Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 13 Nov 2013 08:27:41 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/13/t13843496808myr29npnfuq0ta.htm/, Retrieved Sun, 28 Apr 2024 22:03:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=224718, Retrieved Sun, 28 Apr 2024 22:03:13 +0000
QR Codes:

Original text written by user:Howard Van den Branden
IsPrivate?No (this computation is public)
User-defined keywordsHoward Van den Branden
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [WS8: double expon...] [2013-11-13 13:27:41] [c48df00dfd28bb130a7db97d228aa375] [Current]
Feedback Forum

Post a new message
Dataseries X:
6.02
5.62
4.87
4.24
4.02
3.74
3.45
3.34
3.21
3.12
3.04
2.97
2.93
2.95
2.92
2.9
2.95
2.91
2.89
2.84
2.82
2.78
2.86
2.87
2.94
3.04
3.12
3.19
3.27
3.34
3.4
3.55
3.64
3.76
3.78
3.77
3.81
3.81
3.82
3.96
3.86
3.84
3.68
3.56
3.48
3.4
3.42
3.2
3.11
3.1
2.99
3.1
3
3.05
3.1
3.2
3.1
3.3
3.13
3.14




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224718&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224718&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224718&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.851325467801
beta0.618181084049635
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.851325467801 \tabularnewline
beta & 0.618181084049635 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224718&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]0.851325467801[/C][/ROW]
[ROW][C]beta[/C][C]0.618181084049635[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224718&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224718&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
alpha0.851325467801
beta0.618181084049635
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
34.875.22-0.350000000000001
44.244.33784043107215-0.097840431072151
54.023.618859918533330.401140081466671
63.743.535783538917290.204216461082708
73.453.392534737060370.0574652629396337
83.343.154595336388970.185404663611034
93.213.123147530102920.0868524698970847
103.123.053507867395420.0664921326045795
113.043.001527965105170.038472034894832
122.972.945940644807860.0240593551921378
132.932.890745239486810.0392547605131908
142.952.869144802087270.0808551979127348
152.922.92551180839093-0.0055118083909278
162.92.90545166505658-0.00545166505658123
172.952.882573657511580.0674263424884161
182.912.95722323763859-0.0472232376385935
192.892.90941638119539-0.019416381195394
202.842.87506388680506-0.0350638868050623
212.822.808937084942150.0110629150578521
222.782.7879013210747-0.00790132107470143
232.862.746562565689420.113437434310581
242.872.868221675957080.00177832404292344
252.942.895758426405420.0442415735945803
263.042.982728381600460.057271618399545
273.123.110931669428330.00906833057166834
283.193.20287069095716-0.0128706909571554
293.273.269358963709290.000641036290708552
303.343.34768747426601-0.00768747426600802
313.43.41487999922197-0.0148799992219666
323.553.468118398202190.0818816017978148
333.643.64682451326937-0.00682451326936917
343.763.746421294307160.0135787056928418
353.783.87053396553496-0.0905339655349602
363.773.85836725937049-0.0883672593704854
