Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 May 2017 12:04:38 +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/01/t1493636783cra9lonzdtd4k1z.htm/, Retrieved Wed, 15 May 2024 22:32:01 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 22:32:01 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
101.74
100.73
100.86
100.78
100.76
100.77
100.77
101.93
101.98
102.47
102.59
102.54
102.54
101.29
101.49
101.71
101.98
102.11
102.11
103.13
103.43
103.8
103.99
104.03
104.03
102.58
102.65
102.81
102.98
103.12
103.12
104.33
104.41
104.66
104.81
104.9
100.15
98.74
98.74
98.96
99.34
99.4
99.5
100.5
100.77
101.08
101.39
101.43
101.43
101.29
101.33
101.15
101.25
101.13
101.07
101.33
101.61
101.29
101.39
101.46
101.81
101.78
101.93
102.01
102.03
102.14
101.81
101.52
101.38
101.5
101.65
101.64




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
beta0.00514594280109315
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00514594280109315 \tabularnewline
gamma & 0 \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]0.00514594280109315[/C][/ROW]
[ROW][C]gamma[/C][C]0[/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
beta0.00514594280109315
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13102.54102.0132040255370.526795974462928
14101.29101.2846826532350.00531734676525275
15101.49101.4801547872080.00984521279212913
16101.71101.6948118971280.0151881028723722
17101.98101.9669405061690.0130594938306103
18102.11102.0903697859590.0196302140407454
19102.11101.907673143510.20232685649033
20103.13103.330004716516-0.200004716515693
21103.43103.2314169233380.198583076662132
22103.8103.963156306894-0.163156306893939
23103.99103.931899871280.0581001287201417
24104.03103.9324563114110.0975436885889849
25104.03104.0184535111110.0115464888885413
26102.58102.756371552999-0.17637155299947
27102.65102.771749223792-0.121749223791809
28102.81102.855776653243-0.0457766532432231
29102.98103.068087497296-0.0880874972957315
30103.12103.0893999492270.0306000507729607
31103.12102.9136725866530.20632741334687
32104.33104.350061373451-0.0200613734509574
33104.41104.431345892227-0.0213458922272025
34104.66104.946024995195-0.28602499519539
35104.81104.790305708360.0196942916395955
36104.9104.7491606566810.150839343318978
37100.15104.885739284791-4.73573928479104
3898.7498.9017975629835-0.161797562983509
3998.7498.9025300627479-0.162530062747862
4098.9698.91570643125460.0442935687453598
4199.3499.18654755658320.153452443416839
4299.499.4246734271098-0.0246734271097608
4399.599.18011195076340.319888049236567
44100.5100.666178039321-0.166178039321053
45100.77100.5763298223670.19367017763345
46101.08101.266873163459-0.186873163459154
47101.39101.1857713296590.204228670341081
48101.43101.3118937243420.118106275657652
49101.43101.3968821080740.0331178919264232
50101.29100.1667429654121.12325703458841
51101.33101.463285178323-0.13328517832268
52101.15101.517022213404-0.367022213404056
53101.25101.386455960468-0.136455960467657
54101.13101.339904506796-0.209904506795937
55101.07100.9090651003210.160934899679205
56101.33102.25665883764-0.926658837639707
57101.61101.4057122848590.204287715141007
