Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Apr 2017 21:04:36 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Apr/28/t1493410119vdly6egiz7q0iz9.htm/, Retrieved Fri, 10 May 2024 12:07:34 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 10 May 2024 12:07:34 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
94,47
94,19
94,34
94,3
94,4
94,54
94,09
95,87
98,46
98,7
98,75
98,72
98,72
98,67
98,82
99,39
99,33
99,22
99,05
98,83
98,84
98,89
98,8
99,4
98,89
98,85
98,69
98,48
98,39
98,35
98,26
98,06
98,14
98,17
98,41
98,64
99,25
99,61
100,28
100,31
100,55
100,45
100,78
100,68
101,69
98,09
99,13
99,18
96,22
96,11
96
95,96
97,95
98,43
98,32
97,45
96,42
95,36
95,1
95,54
94,07
93,48
92,86
90,98
91,45
91,16
90,71
90,31
89,78
91,02
90,77
90,69




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0488170816392544
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0488170816392544 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0488170816392544[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha1
beta0.0488170816392544
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
394.3493.910.430000000000007
494.394.08099134510490.21900865489512
594.494.05168270849060.348317291509417
694.5494.16868654214660.371313457853418
794.0994.3268129815324-0.236812981532367
895.8793.86525246287972.00474753712034
998.4695.74311838706542.71688161293463
1098.798.46574861856820.234251381431832
1198.7598.71718408737960.0328159126203502
1298.7298.7687860644651-0.048786064465105
1398.7298.7364044711732-0.0164044711732458
1498.6798.7356036527647-0.0656036527647359
1598.8298.68240107389190.137598926108112
1699.3998.83911825190120.550881748098831
1799.3399.4360106911717-0.10601069117169
1899.2299.3708355586061-0.150835558606133
1999.0599.2534722068276-0.203472206827556
2098.8399.0735392874955-0.243539287495537
2198.8498.8416504102155-0.00165041021548973
2298.8998.85156984200530.0384301579947248
2398.898.9034458901655-0.103445890165517
2499.498.80839596370010.591604036299955
2598.8999.4372763462382-0.54727634623822
2698.8598.9005599121647-0.0505599121646867
2798.6998.8580917248049-0.168091724804853
2898.4898.6898859773522-0.209885977352172
2998.3998.4696399564608-0.0796399564608379
3098.3598.3757521662045-0.0257521662045548
3198.2698.3344950206045-0.0744950206045445
3298.0698.240858391102-0.180858391101978
3398.1498.03202941225840.10797058774159
3498.1798.11730022125480.0526997787451648
3598.4198.14987287065620.260127129343786
3698.6498.4025715179660.237428482034034
3799.2598.64416208355690.605837916443093
3899.6199.28373732258410.32626267741594
39100.2899.65966451434330.620335485656682
40100.31100.35994748239-0.0499474823903512
41100.55100.3875091920650.162490807935171
42100.45100.635441519101-0.185441519101417
43100.78100.5263888053240.253611194675855
44100.68100.868769363719-0.18876936371926
45101.69100.759554194280.930445805720396
4698.09101.814975843138-3.72497584313834
4799.1398.03313339329961.09686660670039
