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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 04 Jan 2013 13:59:18 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Jan/04/t1357326100ys58ivk6s0dgtwe.htm/, Retrieved Sun, 28 Apr 2024 09:20:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205013, Retrieved Sun, 28 Apr 2024 09:20:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-04 18:59:18] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
246.24
247.57
247.84
248.27
248.3
248.31
248.31
248.38
248.37
248.41
248.68
248.75
248.75
247.95
248.13
247.86
246.23
245.98
245.98
246.27
246.31
246.3
246.67
246.78
246.78
247.91
247.99
248.6
248.68
248.75
248.75
249.03
249.05
249.57
249.35
249.46
249.46
250.82
254.19
255.18
256.68
256.73
256.73
257.39
257.78
258.67
258.71
258.91
258.91
261.38
262.42
262.77
263.24
262.83
262.83
263.09
263.6
265.68
266.08
266.28
266.28
269.14
270.96
272.97
273.13
274.73
274.73
274.59
275.15
275.16
275.38
275.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205013&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205013&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205013&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.309031250642435
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.309031250642435 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205013&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]0.309031250642435[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205013&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205013&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
beta0.309031250642435
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3247.84248.9-1.05999999999997
4248.27248.842426874319-0.572426874319007
5248.3249.095529081447-0.795529081446858
6248.31248.879685734485-0.569685734484921
7248.31248.713635039484-0.403635039483873
8248.38248.588899198429-0.208899198429066
9248.37248.59434281788-0.224342817880313
10248.41248.515013876298-0.105013876298131
11248.68248.5225613067710.157438693229096
12248.75248.841214783039-0.0912147830390211
13248.75248.883026564559-0.133026564559373
14247.95248.841917198945-0.891917198944952
15248.13247.7662869114850.363713088514544
16247.86248.058685622104-0.198685622104136
17246.23247.727285555821-1.49728555582067
18245.98245.6345775279370.34542247206349
19245.98245.4913238664780.488676133521693
20246.27245.642340063180.627659936820407
21246.31246.1263065984330.183693401566615
22246.3246.2230736000540.0769263999457337
23246.67246.2368462616370.433153738363046
24246.78246.7407043031240.0392956968763087
25246.78246.862847901474-0.0828479014742527
26247.91246.8372453108691.07275468913144
27247.99248.298760034083-0.308760034083377
28248.6248.2833435346020.316656465397784
29248.68248.991200278128-0.311200278128069
30248.75248.975029666978-0.225029666977917
31248.75248.97548846756-0.225488467560069
32249.03248.9058054844250.124194515575482
33249.05249.224185470896-0.174185470895736
34249.57249.1903567169810.379643283018879
35249.35249.82767835553-0.477678355530429
36249.46249.460060815916-6.08159160151445e-05
37249.46249.570042021897-0.110042021897442
