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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 Nov 2012 11:57:02 -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/2012/Nov/28/t13541218526d9nhmzi4hdrxc3.htm/, Retrieved Fri, 29 Mar 2024 05:12:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=194193, Retrieved Fri, 29 Mar 2024 05:12:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Triple Exponentia...] [2012-11-28 16:57:02] [64435dfec13c3cda39d1733fd4b6eb52] [Current]
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Dataseries X:
54.3
55.9
63.9
64
60.7
67.8
70.5
76.6
76.2
71.8
67.8
69.7
76.7
74.2
75.8
84.3
84.9
84.4
89.4
88.5
76.5
71.4
72.1
75.8
66.6
71.7
75.4
80.9
80.7
85
91.5
87.7
95.3
102.4
114.2
111.7
113.7
118.8
129
136.4
155
166
168.7
145.5
127.3
91.5
69
54
56.3
54.2
59.3
63.4
73.3
86.7
81.3
89.6
85.3
92.4
96.8
93.6
97.6
94.2
99.9
106.4
96
94.9
94.8
95.9
96.2
103.1
106.9
114.2
118.2
123.9
137.1
146.2
136.4
133.2
135.9
127.1
128.5
126.6
132.6
130.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194193&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194193&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194193&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194193&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[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194193&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194193&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
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1376.767.42443299334899.27556700665107
1474.274.03032073134960.169679268650412
1575.876.3746592967267-0.574659296726693
1684.385.4884504333415-1.18845043334146
1784.985.9149012537773-1.01490125377725
1884.485.1149588053522-0.714958805352239
1989.483.88017356642165.51982643357836
2088.595.9781393574596-7.4781393574596
2176.587.6603721414208-11.1603721414208
2271.471.8404575428382-0.440457542838189
2372.166.74210067823615.35789932176391
2475.873.47033009801212.32966990198791
2566.682.9097015791909-16.3097015791909
2671.764.41998423351177.28001576648829
2775.473.8372565731511.562743426849
2880.985.043571984853-4.14357198485304
2980.782.4977621702391-1.79776217023908
308580.96252503863544.03747496136458
3191.584.46828032605827.03171967394178
3287.798.203949052621-10.503949052621
3395.386.87875660212148.42124339787864
34102.489.224012775822513.1759872241775
35114.295.278456189631118.9215438103689
36111.7115.774103502643-4.07410350264279
37113.7121.654897895226-7.95489789522566
38118.8109.2365039412519.56349605874932
39129121.6419238853177.3580761146833
40136.4144.657284082302-8.25728408230222
41155138.27753250446516.7224674955348
42166154.42105572126911.5789442787312
43168.7163.8626928769964.83730712300445
44145.5180.028953084268-34.528953084268
45127.3143.350479316507-16.0504793165074
4691.5118.813042959626-27.3130429596257
476985.2447053807858-16.2447053807858
485470.3553254055096-16.3553254055096
4956.359.381977910958-3.08197791095803
5054.254.6193440426474-0.419344042647353
5159.356.07543750812133.22456249187871