4899.1899.12667921998630.0533207800137347
4996.2299.1792821848573-2.95928218485729
5096.1196.07481866484550.0351813351544905
519695.96653611495590.0334638850440854
5295.9695.85816972416410.101830275835908
5397.9595.82314078105292.1268592189471
5498.4397.91696784117950.51303215882055
5598.3298.4220125739602-0.102012573960167
5697.4598.3070326178089-0.857032617808898
5796.4297.3951947865378-0.975194786537841
5895.3696.3175886230292-0.957588623029238
5995.195.210841941042-0.110841941042011
6095.5494.94543096095710.594569039042909
6194.0795.4144560862762-1.34445608627624
6293.4893.8788236637521-0.398823663752083
6392.8693.269354256399-0.409354256399041
6490.9892.629370776245-1.64937077624502
6591.4590.66885330840770.781146691592326
6691.1691.1769866102234-0.016986610223384
6790.7190.8861573734853-0.176157373485324
6890.3190.4275578846025-0.117557884602519
6989.7890.0218190517526-0.241819051752557
7091.0289.48001415136121.53998584863878
7190.7790.7951917662575-0.025191766257521
7290.6990.54396197774750.146038022252512

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 94.34 & 93.91 & 0.430000000000007 \tabularnewline
4 & 94.3 & 94.0809913451049 & 0.21900865489512 \tabularnewline
5 & 94.4 & 94.0516827084906 & 0.348317291509417 \tabularnewline
6 & 94.54 & 94.1686865421466 & 0.371313457853418 \tabularnewline
7 & 94.09 & 94.3268129815324 & -0.236812981532367 \tabularnewline
8 & 95.87 & 93.8652524628797 & 2.00474753712034 \tabularnewline
9 & 98.46 & 95.7431183870654 & 2.71688161293463 \tabularnewline
10 & 98.7 & 98.4657486185682 & 0.234251381431832 \tabularnewline
11 & 98.75 & 98.7171840873796 & 0.0328159126203502 \tabularnewline
12 & 98.72 & 98.7687860644651 & -0.048786064465105 \tabularnewline
13 & 98.72 & 98.7364044711732 & -0.0164044711732458 \tabularnewline
14 & 98.67 & 98.7356036527647 & -0.0656036527647359 \tabularnewline
15 & 98.82 & 98.6824010738919 & 0.137598926108112 \tabularnewline
16 & 99.39 & 98.8391182519012 & 0.550881748098831 \tabularnewline
17 & 99.33 & 99.4360106911717 & -0.10601069117169 \tabularnewline
18 & 99.22 & 99.3708355586061 & -0.150835558606133 \tabularnewline
19 & 99.05 & 99.2534722068276 & -0.203472206827556 \tabularnewline
20 & 98.83 & 99.0735392874955 & -0.243539287495537 \tabularnewline
21 & 98.84 & 98.8416504102155 & -0.00165041021548973 \tabularnewline
22 & 98.89 & 98.8515698420053 & 0.0384301579947248 \tabularnewline
23 & 98.8 & 98.9034458901655 & -0.103445890165517 \tabularnewline
24 & 99.4 & 98.8083959637001 & 0.591604036299955 \tabularnewline
25 & 98.89 & 99.4372763462382 & -0.54727634623822 \tabularnewline
26 & 98.85 & 98.9005599121647 & -0.0505599121646867 \tabularnewline
27 & 98.69 & 98.8580917248049 & -0.168091724804853 \tabularnewline
28 & 98.48 & 98.6898859773522 & -0.209885977352172 \tabularnewline
29 & 98.39 & 98.4696399564608 & -0.0796399564608379 \tabularnewline
30 & 98.35 & 98.3757521662045 & -0.0257521662045548 \tabularnewline