38250.82249.5360355982471.28396440175274
39254.19251.2928207231012.89717927689873
40255.18255.558139658377-0.378139658376625
41256.68256.4312826868310.248717313168981
42256.73258.008144109176-1.27814410917603
43256.73257.663157636616-0.933157636616102
44257.39257.3747827651260.0152172348738873
45257.78258.03948536625-0.259485366250487
46258.67258.3492962789950.320703721005373
47258.71259.338403750983-0.62840375098267
48258.91259.184207353908-0.274207353908025
49258.91259.299468712395-0.389468712394546
50261.38259.1791107091172.2008892908828
51262.42262.3292542792040.0907457207958373
52262.77263.397297542792-0.627297542792235
53263.24263.553442998618-0.313442998618143
54262.83263.92657931675-1.09657931675014
55262.83263.177702039066-0.347702039066178
56263.09263.0702512430830.0197487569173518
57263.6263.3363542261310.263645773868632
58265.68263.9278290093571.75217099064332
59266.08266.549304601935-0.469304601934596
60266.28266.804274813866-0.524274813866498
61266.28266.842257512457-0.562257512456995
62269.14266.6685023701992.47149762980069
63270.96270.2922723736960.667727626303588
64272.97272.3186210771410.651378922858555
65273.13274.529917520315-1.39991752031466
66274.73274.2572992582160.472700741784479
67274.73276.003378559629-1.27337855962878
68274.59275.609864790805-1.01986479080551
69275.15275.154694699017-0.00469469901662478
70275.16275.713243890308-0.553243890308067
71275.38275.552274238976-0.172274238975945
72275.4275.719036115452-0.319036115451752

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 247.84 & 248.9 & -1.05999999999997 \tabularnewline
4 & 248.27 & 248.842426874319 & -0.572426874319007 \tabularnewline
5 & 248.3 & 249.095529081447 & -0.795529081446858 \tabularnewline
6 & 248.31 & 248.879685734485 & -0.569685734484921 \tabularnewline
7 & 248.31 & 248.713635039484 & -0.403635039483873 \tabularnewline
8 & 248.38 & 248.588899198429 & -0.208899198429066 \tabularnewline
9 & 248.37 & 248.59434281788 & -0.224342817880313 \tabularnewline
10 & 248.41 & 248.515013876298 & -0.105013876298131 \tabularnewline
11 & 248.68 & 248.522561306771 & 0.157438693229096 \tabularnewline
12 & 248.75 & 248.841214783039 & -0.0912147830390211 \tabularnewline
13 & 248.75 & 248.883026564559 & -0.133026564559373 \tabularnewline
14 & 247.95 & 248.841917198945 & -0.891917198944952 \tabularnewline
15 & 248.13 & 247.766286911485 & 0.363713088514544 \tabularnewline
16 & 247.86 & 248.058685622104 & -0.198685622104136 \tabularnewline
17 & 246.23 & 247.727285555821 & -1.49728555582067 \tabularnewline
18 & 245.98 & 245.634577527937 & 0.34542247206349 \tabularnewline
19 & 245.98 & 245.491323866478 & 0.488676133521693 \tabularnewline
20 & 246.27 & 245.64234006318 & 0.627659936820407 \tabularnewline
21 & 246.31 & 246.126306598433 & 0.183693401566615 \tabularnewline
22 & 246.3 & 246.223073600054 & 0.0769263999457337 \tabularnewline
23 & 246.67 & 246.236846261637 & 0.433153738363046 \tabularnewline
24 & 246.78 & 246.740704303124 & 0.0392956968763087 \tabularnewline
25 & 246.78 & 246.862847901474 & -0.0828479014742527 \tabularnewline
26 & 247.91 & 246.837245310869 & 1.07275468913144 \tabularnewline
