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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 29 Nov 2014 11:21:34 +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/2014/Nov/29/t1417260190unlgk0t8j39tnni.htm/, Retrieved Sun, 19 May 2024 13:35:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261084, Retrieved Sun, 19 May 2024 13:35:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [paper 11] [2014-11-29 11:21:34] [7e6d0f152da1c8c00143095b938e0e97] [Current]
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Dataseries X:
4.8
4
3.5
4.1
4.1
3.8
3.5
4.1
4.5
4.1
3.8
4.6
5.2
4.4
4.3
4.7
5.1
4.6
4.7
4.9
5.1
4.6
4.6
4.8
5.1
4.8
4.4
4.8
4.7
4
3.5
4
3.7
3.1
2.9
3.3
3.5
3
2.7
3.2
3.8
3.3
3.1
3.5
3.9
3.4
3.2
3.6
3.9
3.2
3
3.4
3.6
3
3
3.6
3.6
3.3
3.3
3.6
3.8
3.3
3.1
3.4
3.5
3.1
3
3.3
3.7
3.1
2.9
3.1
3.2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261084&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261084&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261084&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.511485164824243
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.511485164824243 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261084&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]0.511485164824243[/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=261084&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261084&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
alpha0.511485164824243
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
244.8-0.8
33.54.39081186814061-0.890811868140606
44.13.935174812937320.164825187062684
54.14.019480450909260.0805195490907398
63.84.06066500574751-0.260665005747511
73.53.92733872231883-0.427338722318833
84.13.70876130549780.391238694502197
94.53.908874093640880.591125906359119
104.14.21122622528686-0.111226225286856
113.84.15433566111323-0.35433566111323
124.63.973098227085620.626901772914378
135.24.293749183733340.906250816266657
144.44.7572830318636-0.357283031863599
154.34.57453806142194-0.274538061421941
164.74.434115915825010.265884084174989
175.14.57011168044340.529888319556601
184.64.84114169491025-0.241141694910248
194.74.71780129534308-0.0178012953430819
204.94.708696196860440.19130380313956
215.14.806545254140780.293454745859217
224.64.95664300319504-0.356643003195041
234.64.77422539792241-0.174225397922412
244.84.68511169154950.114888308450502
255.14.743875356933680.356124643066319
264.84.92602782869043-0.126027828690431
274.44.86156646396026-0.461566463960263
284.84.62548206506420.174517934935795
294.74.71474539977963-0.0147453997796259
3044.70720334654295-0.707203346542945
313.54.34547932627217-0.84547932627217
3243.913029193718360.086970806281641
333.73.95751347090422-0.257513470904221
343.13.82579915079431-0.725799150794313
352.93.45456365252099-0.554563652520988
363.33.170912571305760.129087428694244
373.53.236938876048170.263061123951831
3833.37149073839152-0.371490738391522
392.73.18147873683465-0.481478736834654
403.22.935209505765410.264790494234587
413.83.070645915352880.729354084647116
423.33.44369970955385-0.143699709553849
433.13.3701994399275-0.270199439927503
443.53.231996434860770.268003565139234
