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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 26 Nov 2015 12:35:56 +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/2015/Nov/26/t1448541551b6w1jgfpyjmud53.htm/, Retrieved Tue, 14 May 2024 17:19:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284212, Retrieved Tue, 14 May 2024 17:19:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2015-11-26 12:13:15] [0018d7578cf543a80e31e68d42751f97]
- R PD    [Exponential Smoothing] [] [2015-11-26 12:35:56] [cb8108074d5ede30ed5e3c15decd01d7] [Current]
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Dataseries X:
143,7
149,3
121,7
81
68,1
92,3
107,7
114,4
98,6
106,7
73,9
85,9
118,4
144,2
118,4
82,6
68
99,8
93,4
107,9
101,1
100,4
76,7
89,1
105,3
124,8
111,9
89
88,6
84,5
91,1
118,1
103,6
92,6
70,2
70,2
114,3
125,3
98,9
65,4
66
71,2
84,6
102,6
91,8
97,4
64,1
62,3
96,2
104,9
90,3
65,2
57,8
70,5
93,2
74,2
91,1
85
58,9
68,3
98,1
110,5
77,6
55,1
49,8
58,5
86,5
88,8
94
65
52,2
70,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284212&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284212&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284212&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0567177063295661
beta0.069361414036905
gamma0.49101342602853

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0567177063295661 \tabularnewline
beta & 0.069361414036905 \tabularnewline
gamma & 0.49101342602853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284212&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]0.0567177063295661[/C][/ROW]
[ROW][C]beta[/C][C]0.069361414036905[/C][/ROW]
[ROW][C]gamma[/C][C]0.49101342602853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284212&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284212&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
alpha0.0567177063295661
beta0.069361414036905
gamma0.49101342602853







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13118.4118.3934561965810.00654380341882188
14144.2144.849462063916-0.649462063916332
15118.4118.965705786166-0.565705786166177
1682.683.076141140994-0.476141140994031
176868.3772832481442-0.377283248144238
1899.899.68671477493460.113285225065439
1993.4104.686915886699-11.2869158866994
20107.9111.750287450018-3.8502874500183
21101.195.80363374538915.29636625461089
22100.4104.017426605236-3.61742660523579
2376.770.67808521629986.02191478370023
2489.182.46332216321456.63667783678554
25105.3115.404233408455-10.104233408455
26124.8140.932352304791-16.1323523047912
27111.9114.097736516639-2.19773651663866
288978.039171129404910.9608288705951
2988.663.961853813218824.6381461867812
3084.596.9428025434511-12.4428025434511
3191.195.9267750520273-4.82677505202733
32118.1106.80243562744911.2975643725512
33103.696.01243253831647.58756746168355
3492.6100.297736349713-7.69773634971334
3570.271.2456252979288-1.04562529792877
3670.282.9409976392124-12.7409976392124
37114.3106.9790812363647.3209187636364
38125.3130.722078013568-5.42207801356808
3998.9111.009647523067-12.1096475230673
4065.480.5051919066806-15.1051919066806
416671.2034834110151-5.20348341101509
4271.285.119084235726-13.919084235726
4384.687.3427609844715-2.74276098447154
