Free Statistics

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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 May 2017 16:11:17 +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/t1493651495x8rcy15f9q79gxc.htm/, Retrieved Wed, 15 May 2024 21:50:17 +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 21:50:17 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
 93,65   
 92,68   
 92,70   
 92,73   
 92,80   
 92,86   
 93,02   
 93,02   
 93,04   
 93,09   
 93,11   
 93,11   
 93,20   
 93,21   
 93,22   
 93,23   
 93,29   
 93,42   
 93,43   
 93,45   
 93,45   
 93,49   
 93,50   
 93,56   
 93,68   
 93,70   
 94,01   
 94,07   
 94,33   
 94,43   
 94,47   
 95,35   
 95,37   
 95,46   
 95,83   
 96,00   
 96,85   
 97,84   
 98,38   
 98,90   
 99,51   
 99,93   
 99,95   
 101,40   
 101,56   
 101,65   
 101,70   
 101,91   
 101,91   
 102,29   
 102,33   
 102,44   
 102,57   
 102,59   
 102,84   
 102,88   
 103,04   
 103,16   
 103,20   
 103,23   
 103,27   
 103,31   
 103,59   
 104,35   
 104,55   
 104,60   
 104,67   
 104,93   
 105,08   
 105,15   
 109,25   
 109,82   




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.902104994995845
beta0.237825358930605
gamma0.687727324724698

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.902104994995845 \tabularnewline
beta & 0.237825358930605 \tabularnewline
gamma & 0.687727324724698 \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]0.902104994995845[/C][/ROW]
[ROW][C]beta[/C][C]0.237825358930605[/C][/ROW]
[ROW][C]gamma[/C][C]0.687727324724698[/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
alpha0.902104994995845
beta0.237825358930605
gamma0.687727324724698







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1393.292.95735125907670.2426487409233
1493.2193.2405829858708-0.0305829858708222
1593.2293.2707496476446-0.0507496476445795
1693.2393.2730752856258-0.0430752856257897
1793.2993.3239264541856-0.0339264541855897
1893.4293.4436922723886-0.0236922723885868
1993.4393.4595157667494-0.0295157667493555
2093.4593.4735085250616-0.0235085250616009
2193.4593.4673435059932-0.0173435059932245
2293.4993.4944123791861-0.00441237918606419
2393.593.5033273606038-0.00332736060379091
2493.5693.48991980342040.0700801965796387
2593.6893.66794437318410.0120556268158651
2693.793.68635344210720.0136465578927982
2794.0193.72623852828390.28376147171609
2894.0794.0737263917946-0.00372639179462908
2994.3394.2124680760170.117531923983037
3094.4394.5547170218102-0.124717021810156
3194.4794.5412915391415-0.0712915391415407
3295.3594.57143091063110.778569089368943
3395.3795.5142667879198-0.144266787919747
3495.4695.6261542890307-0.166154289030658
3595.8395.65231690161280.177683098387163
369696.0084596050789-0.00845960507888321
3796.8596.29891110335460.551088896645368
3897.8497.10330815023150.736691849768491
3998.3898.26937401015290.110625989847136
4098.998.85813306528810.0418669347119476
4199.5199.47675751573990.0332424842601
4299.93100.14207538329-0.21207538329007
4399.95100.445073882512-0.495073882512173
44101.4100.4543694306210.945630569379063
45101.56101.817291496443-0.257291496442974
46101.65102.138881803314-0.488881803313575
47101.7102.140581300796-0.440581300795984