31 & 98.26 & 98.3344950206045 & -0.0744950206045445 \tabularnewline
32 & 98.06 & 98.240858391102 & -0.180858391101978 \tabularnewline
33 & 98.14 & 98.0320294122584 & 0.10797058774159 \tabularnewline
34 & 98.17 & 98.1173002212548 & 0.0526997787451648 \tabularnewline
35 & 98.41 & 98.1498728706562 & 0.260127129343786 \tabularnewline
36 & 98.64 & 98.402571517966 & 0.237428482034034 \tabularnewline
37 & 99.25 & 98.6441620835569 & 0.605837916443093 \tabularnewline
38 & 99.61 & 99.2837373225841 & 0.32626267741594 \tabularnewline
39 & 100.28 & 99.6596645143433 & 0.620335485656682 \tabularnewline
40 & 100.31 & 100.35994748239 & -0.0499474823903512 \tabularnewline
41 & 100.55 & 100.387509192065 & 0.162490807935171 \tabularnewline
42 & 100.45 & 100.635441519101 & -0.185441519101417 \tabularnewline
43 & 100.78 & 100.526388805324 & 0.253611194675855 \tabularnewline
44 & 100.68 & 100.868769363719 & -0.18876936371926 \tabularnewline
45 & 101.69 & 100.75955419428 & 0.930445805720396 \tabularnewline
46 & 98.09 & 101.814975843138 & -3.72497584313834 \tabularnewline
47 & 99.13 & 98.0331333932996 & 1.09686660670039 \tabularnewline
48 & 99.18 & 99.1266792199863 & 0.0533207800137347 \tabularnewline
49 & 96.22 & 99.1792821848573 & -2.95928218485729 \tabularnewline
50 & 96.11 & 96.0748186648455 & 0.0351813351544905 \tabularnewline
51 & 96 & 95.9665361149559 & 0.0334638850440854 \tabularnewline
52 & 95.96 & 95.8581697241641 & 0.101830275835908 \tabularnewline
53 & 97.95 & 95.8231407810529 & 2.1268592189471 \tabularnewline
54 & 98.43 & 97.9169678411795 & 0.51303215882055 \tabularnewline
55 & 98.32 & 98.4220125739602 & -0.102012573960167 \tabularnewline
56 & 97.45 & 98.3070326178089 & -0.857032617808898 \tabularnewline
57 & 96.42 & 97.3951947865378 & -0.975194786537841 \tabularnewline
58 & 95.36 & 96.3175886230292 & -0.957588623029238 \tabularnewline
59 & 95.1 & 95.210841941042 & -0.110841941042011 \tabularnewline
60 & 95.54 & 94.9454309609571 & 0.594569039042909 \tabularnewline
61 & 94.07 & 95.4144560862762 & -1.34445608627624 \tabularnewline
62 & 93.48 & 93.8788236637521 & -0.398823663752083 \tabularnewline
63 & 92.86 & 93.269354256399 & -0.409354256399041 \tabularnewline
64 & 90.98 & 92.629370776245 & -1.64937077624502 \tabularnewline
65 & 91.45 & 90.6688533084077 & 0.781146691592326 \tabularnewline
66 & 91.16 & 91.1769866102234 & -0.016986610223384 \tabularnewline
67 & 90.71 & 90.8861573734853 & -0.176157373485324 \tabularnewline
68 & 90.31 & 90.4275578846025 & -0.117557884602519 \tabularnewline
69 & 89.78 & 90.0218190517526 & -0.241819051752557 \tabularnewline
70 & 91.02 & 89.4800141513612 & 1.53998584863878 \tabularnewline
71 & 90.77 & 90.7951917662575 & -0.025191766257521 \tabularnewline
72 & 90.69 & 90.5439619777475 & 0.146038022252512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]94.34[/C][C]93.91[/C][C]0.430000000000007[/C][/ROW]
[ROW][C]4[/C][C]94.3[/C][C]94.0809913451049[/C][C]0.21900865489512[/C][/ROW]
