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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 15:53:30 +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/2016/Apr/25/t1461596058g7fmvt2mh145vk9.htm/, Retrieved Mon, 06 May 2024 08:38:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294728, Retrieved Mon, 06 May 2024 08:38:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 14:53:30] [1af9caed13b550360754d0d82088541b] [Current]
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Dataseries X:
103,71
103,07
103,93
102,9
101,54
102,13
101,08
101,33
101,24
100,58
99,87
99,1
98,98
98,77
98,05
97,94
97,65
97,2
97,39
97,35
98,01
97,81
97,56
98,05
97,82
99,05
98,86
97,64
97,77
98,07
98,36
100
99,52
98,82
98,98
98,6
98,8
99,62
99,35
99,87
99,53
99,88
99,26
99,51
100,64
100,85
101,44
101,26
101,67
102,93
103,81
106,19
106,94
108,51
108,41
108,97
109,25
109,97
108,92
109,01
108,86
107,36
107,99
107,94
108,54
108,37
108,77
107,15
108,61
109,02
109,16
109,55




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=294728&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=294728&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294728&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
alpha0.99994924009082
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99994924009082 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294728&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]0.99994924009082[/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=294728&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294728&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
alpha0.99994924009082
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2103.07103.71-0.640000000000001
3103.93103.0700324863420.859967513658134
4102.9103.929956348127-1.02995634812712
5101.54102.900052280491-1.36005228049068
6102.13101.540069036130.589930963869747
7101.08102.129970055158-1.04997005515784
8101.33101.0800532963850.249946703615365
9101.24101.329987312728-0.0899873127280273
10100.58101.240004567748-0.660004567747819
1199.87100.580033501772-0.710033501771917
1299.199.8700360412361-0.770036041236068
1398.9899.1000390869595-0.120039086959508
1498.7798.9800060931732-0.210006093173163
1598.0598.7700106598902-0.720010659890221
1697.9498.0500365476757-0.110036547675705
1797.6597.9400055854452-0.290005585445158
1897.297.6500147206572-0.45001472065718
1997.3997.20002284270640.18997715729364
2097.3597.3899903567767-0.0399903567767552
2198.0197.35000202990690.65999797009313
2297.8198.009966498563-0.199966498562972
2397.5697.8100101502813-0.250010150281312
2498.0597.56001269049250.48998730950747
2597.8298.0499751282887-0.229975128288672
2699.0597.82001167351661.22998832648338
2798.8699.0499375659042-0.189937565904245
2897.6498.8600096412136-1.22000964121359
2997.7797.64006192757860.12993807242141
3098.0797.76999340435520.30000659564476
3198.3698.06998477169240.290015228307567
3210098.35998527885331.64001472114666
3399.5299.9999167530017-0.479916753001703
3498.8299.5200243605308-0.70002436053079
3598.9898.8200355331730.159964466827049
3698.698.9799918802182-0.379991880218213
