Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 May 2017 14:09:46 +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/2017/May/02/t1493730695q2ft5tsgilefl6j.htm/, Retrieved Fri, 17 May 2024 03:41:11 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 03:41:11 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
78.46
78.59
81.37
83.61
84.65
84.56
83.85
84.08
85.41
85.75
86.38
88.87
90.37
92.21
95.75
97.29
98.29
99.51
99.04
98.9
100.74
100.3
101.68
101.3
103.13
104.17
105.98
106.25
104.01
101.68
101.93
104.41
105.51
104.71
103.14
102.66
102.68
101.89
101.37
101.16
99.34
99.35
99.88
99.31
99.91
98.39
98.02
98.7
98.01
98.42
98.2
93.5
93.17
93.42
93.13
92.31
92.09
92.62
91.43
89.38
86.21
86.65
88.62
87.3
88.33
88.67
88.23
88.85
90.38
89.65
89.2
87.87




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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.123832071086754
gamma0.949968239218729

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.123832071086754 \tabularnewline
gamma & 0.949968239218729 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.123832071086754[/C][/ROW]
[ROW][C]gamma[/C][C]0.949968239218729[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
beta0.123832071086754
gamma0.949968239218729







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1390.3783.43453508082826.93546491917181
1492.2193.0330696021394-0.823069602139412
1595.7596.48284653179-0.732846531789988
1697.2997.9453938431322-0.65539384313216
1798.2998.8639188976377-0.573918897637697
1899.51100.103272316663-0.59327231666262
1999.0498.57213452129470.467865478705349
2098.999.7708331733675-0.870833173367487
21100.74100.7021463738910.0378536261093529
22100.3101.374588916256-1.07458891625566
23101.68101.1830536361130.496946363886934
24101.3104.752035107399-3.45203510739947
25103.13102.6935536872550.436446312745034
26104.17104.970374291053-0.800374291053345
27105.98107.809778035033-1.82977803503327
28106.25107.139103909739-0.889103909739063
29104.01106.708518510371-2.69851851037083
30101.68104.471397527304-2.79139752730427
31101.9399.10157058910312.82842941089686
32104.41101.3535488464243.05645115357592
33105.51105.4293801443040.0806198556961988
34104.71105.317991397321-0.607991397320731
35103.14104.848595526718-1.70859552671777
36102.66105.226090069138-2.56609006913767
37102.68103.156440553835-0.476440553834919
38101.89103.496666526937-1.60666652693662
39101.37104.325930890907-2.95593089090738
40101.16101.225273754435-0.0652737544351538
4199.34100.446894860386-1.10689486038589
4299.3598.81045523365910.539544766340924
4399.8896.27075404959813.60924595040194
4499.3198.86322581344920.44677418655084
4599.9199.53341979323540.376580206764601
4698.3999.0292045734552-0.639204573455217
4798.0297.82257215942730.197427840572701
4898.799.5153742789372-0.815374278937171
4998.0198.8881126459917-0.878112645991692
5098.4298.4470672172435-0.0270672172434985
5198.2100.613923506241-2.41392350624098
5293.597.9562991455408-4.45629914554078
5393.1792.17595611867210.994043881327869
5493.4292.26578209189451.15421790810547
5593.1390.20696761979962.92303238020042
