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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 03 May 2013 05:34:02 -0400
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/May/03/t13675736813q1c2ex9gfxvxyv.htm/, Retrieved Fri, 03 May 2024 06:40:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208684, Retrieved Fri, 03 May 2024 06:40:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opdracht 10 oef2] [2013-05-03 09:34:02] [422c23941b3c44827a9ca757d6dfbb80] [Current]
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Dataseries X:
8.5
8.5
8.5
8.6
8.6
8.4
8.2
8
8
8
8
7.9
7.9
7.9
7.9
8
7.9
7.4
7.2
7
6.9
7.1
7.2
7.2
7.1
6.9
6.8
6.8
6.8
6.9
7.1
7.2
7.2
7.1
7.1
7.2
7.5
7.7
7.8
7.7
7.7
7.8
8
8.1
8.1
8
8.1
8.2
8.4
8.5
8.5
8.5
8.5
8.5
8.4
8.3
8.2
8.1
7.9
7.6
7.3
7.1
7
7.1
7.1
7.1
7.3
7.3
7.3
7.2
7.2
7.1




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=208684&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=208684&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208684&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
alpha0.928637593833649
beta0.91709175727957
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.928637593833649 \tabularnewline
beta & 0.91709175727957 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208684&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]0.928637593833649[/C][/ROW]
[ROW][C]beta[/C][C]0.91709175727957[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208684&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208684&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
alpha0.928637593833649
beta0.91709175727957
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137.98.27147435897436-0.371474358974359
147.97.62290693345970.277093066540303
157.97.816775437353320.0832245626466817
1687.997321549730640.00267845026935554
177.97.892850605261430.0071493947385699
187.47.390286967166590.00971303283341474
197.27.39004275087239-0.190042750872391
2076.838282011239250.161717988760751
216.96.95090597776773-0.0509059777677336
227.16.82272546925180.277274530748199
237.27.2396120976922-0.0396120976921992
247.27.2451570767375-0.045157076737496
257.17.29308563721581-0.193085637215808
266.97.11199422340004-0.211994223400042
276.86.676847989773420.123152010226583
286.86.761733342457290.0382666575427084
296.86.593947628559790.206052371440208
306.96.348988246769430.551011753230567
317.17.37086667218386-0.270866672183859
327.27.23402628752253-0.0340262875225292
337.27.44787058948486-0.247870589484856
347.17.29062617501939-0.190626175019386
357.16.982328202388080.117671797611916
367.26.999426775110640.200573224889364
377.57.340157951908240.159842048091762
387.77.86119326078744-0.161193260787438
397.87.91613815156752-0.116138151567518
407.77.98796015914394-0.287960159143936
417.77.46657994411180.2334200558882
427.87.232338322945470.56766167705453
4388.18589307909243-0.185893079092429
448.18.19209708543809-0.0920970854380858
458.18.33453167971551-0.234531679715506
4688.20289686736101-0.202896867361012
478.17.903891958932740.196108041067259
488.28.065232530444230.134767469555774
498.48.351391242643530.0486087573564706
508.58.66093381834595-0.160933818345953
518.58.63426836561359-0.134268365613588