3798.898.60001928835330.199980711646674
3899.6298.79998984899720.820010151002762
3999.3599.6199583763592-0.269958376359213
4099.8799.35001370306270.519986296937347
4199.5399.8699736055428-0.339973605542795
4299.8899.53001725702930.349982742970653
4399.2699.8799822349077-0.619982234907738
4499.5199.26003147024190.249968529758064
45100.6499.50998731162011.13001268837986
46100.85100.6399426406590.210057359341434
47101.44100.8499893375080.590010662492489
48101.26101.439970051112-0.179970051112349
49101.67101.2600091352630.409990864736542
50102.93101.6699791889011.26002081109905
51103.81102.9299360414580.880063958541925
52106.19103.8099553280332.3800446719666
53106.94106.1898791891490.750120810851399
54108.51106.9399619239361.57003807606424
55108.41108.50992030501-0.09992030500986
56108.97108.4100050719460.559994928054394
57109.25108.9699715747080.28002842529169
58109.97109.2499857857830.720014214217429
59108.92109.969963452144-1.04996345214387
60109.01108.9200532960490.0899467039505311
61108.86109.009995434313-0.149995434313482
62107.36108.860007613755-1.50000761375463
63107.99107.360076140250.629923859749752
64107.94107.989968025122-0.0499680251220838
65108.54107.9400025363720.599997463627588
66108.37108.539969544183-0.169969544183246
67108.77108.3700086276390.399991372361356
68107.15108.769979696474-1.61997969647425
69108.61107.1500822300221.45991776997774
70109.02108.6099258947070.410074105293418
71109.16109.0199791846760.140020815324348
72109.55109.1599928925560.390007107443864

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 103.07 & 103.71 & -0.640000000000001 \tabularnewline
3 & 103.93 & 103.070032486342 & 0.859967513658134 \tabularnewline
4 & 102.9 & 103.929956348127 & -1.02995634812712 \tabularnewline
5 & 101.54 & 102.900052280491 & -1.36005228049068 \tabularnewline
6 & 102.13 & 101.54006903613 & 0.589930963869747 \tabularnewline
7 & 101.08 & 102.129970055158 & -1.04997005515784 \tabularnewline
8 & 101.33 & 101.080053296385 & 0.249946703615365 \tabularnewline
9 & 101.24 & 101.329987312728 & -0.0899873127280273 \tabularnewline
10 & 100.58 & 101.240004567748 & -0.660004567747819 \tabularnewline
11 & 99.87 & 100.580033501772 & -0.710033501771917 \tabularnewline
12 & 99.1 & 99.8700360412361 & -0.770036041236068 \tabularnewline
13 & 98.98 & 99.1000390869595 & -0.120039086959508 \tabularnewline
14 & 98.77 & 98.9800060931732 & -0.210006093173163 \tabularnewline
15 & 98.05 & 98.7700106598902 & -0.720010659890221 \tabularnewline
16 & 97.94 & 98.0500365476757 & -0.110036547675705 \tabularnewline
17 & 97.65 & 97.9400055854452 & -0.290005585445158 \tabularnewline
18 & 97.2 & 97.6500147206572 & -0.45001472065718 \tabularnewline
19 & 97.39 & 97.2000228427064 & 0.18997715729364 \tabularnewline
20 & 97.35 & 97.3899903567767 & -0.0399903567767552 \tabularnewline
21 & 98.01 & 97.3500020299069 & 0.65999797009313 \tabularnewline
22 & 97.81 & 98.009966498563 & -0.199966498562972 \tabularnewline
23 & 97.56 & 97.8100101502813 & -0.250010150281312 \tabularnewline
24 & 98.05 & 97.5600126904925 & 0.48998730950747 \tabularnewline
25 & 97.82 & 98.0499751282887 & -0.229975128288672 \tabularnewline