5692.3191.80939163617670.500608363823261
5792.0992.1547969440213-0.0647969440213245
5892.6290.86825398549571.75174601450431
5991.4391.9669029544623-0.536902954462263
6089.3892.6132589329284-3.23325893292836
6186.2189.0284376473877-2.81843764738775
6286.6585.81153848707360.838461512926429
6388.6287.88904335840080.730956641599178
6487.388.0716808313925-0.771680831392501
6588.3386.17086458180932.15913541819071
6688.6787.74593885570590.924061144294114
6788.2385.86673234001512.36326765998486
6888.8587.17172256448721.67827743551277
6990.3889.04859405377831.33140594622174
7089.6589.7033453470304-0.0533453470304437
7189.289.3172032096516-0.11720320965162
7287.8790.7105024441349-2.84050244413486

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 90.37 & 83.4345350808282 & 6.93546491917181 \tabularnewline
14 & 92.21 & 93.0330696021394 & -0.823069602139412 \tabularnewline
15 & 95.75 & 96.48284653179 & -0.732846531789988 \tabularnewline
16 & 97.29 & 97.9453938431322 & -0.65539384313216 \tabularnewline
17 & 98.29 & 98.8639188976377 & -0.573918897637697 \tabularnewline
18 & 99.51 & 100.103272316663 & -0.59327231666262 \tabularnewline
19 & 99.04 & 98.5721345212947 & 0.467865478705349 \tabularnewline
20 & 98.9 & 99.7708331733675 & -0.870833173367487 \tabularnewline
21 & 100.74 & 100.702146373891 & 0.0378536261093529 \tabularnewline
22 & 100.3 & 101.374588916256 & -1.07458891625566 \tabularnewline
23 & 101.68 & 101.183053636113 & 0.496946363886934 \tabularnewline
24 & 101.3 & 104.752035107399 & -3.45203510739947 \tabularnewline
25 & 103.13 & 102.693553687255 & 0.436446312745034 \tabularnewline
26 & 104.17 & 104.970374291053 & -0.800374291053345 \tabularnewline
27 & 105.98 & 107.809778035033 & -1.82977803503327 \tabularnewline
28 & 106.25 & 107.139103909739 & -0.889103909739063 \tabularnewline
29 & 104.01 & 106.708518510371 & -2.69851851037083 \tabularnewline
30 & 101.68 & 104.471397527304 & -2.79139752730427 \tabularnewline
31 & 101.93 & 99.1015705891031 & 2.82842941089686 \tabularnewline
32 & 104.41 & 101.353548846424 & 3.05645115357592 \tabularnewline
33 & 105.51 & 105.429380144304 & 0.0806198556961988 \tabularnewline
34 & 104.71 & 105.317991397321 & -0.607991397320731 \tabularnewline
35 & 103.14 & 104.848595526718 & -1.70859552671777 \tabularnewline
36 & 102.66 & 105.226090069138 & -2.56609006913767 \tabularnewline
37 & 102.68 & 103.156440553835 & -0.476440553834919 \tabularnewline
38 & 101.89 & 103.496666526937 & -1.60666652693662 \tabularnewline
39 & 101.37 & 104.325930890907 & -2.95593089090738 \tabularnewline
40 & 101.16 & 101.225273754435 & -0.0652737544351538 \tabularnewline
41 & 99.34 & 100.446894860386 & -1.10689486038589 \tabularnewline
42 & 99.35 & 98.8104552336591 & 0.539544766340924 \tabularnewline
43 & 99.88 & 96.2707540495981 & 3.60924595040194 \tabularnewline
44 & 99.31 & 98.8632258134492 & 0.44677418655084 \tabularnewline
45 & 99.91 & 99.5334197932354 & 0.376580206764601 \tabularnewline
46 & 98.39 & 99.0292045734552 & -0.639204573455217 \tabularnewline
47 & 98.02 & 97.8225721594273 & 0.197427840572701 \tabularnewline
48 & 98.7 & 99.5153742789372 & -0.815374278937171 \tabularnewline