373.813.801539796094340.00846020390565627
383.813.83159639772062-0.0215963977206242
393.823.82469944139817-0.00469944139817136
403.963.829714103785920.13028589621408
413.864.01821121048025-0.158211210480254
423.843.87784104693309-0.0378410469330852
433.683.82003033651071-0.140030336510709
443.563.60152905395979-0.0415290539597932
453.483.44502878955880.0349712104411988
463.43.37205956287950.0279404371204981
473.423.307809165876570.112190834123432
483.23.37432631808178-0.174326318081775
493.113.105180834860760.00481916513924041
503.12.99108266189110.108917338108897
512.993.02292620173731-0.0329262017373142
523.12.916686542806060.183313457193941
5333.09101019082689-0.0910101908268879
543.052.983898897356060.0661011026439438
553.13.045327694755470.0546723052445333
563.23.125799440392920.0742005596070796
573.13.26194585971904-0.161945859719041
583.33.111827036035760.18817296396424
593.133.35880369053301-0.228803690533009
603.143.13038422618020.00961577381980483

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4.87 & 5.22 & -0.350000000000001 \tabularnewline
4 & 4.24 & 4.33784043107215 & -0.097840431072151 \tabularnewline
5 & 4.02 & 3.61885991853333 & 0.401140081466671 \tabularnewline
6 & 3.74 & 3.53578353891729 & 0.204216461082708 \tabularnewline
7 & 3.45 & 3.39253473706037 & 0.0574652629396337 \tabularnewline
8 & 3.34 & 3.15459533638897 & 0.185404663611034 \tabularnewline
9 & 3.21 & 3.12314753010292 & 0.0868524698970847 \tabularnewline
10 & 3.12 & 3.05350786739542 & 0.0664921326045795 \tabularnewline
11 & 3.04 & 3.00152796510517 & 0.038472034894832 \tabularnewline
12 & 2.97 & 2.94594064480786 & 0.0240593551921378 \tabularnewline
13 & 2.93 & 2.89074523948681 & 0.0392547605131908 \tabularnewline
14 & 2.95 & 2.86914480208727 & 0.0808551979127348 \tabularnewline
15 & 2.92 & 2.92551180839093 & -0.0055118083909278 \tabularnewline
16 & 2.9 & 2.90545166505658 & -0.00545166505658123 \tabularnewline
17 & 2.95 & 2.88257365751158 & 0.0674263424884161 \tabularnewline
18 & 2.91 & 2.95722323763859 & -0.0472232376385935 \tabularnewline
19 & 2.89 & 2.90941638119539 & -0.019416381195394 \tabularnewline
20 & 2.84 & 2.87506388680506 & -0.0350638868050623 \tabularnewline
21 & 2.82 & 2.80893708494215 & 0.0110629150578521 \tabularnewline
22 & 2.78 & 2.7879013210747 & -0.00790132107470143 \tabularnewline
23 & 2.86 & 2.74656256568942 & 0.113437434310581 \tabularnewline
24 & 2.87 & 2.86822167595708 & 0.00177832404292344 \tabularnewline
25 & 2.94 & 2.89575842640542 & 0.0442415735945803 \tabularnewline
26 & 3.04 & 2.98272838160046 & 0.057271618399545 \tabularnewline
27 & 3.12 & 3.11093166942833 & 0.00906833057166834 \tabularnewline
28 & 3.19 & 3.20287069095716 & -0.0128706909571554 \tabularnewline
29 & 3.27 & 3.26935896370929 & 0.000641036290708552 \tabularnewline
30 & 3.34 & 3.34768747426601 & -0.00768747426600802 \tabularnewline
31 & 3.4 & 3.41487999922197 & -0.0148799992219666 \tabularnewline
32 & 3.55 & 3.46811839820219 & 0.0818816017978148 \tabularnewline
33 & 3.64 & 3.64682451326937 & -0.00682451326936917 \tabularnewline
34 & 3.76 & 3.74642129430716 & 0.0135787056928418 \tabularnewline