44102.6105.609002254726-3.00900225472586
4591.892.0371054701355-0.237105470135489
4697.488.51610272787798.88389727212216
4764.163.26781409035670.832185909643258
4862.369.4425303462928-7.14253034629284
4996.2102.901850902793-6.70185090279291
50104.9119.703983533658-14.8039835336581
5190.396.0816570140928-5.78165701409283
5265.264.29324320621960.906756793780389
5357.860.2933664715166-2.49336647151662
5470.570.14413883053990.355861169460056
5593.278.228304091447314.9716959085527
5674.297.3200170577269-23.1200170577269
5791.183.7562578295417.34374217045898
588584.78451380473490.215486195265143
5958.955.17597389068053.7240261093195
6068.357.693147747537710.6068522524623
6198.192.30514867520675.79485132479327
62110.5106.0544786505194.44552134948101
6377.687.7695185305315-10.1695185305315
6455.158.879567000997-3.77956700099704
6549.853.0701384395836-3.27013843958363
6658.564.2245200026064-5.7245200026064
6786.578.73743757069077.7625624293093
6888.879.75326882995489.04673117004516
699482.225927514083511.7740724859165
706580.3236060984187-15.3236060984187
7152.251.51732165259420.68267834740579
7270.957.096478478465613.8035215215344

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 118.4 & 118.393456196581 & 0.00654380341882188 \tabularnewline
14 & 144.2 & 144.849462063916 & -0.649462063916332 \tabularnewline
15 & 118.4 & 118.965705786166 & -0.565705786166177 \tabularnewline
16 & 82.6 & 83.076141140994 & -0.476141140994031 \tabularnewline
17 & 68 & 68.3772832481442 & -0.377283248144238 \tabularnewline
18 & 99.8 & 99.6867147749346 & 0.113285225065439 \tabularnewline
19 & 93.4 & 104.686915886699 & -11.2869158866994 \tabularnewline
20 & 107.9 & 111.750287450018 & -3.8502874500183 \tabularnewline
21 & 101.1 & 95.8036337453891 & 5.29636625461089 \tabularnewline
22 & 100.4 & 104.017426605236 & -3.61742660523579 \tabularnewline
23 & 76.7 & 70.6780852162998 & 6.02191478370023 \tabularnewline
24 & 89.1 & 82.4633221632145 & 6.63667783678554 \tabularnewline
25 & 105.3 & 115.404233408455 & -10.104233408455 \tabularnewline
26 & 124.8 & 140.932352304791 & -16.1323523047912 \tabularnewline
27 & 111.9 & 114.097736516639 & -2.19773651663866 \tabularnewline
28 & 89 & 78.0391711294049 & 10.9608288705951 \tabularnewline
29 & 88.6 & 63.9618538132188 & 24.6381461867812 \tabularnewline
30 & 84.5 & 96.9428025434511 & -12.4428025434511 \tabularnewline
31 & 91.1 & 95.9267750520273 & -4.82677505202733 \tabularnewline
32 & 118.1 & 106.802435627449 & 11.2975643725512 \tabularnewline
33 & 103.6 & 96.0124325383164 & 7.58756746168355 \tabularnewline
34 & 92.6 & 100.297736349713 & -7.69773634971334 \tabularnewline
35 & 70.2 & 71.2456252979288 & -1.04562529792877 \tabularnewline
36 & 70.2 & 82.9409976392124 & -12.7409976392124 \tabularnewline
37 & 114.3 & 106.979081236364 & 7.3209187636364 \tabularnewline
38 & 125.3 & 130.722078013568 & -5.42207801356808 \tabularnewline
39 & 98.9 & 111.009647523067 & -12.1096475230673 \tabularnewline
40 & 65.4 & 80.5051919066806 & -15.1051919066806 \tabularnewline
41 & 66 & 71.2034834110151 & -5.20348341101509 \tabularnewline
42 & 71.2 & 85.119084235726 & -13.919084235726 \tabularnewline
43 & 84.6 & 87.3427609844715 & -2.74276098447154 \tabularnewline