58101.29102.109802519332-0.819802519332129
59101.39101.392006824629-0.00200682462880764
60101.46101.307014550080.152985449920322
61101.81101.4221547235770.387845276423434
62101.78100.5388903549851.24110964501536
63101.93101.951495626298-0.0214956262981758
64102.01102.11598905004-0.105989050039824
65102.03102.247471141319-0.217471141318654
66102.14102.1192545776220.0207454223779564
67101.81101.916532396857-0.106532396857475
68101.52103.003831447189-1.48383144718915
69101.38101.591917308839-0.21191730883902
70101.5101.87288319223-0.372883192229551
71101.65101.5984045532240.0515954467764885
72101.64101.5632336569920.0767663430075203

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 102.54 & 102.013204025537 & 0.526795974462928 \tabularnewline
14 & 101.29 & 101.284682653235 & 0.00531734676525275 \tabularnewline
15 & 101.49 & 101.480154787208 & 0.00984521279212913 \tabularnewline
16 & 101.71 & 101.694811897128 & 0.0151881028723722 \tabularnewline
17 & 101.98 & 101.966940506169 & 0.0130594938306103 \tabularnewline
18 & 102.11 & 102.090369785959 & 0.0196302140407454 \tabularnewline
19 & 102.11 & 101.90767314351 & 0.20232685649033 \tabularnewline
20 & 103.13 & 103.330004716516 & -0.200004716515693 \tabularnewline
21 & 103.43 & 103.231416923338 & 0.198583076662132 \tabularnewline
22 & 103.8 & 103.963156306894 & -0.163156306893939 \tabularnewline
23 & 103.99 & 103.93189987128 & 0.0581001287201417 \tabularnewline
24 & 104.03 & 103.932456311411 & 0.0975436885889849 \tabularnewline
25 & 104.03 & 104.018453511111 & 0.0115464888885413 \tabularnewline
26 & 102.58 & 102.756371552999 & -0.17637155299947 \tabularnewline
27 & 102.65 & 102.771749223792 & -0.121749223791809 \tabularnewline
28 & 102.81 & 102.855776653243 & -0.0457766532432231 \tabularnewline
29 & 102.98 & 103.068087497296 & -0.0880874972957315 \tabularnewline
30 & 103.12 & 103.089399949227 & 0.0306000507729607 \tabularnewline
31 & 103.12 & 102.913672586653 & 0.20632741334687 \tabularnewline
32 & 104.33 & 104.350061373451 & -0.0200613734509574 \tabularnewline
33 & 104.41 & 104.431345892227 & -0.0213458922272025 \tabularnewline
34 & 104.66 & 104.946024995195 & -0.28602499519539 \tabularnewline
35 & 104.81 & 104.79030570836 & 0.0196942916395955 \tabularnewline
36 & 104.9 & 104.749160656681 & 0.150839343318978 \tabularnewline
37 & 100.15 & 104.885739284791 & -4.73573928479104 \tabularnewline
38 & 98.74 & 98.9017975629835 & -0.161797562983509 \tabularnewline
39 & 98.74 & 98.9025300627479 & -0.162530062747862 \tabularnewline
40 & 98.96 & 98.9157064312546 & 0.0442935687453598 \tabularnewline
41 & 99.34 & 99.1865475565832 & 0.153452443416839 \tabularnewline
42 & 99.4 & 99.4246734271098 & -0.0246734271097608 \tabularnewline
43 & 99.5 & 99.1801119507634 & 0.319888049236567 \tabularnewline
44 & 100.5 & 100.666178039321 & -0.166178039321053 \tabularnewline
45 & 100.77 & 100.576329822367 & 0.19367017763345 \tabularnewline
46 & 101.08 & 101.266873163459 & -0.186873163459154 \tabularnewline
47 & 101.39 & 101.185771329659 & 0.204228670341081 \tabularnewline
48 & 101.43 & 101.311893724342 & 0.118106275657652 \tabularnewline