[ROW][C]5[/C][C]94.4[/C][C]94.0516827084906[/C][C]0.348317291509417[/C][/ROW]
[ROW][C]6[/C][C]94.54[/C][C]94.1686865421466[/C][C]0.371313457853418[/C][/ROW]
[ROW][C]7[/C][C]94.09[/C][C]94.3268129815324[/C][C]-0.236812981532367[/C][/ROW]
[ROW][C]8[/C][C]95.87[/C][C]93.8652524628797[/C][C]2.00474753712034[/C][/ROW]
[ROW][C]9[/C][C]98.46[/C][C]95.7431183870654[/C][C]2.71688161293463[/C][/ROW]
[ROW][C]10[/C][C]98.7[/C][C]98.4657486185682[/C][C]0.234251381431832[/C][/ROW]
[ROW][C]11[/C][C]98.75[/C][C]98.7171840873796[/C][C]0.0328159126203502[/C][/ROW]
[ROW][C]12[/C][C]98.72[/C][C]98.7687860644651[/C][C]-0.048786064465105[/C][/ROW]
[ROW][C]13[/C][C]98.72[/C][C]98.7364044711732[/C][C]-0.0164044711732458[/C][/ROW]
[ROW][C]14[/C][C]98.67[/C][C]98.7356036527647[/C][C]-0.0656036527647359[/C][/ROW]
[ROW][C]15[/C][C]98.82[/C][C]98.6824010738919[/C][C]0.137598926108112[/C][/ROW]
[ROW][C]16[/C][C]99.39[/C][C]98.8391182519012[/C][C]0.550881748098831[/C][/ROW]
[ROW][C]17[/C][C]99.33[/C][C]99.4360106911717[/C][C]-0.10601069117169[/C][/ROW]
[ROW][C]18[/C][C]99.22[/C][C]99.3708355586061[/C][C]-0.150835558606133[/C][/ROW]
[ROW][C]19[/C][C]99.05[/C][C]99.2534722068276[/C][C]-0.203472206827556[/C][/ROW]
[ROW][C]20[/C][C]98.83[/C][C]99.0735392874955[/C][C]-0.243539287495537[/C][/ROW]
[ROW][C]21[/C][C]98.84[/C][C]98.8416504102155[/C][C]-0.00165041021548973[/C][/ROW]
[ROW][C]22[/C][C]98.89[/C][C]98.8515698420053[/C][C]0.0384301579947248[/C][/ROW]
[ROW][C]23[/C][C]98.8[/C][C]98.9034458901655[/C][C]-0.103445890165517[/C][/ROW]
[ROW][C]24[/C][C]99.4[/C][C]98.8083959637001[/C][C]0.591604036299955[/C][/ROW]
[ROW][C]25[/C][C]98.89[/C][C]99.4372763462382[/C][C]-0.54727634623822[/C][/ROW]
[ROW][C]26[/C][C]98.85[/C][C]98.9005599121647[/C][C]-0.0505599121646867[/C][/ROW]
[ROW][C]27[/C][C]98.69[/C][C]98.8580917248049[/C][C]-0.168091724804853[/C][/ROW]
[ROW][C]28[/C][C]98.48[/C][C]98.6898859773522[/C][C]-0.209885977352172[/C][/ROW]
[ROW][C]29[/C][C]98.39[/C][C]98.4696399564608[/C][C]-0.0796399564608379[/C][/ROW]
[ROW][C]30[/C][C]98.35[/C][C]98.3757521662045[/C][C]-0.0257521662045548[/C][/ROW]
[ROW][C]31[/C][C]98.26[/C][C]98.3344950206045[/C][C]-0.0744950206045445[/C][/ROW]
[ROW][C]32[/C][C]98.06[/C][C]98.240858391102[/C][C]-0.180858391101978[/C][/ROW]
[ROW][C]33[/C][C]98.14[/C][C]98.0320294122584[/C][C]0.10797058774159[/C][/ROW]
[ROW][C]34[/C][C]98.17[/C][C]98.1173002212548[/C][C]0.0526997787451648[/C][/ROW]
[ROW][C]35[/C][C]98.41[/C][C]98.1498728706562[/C][C]0.260127129343786[/C][/ROW]
[ROW][C]36[/C][C]98.64[/C][C]98.402571517966[/C][C]0.237428482034034[/C][/ROW]
[ROW][C]37[/C][C]99.25[/C][C]98.6441620835569[/C][C]0.605837916443093[/C][/ROW]
[ROW][C]38[/C][C]99.61[/C][C]99.2837373225841[/C][C]0.32626267741594[/C][/ROW]
[ROW][C]39[/C][C]100.28[/C][C]99.6596645143433[/C][C]0.620335485656682[/C][/ROW]
[ROW][C]40[/C][C]100.31[/C][C]100.35994748239[/C][C]-0.0499474823903512[/C][/ROW]
[ROW][C]41[/C][C]100.55[/C][C]100.387509192065[/C][C]0.162490807935171[/C][/ROW]