44 & 102.6 & 105.609002254726 & -3.00900225472586 \tabularnewline
45 & 91.8 & 92.0371054701355 & -0.237105470135489 \tabularnewline
46 & 97.4 & 88.5161027278779 & 8.88389727212216 \tabularnewline
47 & 64.1 & 63.2678140903567 & 0.832185909643258 \tabularnewline
48 & 62.3 & 69.4425303462928 & -7.14253034629284 \tabularnewline
49 & 96.2 & 102.901850902793 & -6.70185090279291 \tabularnewline
50 & 104.9 & 119.703983533658 & -14.8039835336581 \tabularnewline
51 & 90.3 & 96.0816570140928 & -5.78165701409283 \tabularnewline
52 & 65.2 & 64.2932432062196 & 0.906756793780389 \tabularnewline
53 & 57.8 & 60.2933664715166 & -2.49336647151662 \tabularnewline
54 & 70.5 & 70.1441388305399 & 0.355861169460056 \tabularnewline
55 & 93.2 & 78.2283040914473 & 14.9716959085527 \tabularnewline
56 & 74.2 & 97.3200170577269 & -23.1200170577269 \tabularnewline
57 & 91.1 & 83.756257829541 & 7.34374217045898 \tabularnewline
58 & 85 & 84.7845138047349 & 0.215486195265143 \tabularnewline
59 & 58.9 & 55.1759738906805 & 3.7240261093195 \tabularnewline
60 & 68.3 & 57.6931477475377 & 10.6068522524623 \tabularnewline
61 & 98.1 & 92.3051486752067 & 5.79485132479327 \tabularnewline
62 & 110.5 & 106.054478650519 & 4.44552134948101 \tabularnewline
63 & 77.6 & 87.7695185305315 & -10.1695185305315 \tabularnewline
64 & 55.1 & 58.879567000997 & -3.77956700099704 \tabularnewline
65 & 49.8 & 53.0701384395836 & -3.27013843958363 \tabularnewline
66 & 58.5 & 64.2245200026064 & -5.7245200026064 \tabularnewline
67 & 86.5 & 78.7374375706907 & 7.7625624293093 \tabularnewline
68 & 88.8 & 79.7532688299548 & 9.04673117004516 \tabularnewline
69 & 94 & 82.2259275140835 & 11.7740724859165 \tabularnewline
70 & 65 & 80.3236060984187 & -15.3236060984187 \tabularnewline
71 & 52.2 & 51.5173216525942 & 0.68267834740579 \tabularnewline
72 & 70.9 & 57.0964784784656 & 13.8035215215344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284212&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]118.4[/C][C]118.393456196581[/C][C]0.00654380341882188[/C][/ROW]
[ROW][C]14[/C][C]144.2[/C][C]144.849462063916[/C][C]-0.649462063916332[/C][/ROW]
[ROW][C]15[/C][C]118.4[/C][C]118.965705786166[/C][C]-0.565705786166177[/C][/ROW]
[ROW][C]16[/C][C]82.6[/C][C]83.076141140994[/C][C]-0.476141140994031[/C][/ROW]
[ROW][C]17[/C][C]68[/C][C]68.3772832481442[/C][C]-0.377283248144238[/C][/ROW]
[ROW][C]18[/C][C]99.8[/C][C]99.6867147749346[/C][C]0.113285225065439[/C][/ROW]
[ROW][C]19[/C][C]93.4[/C][C]104.686915886699[/C][C]-11.2869158866994[/C][/ROW]
[ROW][C]20[/C][C]107.9[/C][C]111.750287450018[/C][C]-3.8502874500183[/C][/ROW]
[ROW][C]21[/C][C]101.1[/C][C]95.8036337453891[/C][C]5.29636625461089[/C][/ROW]
[ROW][C]22[/C][C]100.4[/C][C]104.017426605236[/C][C]-3.61742660523579[/C][/ROW]
[ROW][C]23[/C][C]76.7[/C][C]70.6780852162998[/C][C]6.02191478370023[/C][/ROW]
[ROW][C]24[/C][C]89.1[/C][C]82.4633221632145[/C][C]6.63667783678554[/C][/ROW]
[ROW][C]25[/C][C]105.3[/C][C]115.404233408455[/C][C]-10.104233408455[/C][/ROW]
[ROW][C]26[/C][C]124.8[/C][C]140.932352304791[/C][C]-16.1323523047912[/C][/ROW]
[ROW][C]27[/C][C]111.9[/C][C]114.097736516639[/C][C]-2.19773651663866[/C][/ROW]
[ROW][C]28[/C][C]89[/C][C]78.0391711294049[/C][C]10.9608288705951[/C][/ROW]