35 & 3.78 & 3.87053396553496 & -0.0905339655349602 \tabularnewline
36 & 3.77 & 3.85836725937049 & -0.0883672593704854 \tabularnewline
37 & 3.81 & 3.80153979609434 & 0.00846020390565627 \tabularnewline
38 & 3.81 & 3.83159639772062 & -0.0215963977206242 \tabularnewline
39 & 3.82 & 3.82469944139817 & -0.00469944139817136 \tabularnewline
40 & 3.96 & 3.82971410378592 & 0.13028589621408 \tabularnewline
41 & 3.86 & 4.01821121048025 & -0.158211210480254 \tabularnewline
42 & 3.84 & 3.87784104693309 & -0.0378410469330852 \tabularnewline
43 & 3.68 & 3.82003033651071 & -0.140030336510709 \tabularnewline
44 & 3.56 & 3.60152905395979 & -0.0415290539597932 \tabularnewline
45 & 3.48 & 3.4450287895588 & 0.0349712104411988 \tabularnewline
46 & 3.4 & 3.3720595628795 & 0.0279404371204981 \tabularnewline
47 & 3.42 & 3.30780916587657 & 0.112190834123432 \tabularnewline
48 & 3.2 & 3.37432631808178 & -0.174326318081775 \tabularnewline
49 & 3.11 & 3.10518083486076 & 0.00481916513924041 \tabularnewline
50 & 3.1 & 2.9910826618911 & 0.108917338108897 \tabularnewline
51 & 2.99 & 3.02292620173731 & -0.0329262017373142 \tabularnewline
52 & 3.1 & 2.91668654280606 & 0.183313457193941 \tabularnewline
53 & 3 & 3.09101019082689 & -0.0910101908268879 \tabularnewline
54 & 3.05 & 2.98389889735606 & 0.0661011026439438 \tabularnewline
55 & 3.1 & 3.04532769475547 & 0.0546723052445333 \tabularnewline
56 & 3.2 & 3.12579944039292 & 0.0742005596070796 \tabularnewline
57 & 3.1 & 3.26194585971904 & -0.161945859719041 \tabularnewline
58 & 3.3 & 3.11182703603576 & 0.18817296396424 \tabularnewline
59 & 3.13 & 3.35880369053301 & -0.228803690533009 \tabularnewline
60 & 3.14 & 3.1303842261802 & 0.00961577381980483 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224718&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]3[/C][C]4.87[/C][C]5.22[/C][C]-0.350000000000001[/C][/ROW]
[ROW][C]4[/C][C]4.24[/C][C]4.33784043107215[/C][C]-0.097840431072151[/C][/ROW]
[ROW][C]5[/C][C]4.02[/C][C]3.61885991853333[/C][C]0.401140081466671[/C][/ROW]
[ROW][C]6[/C][C]3.74[/C][C]3.53578353891729[/C][C]0.204216461082708[/C][/ROW]
[ROW][C]7[/C][C]3.45[/C][C]3.39253473706037[/C][C]0.0574652629396337[/C][/ROW]
[ROW][C]8[/C][C]3.34[/C][C]3.15459533638897[/C][C]0.185404663611034[/C][/ROW]
[ROW][C]9[/C][C]3.21[/C][C]3.12314753010292[/C][C]0.0868524698970847[/C][/ROW]
[ROW][C]10[/C][C]3.12[/C][C]3.05350786739542[/C][C]0.0664921326045795[/C][/ROW]
[ROW][C]11[/C][C]3.04[/C][C]3.00152796510517[/C][C]0.038472034894832[/C][/ROW]
[ROW][C]12[/C][C]2.97[/C][C]2.94594064480786[/C][C]0.0240593551921378[/C][/ROW]
[ROW][C]13[/C][C]2.93[/C][C]2.89074523948681[/C][C]0.0392547605131908[/C][/ROW]
[ROW][C]14[/C][C]2.95[/C][C]2.86914480208727[/C][C]0.0808551979127348[/C][/ROW]
[ROW][C]15[/C][C]2.92[/C][C]2.92551180839093[/C][C]-0.0055118083909278[/C][/ROW]
[ROW][C]16[/C][C]2.9[/C][C]2.90545166505658[/C][C]-0.00545166505658123[/C][/ROW]
[ROW][C]17[/C][C]2.95[/C][C]2.88257365751158[/C][C]0.0674263424884161[/C][/ROW]
[ROW][C]18[/C][C]2.91[/C][C]2.95722323763859[/C][C]-0.0472232376385935[/C][/ROW]
[ROW][C]19[/C][C]2.89[/C][C]2.90941638119539[/C][C]-0.019416381195394[/C][/ROW]