453.93.369076282549490.530923717450508
463.43.64063588767876-0.240635887678765
473.23.51755420100676-0.317554201006764
483.63.355129938164190.244870061835812
493.93.48037734210280.419622657897199
503.23.69500810644134-0.495008106441337
5133.44181880352885-0.441818803528853
523.43.215835039983450.184164960016552
533.63.310032684912360.289967315087636
5433.45834666486361-0.458346664863607
5533.2239091454392-0.223909145439203
563.63.109382939278580.490617060721423
573.63.360326287447260.23967371255274
583.33.48291583581634-0.182915835816337
593.33.38935709938485-0.0893570993848534
603.63.343652268677780.256347731322225
613.83.474770330285440.325229669714556
623.33.64112048150513-0.341120481505128
633.13.46664241579755-0.366642415797552
643.43.279110259321780.120889740678217
653.53.340943568258140.15905643174186
663.13.42229857346398-0.322298573463981
6733.25744763449314-0.257447634493138
683.33.12576698873080.174233011269196
693.73.214884589217650.485115410782348
703.13.46301392506044-0.363013925060442
712.93.27733768776741-0.377337687767406
723.13.08433505834530.0156649416547046
733.23.092347443609510.107652556390486

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 4 & 4.8 & -0.8 \tabularnewline
3 & 3.5 & 4.39081186814061 & -0.890811868140606 \tabularnewline
4 & 4.1 & 3.93517481293732 & 0.164825187062684 \tabularnewline
5 & 4.1 & 4.01948045090926 & 0.0805195490907398 \tabularnewline
6 & 3.8 & 4.06066500574751 & -0.260665005747511 \tabularnewline
7 & 3.5 & 3.92733872231883 & -0.427338722318833 \tabularnewline
8 & 4.1 & 3.7087613054978 & 0.391238694502197 \tabularnewline
9 & 4.5 & 3.90887409364088 & 0.591125906359119 \tabularnewline
10 & 4.1 & 4.21122622528686 & -0.111226225286856 \tabularnewline
11 & 3.8 & 4.15433566111323 & -0.35433566111323 \tabularnewline
12 & 4.6 & 3.97309822708562 & 0.626901772914378 \tabularnewline
13 & 5.2 & 4.29374918373334 & 0.906250816266657 \tabularnewline
14 & 4.4 & 4.7572830318636 & -0.357283031863599 \tabularnewline
15 & 4.3 & 4.57453806142194 & -0.274538061421941 \tabularnewline
16 & 4.7 & 4.43411591582501 & 0.265884084174989 \tabularnewline
17 & 5.1 & 4.5701116804434 & 0.529888319556601 \tabularnewline
18 & 4.6 & 4.84114169491025 & -0.241141694910248 \tabularnewline
19 & 4.7 & 4.71780129534308 & -0.0178012953430819 \tabularnewline
20 & 4.9 & 4.70869619686044 & 0.19130380313956 \tabularnewline
21 & 5.1 & 4.80654525414078 & 0.293454745859217 \tabularnewline
22 & 4.6 & 4.95664300319504 & -0.356643003195041 \tabularnewline
23 & 4.6 & 4.77422539792241 & -0.174225397922412 \tabularnewline
24 & 4.8 & 4.6851116915495 & 0.114888308450502 \tabularnewline
25 & 5.1 & 4.74387535693368 & 0.356124643066319 \tabularnewline
26 & 4.8 & 4.92602782869043 & -0.126027828690431 \tabularnewline
27 & 4.4 & 4.86156646396026 & -0.461566463960263 \tabularnewline
28 & 4.8 & 4.6254820650642 & 0.174517934935795 \tabularnewline
29 & 4.7 & 4.71474539977963 & -0.0147453997796259 \tabularnewline
30 & 4 & 4.70720334654295 & -0.707203346542945 \tabularnewline
31 & 3.5 & 4.34547932627217 & -0.84547932627217 \tabularnewline
32 & 4 & 3.91302919371836 & 0.086970806281641 \tabularnewline
33 & 3.7 & 3.95751347090422 & -0.257513470904221 \tabularnewline