27 & 247.99 & 248.298760034083 & -0.308760034083377 \tabularnewline
28 & 248.6 & 248.283343534602 & 0.316656465397784 \tabularnewline
29 & 248.68 & 248.991200278128 & -0.311200278128069 \tabularnewline
30 & 248.75 & 248.975029666978 & -0.225029666977917 \tabularnewline
31 & 248.75 & 248.97548846756 & -0.225488467560069 \tabularnewline
32 & 249.03 & 248.905805484425 & 0.124194515575482 \tabularnewline
33 & 249.05 & 249.224185470896 & -0.174185470895736 \tabularnewline
34 & 249.57 & 249.190356716981 & 0.379643283018879 \tabularnewline
35 & 249.35 & 249.82767835553 & -0.477678355530429 \tabularnewline
36 & 249.46 & 249.460060815916 & -6.08159160151445e-05 \tabularnewline
37 & 249.46 & 249.570042021897 & -0.110042021897442 \tabularnewline
38 & 250.82 & 249.536035598247 & 1.28396440175274 \tabularnewline
39 & 254.19 & 251.292820723101 & 2.89717927689873 \tabularnewline
40 & 255.18 & 255.558139658377 & -0.378139658376625 \tabularnewline
41 & 256.68 & 256.431282686831 & 0.248717313168981 \tabularnewline
42 & 256.73 & 258.008144109176 & -1.27814410917603 \tabularnewline
43 & 256.73 & 257.663157636616 & -0.933157636616102 \tabularnewline
44 & 257.39 & 257.374782765126 & 0.0152172348738873 \tabularnewline
45 & 257.78 & 258.03948536625 & -0.259485366250487 \tabularnewline
46 & 258.67 & 258.349296278995 & 0.320703721005373 \tabularnewline
47 & 258.71 & 259.338403750983 & -0.62840375098267 \tabularnewline
48 & 258.91 & 259.184207353908 & -0.274207353908025 \tabularnewline
49 & 258.91 & 259.299468712395 & -0.389468712394546 \tabularnewline
50 & 261.38 & 259.179110709117 & 2.2008892908828 \tabularnewline
51 & 262.42 & 262.329254279204 & 0.0907457207958373 \tabularnewline
52 & 262.77 & 263.397297542792 & -0.627297542792235 \tabularnewline
53 & 263.24 & 263.553442998618 & -0.313442998618143 \tabularnewline
54 & 262.83 & 263.92657931675 & -1.09657931675014 \tabularnewline
55 & 262.83 & 263.177702039066 & -0.347702039066178 \tabularnewline
56 & 263.09 & 263.070251243083 & 0.0197487569173518 \tabularnewline
57 & 263.6 & 263.336354226131 & 0.263645773868632 \tabularnewline
58 & 265.68 & 263.927829009357 & 1.75217099064332 \tabularnewline
59 & 266.08 & 266.549304601935 & -0.469304601934596 \tabularnewline
60 & 266.28 & 266.804274813866 & -0.524274813866498 \tabularnewline
61 & 266.28 & 266.842257512457 & -0.562257512456995 \tabularnewline
62 & 269.14 & 266.668502370199 & 2.47149762980069 \tabularnewline
63 & 270.96 & 270.292272373696 & 0.667727626303588 \tabularnewline
64 & 272.97 & 272.318621077141 & 0.651378922858555 \tabularnewline
65 & 273.13 & 274.529917520315 & -1.39991752031466 \tabularnewline
66 & 274.73 & 274.257299258216 & 0.472700741784479 \tabularnewline
67 & 274.73 & 276.003378559629 & -1.27337855962878 \tabularnewline
68 & 274.59 & 275.609864790805 & -1.01986479080551 \tabularnewline
69 & 275.15 & 275.154694699017 & -0.00469469901662478 \tabularnewline
70 & 275.16 & 275.713243890308 & -0.553243890308067 \tabularnewline
71 & 275.38 & 275.552274238976 & -0.172274238975945 \tabularnewline