[ROW][C]29[/C][C]88.6[/C][C]63.9618538132188[/C][C]24.6381461867812[/C][/ROW]
[ROW][C]30[/C][C]84.5[/C][C]96.9428025434511[/C][C]-12.4428025434511[/C][/ROW]
[ROW][C]31[/C][C]91.1[/C][C]95.9267750520273[/C][C]-4.82677505202733[/C][/ROW]
[ROW][C]32[/C][C]118.1[/C][C]106.802435627449[/C][C]11.2975643725512[/C][/ROW]
[ROW][C]33[/C][C]103.6[/C][C]96.0124325383164[/C][C]7.58756746168355[/C][/ROW]
[ROW][C]34[/C][C]92.6[/C][C]100.297736349713[/C][C]-7.69773634971334[/C][/ROW]
[ROW][C]35[/C][C]70.2[/C][C]71.2456252979288[/C][C]-1.04562529792877[/C][/ROW]
[ROW][C]36[/C][C]70.2[/C][C]82.9409976392124[/C][C]-12.7409976392124[/C][/ROW]
[ROW][C]37[/C][C]114.3[/C][C]106.979081236364[/C][C]7.3209187636364[/C][/ROW]
[ROW][C]38[/C][C]125.3[/C][C]130.722078013568[/C][C]-5.42207801356808[/C][/ROW]
[ROW][C]39[/C][C]98.9[/C][C]111.009647523067[/C][C]-12.1096475230673[/C][/ROW]
[ROW][C]40[/C][C]65.4[/C][C]80.5051919066806[/C][C]-15.1051919066806[/C][/ROW]
[ROW][C]41[/C][C]66[/C][C]71.2034834110151[/C][C]-5.20348341101509[/C][/ROW]
[ROW][C]42[/C][C]71.2[/C][C]85.119084235726[/C][C]-13.919084235726[/C][/ROW]
[ROW][C]43[/C][C]84.6[/C][C]87.3427609844715[/C][C]-2.74276098447154[/C][/ROW]
[ROW][C]44[/C][C]102.6[/C][C]105.609002254726[/C][C]-3.00900225472586[/C][/ROW]
[ROW][C]45[/C][C]91.8[/C][C]92.0371054701355[/C][C]-0.237105470135489[/C][/ROW]
[ROW][C]46[/C][C]97.4[/C][C]88.5161027278779[/C][C]8.88389727212216[/C][/ROW]
[ROW][C]47[/C][C]64.1[/C][C]63.2678140903567[/C][C]0.832185909643258[/C][/ROW]
[ROW][C]48[/C][C]62.3[/C][C]69.4425303462928[/C][C]-7.14253034629284[/C][/ROW]
[ROW][C]49[/C][C]96.2[/C][C]102.901850902793[/C][C]-6.70185090279291[/C][/ROW]
[ROW][C]50[/C][C]104.9[/C][C]119.703983533658[/C][C]-14.8039835336581[/C][/ROW]
[ROW][C]51[/C][C]90.3[/C][C]96.0816570140928[/C][C]-5.78165701409283[/C][/ROW]
[ROW][C]52[/C][C]65.2[/C][C]64.2932432062196[/C][C]0.906756793780389[/C][/ROW]
[ROW][C]53[/C][C]57.8[/C][C]60.2933664715166[/C][C]-2.49336647151662[/C][/ROW]
[ROW][C]54[/C][C]70.5[/C][C]70.1441388305399[/C][C]0.355861169460056[/C][/ROW]
[ROW][C]55[/C][C]93.2[/C][C]78.2283040914473[/C][C]14.9716959085527[/C][/ROW]
[ROW][C]56[/C][C]74.2[/C][C]97.3200170577269[/C][C]-23.1200170577269[/C][/ROW]
[ROW][C]57[/C][C]91.1[/C][C]83.756257829541[/C][C]7.34374217045898[/C][/ROW]
[ROW][C]58[/C][C]85[/C][C]84.7845138047349[/C][C]0.215486195265143[/C][/ROW]
[ROW][C]59[/C][C]58.9[/C][C]55.1759738906805[/C][C]3.7240261093195[/C][/ROW]
[ROW][C]60[/C][C]68.3[/C][C]57.6931477475377[/C][C]10.6068522524623[/C][/ROW]
[ROW][C]61[/C][C]98.1[/C][C]92.3051486752067[/C][C]5.79485132479327[/C][/ROW]
[ROW][C]62[/C][C]110.5[/C][C]106.054478650519[/C][C]4.44552134948101[/C][/ROW]
[ROW][C]63[/C][C]77.6[/C][C]87.7695185305315[/C][C]-10.1695185305315[/C][/ROW]
[ROW][C]64[/C][C]55.1[/C][C]58.879567000997[/C][C]-3.77956700099704[/C][/ROW]
[ROW][C]65[/C][C]49.8[/C][C]53.0701384395836[/C][C]-3.27013843958363[/C][/ROW]
[ROW][C]66[/C][C]58.5[/C][C]64.2245200026064[/C][C]-5.7245200026064[/C][/ROW]
[ROW][C]67[/C][C]86.5[/C][C]78.7374375706907[/C][C]7.7625624293093[/C][/ROW]
[ROW][C]68[/C][C]88.8[/C][C]79.7532688299548[/C][C]9.04673117004516[/C][/ROW]
[ROW][C]69[/C][C]94[/C][C]82.2259275140835[/C][C]11.7740724859165[/C][/ROW]