49 & 98.01 & 98.8881126459917 & -0.878112645991692 \tabularnewline
50 & 98.42 & 98.4470672172435 & -0.0270672172434985 \tabularnewline
51 & 98.2 & 100.613923506241 & -2.41392350624098 \tabularnewline
52 & 93.5 & 97.9562991455408 & -4.45629914554078 \tabularnewline
53 & 93.17 & 92.1759561186721 & 0.994043881327869 \tabularnewline
54 & 93.42 & 92.2657820918945 & 1.15421790810547 \tabularnewline
55 & 93.13 & 90.2069676197996 & 2.92303238020042 \tabularnewline
56 & 92.31 & 91.8093916361767 & 0.500608363823261 \tabularnewline
57 & 92.09 & 92.1547969440213 & -0.0647969440213245 \tabularnewline
58 & 92.62 & 90.8682539854957 & 1.75174601450431 \tabularnewline
59 & 91.43 & 91.9669029544623 & -0.536902954462263 \tabularnewline
60 & 89.38 & 92.6132589329284 & -3.23325893292836 \tabularnewline
61 & 86.21 & 89.0284376473877 & -2.81843764738775 \tabularnewline
62 & 86.65 & 85.8115384870736 & 0.838461512926429 \tabularnewline
63 & 88.62 & 87.8890433584008 & 0.730956641599178 \tabularnewline
64 & 87.3 & 88.0716808313925 & -0.771680831392501 \tabularnewline
65 & 88.33 & 86.1708645818093 & 2.15913541819071 \tabularnewline
66 & 88.67 & 87.7459388557059 & 0.924061144294114 \tabularnewline
67 & 88.23 & 85.8667323400151 & 2.36326765998486 \tabularnewline
68 & 88.85 & 87.1717225644872 & 1.67827743551277 \tabularnewline
69 & 90.38 & 89.0485940537783 & 1.33140594622174 \tabularnewline
70 & 89.65 & 89.7033453470304 & -0.0533453470304437 \tabularnewline
71 & 89.2 & 89.3172032096516 & -0.11720320965162 \tabularnewline
72 & 87.87 & 90.7105024441349 & -2.84050244413486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]90.37[/C][C]83.4345350808282[/C][C]6.93546491917181[/C][/ROW]
[ROW][C]14[/C][C]92.21[/C][C]93.0330696021394[/C][C]-0.823069602139412[/C][/ROW]
[ROW][C]15[/C][C]95.75[/C][C]96.48284653179[/C][C]-0.732846531789988[/C][/ROW]
[ROW][C]16[/C][C]97.29[/C][C]97.9453938431322[/C][C]-0.65539384313216[/C][/ROW]
[ROW][C]17[/C][C]98.29[/C][C]98.8639188976377[/C][C]-0.573918897637697[/C][/ROW]
[ROW][C]18[/C][C]99.51[/C][C]100.103272316663[/C][C]-0.59327231666262[/C][/ROW]
[ROW][C]19[/C][C]99.04[/C][C]98.5721345212947[/C][C]0.467865478705349[/C][/ROW]
[ROW][C]20[/C][C]98.9[/C][C]99.7708331733675[/C][C]-0.870833173367487[/C][/ROW]
[ROW][C]21[/C][C]100.74[/C][C]100.702146373891[/C][C]0.0378536261093529[/C][/ROW]
[ROW][C]22[/C][C]100.3[/C][C]101.374588916256[/C][C]-1.07458891625566[/C][/ROW]
[ROW][C]23[/C][C]101.68[/C][C]101.183053636113[/C][C]0.496946363886934[/C][/ROW]
[ROW][C]24[/C][C]101.3[/C][C]104.752035107399[/C][C]-3.45203510739947[/C][/ROW]
[ROW][C]25[/C][C]103.13[/C][C]102.693553687255[/C][C]0.436446312745034[/C][/ROW]
[ROW][C]26[/C][C]104.17[/C][C]104.970374291053[/C][C]-0.800374291053345[/C][/ROW]
[ROW][C]27[/C][C]105.98[/C][C]107.809778035033[/C][C]-1.82977803503327[/C][/ROW]
[ROW][C]28[/C][C]106.25[/C][C]107.139103909739[/C][C]-0.889103909739063[/C][/ROW]
[ROW][C]29[/C][C]104.01[/C][C]106.708518510371[/C][C]-2.69851851037083[/C][/ROW]
[ROW][C]30[/C][C]101.68[/C][C]104.471397527304[/C][C]-2.79139752730427[/C][/ROW]