[ROW][C]20[/C][C]2.84[/C][C]2.87506388680506[/C][C]-0.0350638868050623[/C][/ROW]
[ROW][C]21[/C][C]2.82[/C][C]2.80893708494215[/C][C]0.0110629150578521[/C][/ROW]
[ROW][C]22[/C][C]2.78[/C][C]2.7879013210747[/C][C]-0.00790132107470143[/C][/ROW]
[ROW][C]23[/C][C]2.86[/C][C]2.74656256568942[/C][C]0.113437434310581[/C][/ROW]
[ROW][C]24[/C][C]2.87[/C][C]2.86822167595708[/C][C]0.00177832404292344[/C][/ROW]
[ROW][C]25[/C][C]2.94[/C][C]2.89575842640542[/C][C]0.0442415735945803[/C][/ROW]
[ROW][C]26[/C][C]3.04[/C][C]2.98272838160046[/C][C]0.057271618399545[/C][/ROW]
[ROW][C]27[/C][C]3.12[/C][C]3.11093166942833[/C][C]0.00906833057166834[/C][/ROW]
[ROW][C]28[/C][C]3.19[/C][C]3.20287069095716[/C][C]-0.0128706909571554[/C][/ROW]
[ROW][C]29[/C][C]3.27[/C][C]3.26935896370929[/C][C]0.000641036290708552[/C][/ROW]
[ROW][C]30[/C][C]3.34[/C][C]3.34768747426601[/C][C]-0.00768747426600802[/C][/ROW]
[ROW][C]31[/C][C]3.4[/C][C]3.41487999922197[/C][C]-0.0148799992219666[/C][/ROW]
[ROW][C]32[/C][C]3.55[/C][C]3.46811839820219[/C][C]0.0818816017978148[/C][/ROW]
[ROW][C]33[/C][C]3.64[/C][C]3.64682451326937[/C][C]-0.00682451326936917[/C][/ROW]
[ROW][C]34[/C][C]3.76[/C][C]3.74642129430716[/C][C]0.0135787056928418[/C][/ROW]
[ROW][C]35[/C][C]3.78[/C][C]3.87053396553496[/C][C]-0.0905339655349602[/C][/ROW]
[ROW][C]36[/C][C]3.77[/C][C]3.85836725937049[/C][C]-0.0883672593704854[/C][/ROW]
[ROW][C]37[/C][C]3.81[/C][C]3.80153979609434[/C][C]0.00846020390565627[/C][/ROW]
[ROW][C]38[/C][C]3.81[/C][C]3.83159639772062[/C][C]-0.0215963977206242[/C][/ROW]
[ROW][C]39[/C][C]3.82[/C][C]3.82469944139817[/C][C]-0.00469944139817136[/C][/ROW]
[ROW][C]40[/C][C]3.96[/C][C]3.82971410378592[/C][C]0.13028589621408[/C][/ROW]
[ROW][C]41[/C][C]3.86[/C][C]4.01821121048025[/C][C]-0.158211210480254[/C][/ROW]
[ROW][C]42[/C][C]3.84[/C][C]3.87784104693309[/C][C]-0.0378410469330852[/C][/ROW]
[ROW][C]43[/C][C]3.68[/C][C]3.82003033651071[/C][C]-0.140030336510709[/C][/ROW]
[ROW][C]44[/C][C]3.56[/C][C]3.60152905395979[/C][C]-0.0415290539597932[/C][/ROW]
[ROW][C]45[/C][C]3.48[/C][C]3.4450287895588[/C][C]0.0349712104411988[/C][/ROW]
[ROW][C]46[/C][C]3.4[/C][C]3.3720595628795[/C][C]0.0279404371204981[/C][/ROW]
[ROW][C]47[/C][C]3.42[/C][C]3.30780916587657[/C][C]0.112190834123432[/C][/ROW]
[ROW][C]48[/C][C]3.2[/C][C]3.37432631808178[/C][C]-0.174326318081775[/C][/ROW]
[ROW][C]49[/C][C]3.11[/C][C]3.10518083486076[/C][C]0.00481916513924041[/C][/ROW]
[ROW][C]50[/C][C]3.1[/C][C]2.9910826618911[/C][C]0.108917338108897[/C][/ROW]
[ROW][C]51[/C][C]2.99[/C][C]3.02292620173731[/C][C]-0.0329262017373142[/C][/ROW]
[ROW][C]52[/C][C]3.1[/C][C]2.91668654280606[/C][C]0.183313457193941[/C][/ROW]
[ROW][C]53[/C][C]3[/C][C]3.09101019082689[/C][C]-0.0910101908268879[/C][/ROW]
[ROW][C]54[/C][C]3.05[/C][C]2.98389889735606[/C][C]0.0661011026439438[/C][/ROW]
[ROW][C]55[/C][C]3.1[/C][C]3.04532769475547[/C][C]0.0546723052445333[/C][/ROW]
[ROW][C]56[/C][C]3.2[/C][C]3.12579944039292[/C][C]0.0742005596070796[/C][/ROW]
[ROW][C]57[/C][C]3.1[/C][C]3.26194585971904[/C][C]-0.161945859719041[/C][/ROW]
[ROW][C]58[/C][C]3.3[/C][C]3.11182703603576[/C][C]0.18817296396424[/C][/ROW]
