[/C][C]86.17[/C][C]90.7504000573439[/C][C]-4.58040005734394[/C][/ROW]
[ROW][C]38[/C][C]89.15[/C][C]86.6439182205116[/C][C]2.5060817794884[/C][/ROW]
[ROW][C]39[/C][C]89.73[/C][C]88.8907043484144[/C][C]0.839295651585587[/C][/ROW]
[ROW][C]40[/C][C]91.07[/C][C]89.6431609691942[/C][C]1.42683903080578[/C][/ROW]
[ROW][C]41[/C][C]93.36[/C][C]90.9223698790563[/C][C]2.43763012094365[/C][/ROW]
[ROW][C]42[/C][C]96.27[/C][C]93.1077868057986[/C][C]3.16221319420143[/C][/ROW]
[ROW][C]43[/C][C]95[/C][C]95.9428166904392[/C][C]-0.942816690439201[/C][/ROW]
[ROW][C]44[/C][C]94.72[/C][C]95.0975499962029[/C][C]-0.377549996202873[/C][/ROW]
[ROW][C]45[/C][C]97.16[/C][C]94.7590637979466[/C][C]2.4009362020534[/C][/ROW]
[ROW][C]46[/C][C]100.92[/C][C]96.9115833992241[/C][C]4.00841660077589[/C][/ROW]
[ROW][C]47[/C][C]98.66[/C][C]100.505262938013[/C][C]-1.84526293801279[/C][/ROW]
[ROW][C]48[/C][C]95.87[/C][C]98.8509230017053[/C][C]-2.98092300170525[/C][/ROW]
[ROW][C]49[/C][C]94.6[/C][C]96.1784258376482[/C][C]-1.57842583764823[/C][/ROW]
[ROW][C]50[/C][C]98.41[/C][C]94.7633142858315[/C][C]3.64668571416848[/C][/ROW]
[ROW][C]51[/C][C]98.05[/C][C]98.0326899871654[/C][C]0.0173100128345567[/C][/ROW]
[ROW][C]52[/C][C]99.82[/C][C]98.0482089925821[/C][C]1.77179100741787[/C][/ROW]
[ROW][C]53[/C][C]106.96[/C][C]99.6366788859397[/C][C]7.32332111406025[/C][/ROW]
[ROW][C]54[/C][C]107.45[/C][C]106.202281183486[/C][C]1.24771881651384[/C][/ROW]
[ROW][C]55[/C][C]100.25[/C][C]107.320902830797[/C][C]-7.07090283079685[/C][/ROW]
[ROW][C]56[/C][C]99.28[/C][C]100.981601965992[/C][C]-1.7016019659918[/C][/ROW]
[ROW][C]57[/C][C]101.38[/C][C]99.4560588956523[/C][C]1.92394110434766[/C][/ROW]
[ROW][C]58[/C][C]101[/C][C]101.180936439366[/C][C]-0.18093643936632[/C][/ROW]
[ROW][C]59[/C][C]97.43[/C][C]101.018720870294[/C][C]-3.58872087029442[/C][/ROW]
[ROW][C]60[/C][C]95.38[/C][C]97.8013125900512[/C][C]-2.42131259005116[/C][/ROW]
[ROW][C]61[/C][C]95.17[/C][C]95.6305248754723[/C][C]-0.460524875472288[/C][/ROW]
[ROW][C]62[/C][C]94.13[/C][C]95.2176489229659[/C][C]-1.08764892296585[/C][/ROW]
[ROW][C]63[/C][C]96.43[/C][C]94.2425352885469[/C][C]2.18746471145313[/C][/ROW]
[ROW][C]64[/C][C]105.38[/C][C]96.2036705592295[/C][C]9.17632944077049[/C][/ROW]
[ROW][C]65[/C][C]98.39[/C][C]104.430556793085[/C][C]-6.04055679308502[/C][/ROW]
[ROW][C]66[/C][C]99.8[/C][C]99.0149956096495[/C][C]0.785004390350522[/C][/ROW]
[ROW][C]67[/C][C]94.43[/C][C]99.7187782990326[/C][C]-5.28877829903257[/C][/ROW]
[ROW][C]68[/C][C]90.16[/C][C]94.9772116777527[/C][C]-4.81721167775274[/C][/ROW]
[ROW][C]69[/C][C]85.49[/C][C]90.6584203033724[/C][C]-5.1684203033724[/C][/ROW]
[ROW][C]70[/C][C]90.57[/C][C]86.0247586504159[/C][C]4.54524134958406[/C][/ROW]
[ROW][C]71[/C][C]88.22[/C][C]90.099719529905[/C][C]-1.87971952990503[/C][/ROW]
[ROW][C]72[/C][C]89.66[/C][C]88.4144881066109[/C][C]1.24551189338905[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284037&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284037&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
294.3692.441.92
393.4294.1613442118613-0.741344211861275
492.9793.4967043326507-0.526704332650709
594.8393.02449628349941.80550371650062