72 & 275.4 & 275.719036115452 & -0.319036115451752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205013&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]247.84[/C][C]248.9[/C][C]-1.05999999999997[/C][/ROW]
[ROW][C]4[/C][C]248.27[/C][C]248.842426874319[/C][C]-0.572426874319007[/C][/ROW]
[ROW][C]5[/C][C]248.3[/C][C]249.095529081447[/C][C]-0.795529081446858[/C][/ROW]
[ROW][C]6[/C][C]248.31[/C][C]248.879685734485[/C][C]-0.569685734484921[/C][/ROW]
[ROW][C]7[/C][C]248.31[/C][C]248.713635039484[/C][C]-0.403635039483873[/C][/ROW]
[ROW][C]8[/C][C]248.38[/C][C]248.588899198429[/C][C]-0.208899198429066[/C][/ROW]
[ROW][C]9[/C][C]248.37[/C][C]248.59434281788[/C][C]-0.224342817880313[/C][/ROW]
[ROW][C]10[/C][C]248.41[/C][C]248.515013876298[/C][C]-0.105013876298131[/C][/ROW]
[ROW][C]11[/C][C]248.68[/C][C]248.522561306771[/C][C]0.157438693229096[/C][/ROW]
[ROW][C]12[/C][C]248.75[/C][C]248.841214783039[/C][C]-0.0912147830390211[/C][/ROW]
[ROW][C]13[/C][C]248.75[/C][C]248.883026564559[/C][C]-0.133026564559373[/C][/ROW]
[ROW][C]14[/C][C]247.95[/C][C]248.841917198945[/C][C]-0.891917198944952[/C][/ROW]
[ROW][C]15[/C][C]248.13[/C][C]247.766286911485[/C][C]0.363713088514544[/C][/ROW]
[ROW][C]16[/C][C]247.86[/C][C]248.058685622104[/C][C]-0.198685622104136[/C][/ROW]
[ROW][C]17[/C][C]246.23[/C][C]247.727285555821[/C][C]-1.49728555582067[/C][/ROW]
[ROW][C]18[/C][C]245.98[/C][C]245.634577527937[/C][C]0.34542247206349[/C][/ROW]
[ROW][C]19[/C][C]245.98[/C][C]245.491323866478[/C][C]0.488676133521693[/C][/ROW]
[ROW][C]20[/C][C]246.27[/C][C]245.64234006318[/C][C]0.627659936820407[/C][/ROW]
[ROW][C]21[/C][C]246.31[/C][C]246.126306598433[/C][C]0.183693401566615[/C][/ROW]
[ROW][C]22[/C][C]246.3[/C][C]246.223073600054[/C][C]0.0769263999457337[/C][/ROW]
[ROW][C]23[/C][C]246.67[/C][C]246.236846261637[/C][C]0.433153738363046[/C][/ROW]
[ROW][C]24[/C][C]246.78[/C][C]246.740704303124[/C][C]0.0392956968763087[/C][/ROW]
[ROW][C]25[/C][C]246.78[/C][C]246.862847901474[/C][C]-0.0828479014742527[/C][/ROW]
[ROW][C]26[/C][C]247.91[/C][C]246.837245310869[/C][C]1.07275468913144[/C][/ROW]
[ROW][C]27[/C][C]247.99[/C][C]248.298760034083[/C][C]-0.308760034083377[/C][/ROW]
[ROW][C]28[/C][C]248.6[/C][C]248.283343534602[/C][C]0.316656465397784[/C][/ROW]
[ROW][C]29[/C][C]248.68[/C][C]248.991200278128[/C][C]-0.311200278128069[/C][/ROW]
[ROW][C]30[/C][C]248.75[/C][C]248.975029666978[/C][C]-0.225029666977917[/C][/ROW]
[ROW][C]31[/C][C]248.75[/C][C]248.97548846756[/C][C]-0.225488467560069[/C][/ROW]
[ROW][C]32[/C][C]249.03[/C][C]248.905805484425[/C][C]0.124194515575482[/C][/ROW]
[ROW][C]33[/C][C]249.05[/C][C]249.224185470896[/C][C]-0.174185470895736[/C][/ROW]
[ROW][C]34[/C][C]249.57[/C][C]249.190356716981[/C][C]0.379643283018879[/C][/ROW]
[ROW][C]35[/C][C]249.35[/C][C]249.82767835553[/C][C]-0.477678355530429[/C][/ROW]
[ROW][C]36[/C][C]249.46[/C][C]249.460060815916[/C][C]-6.08159160151445e-05[/C][/ROW]
[ROW][C]37[/C][C]249.46[/C][C]249.570042021897[/C][C]-0.110042021897442[/C][/ROW]
[ROW][C]38[/C][C]250.82[/C][C]249.536035598247[/C][C]1.28396440175274[/C][/ROW]
[ROW][C]39[/C][C]254.19[/C][C]251.292820723101[/C][C]2.89717927689873[/C][/ROW]
[ROW][C]40[/C][C]255.18[/C][C]255.558139658377[/C][C]-0.378139658376625[/C][/ROW]