[ROW][C]59[/C][C]3.13[/C][C]3.35880369053301[/C][C]-0.228803690533009[/C][/ROW]
[ROW][C]60[/C][C]3.14[/C][C]3.1303842261802[/C][C]0.00961577381980483[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224718&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224718&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
34.875.22-0.350000000000001
44.244.33784043107215-0.097840431072151
54.023.618859918533330.401140081466671
63.743.535783538917290.204216461082708
73.453.392534737060370.0574652629396337
83.343.154595336388970.185404663611034
93.213.123147530102920.0868524698970847
103.123.053507867395420.0664921326045795
113.043.001527965105170.038472034894832
122.972.945940644807860.0240593551921378
132.932.890745239486810.0392547605131908
142.952.869144802087270.0808551979127348
152.922.92551180839093-0.0055118083909278
162.92.90545166505658-0.00545166505658123
172.952.882573657511580.0674263424884161
182.912.95722323763859-0.0472232376385935
192.892.90941638119539-0.019416381195394
202.842.87506388680506-0.0350638868050623
212.822.808937084942150.0110629150578521
222.782.7879013210747-0.00790132107470143
232.862.746562565689420.113437434310581
242.872.868221675957080.00177832404292344
252.942.895758426405420.0442415735945803
263.042.982728381600460.057271618399545
273.123.110931669428330.00906833057166834
283.193.20287069095716-0.0128706909571554
293.273.269358963709290.000641036290708552
303.343.34768747426601-0.00768747426600802
313.43.41487999922197-0.0148799992219666
323.553.468118398202190.0818816017978148
333.643.64682451326937-0.00682451326936917
343.763.746421294307160.0135787056928418
353.783.87053396553496-0.0905339655349602
363.773.85836725937049-0.0883672593704854
373.813.801539796094340.00846020390565627
383.813.83159639772062-0.0215963977206242
393.823.82469944139817-0.00469944139817136
403.963.829714103785920.13028589621408
413.864.01821121048025-0.158211210480254
423.843.87784104693309-0.0378410469330852
433.683.82003033651071-0.140030336510709
443.563.60152905395979-0.0415290539597932
453.483.44502878955880.0349712104411988
463.43.37205956287950.0279404371204981
473.423.307809165876570.112190834123432
483.23.37432631808178-0.174326318081775
493.113.105180834860760.00481916513924041
503.12.99108266189110.108917338108897
512.993.02292620173731-0.0329262017373142
523.12.916686542806060.183313457193941
5333.09101019082689-0.0910101908268879
543.052.983898897356060.0661011026439438
553.13.045327694755470.0546723052445333
563.23.125799440392920.0742005596070796
573.13.26194585971904-0.161945859719041
583.33.111827036035760.18817296396424
593.133.35880369053301-0.228803690533009
603.143.13038422618020.00961577381980483







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
613.109997848876032.888466374036173.3315293237159
623.081425318426462.704315342043863.45853529480905
633.052852787976882.487079130040383.61862644591338
643.02428025752732.243303609246223.80525690580839
652.995707727077731.976457683488444.01495777066702
662.967135196628151.688807050870184.24546334238612
672.938562666178581.382006932054674.49511840030249
682.9099901357291.057347697323594.76263257413441
692.881417605279420.7158778944197655.04695731613908