[ROW][C]42[/C][C]100.45[/C][C]100.635441519101[/C][C]-0.185441519101417[/C][/ROW]
[ROW][C]43[/C][C]100.78[/C][C]100.526388805324[/C][C]0.253611194675855[/C][/ROW]
[ROW][C]44[/C][C]100.68[/C][C]100.868769363719[/C][C]-0.18876936371926[/C][/ROW]
[ROW][C]45[/C][C]101.69[/C][C]100.75955419428[/C][C]0.930445805720396[/C][/ROW]
[ROW][C]46[/C][C]98.09[/C][C]101.814975843138[/C][C]-3.72497584313834[/C][/ROW]
[ROW][C]47[/C][C]99.13[/C][C]98.0331333932996[/C][C]1.09686660670039[/C][/ROW]
[ROW][C]48[/C][C]99.18[/C][C]99.1266792199863[/C][C]0.0533207800137347[/C][/ROW]
[ROW][C]49[/C][C]96.22[/C][C]99.1792821848573[/C][C]-2.95928218485729[/C][/ROW]
[ROW][C]50[/C][C]96.11[/C][C]96.0748186648455[/C][C]0.0351813351544905[/C][/ROW]
[ROW][C]51[/C][C]96[/C][C]95.9665361149559[/C][C]0.0334638850440854[/C][/ROW]
[ROW][C]52[/C][C]95.96[/C][C]95.8581697241641[/C][C]0.101830275835908[/C][/ROW]
[ROW][C]53[/C][C]97.95[/C][C]95.8231407810529[/C][C]2.1268592189471[/C][/ROW]
[ROW][C]54[/C][C]98.43[/C][C]97.9169678411795[/C][C]0.51303215882055[/C][/ROW]
[ROW][C]55[/C][C]98.32[/C][C]98.4220125739602[/C][C]-0.102012573960167[/C][/ROW]
[ROW][C]56[/C][C]97.45[/C][C]98.3070326178089[/C][C]-0.857032617808898[/C][/ROW]
[ROW][C]57[/C][C]96.42[/C][C]97.3951947865378[/C][C]-0.975194786537841[/C][/ROW]
[ROW][C]58[/C][C]95.36[/C][C]96.3175886230292[/C][C]-0.957588623029238[/C][/ROW]
[ROW][C]59[/C][C]95.1[/C][C]95.210841941042[/C][C]-0.110841941042011[/C][/ROW]
[ROW][C]60[/C][C]95.54[/C][C]94.9454309609571[/C][C]0.594569039042909[/C][/ROW]
[ROW][C]61[/C][C]94.07[/C][C]95.4144560862762[/C][C]-1.34445608627624[/C][/ROW]
[ROW][C]62[/C][C]93.48[/C][C]93.8788236637521[/C][C]-0.398823663752083[/C][/ROW]
[ROW][C]63[/C][C]92.86[/C][C]93.269354256399[/C][C]-0.409354256399041[/C][/ROW]
[ROW][C]64[/C][C]90.98[/C][C]92.629370776245[/C][C]-1.64937077624502[/C][/ROW]
[ROW][C]65[/C][C]91.45[/C][C]90.6688533084077[/C][C]0.781146691592326[/C][/ROW]
[ROW][C]66[/C][C]91.16[/C][C]91.1769866102234[/C][C]-0.016986610223384[/C][/ROW]
[ROW][C]67[/C][C]90.71[/C][C]90.8861573734853[/C][C]-0.176157373485324[/C][/ROW]
[ROW][C]68[/C][C]90.31[/C][C]90.4275578846025[/C][C]-0.117557884602519[/C][/ROW]
[ROW][C]69[/C][C]89.78[/C][C]90.0218190517526[/C][C]-0.241819051752557[/C][/ROW]
[ROW][C]70[/C][C]91.02[/C][C]89.4800141513612[/C][C]1.53998584863878[/C][/ROW]
[ROW][C]71[/C][C]90.77[/C][C]90.7951917662575[/C][C]-0.025191766257521[/C][/ROW]
[ROW][C]72[/C][C]90.69[/C][C]90.5439619777475[/C][C]0.146038022252512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
394.3493.910.430000000000007
494.394.08099134510490.21900865489512
594.494.05168270849060.348317291509417
694.5494.16868654214660.371313457853418
794.0994.3268129815324-0.236812981532367
895.8793.86525246287972.00474753712034
998.4695.74311838706542.71688161293463
1098.798.46574861856820.234251381431832
1198.7598.71718408737960.0328159126203502
1298.7298.7687860644651-0.048786064465105
1398.7298.7364044711732-0.0164044711732458