[ROW][C]31[/C][C]101.93[/C][C]99.1015705891031[/C][C]2.82842941089686[/C][/ROW]
[ROW][C]32[/C][C]104.41[/C][C]101.353548846424[/C][C]3.05645115357592[/C][/ROW]
[ROW][C]33[/C][C]105.51[/C][C]105.429380144304[/C][C]0.0806198556961988[/C][/ROW]
[ROW][C]34[/C][C]104.71[/C][C]105.317991397321[/C][C]-0.607991397320731[/C][/ROW]
[ROW][C]35[/C][C]103.14[/C][C]104.848595526718[/C][C]-1.70859552671777[/C][/ROW]
[ROW][C]36[/C][C]102.66[/C][C]105.226090069138[/C][C]-2.56609006913767[/C][/ROW]
[ROW][C]37[/C][C]102.68[/C][C]103.156440553835[/C][C]-0.476440553834919[/C][/ROW]
[ROW][C]38[/C][C]101.89[/C][C]103.496666526937[/C][C]-1.60666652693662[/C][/ROW]
[ROW][C]39[/C][C]101.37[/C][C]104.325930890907[/C][C]-2.95593089090738[/C][/ROW]
[ROW][C]40[/C][C]101.16[/C][C]101.225273754435[/C][C]-0.0652737544351538[/C][/ROW]
[ROW][C]41[/C][C]99.34[/C][C]100.446894860386[/C][C]-1.10689486038589[/C][/ROW]
[ROW][C]42[/C][C]99.35[/C][C]98.8104552336591[/C][C]0.539544766340924[/C][/ROW]
[ROW][C]43[/C][C]99.88[/C][C]96.2707540495981[/C][C]3.60924595040194[/C][/ROW]
[ROW][C]44[/C][C]99.31[/C][C]98.8632258134492[/C][C]0.44677418655084[/C][/ROW]
[ROW][C]45[/C][C]99.91[/C][C]99.5334197932354[/C][C]0.376580206764601[/C][/ROW]
[ROW][C]46[/C][C]98.39[/C][C]99.0292045734552[/C][C]-0.639204573455217[/C][/ROW]
[ROW][C]47[/C][C]98.02[/C][C]97.8225721594273[/C][C]0.197427840572701[/C][/ROW]
[ROW][C]48[/C][C]98.7[/C][C]99.5153742789372[/C][C]-0.815374278937171[/C][/ROW]
[ROW][C]49[/C][C]98.01[/C][C]98.8881126459917[/C][C]-0.878112645991692[/C][/ROW]
[ROW][C]50[/C][C]98.42[/C][C]98.4470672172435[/C][C]-0.0270672172434985[/C][/ROW]
[ROW][C]51[/C][C]98.2[/C][C]100.613923506241[/C][C]-2.41392350624098[/C][/ROW]
[ROW][C]52[/C][C]93.5[/C][C]97.9562991455408[/C][C]-4.45629914554078[/C][/ROW]
[ROW][C]53[/C][C]93.17[/C][C]92.1759561186721[/C][C]0.994043881327869[/C][/ROW]
[ROW][C]54[/C][C]93.42[/C][C]92.2657820918945[/C][C]1.15421790810547[/C][/ROW]
[ROW][C]55[/C][C]93.13[/C][C]90.2069676197996[/C][C]2.92303238020042[/C][/ROW]
[ROW][C]56[/C][C]92.31[/C][C]91.8093916361767[/C][C]0.500608363823261[/C][/ROW]
[ROW][C]57[/C][C]92.09[/C][C]92.1547969440213[/C][C]-0.0647969440213245[/C][/ROW]
[ROW][C]58[/C][C]92.62[/C][C]90.8682539854957[/C][C]1.75174601450431[/C][/ROW]
[ROW][C]59[/C][C]91.43[/C][C]91.9669029544623[/C][C]-0.536902954462263[/C][/ROW]
[ROW][C]60[/C][C]89.38[/C][C]92.6132589329284[/C][C]-3.23325893292836[/C][/ROW]
[ROW][C]61[/C][C]86.21[/C][C]89.0284376473877[/C][C]-2.81843764738775[/C][/ROW]
[ROW][C]62[/C][C]86.65[/C][C]85.8115384870736[/C][C]0.838461512926429[/C][/ROW]
[ROW][C]63[/C][C]88.62[/C][C]87.8890433584008[/C][C]0.730956641599178[/C][/ROW]
[ROW][C]64[/C][C]87.3[/C][C]88.0716808313925[/C][C]-0.771680831392501[/C][/ROW]
[ROW][C]65[/C][C]88.33[/C][C]86.1708645818093[/C][C]2.15913541819071[/C][/ROW]
[ROW][C]66[/C][C]88.67[/C][C]87.7459388557059[/C][C]0.924061144294114[/C][/ROW]
[ROW][C]67[/C][C]88.23[/C][C]85.8667323400151[/C][C]2.36326765998486[/C][/ROW]
[ROW][C]68[/C][C]88.85[/C][C]87.1717225644872[/C][C]1.67827743551277[/C][/ROW]
[ROW][C]69[/C][C]90.38[/C][C]89.0485940537783[/C][C]1.33140594622174[/C][/ROW]