48101.91102.033953435099-0.123953435099054
49101.91102.350003757552-0.440003757552006
50102.29102.1441661769890.145833823011245
51102.33102.479444608785-0.149444608784577
52102.44102.518034008042-0.0780340080421098
53102.57102.694467816803-0.124467816802905
54102.59102.834206441461-0.244206441460804
55102.84102.7125583282580.127441671741792
56102.88103.141758903974-0.261758903973714
57103.04102.8310272150860.208972784914138
58103.16103.1566178356340.00338216436639982
59103.2103.310390835231-0.110390835230845
60103.23103.298113807757-0.0681138077574417
61103.27103.431744638568-0.161744638568464
62103.31103.363562581814-0.0535625818135088
63103.59103.3028382349940.287161765006289
64104.35103.6377548599110.71224514008901
65104.55104.592395254966-0.0423952549664932
66104.6104.88472675664-0.284726756639785
67104.67104.828169398207-0.158169398206851
68104.93104.991319336638-0.0613193366378795
69105.08104.9486130380360.131386961963841
70105.15105.231672016615-0.0816720166151583
71109.25105.3244801351173.92551986488294
72109.82109.843189575904-0.0231895759035865

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 93.2 & 92.9573512590767 & 0.2426487409233 \tabularnewline
14 & 93.21 & 93.2405829858708 & -0.0305829858708222 \tabularnewline
15 & 93.22 & 93.2707496476446 & -0.0507496476445795 \tabularnewline
16 & 93.23 & 93.2730752856258 & -0.0430752856257897 \tabularnewline
17 & 93.29 & 93.3239264541856 & -0.0339264541855897 \tabularnewline
18 & 93.42 & 93.4436922723886 & -0.0236922723885868 \tabularnewline
19 & 93.43 & 93.4595157667494 & -0.0295157667493555 \tabularnewline
20 & 93.45 & 93.4735085250616 & -0.0235085250616009 \tabularnewline
21 & 93.45 & 93.4673435059932 & -0.0173435059932245 \tabularnewline
22 & 93.49 & 93.4944123791861 & -0.00441237918606419 \tabularnewline
23 & 93.5 & 93.5033273606038 & -0.00332736060379091 \tabularnewline
24 & 93.56 & 93.4899198034204 & 0.0700801965796387 \tabularnewline
25 & 93.68 & 93.6679443731841 & 0.0120556268158651 \tabularnewline
26 & 93.7 & 93.6863534421072 & 0.0136465578927982 \tabularnewline
27 & 94.01 & 93.7262385282839 & 0.28376147171609 \tabularnewline
28 & 94.07 & 94.0737263917946 & -0.00372639179462908 \tabularnewline
29 & 94.33 & 94.212468076017 & 0.117531923983037 \tabularnewline
30 & 94.43 & 94.5547170218102 & -0.124717021810156 \tabularnewline
31 & 94.47 & 94.5412915391415 & -0.0712915391415407 \tabularnewline
32 & 95.35 & 94.5714309106311 & 0.778569089368943 \tabularnewline
33 & 95.37 & 95.5142667879198 & -0.144266787919747 \tabularnewline
34 & 95.46 & 95.6261542890307 & -0.166154289030658 \tabularnewline
35 & 95.83 & 95.6523169016128 & 0.177683098387163 \tabularnewline
36 & 96 & 96.0084596050789 & -0.00845960507888321 \tabularnewline
37 & 96.85 & 96.2989111033546 & 0.551088896645368 \tabularnewline
38 & 97.84 & 97.1033081502315 & 0.736691849768491 \tabularnewline
39 & 98.38 & 98.2693740101529 & 0.110625989847136 \tabularnewline
40 & 98.9 & 98.8581330652881 & 0.0418669347119476 \tabularnewline
41 & 99.51 & 99.4767575157399 & 0.0332424842601 \tabularnewline
42 & 99.93 & 100.14207538329 & -0.21207538329007 \tabularnewline
43 & 99.95 & 100.445073882512 & -0.495073882512173 \tabularnewline