26 & 99.05 & 97.8200116735166 & 1.22998832648338 \tabularnewline
27 & 98.86 & 99.0499375659042 & -0.189937565904245 \tabularnewline
28 & 97.64 & 98.8600096412136 & -1.22000964121359 \tabularnewline
29 & 97.77 & 97.6400619275786 & 0.12993807242141 \tabularnewline
30 & 98.07 & 97.7699934043552 & 0.30000659564476 \tabularnewline
31 & 98.36 & 98.0699847716924 & 0.290015228307567 \tabularnewline
32 & 100 & 98.3599852788533 & 1.64001472114666 \tabularnewline
33 & 99.52 & 99.9999167530017 & -0.479916753001703 \tabularnewline
34 & 98.82 & 99.5200243605308 & -0.70002436053079 \tabularnewline
35 & 98.98 & 98.820035533173 & 0.159964466827049 \tabularnewline
36 & 98.6 & 98.9799918802182 & -0.379991880218213 \tabularnewline
37 & 98.8 & 98.6000192883533 & 0.199980711646674 \tabularnewline
38 & 99.62 & 98.7999898489972 & 0.820010151002762 \tabularnewline
39 & 99.35 & 99.6199583763592 & -0.269958376359213 \tabularnewline
40 & 99.87 & 99.3500137030627 & 0.519986296937347 \tabularnewline
41 & 99.53 & 99.8699736055428 & -0.339973605542795 \tabularnewline
42 & 99.88 & 99.5300172570293 & 0.349982742970653 \tabularnewline
43 & 99.26 & 99.8799822349077 & -0.619982234907738 \tabularnewline
44 & 99.51 & 99.2600314702419 & 0.249968529758064 \tabularnewline
45 & 100.64 & 99.5099873116201 & 1.13001268837986 \tabularnewline
46 & 100.85 & 100.639942640659 & 0.210057359341434 \tabularnewline
47 & 101.44 & 100.849989337508 & 0.590010662492489 \tabularnewline
48 & 101.26 & 101.439970051112 & -0.179970051112349 \tabularnewline
49 & 101.67 & 101.260009135263 & 0.409990864736542 \tabularnewline
50 & 102.93 & 101.669979188901 & 1.26002081109905 \tabularnewline
51 & 103.81 & 102.929936041458 & 0.880063958541925 \tabularnewline
52 & 106.19 & 103.809955328033 & 2.3800446719666 \tabularnewline
53 & 106.94 & 106.189879189149 & 0.750120810851399 \tabularnewline
54 & 108.51 & 106.939961923936 & 1.57003807606424 \tabularnewline
55 & 108.41 & 108.50992030501 & -0.09992030500986 \tabularnewline
56 & 108.97 & 108.410005071946 & 0.559994928054394 \tabularnewline
57 & 109.25 & 108.969971574708 & 0.28002842529169 \tabularnewline
58 & 109.97 & 109.249985785783 & 0.720014214217429 \tabularnewline
59 & 108.92 & 109.969963452144 & -1.04996345214387 \tabularnewline
60 & 109.01 & 108.920053296049 & 0.0899467039505311 \tabularnewline
61 & 108.86 & 109.009995434313 & -0.149995434313482 \tabularnewline
62 & 107.36 & 108.860007613755 & -1.50000761375463 \tabularnewline
63 & 107.99 & 107.36007614025 & 0.629923859749752 \tabularnewline
64 & 107.94 & 107.989968025122 & -0.0499680251220838 \tabularnewline
65 & 108.54 & 107.940002536372 & 0.599997463627588 \tabularnewline
66 & 108.37 & 108.539969544183 & -0.169969544183246 \tabularnewline
67 & 108.77 & 108.370008627639 & 0.399991372361356 \tabularnewline
68 & 107.15 & 108.769979696474 & -1.61997969647425 \tabularnewline
69 & 108.61 & 107.150082230022 & 1.45991776997774 \tabularnewline
70 & 109.02 & 108.609925894707 & 0.410074105293418 \tabularnewline
71 & 109.16 & 109.019979184676 & 0.140020815324348 \tabularnewline