[ROW][C]70[/C][C]89.65[/C][C]89.7033453470304[/C][C]-0.0533453470304437[/C][/ROW]
[ROW][C]71[/C][C]89.2[/C][C]89.3172032096516[/C][C]-0.11720320965162[/C][/ROW]
[ROW][C]72[/C][C]87.87[/C][C]90.7105024441349[/C][C]-2.84050244413486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1390.3783.43453508082826.93546491917181
1492.2193.0330696021394-0.823069602139412
1595.7596.48284653179-0.732846531789988
1697.2997.9453938431322-0.65539384313216
1798.2998.8639188976377-0.573918897637697
1899.51100.103272316663-0.59327231666262
1999.0498.57213452129470.467865478705349
2098.999.7708331733675-0.870833173367487
21100.74100.7021463738910.0378536261093529
22100.3101.374588916256-1.07458891625566
23101.68101.1830536361130.496946363886934
24101.3104.752035107399-3.45203510739947
25103.13102.6935536872550.436446312745034
26104.17104.970374291053-0.800374291053345
27105.98107.809778035033-1.82977803503327
28106.25107.139103909739-0.889103909739063
29104.01106.708518510371-2.69851851037083
30101.68104.471397527304-2.79139752730427
31101.9399.10157058910312.82842941089686
32104.41101.3535488464243.05645115357592
33105.51105.4293801443040.0806198556961988
34104.71105.317991397321-0.607991397320731
35103.14104.848595526718-1.70859552671777
36102.66105.226090069138-2.56609006913767
37102.68103.156440553835-0.476440553834919
38101.89103.496666526937-1.60666652693662
39101.37104.325930890907-2.95593089090738
40101.16101.225273754435-0.0652737544351538
4199.34100.446894860386-1.10689486038589
4299.3598.81045523365910.539544766340924
4399.8896.27075404959813.60924595040194
4499.3198.86322581344920.44677418655084
4599.9199.53341979323540.376580206764601
4698.3999.0292045734552-0.639204573455217
4798.0297.82257215942730.197427840572701
4898.799.5153742789372-0.815374278937171
4998.0198.8881126459917-0.878112645991692
5098.4298.4470672172435-0.0270672172434985
5198.2100.613923506241-2.41392350624098
5293.597.9562991455408-4.45629914554078
5393.1792.17595611867210.994043881327869
5493.4292.26578209189451.15421790810547
5593.1390.20696761979962.92303238020042
5692.3191.80939163617670.500608363823261
5792.0992.1547969440213-0.0647969440213245
5892.6290.86825398549571.75174601450431
5991.4391.9669029544623-0.536902954462263
6089.3892.6132589329284-3.23325893292836
6186.2189.0284376473877-2.81843764738775
6286.6585.81153848707360.838461512926429
6388.6287.88904335840080.730956641599178
6487.388.0716808313925-0.771680831392501
6588.3386.17086458180932.15913541819071
6688.6787.74593885570590.924061144294114
6788.2385.86673234001512.36326765998486
6888.8587.17172256448721.67827743551277
6990.3889.04859405377831.33140594622174
7089.6589.7033453470304-0.0533453470304437
7189.289.3172032096516-0.11720320965162
7287.8790.7105024441349-2.84050244413486







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7387.925062214878684.121480516749491.7286439130077
7488.302865525636482.560019141633394.0457119096395
7590.259725079176882.670689030800597.8487611275531
7690.304413257011181.046565816799799.5622606972225
7789.849071008710778.9808251994059100.717316818016
7889.680549388473377.1606755224992102.200423254447