44 & 101.4 & 100.454369430621 & 0.945630569379063 \tabularnewline
45 & 101.56 & 101.817291496443 & -0.257291496442974 \tabularnewline
46 & 101.65 & 102.138881803314 & -0.488881803313575 \tabularnewline
47 & 101.7 & 102.140581300796 & -0.440581300795984 \tabularnewline
48 & 101.91 & 102.033953435099 & -0.123953435099054 \tabularnewline
49 & 101.91 & 102.350003757552 & -0.440003757552006 \tabularnewline
50 & 102.29 & 102.144166176989 & 0.145833823011245 \tabularnewline
51 & 102.33 & 102.479444608785 & -0.149444608784577 \tabularnewline
52 & 102.44 & 102.518034008042 & -0.0780340080421098 \tabularnewline
53 & 102.57 & 102.694467816803 & -0.124467816802905 \tabularnewline
54 & 102.59 & 102.834206441461 & -0.244206441460804 \tabularnewline
55 & 102.84 & 102.712558328258 & 0.127441671741792 \tabularnewline
56 & 102.88 & 103.141758903974 & -0.261758903973714 \tabularnewline
57 & 103.04 & 102.831027215086 & 0.208972784914138 \tabularnewline
58 & 103.16 & 103.156617835634 & 0.00338216436639982 \tabularnewline
59 & 103.2 & 103.310390835231 & -0.110390835230845 \tabularnewline
60 & 103.23 & 103.298113807757 & -0.0681138077574417 \tabularnewline
61 & 103.27 & 103.431744638568 & -0.161744638568464 \tabularnewline
62 & 103.31 & 103.363562581814 & -0.0535625818135088 \tabularnewline
63 & 103.59 & 103.302838234994 & 0.287161765006289 \tabularnewline
64 & 104.35 & 103.637754859911 & 0.71224514008901 \tabularnewline
65 & 104.55 & 104.592395254966 & -0.0423952549664932 \tabularnewline
66 & 104.6 & 104.88472675664 & -0.284726756639785 \tabularnewline
67 & 104.67 & 104.828169398207 & -0.158169398206851 \tabularnewline
68 & 104.93 & 104.991319336638 & -0.0613193366378795 \tabularnewline
69 & 105.08 & 104.948613038036 & 0.131386961963841 \tabularnewline
70 & 105.15 & 105.231672016615 & -0.0816720166151583 \tabularnewline
71 & 109.25 & 105.324480135117 & 3.92551986488294 \tabularnewline
72 & 109.82 & 109.843189575904 & -0.0231895759035865 \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]93.2[/C][C]92.9573512590767[/C][C]0.2426487409233[/C][/ROW]
[ROW][C]14[/C][C]93.21[/C][C]93.2405829858708[/C][C]-0.0305829858708222[/C][/ROW]
[ROW][C]15[/C][C]93.22[/C][C]93.2707496476446[/C][C]-0.0507496476445795[/C][/ROW]
[ROW][C]16[/C][C]93.23[/C][C]93.2730752856258[/C][C]-0.0430752856257897[/C][/ROW]
[ROW][C]17[/C][C]93.29[/C][C]93.3239264541856[/C][C]-0.0339264541855897[/C][/ROW]
[ROW][C]18[/C][C]93.42[/C][C]93.4436922723886[/C][C]-0.0236922723885868[/C][/ROW]
[ROW][C]19[/C][C]93.43[/C][C]93.4595157667494[/C][C]-0.0295157667493555[/C][/ROW]
[ROW][C]20[/C][C]93.45[/C][C]93.4735085250616[/C][C]-0.0235085250616009[/C][/ROW]
[ROW][C]21[/C][C]93.45[/C][C]93.4673435059932[/C][C]-0.0173435059932245[/C][/ROW]
[ROW][C]22[/C][C]93.49[/C][C]93.4944123791861[/C][C]-0.00441237918606419[/C][/ROW]
[ROW][C]23[/C][C]93.5[/C][C]93.5033273606038[/C][C]-0.00332736060379091[/C][/ROW]
[ROW][C]24[/C][C]93.56[/C][C]93.4899198034204[/C][C]0.0700801965796387[/C][/ROW]
[ROW][C]25[/C][C]93.68[/C][C]93.6679443731841[/C][C]0.0120556268158651[/C][/ROW]
[ROW][C]26[/C][C]93.7[/C][C]93.6863534421072[/C][C]0.0136465578927982[/C][/ROW]
[ROW][C]27[/C][C]94.01[/C][C]93.7262385282839[/C][C]0.28376147171609[/C][/ROW]