72 & 109.55 & 109.159992892556 & 0.390007107443864 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294728&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]103.07[/C][C]103.71[/C][C]-0.640000000000001[/C][/ROW]
[ROW][C]3[/C][C]103.93[/C][C]103.070032486342[/C][C]0.859967513658134[/C][/ROW]
[ROW][C]4[/C][C]102.9[/C][C]103.929956348127[/C][C]-1.02995634812712[/C][/ROW]
[ROW][C]5[/C][C]101.54[/C][C]102.900052280491[/C][C]-1.36005228049068[/C][/ROW]
[ROW][C]6[/C][C]102.13[/C][C]101.54006903613[/C][C]0.589930963869747[/C][/ROW]
[ROW][C]7[/C][C]101.08[/C][C]102.129970055158[/C][C]-1.04997005515784[/C][/ROW]
[ROW][C]8[/C][C]101.33[/C][C]101.080053296385[/C][C]0.249946703615365[/C][/ROW]
[ROW][C]9[/C][C]101.24[/C][C]101.329987312728[/C][C]-0.0899873127280273[/C][/ROW]
[ROW][C]10[/C][C]100.58[/C][C]101.240004567748[/C][C]-0.660004567747819[/C][/ROW]
[ROW][C]11[/C][C]99.87[/C][C]100.580033501772[/C][C]-0.710033501771917[/C][/ROW]
[ROW][C]12[/C][C]99.1[/C][C]99.8700360412361[/C][C]-0.770036041236068[/C][/ROW]
[ROW][C]13[/C][C]98.98[/C][C]99.1000390869595[/C][C]-0.120039086959508[/C][/ROW]
[ROW][C]14[/C][C]98.77[/C][C]98.9800060931732[/C][C]-0.210006093173163[/C][/ROW]
[ROW][C]15[/C][C]98.05[/C][C]98.7700106598902[/C][C]-0.720010659890221[/C][/ROW]
[ROW][C]16[/C][C]97.94[/C][C]98.0500365476757[/C][C]-0.110036547675705[/C][/ROW]
[ROW][C]17[/C][C]97.65[/C][C]97.9400055854452[/C][C]-0.290005585445158[/C][/ROW]
[ROW][C]18[/C][C]97.2[/C][C]97.6500147206572[/C][C]-0.45001472065718[/C][/ROW]
[ROW][C]19[/C][C]97.39[/C][C]97.2000228427064[/C][C]0.18997715729364[/C][/ROW]
[ROW][C]20[/C][C]97.35[/C][C]97.3899903567767[/C][C]-0.0399903567767552[/C][/ROW]
[ROW][C]21[/C][C]98.01[/C][C]97.3500020299069[/C][C]0.65999797009313[/C][/ROW]
[ROW][C]22[/C][C]97.81[/C][C]98.009966498563[/C][C]-0.199966498562972[/C][/ROW]
[ROW][C]23[/C][C]97.56[/C][C]97.8100101502813[/C][C]-0.250010150281312[/C][/ROW]
[ROW][C]24[/C][C]98.05[/C][C]97.5600126904925[/C][C]0.48998730950747[/C][/ROW]
[ROW][C]25[/C][C]97.82[/C][C]98.0499751282887[/C][C]-0.229975128288672[/C][/ROW]
[ROW][C]26[/C][C]99.05[/C][C]97.8200116735166[/C][C]1.22998832648338[/C][/ROW]
[ROW][C]27[/C][C]98.86[/C][C]99.0499375659042[/C][C]-0.189937565904245[/C][/ROW]
[ROW][C]28[/C][C]97.64[/C][C]98.8600096412136[/C][C]-1.22000964121359[/C][/ROW]
[ROW][C]29[/C][C]97.77[/C][C]97.6400619275786[/C][C]0.12993807242141[/C][/ROW]
[ROW][C]30[/C][C]98.07[/C][C]97.7699934043552[/C][C]0.30000659564476[/C][/ROW]
[ROW][C]31[/C][C]98.36[/C][C]98.0699847716924[/C][C]0.290015228307567[/C][/ROW]
[ROW][C]32[/C][C]100[/C][C]98.3599852788533[/C][C]1.64001472114666[/C][/ROW]
[ROW][C]33[/C][C]99.52[/C][C]99.9999167530017[/C][C]-0.479916753001703[/C][/ROW]
[ROW][C]34[/C][C]98.82[/C][C]99.5200243605308[/C][C]-0.70002436053079[/C][/ROW]
[ROW][C]35[/C][C]98.98[/C][C]98.820035533173[/C][C]0.159964466827049[/C][/ROW]
[ROW][C]36[/C][C]98.6[/C][C]98.9799918802182[/C][C]-0.379991880218213[/C][/ROW]
[ROW][C]37[/C][C]98.8[/C][C]98.6000192883533[/C][C]0.199980711646674[/C][/ROW]
[ROW][C]38[/C][C]99.62[/C][C]98.7999898489972[/C][C]0.820010151002762[/C][/ROW]
[ROW][C]39[/C][C]99.35[/C][C]99.6199583763592[/C][C]-0.269958376359213[/C][/ROW]