5263.467.1372144331938-3.73721443319383
5373.364.90954629908678.39045370091328
5486.773.646332211562913.0536677884371
5581.386.1345828116952-4.83458281169517
5689.687.39287339040862.20712660959144
5785.388.7350935079576-3.43509350795756
5892.479.977440843384112.4225591566159
5996.886.073180218213410.7268197817866
6093.698.2898836156933-4.68988361569328
6197.6102.120411730317-4.52041173031675
6294.293.9170566526180.282943347381959
6399.996.67388108533213.22611891466792
64106.4112.292376954769-5.89237695476918
6596108.126305296775-12.1263052967754
6694.996.089248045961-1.18924804596098
6794.894.17204186006170.627958139938329
6895.9101.70165000216-5.8016500021603
6996.294.89031587994081.30968412005917
70103.190.05620424974213.043795750258
71106.995.922825507630310.9771744923697
72114.2108.4387698719115.76123012808891
73118.2124.353031343417-6.1530313434175
74123.9113.51833703434710.3816629656533
75137.1126.81822544141110.2817745585889
76146.2153.666072664193-7.46607266419286
77136.4148.12693339231-11.7269333923105
78133.2136.031706182951-2.83170618295142
79135.9131.712856683534.18714331647047
80127.1145.263925464605-18.1639254646045
81128.5125.373321912623.12667808738018
82126.6119.9226315915186.67736840848168
83132.6117.55522404046215.0447759595379
84130.9134.26316361298-3.36316361298014

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 76.7 & 67.4244329933489 & 9.27556700665107 \tabularnewline
14 & 74.2 & 74.0303207313496 & 0.169679268650412 \tabularnewline
15 & 75.8 & 76.3746592967267 & -0.574659296726693 \tabularnewline
16 & 84.3 & 85.4884504333415 & -1.18845043334146 \tabularnewline
17 & 84.9 & 85.9149012537773 & -1.01490125377725 \tabularnewline
18 & 84.4 & 85.1149588053522 & -0.714958805352239 \tabularnewline
19 & 89.4 & 83.8801735664216 & 5.51982643357836 \tabularnewline
20 & 88.5 & 95.9781393574596 & -7.4781393574596 \tabularnewline
21 & 76.5 & 87.6603721414208 & -11.1603721414208 \tabularnewline
22 & 71.4 & 71.8404575428382 & -0.440457542838189 \tabularnewline
23 & 72.1 & 66.7421006782361 & 5.35789932176391 \tabularnewline
24 & 75.8 & 73.4703300980121 & 2.32966990198791 \tabularnewline
25 & 66.6 & 82.9097015791909 & -16.3097015791909 \tabularnewline
26 & 71.7 & 64.4199842335117 & 7.28001576648829 \tabularnewline
27 & 75.4 & 73.837256573151 & 1.562743426849 \tabularnewline
28 & 80.9 & 85.043571984853 & -4.14357198485304 \tabularnewline
29 & 80.7 & 82.4977621702391 & -1.79776217023908 \tabularnewline
30 & 85 & 80.9625250386354 & 4.03747496136458 \tabularnewline
31 & 91.5 & 84.4682803260582 & 7.03171967394178 \tabularnewline
32 & 87.7 & 98.203949052621 & -10.503949052621 \tabularnewline
33 & 95.3 & 86.8787566021214 & 8.42124339787864 \tabularnewline
34 & 102.4 & 89.2240127758225 & 13.1759872241775 \tabularnewline
35 & 114.2 & 95.2784561896311 & 18.9215438103689 \tabularnewline
36 & 111.7 & 115.774103502643 & -4.07410350264279 \tabularnewline
37 & 113.7 & 121.654897895226 & -7.95489789522566 \tabularnewline
38 & 118.8 & 109.236503941251 & 9.56349605874932 \tabularnewline
39 & 129 & 121.641923885317 & 7.3580761146833 \tabularnewline