[ROW][C]28[/C][C]94.07[/C][C]94.0737263917946[/C][C]-0.00372639179462908[/C][/ROW]
[ROW][C]29[/C][C]94.33[/C][C]94.212468076017[/C][C]0.117531923983037[/C][/ROW]
[ROW][C]30[/C][C]94.43[/C][C]94.5547170218102[/C][C]-0.124717021810156[/C][/ROW]
[ROW][C]31[/C][C]94.47[/C][C]94.5412915391415[/C][C]-0.0712915391415407[/C][/ROW]
[ROW][C]32[/C][C]95.35[/C][C]94.5714309106311[/C][C]0.778569089368943[/C][/ROW]
[ROW][C]33[/C][C]95.37[/C][C]95.5142667879198[/C][C]-0.144266787919747[/C][/ROW]
[ROW][C]34[/C][C]95.46[/C][C]95.6261542890307[/C][C]-0.166154289030658[/C][/ROW]
[ROW][C]35[/C][C]95.83[/C][C]95.6523169016128[/C][C]0.177683098387163[/C][/ROW]
[ROW][C]36[/C][C]96[/C][C]96.0084596050789[/C][C]-0.00845960507888321[/C][/ROW]
[ROW][C]37[/C][C]96.85[/C][C]96.2989111033546[/C][C]0.551088896645368[/C][/ROW]
[ROW][C]38[/C][C]97.84[/C][C]97.1033081502315[/C][C]0.736691849768491[/C][/ROW]
[ROW][C]39[/C][C]98.38[/C][C]98.2693740101529[/C][C]0.110625989847136[/C][/ROW]
[ROW][C]40[/C][C]98.9[/C][C]98.8581330652881[/C][C]0.0418669347119476[/C][/ROW]
[ROW][C]41[/C][C]99.51[/C][C]99.4767575157399[/C][C]0.0332424842601[/C][/ROW]
[ROW][C]42[/C][C]99.93[/C][C]100.14207538329[/C][C]-0.21207538329007[/C][/ROW]
[ROW][C]43[/C][C]99.95[/C][C]100.445073882512[/C][C]-0.495073882512173[/C][/ROW]
[ROW][C]44[/C][C]101.4[/C][C]100.454369430621[/C][C]0.945630569379063[/C][/ROW]
[ROW][C]45[/C][C]101.56[/C][C]101.817291496443[/C][C]-0.257291496442974[/C][/ROW]
[ROW][C]46[/C][C]101.65[/C][C]102.138881803314[/C][C]-0.488881803313575[/C][/ROW]
[ROW][C]47[/C][C]101.7[/C][C]102.140581300796[/C][C]-0.440581300795984[/C][/ROW]
[ROW][C]48[/C][C]101.91[/C][C]102.033953435099[/C][C]-0.123953435099054[/C][/ROW]
[ROW][C]49[/C][C]101.91[/C][C]102.350003757552[/C][C]-0.440003757552006[/C][/ROW]
[ROW][C]50[/C][C]102.29[/C][C]102.144166176989[/C][C]0.145833823011245[/C][/ROW]
[ROW][C]51[/C][C]102.33[/C][C]102.479444608785[/C][C]-0.149444608784577[/C][/ROW]
[ROW][C]52[/C][C]102.44[/C][C]102.518034008042[/C][C]-0.0780340080421098[/C][/ROW]
[ROW][C]53[/C][C]102.57[/C][C]102.694467816803[/C][C]-0.124467816802905[/C][/ROW]
[ROW][C]54[/C][C]102.59[/C][C]102.834206441461[/C][C]-0.244206441460804[/C][/ROW]
[ROW][C]55[/C][C]102.84[/C][C]102.712558328258[/C][C]0.127441671741792[/C][/ROW]
[ROW][C]56[/C][C]102.88[/C][C]103.141758903974[/C][C]-0.261758903973714[/C][/ROW]
[ROW][C]57[/C][C]103.04[/C][C]102.831027215086[/C][C]0.208972784914138[/C][/ROW]
[ROW][C]58[/C][C]103.16[/C][C]103.156617835634[/C][C]0.00338216436639982[/C][/ROW]
[ROW][C]59[/C][C]103.2[/C][C]103.310390835231[/C][C]-0.110390835230845[/C][/ROW]
[ROW][C]60[/C][C]103.23[/C][C]103.298113807757[/C][C]-0.0681138077574417[/C][/ROW]
[ROW][C]61[/C][C]103.27[/C][C]103.431744638568[/C][C]-0.161744638568464[/C][/ROW]
[ROW][C]62[/C][C]103.31[/C][C]103.363562581814[/C][C]-0.0535625818135088[/C][/ROW]
[ROW][C]63[/C][C]103.59[/C][C]103.302838234994[/C][C]0.287161765006289[/C][/ROW]
[ROW][C]64[/C][C]104.35[/C][C]103.637754859911[/C][C]0.71224514008901[/C][/ROW]
[ROW][C]65[/C][C]104.55[/C][C]104.592395254966[/C][C]-0.0423952549664932[/C][/ROW]
[ROW][C]66[/C][C]104.6[/C][C]104.88472675664[/C][C]-0.284726756639785[/C][/ROW]
[ROW][C]67[/C][C]104.67[/C][C]104.828169398207[/C][C]-0.158169398206851[/C][/ROW]