[ROW][C]41[/C][C]256.68[/C][C]256.431282686831[/C][C]0.248717313168981[/C][/ROW]
[ROW][C]42[/C][C]256.73[/C][C]258.008144109176[/C][C]-1.27814410917603[/C][/ROW]
[ROW][C]43[/C][C]256.73[/C][C]257.663157636616[/C][C]-0.933157636616102[/C][/ROW]
[ROW][C]44[/C][C]257.39[/C][C]257.374782765126[/C][C]0.0152172348738873[/C][/ROW]
[ROW][C]45[/C][C]257.78[/C][C]258.03948536625[/C][C]-0.259485366250487[/C][/ROW]
[ROW][C]46[/C][C]258.67[/C][C]258.349296278995[/C][C]0.320703721005373[/C][/ROW]
[ROW][C]47[/C][C]258.71[/C][C]259.338403750983[/C][C]-0.62840375098267[/C][/ROW]
[ROW][C]48[/C][C]258.91[/C][C]259.184207353908[/C][C]-0.274207353908025[/C][/ROW]
[ROW][C]49[/C][C]258.91[/C][C]259.299468712395[/C][C]-0.389468712394546[/C][/ROW]
[ROW][C]50[/C][C]261.38[/C][C]259.179110709117[/C][C]2.2008892908828[/C][/ROW]
[ROW][C]51[/C][C]262.42[/C][C]262.329254279204[/C][C]0.0907457207958373[/C][/ROW]
[ROW][C]52[/C][C]262.77[/C][C]263.397297542792[/C][C]-0.627297542792235[/C][/ROW]
[ROW][C]53[/C][C]263.24[/C][C]263.553442998618[/C][C]-0.313442998618143[/C][/ROW]
[ROW][C]54[/C][C]262.83[/C][C]263.92657931675[/C][C]-1.09657931675014[/C][/ROW]
[ROW][C]55[/C][C]262.83[/C][C]263.177702039066[/C][C]-0.347702039066178[/C][/ROW]
[ROW][C]56[/C][C]263.09[/C][C]263.070251243083[/C][C]0.0197487569173518[/C][/ROW]
[ROW][C]57[/C][C]263.6[/C][C]263.336354226131[/C][C]0.263645773868632[/C][/ROW]
[ROW][C]58[/C][C]265.68[/C][C]263.927829009357[/C][C]1.75217099064332[/C][/ROW]
[ROW][C]59[/C][C]266.08[/C][C]266.549304601935[/C][C]-0.469304601934596[/C][/ROW]
[ROW][C]60[/C][C]266.28[/C][C]266.804274813866[/C][C]-0.524274813866498[/C][/ROW]
[ROW][C]61[/C][C]266.28[/C][C]266.842257512457[/C][C]-0.562257512456995[/C][/ROW]
[ROW][C]62[/C][C]269.14[/C][C]266.668502370199[/C][C]2.47149762980069[/C][/ROW]
[ROW][C]63[/C][C]270.96[/C][C]270.292272373696[/C][C]0.667727626303588[/C][/ROW]
[ROW][C]64[/C][C]272.97[/C][C]272.318621077141[/C][C]0.651378922858555[/C][/ROW]
[ROW][C]65[/C][C]273.13[/C][C]274.529917520315[/C][C]-1.39991752031466[/C][/ROW]
[ROW][C]66[/C][C]274.73[/C][C]274.257299258216[/C][C]0.472700741784479[/C][/ROW]
[ROW][C]67[/C][C]274.73[/C][C]276.003378559629[/C][C]-1.27337855962878[/C][/ROW]
[ROW][C]68[/C][C]274.59[/C][C]275.609864790805[/C][C]-1.01986479080551[/C][/ROW]
[ROW][C]69[/C][C]275.15[/C][C]275.154694699017[/C][C]-0.00469469901662478[/C][/ROW]
[ROW][C]70[/C][C]275.16[/C][C]275.713243890308[/C][C]-0.553243890308067[/C][/ROW]
[ROW][C]71[/C][C]275.38[/C][C]275.552274238976[/C][C]-0.172274238975945[/C][/ROW]
[ROW][C]72[/C][C]275.4[/C][C]275.719036115452[/C][C]-0.319036115451752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205013&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205013&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
3247.84248.9-1.05999999999997
4248.27248.842426874319-0.572426874319007
5248.3249.095529081447-0.795529081446858
6248.31248.879685734485-0.569685734484921
7248.31248.713635039484-0.403635039483873
8248.38248.588899198429-0.208899198429066
9248.37248.59434281788-0.224342817880313
10248.41248.515013876298-0.105013876298131