[ROW][C]40[/C][C]99.87[/C][C]99.3500137030627[/C][C]0.519986296937347[/C][/ROW]
[ROW][C]41[/C][C]99.53[/C][C]99.8699736055428[/C][C]-0.339973605542795[/C][/ROW]
[ROW][C]42[/C][C]99.88[/C][C]99.5300172570293[/C][C]0.349982742970653[/C][/ROW]
[ROW][C]43[/C][C]99.26[/C][C]99.8799822349077[/C][C]-0.619982234907738[/C][/ROW]
[ROW][C]44[/C][C]99.51[/C][C]99.2600314702419[/C][C]0.249968529758064[/C][/ROW]
[ROW][C]45[/C][C]100.64[/C][C]99.5099873116201[/C][C]1.13001268837986[/C][/ROW]
[ROW][C]46[/C][C]100.85[/C][C]100.639942640659[/C][C]0.210057359341434[/C][/ROW]
[ROW][C]47[/C][C]101.44[/C][C]100.849989337508[/C][C]0.590010662492489[/C][/ROW]
[ROW][C]48[/C][C]101.26[/C][C]101.439970051112[/C][C]-0.179970051112349[/C][/ROW]
[ROW][C]49[/C][C]101.67[/C][C]101.260009135263[/C][C]0.409990864736542[/C][/ROW]
[ROW][C]50[/C][C]102.93[/C][C]101.669979188901[/C][C]1.26002081109905[/C][/ROW]
[ROW][C]51[/C][C]103.81[/C][C]102.929936041458[/C][C]0.880063958541925[/C][/ROW]
[ROW][C]52[/C][C]106.19[/C][C]103.809955328033[/C][C]2.3800446719666[/C][/ROW]
[ROW][C]53[/C][C]106.94[/C][C]106.189879189149[/C][C]0.750120810851399[/C][/ROW]
[ROW][C]54[/C][C]108.51[/C][C]106.939961923936[/C][C]1.57003807606424[/C][/ROW]
[ROW][C]55[/C][C]108.41[/C][C]108.50992030501[/C][C]-0.09992030500986[/C][/ROW]
[ROW][C]56[/C][C]108.97[/C][C]108.410005071946[/C][C]0.559994928054394[/C][/ROW]
[ROW][C]57[/C][C]109.25[/C][C]108.969971574708[/C][C]0.28002842529169[/C][/ROW]
[ROW][C]58[/C][C]109.97[/C][C]109.249985785783[/C][C]0.720014214217429[/C][/ROW]
[ROW][C]59[/C][C]108.92[/C][C]109.969963452144[/C][C]-1.04996345214387[/C][/ROW]
[ROW][C]60[/C][C]109.01[/C][C]108.920053296049[/C][C]0.0899467039505311[/C][/ROW]
[ROW][C]61[/C][C]108.86[/C][C]109.009995434313[/C][C]-0.149995434313482[/C][/ROW]
[ROW][C]62[/C][C]107.36[/C][C]108.860007613755[/C][C]-1.50000761375463[/C][/ROW]
[ROW][C]63[/C][C]107.99[/C][C]107.36007614025[/C][C]0.629923859749752[/C][/ROW]
[ROW][C]64[/C][C]107.94[/C][C]107.989968025122[/C][C]-0.0499680251220838[/C][/ROW]
[ROW][C]65[/C][C]108.54[/C][C]107.940002536372[/C][C]0.599997463627588[/C][/ROW]
[ROW][C]66[/C][C]108.37[/C][C]108.539969544183[/C][C]-0.169969544183246[/C][/ROW]
[ROW][C]67[/C][C]108.77[/C][C]108.370008627639[/C][C]0.399991372361356[/C][/ROW]
[ROW][C]68[/C][C]107.15[/C][C]108.769979696474[/C][C]-1.61997969647425[/C][/ROW]
[ROW][C]69[/C][C]108.61[/C][C]107.150082230022[/C][C]1.45991776997774[/C][/ROW]
[ROW][C]70[/C][C]109.02[/C][C]108.609925894707[/C][C]0.410074105293418[/C][/ROW]
[ROW][C]71[/C][C]109.16[/C][C]109.019979184676[/C][C]0.140020815324348[/C][/ROW]
[ROW][C]72[/C][C]109.55[/C][C]109.159992892556[/C][C]0.390007107443864[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294728&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294728&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
2103.07103.71-0.640000000000001
3103.93103.0700324863420.859967513658134
4102.9103.929956348127-1.02995634812712
5101.54102.900052280491-1.36005228049068
6102.13101.540069036130.589930963869747
7101.08102.129970055158-1.04997005515784
8101.33101.0800532963850.249946703615365
9101.24101.329987312728-0.0899873127280273