[ROW][C]68[/C][C]104.93[/C][C]104.991319336638[/C][C]-0.0613193366378795[/C][/ROW]
[ROW][C]69[/C][C]105.08[/C][C]104.948613038036[/C][C]0.131386961963841[/C][/ROW]
[ROW][C]70[/C][C]105.15[/C][C]105.231672016615[/C][C]-0.0816720166151583[/C][/ROW]
[ROW][C]71[/C][C]109.25[/C][C]105.324480135117[/C][C]3.92551986488294[/C][/ROW]
[ROW][C]72[/C][C]109.82[/C][C]109.843189575904[/C][C]-0.0231895759035865[/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
1393.292.95735125907670.2426487409233
1493.2193.2405829858708-0.0305829858708222
1593.2293.2707496476446-0.0507496476445795
1693.2393.2730752856258-0.0430752856257897
1793.2993.3239264541856-0.0339264541855897
1893.4293.4436922723886-0.0236922723885868
1993.4393.4595157667494-0.0295157667493555
2093.4593.4735085250616-0.0235085250616009
2193.4593.4673435059932-0.0173435059932245
2293.4993.4944123791861-0.00441237918606419
2393.593.5033273606038-0.00332736060379091
2493.5693.48991980342040.0700801965796387
2593.6893.66794437318410.0120556268158651
2693.793.68635344210720.0136465578927982
2794.0193.72623852828390.28376147171609
2894.0794.0737263917946-0.00372639179462908
2994.3394.2124680760170.117531923983037
3094.4394.5547170218102-0.124717021810156
3194.4794.5412915391415-0.0712915391415407
3295.3594.57143091063110.778569089368943
3395.3795.5142667879198-0.144266787919747
3495.4695.6261542890307-0.166154289030658
3595.8395.65231690161280.177683098387163
369696.0084596050789-0.00845960507888321
3796.8596.29891110335460.551088896645368
3897.8497.10330815023150.736691849768491
3998.3898.26937401015290.110625989847136
4098.998.85813306528810.0418669347119476
4199.5199.47675751573990.0332424842601
4299.93100.14207538329-0.21207538329007
4399.95100.445073882512-0.495073882512173
44101.4100.4543694306210.945630569379063
45101.56101.817291496443-0.257291496442974
46101.65102.138881803314-0.488881803313575
47101.7102.140581300796-0.440581300795984
48101.91102.033953435099-0.123953435099054
49101.91102.350003757552-0.440003757552006
50102.29102.1441661769890.145833823011245
51102.33102.479444608785-0.149444608784577
52102.44102.518034008042-0.0780340080421098
53102.57102.694467816803-0.124467816802905
54102.59102.834206441461-0.244206441460804
55102.84102.7125583282580.127441671741792
56102.88103.141758903974-0.261758903973714
57103.04102.8310272150860.208972784914138
58103.16103.1566178356340.00338216436639982
59103.2103.310390835231-0.110390835230845
60103.23103.298113807757-0.0681138077574417
61103.27103.431744638568-0.161744638568464
62103.31103.363562581814-0.0535625818135088
63103.59103.3028382349940.287161765006289
64104.35103.6377548599110.71224514008901
65104.55104.592395254966-0.0423952549664932
66104.6104.88472675664-0.284726756639785
67104.67104.828169398207-0.158169398206851
68104.93104.991319336638-0.0613193366378795
69105.08104.9486130380360.131386961963841
70105.15105.231672016615-0.0816720166151583
71109.25105.3244801351173.92551986488294
72109.82109.843189575904-0.0231895759035865







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73110.915633852571109.817074646075112.014193059068
74111.935770308745110.2599390312113.61160158629
75112.887261678022110.63330076126115.141222594783