691.4794.6431907480267-3.17319074802666
788.4291.7983191192519-3.37831911925194
886.3688.7695430454266-2.40954304542662
986.0186.6093071212205-0.599307121220519
1087.8786.07200824401211.79799175598791
1189.8187.68396798471212.12603201528786
1288.4189.5900267887473-1.18002678874731
1386.3388.5320933081997-2.20209330819968
1489.6486.55784301129973.08215698870032
1589.5389.32109983033460.20890016966537
1688.389.5083858188296-1.2083858188296
1799.4988.425027519382911.0649724806171
1898.8198.34514540163010.464854598369897
1990.9798.7619030955161-7.79190309551612
2092.5891.77620138048970.803798619510275
2192.9892.49683372486270.483166275137307
229592.93000844938052.06999155061951
2392.4794.7858251026412-2.31582510264124
2488.6592.7096104484149-4.0596104484149
2584.8189.0700339131073-4.26003391310732
2688.685.25077103880523.34922896119478
2789.3188.25346681305041.05653318694958
2892.3489.20068414950623.13931585049384
2991.5392.0151857997415-0.485185799741544
3096.9591.58020050387575.36979949612429
3195.4496.3944053379951-0.95440533799507
3289.5995.5387490336579-5.9487490336579
3389.8690.2054965769379-0.34549657693789
3491.6689.89574734103691.7642526589631
3592.791.47745885289471.22254114710528
3690.5492.5735078775468-2.03350787754677
3786.1790.7504000573439-4.58040005734394
3889.1586.64391822051162.5060817794884
3989.7388.89070434841440.839295651585587
4091.0789.64316096919421.42683903080578
4193.3690.92236987905632.43763012094365
4296.2793.10778680579863.16221319420143
439595.9428166904392-0.942816690439201
4494.7295.0975499962029-0.377549996202873
4597.1694.75906379794662.4009362020534
46100.9296.91158339922414.00841660077589
4798.66100.505262938013-1.84526293801279
4895.8798.8509230017053-2.98092300170525
4994.696.1784258376482-1.57842583764823
5098.4194.76331428583153.64668571416848
5198.0598.03268998716540.0173100128345567
5299.8298.04820899258211.77179100741787
53106.9699.63667888593977.32332111406025
54107.45106.2022811834861.24771881651384
55100.25107.320902830797-7.07090283079685
5699.28100.981601965992-1.7016019659918
57101.3899.45605889565231.92394110434766
58101101.180936439366-0.18093643936632
5997.43101.018720870294-3.58872087029442
6095.3897.8013125900512-2.42131259005116
6195.1795.6305248754723-0.460524875472288
6294.1395.2176489229659-1.08764892296585
6396.4394.24253528854692.18746471145313
64105.3896.20367055922959.17632944077049
6598.39104.430556793085-6.04055679308502
6699.899.01499560964950.785004390350522
6794.4399.7187782990326-5.28877829903257
6890.1694.9772116777527-4.81721167775274
6985.4990.6584203033724-5.1684203033724
7090.5786.02475865041594.54524134958406
7188.2290.099719529905-1.87971952990503
7289.6688.41448810661091.24551189338905







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7389.531131173532682.713730396187396.348531950878
7489.531131173532680.375049198357498.6872131487079
7589.531131173532678.5224654545044100.539796892561
7689.531131173532676.9395623796735102.122699967392
7789.531131173532675.5345427153523103.527719631713
7889.531131173532674.2582345181877104.804027828878
7989.531131173532673.080652274059105.981610073006
8089.531131173532671.9819106837443107.080351663321