10100.58101.240004567748-0.660004567747819
1199.87100.580033501772-0.710033501771917
1299.199.8700360412361-0.770036041236068
1398.9899.1000390869595-0.120039086959508
1498.7798.9800060931732-0.210006093173163
1598.0598.7700106598902-0.720010659890221
1697.9498.0500365476757-0.110036547675705
1797.6597.9400055854452-0.290005585445158
1897.297.6500147206572-0.45001472065718
1997.3997.20002284270640.18997715729364
2097.3597.3899903567767-0.0399903567767552
2198.0197.35000202990690.65999797009313
2297.8198.009966498563-0.199966498562972
2397.5697.8100101502813-0.250010150281312
2498.0597.56001269049250.48998730950747
2597.8298.0499751282887-0.229975128288672
2699.0597.82001167351661.22998832648338
2798.8699.0499375659042-0.189937565904245
2897.6498.8600096412136-1.22000964121359
2997.7797.64006192757860.12993807242141
3098.0797.76999340435520.30000659564476
3198.3698.06998477169240.290015228307567
3210098.35998527885331.64001472114666
3399.5299.9999167530017-0.479916753001703
3498.8299.5200243605308-0.70002436053079
3598.9898.8200355331730.159964466827049
3698.698.9799918802182-0.379991880218213
3798.898.60001928835330.199980711646674
3899.6298.79998984899720.820010151002762
3999.3599.6199583763592-0.269958376359213
4099.8799.35001370306270.519986296937347
4199.5399.8699736055428-0.339973605542795
4299.8899.53001725702930.349982742970653
4399.2699.8799822349077-0.619982234907738
4499.5199.26003147024190.249968529758064
45100.6499.50998731162011.13001268837986
46100.85100.6399426406590.210057359341434
47101.44100.8499893375080.590010662492489
48101.26101.439970051112-0.179970051112349
49101.67101.2600091352630.409990864736542
50102.93101.6699791889011.26002081109905
51103.81102.9299360414580.880063958541925
52106.19103.8099553280332.3800446719666
53106.94106.1898791891490.750120810851399
54108.51106.9399619239361.57003807606424
55108.41108.50992030501-0.09992030500986
56108.97108.4100050719460.559994928054394
57109.25108.9699715747080.28002842529169
58109.97109.2499857857830.720014214217429
59108.92109.969963452144-1.04996345214387
60109.01108.9200532960490.0899467039505311
61108.86109.009995434313-0.149995434313482
62107.36108.860007613755-1.50000761375463
63107.99107.360076140250.629923859749752
64107.94107.989968025122-0.0499680251220838
65108.54107.9400025363720.599997463627588
66108.37108.539969544183-0.169969544183246
67108.77108.3700086276390.399991372361356
68107.15108.769979696474-1.61997969647425
69108.61107.1500822300221.45991776997774
70109.02108.6099258947070.410074105293418
71109.16109.0199791846760.140020815324348
72109.55109.1599928925560.390007107443864







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73109.549980203275108.064729577892111.035230828657
74109.549980203275107.449571934278111.650388472271
75109.549980203275106.977537711646112.122422694903
76109.549980203275106.579592038572112.520368367977
77109.549980203275106.228993704465112.870966702084
78109.549980203275105.912027921902113.187932484647
79109.549980203275105.62054738443113.479413022119
80109.549980203275105.349243630472113.750716776077
81109.549980203275105.094429369724114.005531036825