11248.68248.5225613067710.157438693229096
12248.75248.841214783039-0.0912147830390211
13248.75248.883026564559-0.133026564559373
14247.95248.841917198945-0.891917198944952
15248.13247.7662869114850.363713088514544
16247.86248.058685622104-0.198685622104136
17246.23247.727285555821-1.49728555582067
18245.98245.6345775279370.34542247206349
19245.98245.4913238664780.488676133521693
20246.27245.642340063180.627659936820407
21246.31246.1263065984330.183693401566615
22246.3246.2230736000540.0769263999457337
23246.67246.2368462616370.433153738363046
24246.78246.7407043031240.0392956968763087
25246.78246.862847901474-0.0828479014742527
26247.91246.8372453108691.07275468913144
27247.99248.298760034083-0.308760034083377
28248.6248.2833435346020.316656465397784
29248.68248.991200278128-0.311200278128069
30248.75248.975029666978-0.225029666977917
31248.75248.97548846756-0.225488467560069
32249.03248.9058054844250.124194515575482
33249.05249.224185470896-0.174185470895736
34249.57249.1903567169810.379643283018879
35249.35249.82767835553-0.477678355530429
36249.46249.460060815916-6.08159160151445e-05
37249.46249.570042021897-0.110042021897442
38250.82249.5360355982471.28396440175274
39254.19251.2928207231012.89717927689873
40255.18255.558139658377-0.378139658376625
41256.68256.4312826868310.248717313168981
42256.73258.008144109176-1.27814410917603
43256.73257.663157636616-0.933157636616102
44257.39257.3747827651260.0152172348738873
45257.78258.03948536625-0.259485366250487
46258.67258.3492962789950.320703721005373
47258.71259.338403750983-0.62840375098267
48258.91259.184207353908-0.274207353908025
49258.91259.299468712395-0.389468712394546
50261.38259.1791107091172.2008892908828
51262.42262.3292542792040.0907457207958373
52262.77263.397297542792-0.627297542792235
53263.24263.553442998618-0.313442998618143
54262.83263.92657931675-1.09657931675014
55262.83263.177702039066-0.347702039066178
56263.09263.0702512430830.0197487569173518
57263.6263.3363542261310.263645773868632
58265.68263.9278290093571.75217099064332
59266.08266.549304601935-0.469304601934596
60266.28266.804274813866-0.524274813866498
61266.28266.842257512457-0.562257512456995
62269.14266.6685023701992.47149762980069
63270.96270.2922723736960.667727626303588
64272.97272.3186210771410.651378922858555
65273.13274.529917520315-1.39991752031466
66274.73274.2572992582160.472700741784479
67274.73276.003378559629-1.27337855962878
68274.59275.609864790805-1.01986479080551
69275.15275.154694699017-0.00469469901662478
70275.16275.713243890308-0.553243890308067
71275.38275.552274238976-0.172274238975945
72275.4275.719036115452-0.319036115451752







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73275.640443985694274.05508740171277.225800569677
74275.880887971387273.269346659886278.492429282888
75276.121331957081272.460672173949279.781991740212
76276.361775942774271.59373084496281.129821040589
77276.602219928468270.660698867283282.543740989652
78276.842663914161269.660551556164284.024776272158
79277.083107899855268.594438820434285.571776979276
80277.323551885549267.464240578489287.182863192608
81277.563995871242266.272036761786288.855954980698