40 & 136.4 & 144.657284082302 & -8.25728408230222 \tabularnewline
41 & 155 & 138.277532504465 & 16.7224674955348 \tabularnewline
42 & 166 & 154.421055721269 & 11.5789442787312 \tabularnewline
43 & 168.7 & 163.862692876996 & 4.83730712300445 \tabularnewline
44 & 145.5 & 180.028953084268 & -34.528953084268 \tabularnewline
45 & 127.3 & 143.350479316507 & -16.0504793165074 \tabularnewline
46 & 91.5 & 118.813042959626 & -27.3130429596257 \tabularnewline
47 & 69 & 85.2447053807858 & -16.2447053807858 \tabularnewline
48 & 54 & 70.3553254055096 & -16.3553254055096 \tabularnewline
49 & 56.3 & 59.381977910958 & -3.08197791095803 \tabularnewline
50 & 54.2 & 54.6193440426474 & -0.419344042647353 \tabularnewline
51 & 59.3 & 56.0754375081213 & 3.22456249187871 \tabularnewline
52 & 63.4 & 67.1372144331938 & -3.73721443319383 \tabularnewline
53 & 73.3 & 64.9095462990867 & 8.39045370091328 \tabularnewline
54 & 86.7 & 73.6463322115629 & 13.0536677884371 \tabularnewline
55 & 81.3 & 86.1345828116952 & -4.83458281169517 \tabularnewline
56 & 89.6 & 87.3928733904086 & 2.20712660959144 \tabularnewline
57 & 85.3 & 88.7350935079576 & -3.43509350795756 \tabularnewline
58 & 92.4 & 79.9774408433841 & 12.4225591566159 \tabularnewline
59 & 96.8 & 86.0731802182134 & 10.7268197817866 \tabularnewline
60 & 93.6 & 98.2898836156933 & -4.68988361569328 \tabularnewline
61 & 97.6 & 102.120411730317 & -4.52041173031675 \tabularnewline
62 & 94.2 & 93.917056652618 & 0.282943347381959 \tabularnewline
63 & 99.9 & 96.6738810853321 & 3.22611891466792 \tabularnewline
64 & 106.4 & 112.292376954769 & -5.89237695476918 \tabularnewline
65 & 96 & 108.126305296775 & -12.1263052967754 \tabularnewline
66 & 94.9 & 96.089248045961 & -1.18924804596098 \tabularnewline
67 & 94.8 & 94.1720418600617 & 0.627958139938329 \tabularnewline
68 & 95.9 & 101.70165000216 & -5.8016500021603 \tabularnewline
69 & 96.2 & 94.8903158799408 & 1.30968412005917 \tabularnewline
70 & 103.1 & 90.056204249742 & 13.043795750258 \tabularnewline
71 & 106.9 & 95.9228255076303 & 10.9771744923697 \tabularnewline
72 & 114.2 & 108.438769871911 & 5.76123012808891 \tabularnewline
73 & 118.2 & 124.353031343417 & -6.1530313434175 \tabularnewline
74 & 123.9 & 113.518337034347 & 10.3816629656533 \tabularnewline
75 & 137.1 & 126.818225441411 & 10.2817745585889 \tabularnewline
76 & 146.2 & 153.666072664193 & -7.46607266419286 \tabularnewline
77 & 136.4 & 148.12693339231 & -11.7269333923105 \tabularnewline
78 & 133.2 & 136.031706182951 & -2.83170618295142 \tabularnewline
79 & 135.9 & 131.71285668353 & 4.18714331647047 \tabularnewline
80 & 127.1 & 145.263925464605 & -18.1639254646045 \tabularnewline
81 & 128.5 & 125.37332191262 & 3.12667808738018 \tabularnewline
82 & 126.6 & 119.922631591518 & 6.67736840848168 \tabularnewline
83 & 132.6 & 117.555224040462 & 15.0447759595379 \tabularnewline
84 & 130.9 & 134.26316361298 & -3.36316361298014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194193&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]13[/C][C]76.7[/C][C]67.4244329933489[/C][C]9.27556700665107[/C][/ROW]