34 & 3.1 & 3.82579915079431 & -0.725799150794313 \tabularnewline
35 & 2.9 & 3.45456365252099 & -0.554563652520988 \tabularnewline
36 & 3.3 & 3.17091257130576 & 0.129087428694244 \tabularnewline
37 & 3.5 & 3.23693887604817 & 0.263061123951831 \tabularnewline
38 & 3 & 3.37149073839152 & -0.371490738391522 \tabularnewline
39 & 2.7 & 3.18147873683465 & -0.481478736834654 \tabularnewline
40 & 3.2 & 2.93520950576541 & 0.264790494234587 \tabularnewline
41 & 3.8 & 3.07064591535288 & 0.729354084647116 \tabularnewline
42 & 3.3 & 3.44369970955385 & -0.143699709553849 \tabularnewline
43 & 3.1 & 3.3701994399275 & -0.270199439927503 \tabularnewline
44 & 3.5 & 3.23199643486077 & 0.268003565139234 \tabularnewline
45 & 3.9 & 3.36907628254949 & 0.530923717450508 \tabularnewline
46 & 3.4 & 3.64063588767876 & -0.240635887678765 \tabularnewline
47 & 3.2 & 3.51755420100676 & -0.317554201006764 \tabularnewline
48 & 3.6 & 3.35512993816419 & 0.244870061835812 \tabularnewline
49 & 3.9 & 3.4803773421028 & 0.419622657897199 \tabularnewline
50 & 3.2 & 3.69500810644134 & -0.495008106441337 \tabularnewline
51 & 3 & 3.44181880352885 & -0.441818803528853 \tabularnewline
52 & 3.4 & 3.21583503998345 & 0.184164960016552 \tabularnewline
53 & 3.6 & 3.31003268491236 & 0.289967315087636 \tabularnewline
54 & 3 & 3.45834666486361 & -0.458346664863607 \tabularnewline
55 & 3 & 3.2239091454392 & -0.223909145439203 \tabularnewline
56 & 3.6 & 3.10938293927858 & 0.490617060721423 \tabularnewline
57 & 3.6 & 3.36032628744726 & 0.23967371255274 \tabularnewline
58 & 3.3 & 3.48291583581634 & -0.182915835816337 \tabularnewline
59 & 3.3 & 3.38935709938485 & -0.0893570993848534 \tabularnewline
60 & 3.6 & 3.34365226867778 & 0.256347731322225 \tabularnewline
61 & 3.8 & 3.47477033028544 & 0.325229669714556 \tabularnewline
62 & 3.3 & 3.64112048150513 & -0.341120481505128 \tabularnewline
63 & 3.1 & 3.46664241579755 & -0.366642415797552 \tabularnewline
64 & 3.4 & 3.27911025932178 & 0.120889740678217 \tabularnewline
65 & 3.5 & 3.34094356825814 & 0.15905643174186 \tabularnewline
66 & 3.1 & 3.42229857346398 & -0.322298573463981 \tabularnewline
67 & 3 & 3.25744763449314 & -0.257447634493138 \tabularnewline
68 & 3.3 & 3.1257669887308 & 0.174233011269196 \tabularnewline
69 & 3.7 & 3.21488458921765 & 0.485115410782348 \tabularnewline
70 & 3.1 & 3.46301392506044 & -0.363013925060442 \tabularnewline
71 & 2.9 & 3.27733768776741 & -0.377337687767406 \tabularnewline
72 & 3.1 & 3.0843350583453 & 0.0156649416547046 \tabularnewline
73 & 3.2 & 3.09234744360951 & 0.107652556390486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261084&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]4[/C][C]4.8[/C][C]-0.8[/C][/ROW]
[ROW][C]3[/C][C]3.5[/C][C]4.39081186814061[/C][C]-0.890811868140606[/C][/ROW]
[ROW][C]4[/C][C]4.1[/C][C]3.93517481293732[/C][C]0.164825187062684[/C][/ROW]
[ROW][C]5[/C][C]4.1[/C][C]4.01948045090926[/C][C]0.0805195490907398[/C][/ROW]
[ROW][C]6[/C][C]3.8[/C][C]4.06066500574751[/C][C]-0.260665005747511[/C][/ROW]
[ROW][C]7[/C][C]3.5[/C][C]3.92733872231883[/C][C]-0.427338722318833[/C][/ROW]
[ROW][C]8[/C][C]4.1[/C][C]3.7087613054978[/C][C]0.391238694502197[/C][/ROW]
[ROW][C]9[/C][C]4.5[/C][C]3.90887409364088[/C][C]0.591125906359119[/C][/ROW]