1498.6798.7356036527647-0.0656036527647359
1598.8298.68240107389190.137598926108112
1699.3998.83911825190120.550881748098831
1799.3399.4360106911717-0.10601069117169
1899.2299.3708355586061-0.150835558606133
1999.0599.2534722068276-0.203472206827556
2098.8399.0735392874955-0.243539287495537
2198.8498.8416504102155-0.00165041021548973
2298.8998.85156984200530.0384301579947248
2398.898.9034458901655-0.103445890165517
2499.498.80839596370010.591604036299955
2598.8999.4372763462382-0.54727634623822
2698.8598.9005599121647-0.0505599121646867
2798.6998.8580917248049-0.168091724804853
2898.4898.6898859773522-0.209885977352172
2998.3998.4696399564608-0.0796399564608379
3098.3598.3757521662045-0.0257521662045548
3198.2698.3344950206045-0.0744950206045445
3298.0698.240858391102-0.180858391101978
3398.1498.03202941225840.10797058774159
3498.1798.11730022125480.0526997787451648
3598.4198.14987287065620.260127129343786
3698.6498.4025715179660.237428482034034
3799.2598.64416208355690.605837916443093
3899.6199.28373732258410.32626267741594
39100.2899.65966451434330.620335485656682
40100.31100.35994748239-0.0499474823903512
41100.55100.3875091920650.162490807935171
42100.45100.635441519101-0.185441519101417
43100.78100.5263888053240.253611194675855
44100.68100.868769363719-0.18876936371926
45101.69100.759554194280.930445805720396
4698.09101.814975843138-3.72497584313834
4799.1398.03313339329961.09686660670039
4899.1899.12667921998630.0533207800137347
4996.2299.1792821848573-2.95928218485729
5096.1196.07481866484550.0351813351544905
519695.96653611495590.0334638850440854
5295.9695.85816972416410.101830275835908
5397.9595.82314078105292.1268592189471
5498.4397.91696784117950.51303215882055
5598.3298.4220125739602-0.102012573960167
5697.4598.3070326178089-0.857032617808898
5796.4297.3951947865378-0.975194786537841
5895.3696.3175886230292-0.957588623029238
5995.195.210841941042-0.110841941042011
6095.5494.94543096095710.594569039042909
6194.0795.4144560862762-1.34445608627624
6293.4893.8788236637521-0.398823663752083
6392.8693.269354256399-0.409354256399041
6490.9892.629370776245-1.64937077624502
6591.4590.66885330840770.781146691592326
6691.1691.1769866102234-0.016986610223384
6790.7190.8861573734853-0.176157373485324
6890.3190.4275578846025-0.117557884602519
6989.7890.0218190517526-0.241819051752557
7091.0289.48001415136121.53998584863878
7190.7790.7951917662575-0.025191766257521
7290.6990.54396197774750.146038022252512







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7390.471091127802288.723888993746192.2182932618584
7490.252182255604587.720235406463992.784129104745
7590.033273383406786.857006935820593.2095398309929
7689.814364511208986.059233848766893.569495173651
7789.595455639011185.298675683984393.8922355940379
7889.376546766813384.561242673302894.1918508603239
7989.157637894615683.838797533936994.4764782552943
8088.938729022417883.126191221479994.7512668233556