[ROW][C]70[/C][C]65[/C][C]80.3236060984187[/C][C]-15.3236060984187[/C][/ROW]
[ROW][C]71[/C][C]52.2[/C][C]51.5173216525942[/C][C]0.68267834740579[/C][/ROW]
[ROW][C]72[/C][C]70.9[/C][C]57.0964784784656[/C][C]13.8035215215344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284212&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284212&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
13118.4118.3934561965810.00654380341882188
14144.2144.849462063916-0.649462063916332
15118.4118.965705786166-0.565705786166177
1682.683.076141140994-0.476141140994031
176868.3772832481442-0.377283248144238
1899.899.68671477493460.113285225065439
1993.4104.686915886699-11.2869158866994
20107.9111.750287450018-3.8502874500183
21101.195.80363374538915.29636625461089
22100.4104.017426605236-3.61742660523579
2376.770.67808521629986.02191478370023
2489.182.46332216321456.63667783678554
25105.3115.404233408455-10.104233408455
26124.8140.932352304791-16.1323523047912
27111.9114.097736516639-2.19773651663866
288978.039171129404910.9608288705951
2988.663.961853813218824.6381461867812
3084.596.9428025434511-12.4428025434511
3191.195.9267750520273-4.82677505202733
32118.1106.80243562744911.2975643725512
33103.696.01243253831647.58756746168355
3492.6100.297736349713-7.69773634971334
3570.271.2456252979288-1.04562529792877
3670.282.9409976392124-12.7409976392124
37114.3106.9790812363647.3209187636364
38125.3130.722078013568-5.42207801356808
3998.9111.009647523067-12.1096475230673
4065.480.5051919066806-15.1051919066806
416671.2034834110151-5.20348341101509
4271.285.119084235726-13.919084235726
4384.687.3427609844715-2.74276098447154
44102.6105.609002254726-3.00900225472586
4591.892.0371054701355-0.237105470135489
4697.488.51610272787798.88389727212216
4764.163.26781409035670.832185909643258
4862.369.4425303462928-7.14253034629284
4996.2102.901850902793-6.70185090279291
50104.9119.703983533658-14.8039835336581
5190.396.0816570140928-5.78165701409283
5265.264.29324320621960.906756793780389
5357.860.2933664715166-2.49336647151662
5470.570.14413883053990.355861169460056
5593.278.228304091447314.9716959085527
5674.297.3200170577269-23.1200170577269
5791.183.7562578295417.34374217045898
588584.78451380473490.215486195265143
5958.955.17597389068053.7240261093195
6068.357.693147747537710.6068522524623
6198.192.30514867520675.79485132479327
62110.5106.0544786505194.44552134948101
6377.687.7695185305315-10.1695185305315
6455.158.879567000997-3.77956700099704
6549.853.0701384395836-3.27013843958363
6658.564.2245200026064-5.7245200026064
6786.578.73743757069077.7625624293093
6888.879.75326882995489.04673117004516
699482.225927514083511.7740724859165
706580.3236060984187-15.3236060984187
7152.251.51732165259420.68267834740579
7270.957.096478478465613.8035215215344







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7389.720218103493371.9141813684834107.526254838503
74102.55229675526584.713539156865120.391054353665
7577.264924588043959.389136217311695.1407129587761
7651.970261171480334.052884977337969.8876373656227
7746.684918090053528.721155514027464.6486806660797
7856.974625349706838.959442522347674.9898081770659
7978.168112430639360.096246928147696.239977933131