[ROW][C]10[/C][C]4.1[/C][C]4.21122622528686[/C][C]-0.111226225286856[/C][/ROW]
[ROW][C]11[/C][C]3.8[/C][C]4.15433566111323[/C][C]-0.35433566111323[/C][/ROW]
[ROW][C]12[/C][C]4.6[/C][C]3.97309822708562[/C][C]0.626901772914378[/C][/ROW]
[ROW][C]13[/C][C]5.2[/C][C]4.29374918373334[/C][C]0.906250816266657[/C][/ROW]
[ROW][C]14[/C][C]4.4[/C][C]4.7572830318636[/C][C]-0.357283031863599[/C][/ROW]
[ROW][C]15[/C][C]4.3[/C][C]4.57453806142194[/C][C]-0.274538061421941[/C][/ROW]
[ROW][C]16[/C][C]4.7[/C][C]4.43411591582501[/C][C]0.265884084174989[/C][/ROW]
[ROW][C]17[/C][C]5.1[/C][C]4.5701116804434[/C][C]0.529888319556601[/C][/ROW]
[ROW][C]18[/C][C]4.6[/C][C]4.84114169491025[/C][C]-0.241141694910248[/C][/ROW]
[ROW][C]19[/C][C]4.7[/C][C]4.71780129534308[/C][C]-0.0178012953430819[/C][/ROW]
[ROW][C]20[/C][C]4.9[/C][C]4.70869619686044[/C][C]0.19130380313956[/C][/ROW]
[ROW][C]21[/C][C]5.1[/C][C]4.80654525414078[/C][C]0.293454745859217[/C][/ROW]
[ROW][C]22[/C][C]4.6[/C][C]4.95664300319504[/C][C]-0.356643003195041[/C][/ROW]
[ROW][C]23[/C][C]4.6[/C][C]4.77422539792241[/C][C]-0.174225397922412[/C][/ROW]
[ROW][C]24[/C][C]4.8[/C][C]4.6851116915495[/C][C]0.114888308450502[/C][/ROW]
[ROW][C]25[/C][C]5.1[/C][C]4.74387535693368[/C][C]0.356124643066319[/C][/ROW]
[ROW][C]26[/C][C]4.8[/C][C]4.92602782869043[/C][C]-0.126027828690431[/C][/ROW]
[ROW][C]27[/C][C]4.4[/C][C]4.86156646396026[/C][C]-0.461566463960263[/C][/ROW]
[ROW][C]28[/C][C]4.8[/C][C]4.6254820650642[/C][C]0.174517934935795[/C][/ROW]
[ROW][C]29[/C][C]4.7[/C][C]4.71474539977963[/C][C]-0.0147453997796259[/C][/ROW]
[ROW][C]30[/C][C]4[/C][C]4.70720334654295[/C][C]-0.707203346542945[/C][/ROW]
[ROW][C]31[/C][C]3.5[/C][C]4.34547932627217[/C][C]-0.84547932627217[/C][/ROW]
[ROW][C]32[/C][C]4[/C][C]3.91302919371836[/C][C]0.086970806281641[/C][/ROW]
[ROW][C]33[/C][C]3.7[/C][C]3.95751347090422[/C][C]-0.257513470904221[/C][/ROW]
[ROW][C]34[/C][C]3.1[/C][C]3.82579915079431[/C][C]-0.725799150794313[/C][/ROW]
[ROW][C]35[/C][C]2.9[/C][C]3.45456365252099[/C][C]-0.554563652520988[/C][/ROW]
[ROW][C]36[/C][C]3.3[/C][C]3.17091257130576[/C][C]0.129087428694244[/C][/ROW]
[ROW][C]37[/C][C]3.5[/C][C]3.23693887604817[/C][C]0.263061123951831[/C][/ROW]
[ROW][C]38[/C][C]3[/C][C]3.37149073839152[/C][C]-0.371490738391522[/C][/ROW]
[ROW][C]39[/C][C]2.7[/C][C]3.18147873683465[/C][C]-0.481478736834654[/C][/ROW]
[ROW][C]40[/C][C]3.2[/C][C]2.93520950576541[/C][C]0.264790494234587[/C][/ROW]
[ROW][C]41[/C][C]3.8[/C][C]3.07064591535288[/C][C]0.729354084647116[/C][/ROW]
[ROW][C]42[/C][C]3.3[/C][C]3.44369970955385[/C][C]-0.143699709553849[/C][/ROW]
[ROW][C]43[/C][C]3.1[/C][C]3.3701994399275[/C][C]-0.270199439927503[/C][/ROW]
[ROW][C]44[/C][C]3.5[/C][C]3.23199643486077[/C][C]0.268003565139234[/C][/ROW]
[ROW][C]45[/C][C]3.9[/C][C]3.36907628254949[/C][C]0.530923717450508[/C][/ROW]
[ROW][C]46[/C][C]3.4[/C][C]3.64063588767876[/C][C]-0.240635887678765[/C][/ROW]
[ROW][C]47[/C][C]3.2[/C][C]3.51755420100676[/C][C]-0.317554201006764[/C][/ROW]
[ROW][C]48[/C][C]3.6[/C][C]3.35512993816419[/C][C]0.244870061835812[/C][/ROW]
[ROW][C]49[/C][C]3.9[/C][C]3.4803773421028[/C][C]0.419622657897199[/C][/ROW]
[ROW][C]50[/C][C]3.2[/C][C]3.69500810644134[/C][C]-0.495008106441337[/C][/ROW]