82277.804439856936265.019897688434290.588982025437
83278.044883842629263.709800804392292.379966880867
84278.285327828323262.343600984205294.227054672441

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 275.640443985694 & 274.05508740171 & 277.225800569677 \tabularnewline
74 & 275.880887971387 & 273.269346659886 & 278.492429282888 \tabularnewline
75 & 276.121331957081 & 272.460672173949 & 279.781991740212 \tabularnewline
76 & 276.361775942774 & 271.59373084496 & 281.129821040589 \tabularnewline
77 & 276.602219928468 & 270.660698867283 & 282.543740989652 \tabularnewline
78 & 276.842663914161 & 269.660551556164 & 284.024776272158 \tabularnewline
79 & 277.083107899855 & 268.594438820434 & 285.571776979276 \tabularnewline
80 & 277.323551885549 & 267.464240578489 & 287.182863192608 \tabularnewline
81 & 277.563995871242 & 266.272036761786 & 288.855954980698 \tabularnewline
82 & 277.804439856936 & 265.019897688434 & 290.588982025437 \tabularnewline
83 & 278.044883842629 & 263.709800804392 & 292.379966880867 \tabularnewline
84 & 278.285327828323 & 262.343600984205 & 294.227054672441 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205013&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]275.640443985694[/C][C]274.05508740171[/C][C]277.225800569677[/C][/ROW]
[ROW][C]74[/C][C]275.880887971387[/C][C]273.269346659886[/C][C]278.492429282888[/C][/ROW]
[ROW][C]75[/C][C]276.121331957081[/C][C]272.460672173949[/C][C]279.781991740212[/C][/ROW]
[ROW][C]76[/C][C]276.361775942774[/C][C]271.59373084496[/C][C]281.129821040589[/C][/ROW]
[ROW][C]77[/C][C]276.602219928468[/C][C]270.660698867283[/C][C]282.543740989652[/C][/ROW]
[ROW][C]78[/C][C]276.842663914161[/C][C]269.660551556164[/C][C]284.024776272158[/C][/ROW]
[ROW][C]79[/C][C]277.083107899855[/C][C]268.594438820434[/C][C]285.571776979276[/C][/ROW]
[ROW][C]80[/C][C]277.323551885549[/C][C]267.464240578489[/C][C]287.182863192608[/C][/ROW]
[ROW][C]81[/C][C]277.563995871242[/C][C]266.272036761786[/C][C]288.855954980698[/C][/ROW]
[ROW][C]82[/C][C]277.804439856936[/C][C]265.019897688434[/C][C]290.588982025437[/C][/ROW]
[ROW][C]83[/C][C]278.044883842629[/C][C]263.709800804392[/C][C]292.379966880867[/C][/ROW]
[ROW][C]84[/C][C]278.285327828323[/C][C]262.343600984205[/C][C]294.227054672441[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205013&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205013&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
73275.640443985694274.05508740171277.225800569677
74275.880887971387273.269346659886278.492429282888
75276.121331957081272.460672173949279.781991740212
76276.361775942774271.59373084496281.129821040589
77276.602219928468270.660698867283282.543740989652
78276.842663914161269.660551556164284.024776272158
79277.083107899855268.594438820434285.571776979276
80277.323551885549267.464240578489287.182863192608
81277.563995871242266.272036761786288.855954980698
82277.804439856936265.019897688434290.588982025437
83278.044883842629263.709800804392292.379966880867
84278.285327828323262.343600984205294.227054672441



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')