8079.41706512334461.283033276827597.5510969698605
8182.68284608451564.4809508280899100.88474134094
8267.55875537026249.28309460797985.8344161325449
8347.092118781966828.736594247409765.447643316524
8458.763964751925540.322291328409177.2056381754418

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 89.7202181034933 & 71.9141813684834 & 107.526254838503 \tabularnewline
74 & 102.552296755265 & 84.713539156865 & 120.391054353665 \tabularnewline
75 & 77.2649245880439 & 59.3891362173116 & 95.1407129587761 \tabularnewline
76 & 51.9702611714803 & 34.0528849773379 & 69.8876373656227 \tabularnewline
77 & 46.6849180900535 & 28.7211555140274 & 64.6486806660797 \tabularnewline
78 & 56.9746253497068 & 38.9594425223476 & 74.9898081770659 \tabularnewline
79 & 78.1681124306393 & 60.0962469281476 & 96.239977933131 \tabularnewline
80 & 79.417065123344 & 61.2830332768275 & 97.5510969698605 \tabularnewline
81 & 82.682846084515 & 64.4809508280899 & 100.88474134094 \tabularnewline
82 & 67.558755370262 & 49.283094607979 & 85.8344161325449 \tabularnewline
83 & 47.0921187819668 & 28.7365942474097 & 65.447643316524 \tabularnewline
84 & 58.7639647519255 & 40.3222913284091 & 77.2056381754418 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284212&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]89.7202181034933[/C][C]71.9141813684834[/C][C]107.526254838503[/C][/ROW]
[ROW][C]74[/C][C]102.552296755265[/C][C]84.713539156865[/C][C]120.391054353665[/C][/ROW]
[ROW][C]75[/C][C]77.2649245880439[/C][C]59.3891362173116[/C][C]95.1407129587761[/C][/ROW]
[ROW][C]76[/C][C]51.9702611714803[/C][C]34.0528849773379[/C][C]69.8876373656227[/C][/ROW]
[ROW][C]77[/C][C]46.6849180900535[/C][C]28.7211555140274[/C][C]64.6486806660797[/C][/ROW]
[ROW][C]78[/C][C]56.9746253497068[/C][C]38.9594425223476[/C][C]74.9898081770659[/C][/ROW]
[ROW][C]79[/C][C]78.1681124306393[/C][C]60.0962469281476[/C][C]96.239977933131[/C][/ROW]
[ROW][C]80[/C][C]79.417065123344[/C][C]61.2830332768275[/C][C]97.5510969698605[/C][/ROW]
[ROW][C]81[/C][C]82.682846084515[/C][C]64.4809508280899[/C][C]100.88474134094[/C][/ROW]
[ROW][C]82[/C][C]67.558755370262[/C][C]49.283094607979[/C][C]85.8344161325449[/C][/ROW]
[ROW][C]83[/C][C]47.0921187819668[/C][C]28.7365942474097[/C][C]65.447643316524[/C][/ROW]
[ROW][C]84[/C][C]58.7639647519255[/C][C]40.3222913284091[/C][C]77.2056381754418[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284212&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284212&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
7389.720218103493371.9141813684834107.526254838503
74102.55229675526584.713539156865120.391054353665
7577.264924588043959.389136217311695.1407129587761
7651.970261171480334.052884977337969.8876373656227
7746.684918090053528.721155514027464.6486806660797
7856.974625349706838.959442522347674.9898081770659
7978.168112430639360.096246928147696.239977933131
8079.41706512334461.283033276827597.5510969698605
8182.68284608451564.4809508280899100.88474134094
8267.55875537026249.28309460797985.8344161325449
8347.092118781966828.736594247409765.447643316524
8458.763964751925540.322291328409177.2056381754418



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