[ROW][C]51[/C][C]3[/C][C]3.44181880352885[/C][C]-0.441818803528853[/C][/ROW]
[ROW][C]52[/C][C]3.4[/C][C]3.21583503998345[/C][C]0.184164960016552[/C][/ROW]
[ROW][C]53[/C][C]3.6[/C][C]3.31003268491236[/C][C]0.289967315087636[/C][/ROW]
[ROW][C]54[/C][C]3[/C][C]3.45834666486361[/C][C]-0.458346664863607[/C][/ROW]
[ROW][C]55[/C][C]3[/C][C]3.2239091454392[/C][C]-0.223909145439203[/C][/ROW]
[ROW][C]56[/C][C]3.6[/C][C]3.10938293927858[/C][C]0.490617060721423[/C][/ROW]
[ROW][C]57[/C][C]3.6[/C][C]3.36032628744726[/C][C]0.23967371255274[/C][/ROW]
[ROW][C]58[/C][C]3.3[/C][C]3.48291583581634[/C][C]-0.182915835816337[/C][/ROW]
[ROW][C]59[/C][C]3.3[/C][C]3.38935709938485[/C][C]-0.0893570993848534[/C][/ROW]
[ROW][C]60[/C][C]3.6[/C][C]3.34365226867778[/C][C]0.256347731322225[/C][/ROW]
[ROW][C]61[/C][C]3.8[/C][C]3.47477033028544[/C][C]0.325229669714556[/C][/ROW]
[ROW][C]62[/C][C]3.3[/C][C]3.64112048150513[/C][C]-0.341120481505128[/C][/ROW]
[ROW][C]63[/C][C]3.1[/C][C]3.46664241579755[/C][C]-0.366642415797552[/C][/ROW]
[ROW][C]64[/C][C]3.4[/C][C]3.27911025932178[/C][C]0.120889740678217[/C][/ROW]
[ROW][C]65[/C][C]3.5[/C][C]3.34094356825814[/C][C]0.15905643174186[/C][/ROW]
[ROW][C]66[/C][C]3.1[/C][C]3.42229857346398[/C][C]-0.322298573463981[/C][/ROW]
[ROW][C]67[/C][C]3[/C][C]3.25744763449314[/C][C]-0.257447634493138[/C][/ROW]
[ROW][C]68[/C][C]3.3[/C][C]3.1257669887308[/C][C]0.174233011269196[/C][/ROW]
[ROW][C]69[/C][C]3.7[/C][C]3.21488458921765[/C][C]0.485115410782348[/C][/ROW]
[ROW][C]70[/C][C]3.1[/C][C]3.46301392506044[/C][C]-0.363013925060442[/C][/ROW]
[ROW][C]71[/C][C]2.9[/C][C]3.27733768776741[/C][C]-0.377337687767406[/C][/ROW]
[ROW][C]72[/C][C]3.1[/C][C]3.0843350583453[/C][C]0.0156649416547046[/C][/ROW]
[ROW][C]73[/C][C]3.2[/C][C]3.09234744360951[/C][C]0.107652556390486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261084&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261084&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
244.8-0.8
33.54.39081186814061-0.890811868140606
44.13.935174812937320.164825187062684
54.14.019480450909260.0805195490907398
63.84.06066500574751-0.260665005747511
73.53.92733872231883-0.427338722318833
84.13.70876130549780.391238694502197
94.53.908874093640880.591125906359119
104.14.21122622528686-0.111226225286856
113.84.15433566111323-0.35433566111323
124.63.973098227085620.626901772914378
135.24.293749183733340.906250816266657
144.44.7572830318636-0.357283031863599
154.34.57453806142194-0.274538061421941
164.74.434115915825010.265884084174989
175.14.57011168044340.529888319556601
184.64.84114169491025-0.241141694910248
194.74.71780129534308-0.0178012953430819
204.94.708696196860440.19130380313956
215.14.806545254140780.293454745859217
224.64.95664300319504-0.356643003195041
234.64.77422539792241-0.174225397922412
244.84.68511169154950.114888308450502
255.14.743875356933680.356124643066319
264.84.92602782869043-0.126027828690431
274.44.86156646396026-0.461566463960263
284.84.62548206506420.174517934935795
294.74.71474539977963-0.0147453997796259
3044.70720334654295-0.707203346542945
313.54.34547932627217-0.84547932627217
3243.913029193718360.086970806281641
333.73.95751347090422-0.257513470904221