7987.143607208913973.2966504050203100.990564012808
8086.095939881796570.7086270284644101.483252735129
8186.080440174160768.9496303305407103.211250017781
8285.074608152252766.3670218012514103.782194503254
8384.406269575680364.0328787905272104.779660360833
8485.492104238157956.4279195938531114.556288882463

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 87.9250622148786 & 84.1214805167494 & 91.7286439130077 \tabularnewline
74 & 88.3028655256364 & 82.5600191416333 & 94.0457119096395 \tabularnewline
75 & 90.2597250791768 & 82.6706890308005 & 97.8487611275531 \tabularnewline
76 & 90.3044132570111 & 81.0465658167997 & 99.5622606972225 \tabularnewline
77 & 89.8490710087107 & 78.9808251994059 & 100.717316818016 \tabularnewline
78 & 89.6805493884733 & 77.1606755224992 & 102.200423254447 \tabularnewline
79 & 87.1436072089139 & 73.2966504050203 & 100.990564012808 \tabularnewline
80 & 86.0959398817965 & 70.7086270284644 & 101.483252735129 \tabularnewline
81 & 86.0804401741607 & 68.9496303305407 & 103.211250017781 \tabularnewline
82 & 85.0746081522527 & 66.3670218012514 & 103.782194503254 \tabularnewline
83 & 84.4062695756803 & 64.0328787905272 & 104.779660360833 \tabularnewline
84 & 85.4921042381579 & 56.4279195938531 & 114.556288882463 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]87.9250622148786[/C][C]84.1214805167494[/C][C]91.7286439130077[/C][/ROW]
[ROW][C]74[/C][C]88.3028655256364[/C][C]82.5600191416333[/C][C]94.0457119096395[/C][/ROW]
[ROW][C]75[/C][C]90.2597250791768[/C][C]82.6706890308005[/C][C]97.8487611275531[/C][/ROW]
[ROW][C]76[/C][C]90.3044132570111[/C][C]81.0465658167997[/C][C]99.5622606972225[/C][/ROW]
[ROW][C]77[/C][C]89.8490710087107[/C][C]78.9808251994059[/C][C]100.717316818016[/C][/ROW]
[ROW][C]78[/C][C]89.6805493884733[/C][C]77.1606755224992[/C][C]102.200423254447[/C][/ROW]
[ROW][C]79[/C][C]87.1436072089139[/C][C]73.2966504050203[/C][C]100.990564012808[/C][/ROW]
[ROW][C]80[/C][C]86.0959398817965[/C][C]70.7086270284644[/C][C]101.483252735129[/C][/ROW]
[ROW][C]81[/C][C]86.0804401741607[/C][C]68.9496303305407[/C][C]103.211250017781[/C][/ROW]
[ROW][C]82[/C][C]85.0746081522527[/C][C]66.3670218012514[/C][C]103.782194503254[/C][/ROW]
[ROW][C]83[/C][C]84.4062695756803[/C][C]64.0328787905272[/C][C]104.779660360833[/C][/ROW]
[ROW][C]84[/C][C]85.4921042381579[/C][C]56.4279195938531[/C][C]114.556288882463[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
7387.925062214878684.121480516749491.7286439130077
7488.302865525636482.560019141633394.0457119096395
7590.259725079176882.670689030800597.8487611275531
7690.304413257011181.046565816799799.5622606972225
7789.849071008710778.9808251994059100.717316818016
7889.680549388473377.1606755224992102.200423254447
7987.143607208913973.2966504050203100.990564012808
8086.095939881796570.7086270284644101.483252735129
8186.080440174160768.9496303305407103.211250017781
8285.074608152252766.3670218012514103.782194503254
8384.406269575680364.0328787905272104.779660360833
8485.492104238157956.4279195938531114.556288882463



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')