49 & 101.43 & 101.396882108074 & 0.0331178919264232 \tabularnewline
50 & 101.29 & 100.166742965412 & 1.12325703458841 \tabularnewline
51 & 101.33 & 101.463285178323 & -0.13328517832268 \tabularnewline
52 & 101.15 & 101.517022213404 & -0.367022213404056 \tabularnewline
53 & 101.25 & 101.386455960468 & -0.136455960467657 \tabularnewline
54 & 101.13 & 101.339904506796 & -0.209904506795937 \tabularnewline
55 & 101.07 & 100.909065100321 & 0.160934899679205 \tabularnewline
56 & 101.33 & 102.25665883764 & -0.926658837639707 \tabularnewline
57 & 101.61 & 101.405712284859 & 0.204287715141007 \tabularnewline
58 & 101.29 & 102.109802519332 & -0.819802519332129 \tabularnewline
59 & 101.39 & 101.392006824629 & -0.00200682462880764 \tabularnewline
60 & 101.46 & 101.30701455008 & 0.152985449920322 \tabularnewline
61 & 101.81 & 101.422154723577 & 0.387845276423434 \tabularnewline
62 & 101.78 & 100.538890354985 & 1.24110964501536 \tabularnewline
63 & 101.93 & 101.951495626298 & -0.0214956262981758 \tabularnewline
64 & 102.01 & 102.11598905004 & -0.105989050039824 \tabularnewline
65 & 102.03 & 102.247471141319 & -0.217471141318654 \tabularnewline
66 & 102.14 & 102.119254577622 & 0.0207454223779564 \tabularnewline
67 & 101.81 & 101.916532396857 & -0.106532396857475 \tabularnewline
68 & 101.52 & 103.003831447189 & -1.48383144718915 \tabularnewline
69 & 101.38 & 101.591917308839 & -0.21191730883902 \tabularnewline
70 & 101.5 & 101.87288319223 & -0.372883192229551 \tabularnewline
71 & 101.65 & 101.598404553224 & 0.0515954467764885 \tabularnewline
72 & 101.64 & 101.563233656992 & 0.0767663430075203 \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]102.54[/C][C]102.013204025537[/C][C]0.526795974462928[/C][/ROW]
[ROW][C]14[/C][C]101.29[/C][C]101.284682653235[/C][C]0.00531734676525275[/C][/ROW]
[ROW][C]15[/C][C]101.49[/C][C]101.480154787208[/C][C]0.00984521279212913[/C][/ROW]
[ROW][C]16[/C][C]101.71[/C][C]101.694811897128[/C][C]0.0151881028723722[/C][/ROW]
[ROW][C]17[/C][C]101.98[/C][C]101.966940506169[/C][C]0.0130594938306103[/C][/ROW]
[ROW][C]18[/C][C]102.11[/C][C]102.090369785959[/C][C]0.0196302140407454[/C][/ROW]
[ROW][C]19[/C][C]102.11[/C][C]101.90767314351[/C][C]0.20232685649033[/C][/ROW]
[ROW][C]20[/C][C]103.13[/C][C]103.330004716516[/C][C]-0.200004716515693[/C][/ROW]
[ROW][C]21[/C][C]103.43[/C][C]103.231416923338[/C][C]0.198583076662132[/C][/ROW]
[ROW][C]22[/C][C]103.8[/C][C]103.963156306894[/C][C]-0.163156306893939[/C][/ROW]
[ROW][C]23[/C][C]103.99[/C][C]103.93189987128[/C][C]0.0581001287201417[/C][/ROW]
[ROW][C]24[/C][C]104.03[/C][C]103.932456311411[/C][C]0.0975436885889849[/C][/ROW]
[ROW][C]25[/C][C]104.03[/C][C]104.018453511111[/C][C]0.0115464888885413[/C][/ROW]
[ROW][C]26[/C][C]102.58[/C][C]102.756371552999[/C][C]-0.17637155299947[/C][/ROW]
[ROW][C]27[/C][C]102.65[/C][C]102.771749223792[/C][C]-0.121749223791809[/C][/ROW]
[ROW][C]28[/C][C]102.81[/C][C]102.855776653243[/C][C]-0.0457766532432231[/C][/ROW]
[ROW][C]29[/C][C]102.98[/C][C]103.068087497296[/C][C]-0.0880874972957315[/C][/ROW]
[ROW][C]30[/C][C]103.12[/C][C]103.089399949227[/C][C]0.0306000507729607[/C][/ROW]