82109.549980203275104.85341989741114.246540509139
83109.549980203275104.624188471696114.475771934853
84109.549980203275104.405160511667114.694799894883

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 109.549980203275 & 108.064729577892 & 111.035230828657 \tabularnewline
74 & 109.549980203275 & 107.449571934278 & 111.650388472271 \tabularnewline
75 & 109.549980203275 & 106.977537711646 & 112.122422694903 \tabularnewline
76 & 109.549980203275 & 106.579592038572 & 112.520368367977 \tabularnewline
77 & 109.549980203275 & 106.228993704465 & 112.870966702084 \tabularnewline
78 & 109.549980203275 & 105.912027921902 & 113.187932484647 \tabularnewline
79 & 109.549980203275 & 105.62054738443 & 113.479413022119 \tabularnewline
80 & 109.549980203275 & 105.349243630472 & 113.750716776077 \tabularnewline
81 & 109.549980203275 & 105.094429369724 & 114.005531036825 \tabularnewline
82 & 109.549980203275 & 104.85341989741 & 114.246540509139 \tabularnewline
83 & 109.549980203275 & 104.624188471696 & 114.475771934853 \tabularnewline
84 & 109.549980203275 & 104.405160511667 & 114.694799894883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294728&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]109.549980203275[/C][C]108.064729577892[/C][C]111.035230828657[/C][/ROW]
[ROW][C]74[/C][C]109.549980203275[/C][C]107.449571934278[/C][C]111.650388472271[/C][/ROW]
[ROW][C]75[/C][C]109.549980203275[/C][C]106.977537711646[/C][C]112.122422694903[/C][/ROW]
[ROW][C]76[/C][C]109.549980203275[/C][C]106.579592038572[/C][C]112.520368367977[/C][/ROW]
[ROW][C]77[/C][C]109.549980203275[/C][C]106.228993704465[/C][C]112.870966702084[/C][/ROW]
[ROW][C]78[/C][C]109.549980203275[/C][C]105.912027921902[/C][C]113.187932484647[/C][/ROW]
[ROW][C]79[/C][C]109.549980203275[/C][C]105.62054738443[/C][C]113.479413022119[/C][/ROW]
[ROW][C]80[/C][C]109.549980203275[/C][C]105.349243630472[/C][C]113.750716776077[/C][/ROW]
[ROW][C]81[/C][C]109.549980203275[/C][C]105.094429369724[/C][C]114.005531036825[/C][/ROW]
[ROW][C]82[/C][C]109.549980203275[/C][C]104.85341989741[/C][C]114.246540509139[/C][/ROW]
[ROW][C]83[/C][C]109.549980203275[/C][C]104.624188471696[/C][C]114.475771934853[/C][/ROW]
[ROW][C]84[/C][C]109.549980203275[/C][C]104.405160511667[/C][C]114.694799894883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294728&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294728&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
73109.549980203275108.064729577892111.035230828657
74109.549980203275107.449571934278111.650388472271
75109.549980203275106.977537711646112.122422694903
76109.549980203275106.579592038572112.520368367977
77109.549980203275106.228993704465112.870966702084
78109.549980203275105.912027921902113.187932484647
79109.549980203275105.62054738443113.479413022119
80109.549980203275105.349243630472113.750716776077
81109.549980203275105.094429369724114.005531036825
82109.549980203275104.85341989741114.246540509139
83109.549980203275104.624188471696114.475771934853
84109.549980203275104.405160511667114.694799894883



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')