528.58.57648530828182-0.0764853082818213
538.58.368290187968540.131709812031463
548.58.056422437972270.44357756202773
558.48.72827035481302-0.328270354813016
568.38.37499377282246-0.0749937728224559
578.28.3037554311859-0.103755431185899
588.18.18780570993469-0.0878057099346865
597.98.01415345172724-0.114153451727237
607.67.60876392778012-0.00876392778011592
617.37.35901537335677-0.0590153733567655
627.17.065532902920080.034467097079915
6376.90051161215020.0994883878497959
647.16.94128999372880.158710006271199
657.17.04402910225960.055970897740397
667.16.697245960776810.402754039223193
677.37.25449848856510.0455015114348969
687.37.56311200388125-0.263112003881254
697.37.45163444716522-0.151634447165219
707.27.38809166288784-0.188091662887843
717.27.129752722129410.070247277870588
727.17.070492481925080.0295075180749222

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7.9 & 8.27147435897436 & -0.371474358974359 \tabularnewline
14 & 7.9 & 7.6229069334597 & 0.277093066540303 \tabularnewline
15 & 7.9 & 7.81677543735332 & 0.0832245626466817 \tabularnewline
16 & 8 & 7.99732154973064 & 0.00267845026935554 \tabularnewline
17 & 7.9 & 7.89285060526143 & 0.0071493947385699 \tabularnewline
18 & 7.4 & 7.39028696716659 & 0.00971303283341474 \tabularnewline
19 & 7.2 & 7.39004275087239 & -0.190042750872391 \tabularnewline
20 & 7 & 6.83828201123925 & 0.161717988760751 \tabularnewline
21 & 6.9 & 6.95090597776773 & -0.0509059777677336 \tabularnewline
22 & 7.1 & 6.8227254692518 & 0.277274530748199 \tabularnewline
23 & 7.2 & 7.2396120976922 & -0.0396120976921992 \tabularnewline
24 & 7.2 & 7.2451570767375 & -0.045157076737496 \tabularnewline
25 & 7.1 & 7.29308563721581 & -0.193085637215808 \tabularnewline
26 & 6.9 & 7.11199422340004 & -0.211994223400042 \tabularnewline
27 & 6.8 & 6.67684798977342 & 0.123152010226583 \tabularnewline
28 & 6.8 & 6.76173334245729 & 0.0382666575427084 \tabularnewline
29 & 6.8 & 6.59394762855979 & 0.206052371440208 \tabularnewline
30 & 6.9 & 6.34898824676943 & 0.551011753230567 \tabularnewline
31 & 7.1 & 7.37086667218386 & -0.270866672183859 \tabularnewline
32 & 7.2 & 7.23402628752253 & -0.0340262875225292 \tabularnewline
33 & 7.2 & 7.44787058948486 & -0.247870589484856 \tabularnewline
34 & 7.1 & 7.29062617501939 & -0.190626175019386 \tabularnewline
35 & 7.1 & 6.98232820238808 & 0.117671797611916 \tabularnewline
36 & 7.2 & 6.99942677511064 & 0.200573224889364 \tabularnewline
37 & 7.5 & 7.34015795190824 & 0.159842048091762 \tabularnewline
38 & 7.7 & 7.86119326078744 & -0.161193260787438 \tabularnewline
39 & 7.8 & 7.91613815156752 & -0.116138151567518 \tabularnewline
40 & 7.7 & 7.98796015914394 & -0.287960159143936 \tabularnewline
41 & 7.7 & 7.4665799441118 & 0.2334200558882 \tabularnewline
42 & 7.8 & 7.23233832294547 & 0.56766167705453 \tabularnewline
43 & 8 & 8.18589307909243 & -0.185893079092429 \tabularnewline
44 & 8.1 & 8.19209708543809 & -0.0920970854380858 \tabularnewline
45 & 8.1 & 8.33453167971551 & -0.234531679715506 \tabularnewline
46 & 8 & 8.20289686736101 & -0.202896867361012 \tabularnewline
47 & 8.1 & 7.90389195893274 & 0.196108041067259 \tabularnewline
48 & 8.2 & 8.06523253044423 & 0.134767469555774 \tabularnewline