8188.7198201502282.419954903644195.0196853967959
8288.500911278022281.717642744886695.2841798111579
8388.282002405824581.017469716974695.5465350946743
8488.063093533626780.318097626175995.8080894410775

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 90.4710911278022 & 88.7238889937461 & 92.2182932618584 \tabularnewline
74 & 90.2521822556045 & 87.7202354064639 & 92.784129104745 \tabularnewline
75 & 90.0332733834067 & 86.8570069358205 & 93.2095398309929 \tabularnewline
76 & 89.8143645112089 & 86.0592338487668 & 93.569495173651 \tabularnewline
77 & 89.5954556390111 & 85.2986756839843 & 93.8922355940379 \tabularnewline
78 & 89.3765467668133 & 84.5612426733028 & 94.1918508603239 \tabularnewline
79 & 89.1576378946156 & 83.8387975339369 & 94.4764782552943 \tabularnewline
80 & 88.9387290224178 & 83.1261912214799 & 94.7512668233556 \tabularnewline
81 & 88.71982015022 & 82.4199549036441 & 95.0196853967959 \tabularnewline
82 & 88.5009112780222 & 81.7176427448866 & 95.2841798111579 \tabularnewline
83 & 88.2820024058245 & 81.0174697169746 & 95.5465350946743 \tabularnewline
84 & 88.0630935336267 & 80.3180976261759 & 95.8080894410775 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]90.4710911278022[/C][C]88.7238889937461[/C][C]92.2182932618584[/C][/ROW]
[ROW][C]74[/C][C]90.2521822556045[/C][C]87.7202354064639[/C][C]92.784129104745[/C][/ROW]
[ROW][C]75[/C][C]90.0332733834067[/C][C]86.8570069358205[/C][C]93.2095398309929[/C][/ROW]
[ROW][C]76[/C][C]89.8143645112089[/C][C]86.0592338487668[/C][C]93.569495173651[/C][/ROW]
[ROW][C]77[/C][C]89.5954556390111[/C][C]85.2986756839843[/C][C]93.8922355940379[/C][/ROW]
[ROW][C]78[/C][C]89.3765467668133[/C][C]84.5612426733028[/C][C]94.1918508603239[/C][/ROW]
[ROW][C]79[/C][C]89.1576378946156[/C][C]83.8387975339369[/C][C]94.4764782552943[/C][/ROW]
[ROW][C]80[/C][C]88.9387290224178[/C][C]83.1261912214799[/C][C]94.7512668233556[/C][/ROW]
[ROW][C]81[/C][C]88.71982015022[/C][C]82.4199549036441[/C][C]95.0196853967959[/C][/ROW]
[ROW][C]82[/C][C]88.5009112780222[/C][C]81.7176427448866[/C][C]95.2841798111579[/C][/ROW]
[ROW][C]83[/C][C]88.2820024058245[/C][C]81.0174697169746[/C][C]95.5465350946743[/C][/ROW]
[ROW][C]84[/C][C]88.0630935336267[/C][C]80.3180976261759[/C][C]95.8080894410775[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
7390.471091127802288.723888993746192.2182932618584
7490.252182255604587.720235406463992.784129104745
7590.033273383406786.857006935820593.2095398309929
7689.814364511208986.059233848766893.569495173651
7789.595455639011185.298675683984393.8922355940379
7889.376546766813384.561242673302894.1918508603239
7989.157637894615683.838797533936994.4764782552943
8088.938729022417883.126191221479994.7512668233556
8188.7198201502282.419954903644195.0196853967959
8288.500911278022281.717642744886695.2841798111579
8388.282002405824581.017469716974695.5465350946743
8488.063093533626780.318097626175995.8080894410775



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')