8189.531131173532670.9480199276625108.114242419403
8289.531131173532669.9686950431943109.093567303871
8389.531131173532669.0361124828667110.026149864199
8489.531131173532668.1441567519852110.91810559508

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 89.5311311735326 & 82.7137303961873 & 96.348531950878 \tabularnewline
74 & 89.5311311735326 & 80.3750491983574 & 98.6872131487079 \tabularnewline
75 & 89.5311311735326 & 78.5224654545044 & 100.539796892561 \tabularnewline
76 & 89.5311311735326 & 76.9395623796735 & 102.122699967392 \tabularnewline
77 & 89.5311311735326 & 75.5345427153523 & 103.527719631713 \tabularnewline
78 & 89.5311311735326 & 74.2582345181877 & 104.804027828878 \tabularnewline
79 & 89.5311311735326 & 73.080652274059 & 105.981610073006 \tabularnewline
80 & 89.5311311735326 & 71.9819106837443 & 107.080351663321 \tabularnewline
81 & 89.5311311735326 & 70.9480199276625 & 108.114242419403 \tabularnewline
82 & 89.5311311735326 & 69.9686950431943 & 109.093567303871 \tabularnewline
83 & 89.5311311735326 & 69.0361124828667 & 110.026149864199 \tabularnewline
84 & 89.5311311735326 & 68.1441567519852 & 110.91810559508 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284037&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]73[/C][C]89.5311311735326[/C][C]82.7137303961873[/C][C]96.348531950878[/C][/ROW]
[ROW][C]74[/C][C]89.5311311735326[/C][C]80.3750491983574[/C][C]98.6872131487079[/C][/ROW]
[ROW][C]75[/C][C]89.5311311735326[/C][C]78.5224654545044[/C][C]100.539796892561[/C][/ROW]
[ROW][C]76[/C][C]89.5311311735326[/C][C]76.9395623796735[/C][C]102.122699967392[/C][/ROW]
[ROW][C]77[/C][C]89.5311311735326[/C][C]75.5345427153523[/C][C]103.527719631713[/C][/ROW]
[ROW][C]78[/C][C]89.5311311735326[/C][C]74.2582345181877[/C][C]104.804027828878[/C][/ROW]
[ROW][C]79[/C][C]89.5311311735326[/C][C]73.080652274059[/C][C]105.981610073006[/C][/ROW]
[ROW][C]80[/C][C]89.5311311735326[/C][C]71.9819106837443[/C][C]107.080351663321[/C][/ROW]
[ROW][C]81[/C][C]89.5311311735326[/C][C]70.9480199276625[/C][C]108.114242419403[/C][/ROW]
[ROW][C]82[/C][C]89.5311311735326[/C][C]69.9686950431943[/C][C]109.093567303871[/C][/ROW]
[ROW][C]83[/C][C]89.5311311735326[/C][C]69.0361124828667[/C][C]110.026149864199[/C][/ROW]
[ROW][C]84[/C][C]89.5311311735326[/C][C]68.1441567519852[/C][C]110.91810559508[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284037&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284037&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
7389.531131173532682.713730396187396.348531950878
7489.531131173532680.375049198357498.6872131487079
7589.531131173532678.5224654545044100.539796892561
7689.531131173532676.9395623796735102.122699967392
7789.531131173532675.5345427153523103.527719631713
7889.531131173532674.2582345181877104.804027828878
7989.531131173532673.080652274059105.981610073006
8089.531131173532671.9819106837443107.080351663321
8189.531131173532670.9480199276625108.114242419403
8289.531131173532669.9686950431943109.093567303871
8389.531131173532669.0361124828667110.026149864199
8489.531131173532668.1441567519852110.91810559508



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')