[ROW][C]14[/C][C]74.2[/C][C]74.0303207313496[/C][C]0.169679268650412[/C][/ROW]
[ROW][C]15[/C][C]75.8[/C][C]76.3746592967267[/C][C]-0.574659296726693[/C][/ROW]
[ROW][C]16[/C][C]84.3[/C][C]85.4884504333415[/C][C]-1.18845043334146[/C][/ROW]
[ROW][C]17[/C][C]84.9[/C][C]85.9149012537773[/C][C]-1.01490125377725[/C][/ROW]
[ROW][C]18[/C][C]84.4[/C][C]85.1149588053522[/C][C]-0.714958805352239[/C][/ROW]
[ROW][C]19[/C][C]89.4[/C][C]83.8801735664216[/C][C]5.51982643357836[/C][/ROW]
[ROW][C]20[/C][C]88.5[/C][C]95.9781393574596[/C][C]-7.4781393574596[/C][/ROW]
[ROW][C]21[/C][C]76.5[/C][C]87.6603721414208[/C][C]-11.1603721414208[/C][/ROW]
[ROW][C]22[/C][C]71.4[/C][C]71.8404575428382[/C][C]-0.440457542838189[/C][/ROW]
[ROW][C]23[/C][C]72.1[/C][C]66.7421006782361[/C][C]5.35789932176391[/C][/ROW]
[ROW][C]24[/C][C]75.8[/C][C]73.4703300980121[/C][C]2.32966990198791[/C][/ROW]
[ROW][C]25[/C][C]66.6[/C][C]82.9097015791909[/C][C]-16.3097015791909[/C][/ROW]
[ROW][C]26[/C][C]71.7[/C][C]64.4199842335117[/C][C]7.28001576648829[/C][/ROW]
[ROW][C]27[/C][C]75.4[/C][C]73.837256573151[/C][C]1.562743426849[/C][/ROW]
[ROW][C]28[/C][C]80.9[/C][C]85.043571984853[/C][C]-4.14357198485304[/C][/ROW]
[ROW][C]29[/C][C]80.7[/C][C]82.4977621702391[/C][C]-1.79776217023908[/C][/ROW]
[ROW][C]30[/C][C]85[/C][C]80.9625250386354[/C][C]4.03747496136458[/C][/ROW]
[ROW][C]31[/C][C]91.5[/C][C]84.4682803260582[/C][C]7.03171967394178[/C][/ROW]
[ROW][C]32[/C][C]87.7[/C][C]98.203949052621[/C][C]-10.503949052621[/C][/ROW]
[ROW][C]33[/C][C]95.3[/C][C]86.8787566021214[/C][C]8.42124339787864[/C][/ROW]
[ROW][C]34[/C][C]102.4[/C][C]89.2240127758225[/C][C]13.1759872241775[/C][/ROW]
[ROW][C]35[/C][C]114.2[/C][C]95.2784561896311[/C][C]18.9215438103689[/C][/ROW]
[ROW][C]36[/C][C]111.7[/C][C]115.774103502643[/C][C]-4.07410350264279[/C][/ROW]
[ROW][C]37[/C][C]113.7[/C][C]121.654897895226[/C][C]-7.95489789522566[/C][/ROW]
[ROW][C]38[/C][C]118.8[/C][C]109.236503941251[/C][C]9.56349605874932[/C][/ROW]
[ROW][C]39[/C][C]129[/C][C]121.641923885317[/C][C]7.3580761146833[/C][/ROW]
[ROW][C]40[/C][C]136.4[/C][C]144.657284082302[/C][C]-8.25728408230222[/C][/ROW]
[ROW][C]41[/C][C]155[/C][C]138.277532504465[/C][C]16.7224674955348[/C][/ROW]
[ROW][C]42[/C][C]166[/C][C]154.421055721269[/C][C]11.5789442787312[/C][/ROW]
[ROW][C]43[/C][C]168.7[/C][C]163.862692876996[/C][C]4.83730712300445[/C][/ROW]
[ROW][C]44[/C][C]145.5[/C][C]180.028953084268[/C][C]-34.528953084268[/C][/ROW]
[ROW][C]45[/C][C]127.3[/C][C]143.350479316507[/C][C]-16.0504793165074[/C][/ROW]
[ROW][C]46[/C][C]91.5[/C][C]118.813042959626[/C][C]-27.3130429596257[/C][/ROW]
[ROW][C]47[/C][C]69[/C][C]85.2447053807858[/C][C]-16.2447053807858[/C][/ROW]
[ROW][C]48[/C][C]54[/C][C]70.3553254055096[/C][C]-16.3553254055096[/C][/ROW]
[ROW][C]49[/C][C]56.3[/C][C]59.381977910958[/C][C]-3.08197791095803[/C][/ROW]
[ROW][C]50[/C][C]54.2[/C][C]54.6193440426474[/C][C]-0.419344042647353[/C][/ROW]
[ROW][C]51[/C][C]59.3[/C][C]56.0754375081213[/C][C]3.22456249187871[/C][/ROW]
[ROW][C]52[/C][C]63.4[/C][C]67.1372144331938[/C][C]-3.73721443319383[/C][/ROW]