[ROW][C]31[/C][C]103.12[/C][C]102.913672586653[/C][C]0.20632741334687[/C][/ROW]
[ROW][C]32[/C][C]104.33[/C][C]104.350061373451[/C][C]-0.0200613734509574[/C][/ROW]
[ROW][C]33[/C][C]104.41[/C][C]104.431345892227[/C][C]-0.0213458922272025[/C][/ROW]
[ROW][C]34[/C][C]104.66[/C][C]104.946024995195[/C][C]-0.28602499519539[/C][/ROW]
[ROW][C]35[/C][C]104.81[/C][C]104.79030570836[/C][C]0.0196942916395955[/C][/ROW]
[ROW][C]36[/C][C]104.9[/C][C]104.749160656681[/C][C]0.150839343318978[/C][/ROW]
[ROW][C]37[/C][C]100.15[/C][C]104.885739284791[/C][C]-4.73573928479104[/C][/ROW]
[ROW][C]38[/C][C]98.74[/C][C]98.9017975629835[/C][C]-0.161797562983509[/C][/ROW]
[ROW][C]39[/C][C]98.74[/C][C]98.9025300627479[/C][C]-0.162530062747862[/C][/ROW]
[ROW][C]40[/C][C]98.96[/C][C]98.9157064312546[/C][C]0.0442935687453598[/C][/ROW]
[ROW][C]41[/C][C]99.34[/C][C]99.1865475565832[/C][C]0.153452443416839[/C][/ROW]
[ROW][C]42[/C][C]99.4[/C][C]99.4246734271098[/C][C]-0.0246734271097608[/C][/ROW]
[ROW][C]43[/C][C]99.5[/C][C]99.1801119507634[/C][C]0.319888049236567[/C][/ROW]
[ROW][C]44[/C][C]100.5[/C][C]100.666178039321[/C][C]-0.166178039321053[/C][/ROW]
[ROW][C]45[/C][C]100.77[/C][C]100.576329822367[/C][C]0.19367017763345[/C][/ROW]
[ROW][C]46[/C][C]101.08[/C][C]101.266873163459[/C][C]-0.186873163459154[/C][/ROW]
[ROW][C]47[/C][C]101.39[/C][C]101.185771329659[/C][C]0.204228670341081[/C][/ROW]
[ROW][C]48[/C][C]101.43[/C][C]101.311893724342[/C][C]0.118106275657652[/C][/ROW]
[ROW][C]49[/C][C]101.43[/C][C]101.396882108074[/C][C]0.0331178919264232[/C][/ROW]
[ROW][C]50[/C][C]101.29[/C][C]100.166742965412[/C][C]1.12325703458841[/C][/ROW]
[ROW][C]51[/C][C]101.33[/C][C]101.463285178323[/C][C]-0.13328517832268[/C][/ROW]
[ROW][C]52[/C][C]101.15[/C][C]101.517022213404[/C][C]-0.367022213404056[/C][/ROW]
[ROW][C]53[/C][C]101.25[/C][C]101.386455960468[/C][C]-0.136455960467657[/C][/ROW]
[ROW][C]54[/C][C]101.13[/C][C]101.339904506796[/C][C]-0.209904506795937[/C][/ROW]
[ROW][C]55[/C][C]101.07[/C][C]100.909065100321[/C][C]0.160934899679205[/C][/ROW]
[ROW][C]56[/C][C]101.33[/C][C]102.25665883764[/C][C]-0.926658837639707[/C][/ROW]
[ROW][C]57[/C][C]101.61[/C][C]101.405712284859[/C][C]0.204287715141007[/C][/ROW]
[ROW][C]58[/C][C]101.29[/C][C]102.109802519332[/C][C]-0.819802519332129[/C][/ROW]
[ROW][C]59[/C][C]101.39[/C][C]101.392006824629[/C][C]-0.00200682462880764[/C][/ROW]
[ROW][C]60[/C][C]101.46[/C][C]101.30701455008[/C][C]0.152985449920322[/C][/ROW]
[ROW][C]61[/C][C]101.81[/C][C]101.422154723577[/C][C]0.387845276423434[/C][/ROW]
[ROW][C]62[/C][C]101.78[/C][C]100.538890354985[/C][C]1.24110964501536[/C][/ROW]
[ROW][C]63[/C][C]101.93[/C][C]101.951495626298[/C][C]-0.0214956262981758[/C][/ROW]
[ROW][C]64[/C][C]102.01[/C][C]102.11598905004[/C][C]-0.105989050039824[/C][/ROW]
[ROW][C]65[/C][C]102.03[/C][C]102.247471141319[/C][C]-0.217471141318654[/C][/ROW]
[ROW][C]66[/C][C]102.14[/C][C]102.119254577622[/C][C]0.0207454223779564[/C][/ROW]
[ROW][C]67[/C][C]101.81[/C][C]101.916532396857[/C][C]-0.106532396857475[/C][/ROW]
[ROW][C]68[/C][C]101.52[/C][C]103.003831447189[/C][C]-1.48383144718915[/C][/ROW]
[ROW][C]69[/C][C]101.38[/C][C]101.591917308839[/C][C]-0.21191730883902[/C][/ROW]