702.852845074829850.3584743936248445.34721575603485
712.82427254438027-0.01411382996143035.66265891872198
722.7957000139307-0.4012365230252125.9926365508866

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 3.10999784887603 & 2.88846637403617 & 3.3315293237159 \tabularnewline
62 & 3.08142531842646 & 2.70431534204386 & 3.45853529480905 \tabularnewline
63 & 3.05285278797688 & 2.48707913004038 & 3.61862644591338 \tabularnewline
64 & 3.0242802575273 & 2.24330360924622 & 3.80525690580839 \tabularnewline
65 & 2.99570772707773 & 1.97645768348844 & 4.01495777066702 \tabularnewline
66 & 2.96713519662815 & 1.68880705087018 & 4.24546334238612 \tabularnewline
67 & 2.93856266617858 & 1.38200693205467 & 4.49511840030249 \tabularnewline
68 & 2.909990135729 & 1.05734769732359 & 4.76263257413441 \tabularnewline
69 & 2.88141760527942 & 0.715877894419765 & 5.04695731613908 \tabularnewline
70 & 2.85284507482985 & 0.358474393624844 & 5.34721575603485 \tabularnewline
71 & 2.82427254438027 & -0.0141138299614303 & 5.66265891872198 \tabularnewline
72 & 2.7957000139307 & -0.401236523025212 & 5.9926365508866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224718&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]61[/C][C]3.10999784887603[/C][C]2.88846637403617[/C][C]3.3315293237159[/C][/ROW]
[ROW][C]62[/C][C]3.08142531842646[/C][C]2.70431534204386[/C][C]3.45853529480905[/C][/ROW]
[ROW][C]63[/C][C]3.05285278797688[/C][C]2.48707913004038[/C][C]3.61862644591338[/C][/ROW]
[ROW][C]64[/C][C]3.0242802575273[/C][C]2.24330360924622[/C][C]3.80525690580839[/C][/ROW]
[ROW][C]65[/C][C]2.99570772707773[/C][C]1.97645768348844[/C][C]4.01495777066702[/C][/ROW]
[ROW][C]66[/C][C]2.96713519662815[/C][C]1.68880705087018[/C][C]4.24546334238612[/C][/ROW]
[ROW][C]67[/C][C]2.93856266617858[/C][C]1.38200693205467[/C][C]4.49511840030249[/C][/ROW]
[ROW][C]68[/C][C]2.909990135729[/C][C]1.05734769732359[/C][C]4.76263257413441[/C][/ROW]
[ROW][C]69[/C][C]2.88141760527942[/C][C]0.715877894419765[/C][C]5.04695731613908[/C][/ROW]
[ROW][C]70[/C][C]2.85284507482985[/C][C]0.358474393624844[/C][C]5.34721575603485[/C][/ROW]
[ROW][C]71[/C][C]2.82427254438027[/C][C]-0.0141138299614303[/C][C]5.66265891872198[/C][/ROW]
[ROW][C]72[/C][C]2.7957000139307[/C][C]-0.401236523025212[/C][C]5.9926365508866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224718&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224718&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
613.109997848876032.888466374036173.3315293237159
623.081425318426462.704315342043863.45853529480905
633.052852787976882.487079130040383.61862644591338
643.02428025752732.243303609246223.80525690580839
652.995707727077731.976457683488444.01495777066702
662.967135196628151.688807050870184.24546334238612
672.938562666178581.382006932054674.49511840030249
682.9099901357291.057347697323594.76263257413441
692.881417605279420.7158778944197655.04695731613908
702.852845074829850.3584743936248445.34721575603485
712.82427254438027-0.01411382996143035.66265891872198
722.7957000139307-0.4012365230252125.9926365508866



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