[ROW][C]53[/C][C]73.3[/C][C]64.9095462990867[/C][C]8.39045370091328[/C][/ROW]
[ROW][C]54[/C][C]86.7[/C][C]73.6463322115629[/C][C]13.0536677884371[/C][/ROW]
[ROW][C]55[/C][C]81.3[/C][C]86.1345828116952[/C][C]-4.83458281169517[/C][/ROW]
[ROW][C]56[/C][C]89.6[/C][C]87.3928733904086[/C][C]2.20712660959144[/C][/ROW]
[ROW][C]57[/C][C]85.3[/C][C]88.7350935079576[/C][C]-3.43509350795756[/C][/ROW]
[ROW][C]58[/C][C]92.4[/C][C]79.9774408433841[/C][C]12.4225591566159[/C][/ROW]
[ROW][C]59[/C][C]96.8[/C][C]86.0731802182134[/C][C]10.7268197817866[/C][/ROW]
[ROW][C]60[/C][C]93.6[/C][C]98.2898836156933[/C][C]-4.68988361569328[/C][/ROW]
[ROW][C]61[/C][C]97.6[/C][C]102.120411730317[/C][C]-4.52041173031675[/C][/ROW]
[ROW][C]62[/C][C]94.2[/C][C]93.917056652618[/C][C]0.282943347381959[/C][/ROW]
[ROW][C]63[/C][C]99.9[/C][C]96.6738810853321[/C][C]3.22611891466792[/C][/ROW]
[ROW][C]64[/C][C]106.4[/C][C]112.292376954769[/C][C]-5.89237695476918[/C][/ROW]
[ROW][C]65[/C][C]96[/C][C]108.126305296775[/C][C]-12.1263052967754[/C][/ROW]
[ROW][C]66[/C][C]94.9[/C][C]96.089248045961[/C][C]-1.18924804596098[/C][/ROW]
[ROW][C]67[/C][C]94.8[/C][C]94.1720418600617[/C][C]0.627958139938329[/C][/ROW]
[ROW][C]68[/C][C]95.9[/C][C]101.70165000216[/C][C]-5.8016500021603[/C][/ROW]
[ROW][C]69[/C][C]96.2[/C][C]94.8903158799408[/C][C]1.30968412005917[/C][/ROW]
[ROW][C]70[/C][C]103.1[/C][C]90.056204249742[/C][C]13.043795750258[/C][/ROW]
[ROW][C]71[/C][C]106.9[/C][C]95.9228255076303[/C][C]10.9771744923697[/C][/ROW]
[ROW][C]72[/C][C]114.2[/C][C]108.438769871911[/C][C]5.76123012808891[/C][/ROW]
[ROW][C]73[/C][C]118.2[/C][C]124.353031343417[/C][C]-6.1530313434175[/C][/ROW]
[ROW][C]74[/C][C]123.9[/C][C]113.518337034347[/C][C]10.3816629656533[/C][/ROW]
[ROW][C]75[/C][C]137.1[/C][C]126.818225441411[/C][C]10.2817745585889[/C][/ROW]
[ROW][C]76[/C][C]146.2[/C][C]153.666072664193[/C][C]-7.46607266419286[/C][/ROW]
[ROW][C]77[/C][C]136.4[/C][C]148.12693339231[/C][C]-11.7269333923105[/C][/ROW]
[ROW][C]78[/C][C]133.2[/C][C]136.031706182951[/C][C]-2.83170618295142[/C][/ROW]
[ROW][C]79[/C][C]135.9[/C][C]131.71285668353[/C][C]4.18714331647047[/C][/ROW]
[ROW][C]80[/C][C]127.1[/C][C]145.263925464605[/C][C]-18.1639254646045[/C][/ROW]
[ROW][C]81[/C][C]128.5[/C][C]125.37332191262[/C][C]3.12667808738018[/C][/ROW]
[ROW][C]82[/C][C]126.6[/C][C]119.922631591518[/C][C]6.67736840848168[/C][/ROW]
[ROW][C]83[/C][C]132.6[/C][C]117.555224040462[/C][C]15.0447759595379[/C][/ROW]
[ROW][C]84[/C][C]130.9[/C][C]134.26316361298[/C][C]-3.36316361298014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194193&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194193&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
1376.767.42443299334899.27556700665107
1474.274.03032073134960.169679268650412
1575.876.3746592967267-0.574659296726693
1684.385.4884504333415-1.18845043334146
1784.985.9149012537773-1.01490125377725
1884.485.1149588053522-0.714958805352239
1989.483.88017356642165.51982643357836
2088.595.9781393574596-7.4781393574596
2176.587.6603721414208-11.1603721414208