76113.873236299802111.019334695326116.727137904279
77114.863715312936111.382566284784118.344864341088
78115.922524497455111.782808399099120.062240595811
79116.932673380859112.106303145899121.75904361582
80118.097522228812112.54827258479123.646771872835
81118.954535558966112.667960395055125.241110722877
82119.919546818597112.86309941504126.975994222153
83121.222683035154113.3480530992129.097312971108
84121.896136902802113.218605789122130.573668016483

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 110.915633852571 & 109.817074646075 & 112.014193059068 \tabularnewline
74 & 111.935770308745 & 110.2599390312 & 113.61160158629 \tabularnewline
75 & 112.887261678022 & 110.63330076126 & 115.141222594783 \tabularnewline
76 & 113.873236299802 & 111.019334695326 & 116.727137904279 \tabularnewline
77 & 114.863715312936 & 111.382566284784 & 118.344864341088 \tabularnewline
78 & 115.922524497455 & 111.782808399099 & 120.062240595811 \tabularnewline
79 & 116.932673380859 & 112.106303145899 & 121.75904361582 \tabularnewline
80 & 118.097522228812 & 112.54827258479 & 123.646771872835 \tabularnewline
81 & 118.954535558966 & 112.667960395055 & 125.241110722877 \tabularnewline
82 & 119.919546818597 & 112.86309941504 & 126.975994222153 \tabularnewline
83 & 121.222683035154 & 113.3480530992 & 129.097312971108 \tabularnewline
84 & 121.896136902802 & 113.218605789122 & 130.573668016483 \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]110.915633852571[/C][C]109.817074646075[/C][C]112.014193059068[/C][/ROW]
[ROW][C]74[/C][C]111.935770308745[/C][C]110.2599390312[/C][C]113.61160158629[/C][/ROW]
[ROW][C]75[/C][C]112.887261678022[/C][C]110.63330076126[/C][C]115.141222594783[/C][/ROW]
[ROW][C]76[/C][C]113.873236299802[/C][C]111.019334695326[/C][C]116.727137904279[/C][/ROW]
[ROW][C]77[/C][C]114.863715312936[/C][C]111.382566284784[/C][C]118.344864341088[/C][/ROW]
[ROW][C]78[/C][C]115.922524497455[/C][C]111.782808399099[/C][C]120.062240595811[/C][/ROW]
[ROW][C]79[/C][C]116.932673380859[/C][C]112.106303145899[/C][C]121.75904361582[/C][/ROW]
[ROW][C]80[/C][C]118.097522228812[/C][C]112.54827258479[/C][C]123.646771872835[/C][/ROW]
[ROW][C]81[/C][C]118.954535558966[/C][C]112.667960395055[/C][C]125.241110722877[/C][/ROW]
[ROW][C]82[/C][C]119.919546818597[/C][C]112.86309941504[/C][C]126.975994222153[/C][/ROW]
[ROW][C]83[/C][C]121.222683035154[/C][C]113.3480530992[/C][C]129.097312971108[/C][/ROW]
[ROW][C]84[/C][C]121.896136902802[/C][C]113.218605789122[/C][C]130.573668016483[/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
73110.915633852571109.817074646075112.014193059068
74111.935770308745110.2599390312113.61160158629
75112.887261678022110.63330076126115.141222594783
76113.873236299802111.019334695326116.727137904279
77114.863715312936111.382566284784118.344864341088
78115.922524497455111.782808399099120.062240595811
79116.932673380859112.106303145899121.75904361582
80118.097522228812112.54827258479123.646771872835
81118.954535558966112.667960395055125.241110722877
82119.919546818597112.86309941504126.975994222153
83121.222683035154113.3480530992129.097312971108
84121.896136902802113.218605789122130.573668016483



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')