[ROW][C]70[/C][C]101.5[/C][C]101.87288319223[/C][C]-0.372883192229551[/C][/ROW]
[ROW][C]71[/C][C]101.65[/C][C]101.598404553224[/C][C]0.0515954467764885[/C][/ROW]
[ROW][C]72[/C][C]101.64[/C][C]101.563233656992[/C][C]0.0767663430075203[/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
13102.54102.0132040255370.526795974462928
14101.29101.2846826532350.00531734676525275
15101.49101.4801547872080.00984521279212913
16101.71101.6948118971280.0151881028723722
17101.98101.9669405061690.0130594938306103
18102.11102.0903697859590.0196302140407454
19102.11101.907673143510.20232685649033
20103.13103.330004716516-0.200004716515693
21103.43103.2314169233380.198583076662132
22103.8103.963156306894-0.163156306893939
23103.99103.931899871280.0581001287201417
24104.03103.9324563114110.0975436885889849
25104.03104.0184535111110.0115464888885413
26102.58102.756371552999-0.17637155299947
27102.65102.771749223792-0.121749223791809
28102.81102.855776653243-0.0457766532432231
29102.98103.068087497296-0.0880874972957315
30103.12103.0893999492270.0306000507729607
31103.12102.9136725866530.20632741334687
32104.33104.350061373451-0.0200613734509574
33104.41104.431345892227-0.0213458922272025
34104.66104.946024995195-0.28602499519539
35104.81104.790305708360.0196942916395955
36104.9104.7491606566810.150839343318978
37100.15104.885739284791-4.73573928479104
3898.7498.9017975629835-0.161797562983509
3998.7498.9025300627479-0.162530062747862
4098.9698.91570643125460.0442935687453598
4199.3499.18654755658320.153452443416839
4299.499.4246734271098-0.0246734271097608
4399.599.18011195076340.319888049236567
44100.5100.666178039321-0.166178039321053
45100.77100.5763298223670.19367017763345
46101.08101.266873163459-0.186873163459154
47101.39101.1857713296590.204228670341081
48101.43101.3118937243420.118106275657652
49101.43101.3968821080740.0331178919264232
50101.29100.1667429654121.12325703458841
51101.33101.463285178323-0.13328517832268
52101.15101.517022213404-0.367022213404056
53101.25101.386455960468-0.136455960467657
54101.13101.339904506796-0.209904506795937
55101.07100.9090651003210.160934899679205
56101.33102.25665883764-0.926658837639707
57101.61101.4057122848590.204287715141007
58101.29102.109802519332-0.819802519332129
59101.39101.392006824629-0.00200682462880764
60101.46101.307014550080.152985449920322
61101.81101.4221547235770.387845276423434
62101.78100.5388903549851.24110964501536
63101.93101.951495626298-0.0214956262981758
64102.01102.11598905004-0.105989050039824
65102.03102.247471141319-0.217471141318654
66102.14102.1192545776220.0207454223779564
67101.81101.916532396857-0.106532396857475
68101.52103.003831447189-1.48383144718915
69101.38101.591917308839-0.21191730883902
70101.5101.87288319223-0.372883192229551
71101.65101.5984045532240.0515954467764885
72101.64101.5632336569920.0767663430075203







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73101.598187458765100.197425001837102.998949915693
74100.3241868888898.351252012556102.297121765203
75100.48229628561698.0529569110552102.911635660176
76100.65480024379397.8375783994496103.472022088136
77100.87872121415297.7156725122072104.041769916097