2271.471.8404575428382-0.440457542838189
2372.166.74210067823615.35789932176391
2475.873.47033009801212.32966990198791
2566.682.9097015791909-16.3097015791909
2671.764.41998423351177.28001576648829
2775.473.8372565731511.562743426849
2880.985.043571984853-4.14357198485304
2980.782.4977621702391-1.79776217023908
308580.96252503863544.03747496136458
3191.584.46828032605827.03171967394178
3287.798.203949052621-10.503949052621
3395.386.87875660212148.42124339787864
34102.489.224012775822513.1759872241775
35114.295.278456189631118.9215438103689
36111.7115.774103502643-4.07410350264279
37113.7121.654897895226-7.95489789522566
38118.8109.2365039412519.56349605874932
39129121.6419238853177.3580761146833
40136.4144.657284082302-8.25728408230222
41155138.27753250446516.7224674955348
42166154.42105572126911.5789442787312
43168.7163.8626928769964.83730712300445
44145.5180.028953084268-34.528953084268
45127.3143.350479316507-16.0504793165074
4691.5118.813042959626-27.3130429596257
476985.2447053807858-16.2447053807858
485470.3553254055096-16.3553254055096
4956.359.381977910958-3.08197791095803
5054.254.6193440426474-0.419344042647353
5159.356.07543750812133.22456249187871
5263.467.1372144331938-3.73721443319383
5373.364.90954629908678.39045370091328
5486.773.646332211562913.0536677884371
5581.386.1345828116952-4.83458281169517
5689.687.39287339040862.20712660959144
5785.388.7350935079576-3.43509350795756
5892.479.977440843384112.4225591566159
5996.886.073180218213410.7268197817866
6093.698.2898836156933-4.68988361569328
6197.6102.120411730317-4.52041173031675
6294.293.9170566526180.282943347381959
6399.996.67388108533213.22611891466792
64106.4112.292376954769-5.89237695476918
6596108.126305296775-12.1263052967754
6694.996.089248045961-1.18924804596098
6794.894.17204186006170.627958139938329
6895.9101.70165000216-5.8016500021603
6996.294.89031587994081.30968412005917
70103.190.05620424974213.043795750258
71106.995.922825507630310.9771744923697
72114.2108.4387698719115.76123012808891
73118.2124.353031343417-6.1530313434175
74123.9113.51833703434710.3816629656533
75137.1126.81822544141110.2817745585889
76146.2153.666072664193-7.46607266419286
77136.4148.12693339231-11.7269333923105
78133.2136.031706182951-2.83170618295142
79135.9131.712856683534.18714331647047
80127.1145.263925464605-18.1639254646045
81128.5125.373321912623.12667808738018
82126.6119.9226315915186.67736840848168
83132.6117.55522404046215.0447759595379
84130.9134.26316361298-3.36316361298014







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85142.376562777339122.665460481867162.087665072811
86136.522782940419109.314411043271163.731154837567
87139.629858966261105.701404641838173.558313290683
88156.479771993704113.906717476784199.052826510625
89158.458524759824111.348955507675205.568094011974
90157.840411672631107.265170559987208.415652785275
91155.864844458367102.517083146931209.212605769802
92166.424851349281106.543902551288226.305800147275
93163.794465531669102.058373655278225.530557408061
94152.55791302707392.1659187301556212.949907323991