343.13.82579915079431-0.725799150794313
352.93.45456365252099-0.554563652520988
363.33.170912571305760.129087428694244
373.53.236938876048170.263061123951831
3833.37149073839152-0.371490738391522
392.73.18147873683465-0.481478736834654
403.22.935209505765410.264790494234587
413.83.070645915352880.729354084647116
423.33.44369970955385-0.143699709553849
433.13.3701994399275-0.270199439927503
443.53.231996434860770.268003565139234
453.93.369076282549490.530923717450508
463.43.64063588767876-0.240635887678765
473.23.51755420100676-0.317554201006764
483.63.355129938164190.244870061835812
493.93.48037734210280.419622657897199
503.23.69500810644134-0.495008106441337
5133.44181880352885-0.441818803528853
523.43.215835039983450.184164960016552
533.63.310032684912360.289967315087636
5433.45834666486361-0.458346664863607
5533.2239091454392-0.223909145439203
563.63.109382939278580.490617060721423
573.63.360326287447260.23967371255274
583.33.48291583581634-0.182915835816337
593.33.38935709938485-0.0893570993848534
603.63.343652268677780.256347731322225
613.83.474770330285440.325229669714556
623.33.64112048150513-0.341120481505128
633.13.46664241579755-0.366642415797552
643.43.279110259321780.120889740678217
653.53.340943568258140.15905643174186
663.13.42229857346398-0.322298573463981
6733.25744763449314-0.257447634493138
683.33.12576698873080.174233011269196
693.73.214884589217650.485115410782348
703.13.46301392506044-0.363013925060442
712.93.27733768776741-0.377337687767406
723.13.08433505834530.0156649416547046
733.23.092347443609510.107652556390486







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
743.147410129158652.372953897036813.9218663612805
753.147410129158652.277527501207744.01729275710956
763.147410129158652.191581108177814.1032391501395
773.147410129158652.11274958178694.18207067653041

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 3.14741012915865 & 2.37295389703681 & 3.9218663612805 \tabularnewline
75 & 3.14741012915865 & 2.27752750120774 & 4.01729275710956 \tabularnewline
76 & 3.14741012915865 & 2.19158110817781 & 4.1032391501395 \tabularnewline
77 & 3.14741012915865 & 2.1127495817869 & 4.18207067653041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261084&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]74[/C][C]3.14741012915865[/C][C]2.37295389703681[/C][C]3.9218663612805[/C][/ROW]
[ROW][C]75[/C][C]3.14741012915865[/C][C]2.27752750120774[/C][C]4.01729275710956[/C][/ROW]
[ROW][C]76[/C][C]3.14741012915865[/C][C]2.19158110817781[/C][C]4.1032391501395[/C][/ROW]
[ROW][C]77[/C][C]3.14741012915865[/C][C]2.1127495817869[/C][C]4.18207067653041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261084&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261084&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
743.147410129158652.372953897036813.9218663612805
753.147410129158652.277527501207744.01729275710956
763.147410129158652.191581108177814.1032391501395
773.147410129158652.11274958178694.18207067653041



Parameters (Session):
par1 = 4 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 4 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '4'
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')