78100.95751825187397.483155315455104.431881188291
79100.72713325315696.974243224579104.480023281734
80101.89913155841797.8367897207695105.961473396065
81101.96870660928297.6522178581744106.285195360389
82102.46278250007197.8868072295548107.038757770587
83102.56212735387197.7532759580017107.370978749741
84102.47435711220481.4956986589354123.453015565474

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 101.598187458765 & 100.197425001837 & 102.998949915693 \tabularnewline
74 & 100.32418688888 & 98.351252012556 & 102.297121765203 \tabularnewline
75 & 100.482296285616 & 98.0529569110552 & 102.911635660176 \tabularnewline
76 & 100.654800243793 & 97.8375783994496 & 103.472022088136 \tabularnewline
77 & 100.878721214152 & 97.7156725122072 & 104.041769916097 \tabularnewline
78 & 100.957518251873 & 97.483155315455 & 104.431881188291 \tabularnewline
79 & 100.727133253156 & 96.974243224579 & 104.480023281734 \tabularnewline
80 & 101.899131558417 & 97.8367897207695 & 105.961473396065 \tabularnewline
81 & 101.968706609282 & 97.6522178581744 & 106.285195360389 \tabularnewline
82 & 102.462782500071 & 97.8868072295548 & 107.038757770587 \tabularnewline
83 & 102.562127353871 & 97.7532759580017 & 107.370978749741 \tabularnewline
84 & 102.474357112204 & 81.4956986589354 & 123.453015565474 \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]101.598187458765[/C][C]100.197425001837[/C][C]102.998949915693[/C][/ROW]
[ROW][C]74[/C][C]100.32418688888[/C][C]98.351252012556[/C][C]102.297121765203[/C][/ROW]
[ROW][C]75[/C][C]100.482296285616[/C][C]98.0529569110552[/C][C]102.911635660176[/C][/ROW]
[ROW][C]76[/C][C]100.654800243793[/C][C]97.8375783994496[/C][C]103.472022088136[/C][/ROW]
[ROW][C]77[/C][C]100.878721214152[/C][C]97.7156725122072[/C][C]104.041769916097[/C][/ROW]
[ROW][C]78[/C][C]100.957518251873[/C][C]97.483155315455[/C][C]104.431881188291[/C][/ROW]
[ROW][C]79[/C][C]100.727133253156[/C][C]96.974243224579[/C][C]104.480023281734[/C][/ROW]
[ROW][C]80[/C][C]101.899131558417[/C][C]97.8367897207695[/C][C]105.961473396065[/C][/ROW]
[ROW][C]81[/C][C]101.968706609282[/C][C]97.6522178581744[/C][C]106.285195360389[/C][/ROW]
[ROW][C]82[/C][C]102.462782500071[/C][C]97.8868072295548[/C][C]107.038757770587[/C][/ROW]
[ROW][C]83[/C][C]102.562127353871[/C][C]97.7532759580017[/C][C]107.370978749741[/C][/ROW]
[ROW][C]84[/C][C]102.474357112204[/C][C]81.4956986589354[/C][C]123.453015565474[/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
73101.598187458765100.197425001837102.998949915693
74100.3241868888898.351252012556102.297121765203
75100.48229628561698.0529569110552102.911635660176
76100.65480024379397.8375783994496103.472022088136
77100.87872121415297.7156725122072104.041769916097
78100.95751825187397.483155315455104.431881188291
79100.72713325315696.974243224579104.480023281734
80101.89913155841797.8367897207695105.961473396065
81101.96870660928297.6522178581744106.285195360389
82102.46278250007197.8868072295548107.038757770587
83102.56212735387197.7532759580017107.370978749741
84102.47435711220481.4956986589354123.453015565474



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')