95141.45019934608982.4666989369978200.433699755181
96143.15619990093281.7760583783363204.536341423528

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 142.376562777339 & 122.665460481867 & 162.087665072811 \tabularnewline
86 & 136.522782940419 & 109.314411043271 & 163.731154837567 \tabularnewline
87 & 139.629858966261 & 105.701404641838 & 173.558313290683 \tabularnewline
88 & 156.479771993704 & 113.906717476784 & 199.052826510625 \tabularnewline
89 & 158.458524759824 & 111.348955507675 & 205.568094011974 \tabularnewline
90 & 157.840411672631 & 107.265170559987 & 208.415652785275 \tabularnewline
91 & 155.864844458367 & 102.517083146931 & 209.212605769802 \tabularnewline
92 & 166.424851349281 & 106.543902551288 & 226.305800147275 \tabularnewline
93 & 163.794465531669 & 102.058373655278 & 225.530557408061 \tabularnewline
94 & 152.557913027073 & 92.1659187301556 & 212.949907323991 \tabularnewline
95 & 141.450199346089 & 82.4666989369978 & 200.433699755181 \tabularnewline
96 & 143.156199900932 & 81.7760583783363 & 204.536341423528 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194193&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]85[/C][C]142.376562777339[/C][C]122.665460481867[/C][C]162.087665072811[/C][/ROW]
[ROW][C]86[/C][C]136.522782940419[/C][C]109.314411043271[/C][C]163.731154837567[/C][/ROW]
[ROW][C]87[/C][C]139.629858966261[/C][C]105.701404641838[/C][C]173.558313290683[/C][/ROW]
[ROW][C]88[/C][C]156.479771993704[/C][C]113.906717476784[/C][C]199.052826510625[/C][/ROW]
[ROW][C]89[/C][C]158.458524759824[/C][C]111.348955507675[/C][C]205.568094011974[/C][/ROW]
[ROW][C]90[/C][C]157.840411672631[/C][C]107.265170559987[/C][C]208.415652785275[/C][/ROW]
[ROW][C]91[/C][C]155.864844458367[/C][C]102.517083146931[/C][C]209.212605769802[/C][/ROW]
[ROW][C]92[/C][C]166.424851349281[/C][C]106.543902551288[/C][C]226.305800147275[/C][/ROW]
[ROW][C]93[/C][C]163.794465531669[/C][C]102.058373655278[/C][C]225.530557408061[/C][/ROW]
[ROW][C]94[/C][C]152.557913027073[/C][C]92.1659187301556[/C][C]212.949907323991[/C][/ROW]
[ROW][C]95[/C][C]141.450199346089[/C][C]82.4666989369978[/C][C]200.433699755181[/C][/ROW]
[ROW][C]96[/C][C]143.156199900932[/C][C]81.7760583783363[/C][C]204.536341423528[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194193&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194193&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
85142.376562777339122.665460481867162.087665072811
86136.522782940419109.314411043271163.731154837567
87139.629858966261105.701404641838173.558313290683
88156.479771993704113.906717476784199.052826510625
89158.458524759824111.348955507675205.568094011974
90157.840411672631107.265170559987208.415652785275
91155.864844458367102.517083146931209.212605769802
92166.424851349281106.543902551288226.305800147275
93163.794465531669102.058373655278225.530557408061
94152.55791302707392.1659187301556212.949907323991
95141.45019934608982.4666989369978200.433699755181
96143.15619990093281.7760583783363204.536341423528



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')