49 & 8.4 & 8.35139124264353 & 0.0486087573564706 \tabularnewline
50 & 8.5 & 8.66093381834595 & -0.160933818345953 \tabularnewline
51 & 8.5 & 8.63426836561359 & -0.134268365613588 \tabularnewline
52 & 8.5 & 8.57648530828182 & -0.0764853082818213 \tabularnewline
53 & 8.5 & 8.36829018796854 & 0.131709812031463 \tabularnewline
54 & 8.5 & 8.05642243797227 & 0.44357756202773 \tabularnewline
55 & 8.4 & 8.72827035481302 & -0.328270354813016 \tabularnewline
56 & 8.3 & 8.37499377282246 & -0.0749937728224559 \tabularnewline
57 & 8.2 & 8.3037554311859 & -0.103755431185899 \tabularnewline
58 & 8.1 & 8.18780570993469 & -0.0878057099346865 \tabularnewline
59 & 7.9 & 8.01415345172724 & -0.114153451727237 \tabularnewline
60 & 7.6 & 7.60876392778012 & -0.00876392778011592 \tabularnewline
61 & 7.3 & 7.35901537335677 & -0.0590153733567655 \tabularnewline
62 & 7.1 & 7.06553290292008 & 0.034467097079915 \tabularnewline
63 & 7 & 6.9005116121502 & 0.0994883878497959 \tabularnewline
64 & 7.1 & 6.9412899937288 & 0.158710006271199 \tabularnewline
65 & 7.1 & 7.0440291022596 & 0.055970897740397 \tabularnewline
66 & 7.1 & 6.69724596077681 & 0.402754039223193 \tabularnewline
67 & 7.3 & 7.2544984885651 & 0.0455015114348969 \tabularnewline
68 & 7.3 & 7.56311200388125 & -0.263112003881254 \tabularnewline
69 & 7.3 & 7.45163444716522 & -0.151634447165219 \tabularnewline
70 & 7.2 & 7.38809166288784 & -0.188091662887843 \tabularnewline
71 & 7.2 & 7.12975272212941 & 0.070247277870588 \tabularnewline
72 & 7.1 & 7.07049248192508 & 0.0295075180749222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208684&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]7.9[/C][C]8.27147435897436[/C][C]-0.371474358974359[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]7.6229069334597[/C][C]0.277093066540303[/C][/ROW]
[ROW][C]15[/C][C]7.9[/C][C]7.81677543735332[/C][C]0.0832245626466817[/C][/ROW]
[ROW][C]16[/C][C]8[/C][C]7.99732154973064[/C][C]0.00267845026935554[/C][/ROW]
[ROW][C]17[/C][C]7.9[/C][C]7.89285060526143[/C][C]0.0071493947385699[/C][/ROW]
[ROW][C]18[/C][C]7.4[/C][C]7.39028696716659[/C][C]0.00971303283341474[/C][/ROW]
[ROW][C]19[/C][C]7.2[/C][C]7.39004275087239[/C][C]-0.190042750872391[/C][/ROW]
[ROW][C]20[/C][C]7[/C][C]6.83828201123925[/C][C]0.161717988760751[/C][/ROW]
[ROW][C]21[/C][C]6.9[/C][C]6.95090597776773[/C][C]-0.0509059777677336[/C][/ROW]
[ROW][C]22[/C][C]7.1[/C][C]6.8227254692518[/C][C]0.277274530748199[/C][/ROW]
[ROW][C]23[/C][C]7.2[/C][C]7.2396120976922[/C][C]-0.0396120976921992[/C][/ROW]
[ROW][C]24[/C][C]7.2[/C][C]7.2451570767375[/C][C]-0.045157076737496[/C][/ROW]
[ROW][C]25[/C][C]7.1[/C][C]7.29308563721581[/C][C]-0.193085637215808[/C][/ROW]
[ROW][C]26[/C][C]6.9[/C][C]7.11199422340004[/C][C]-0.211994223400042[/C][/ROW]
[ROW][C]27[/C][C]6.8[/C][C]6.67684798977342[/C][C]0.123152010226583[/C][/ROW]
[ROW][C]28[/C][C]6.8[/C][C]6.76173334245729[/C][C]0.0382666575427084[/C][/ROW]
[ROW][C]29[/C][C]6.8[/C][C]6.59394762855979[/C][C]0.206052371440208[/C][/ROW]
[ROW][C]30[/C][C]6.9[/C][C]6.34898824676943[/C][C]0.551011753230567[/C][/ROW]
[ROW][C]31[/C][C]7.1[/C][C]7.37086667218386[/C][C]-0.270866672183859[/C][/ROW]
[ROW][C]32[/C][C]7.2[/C][C]7.23402628752253[/C][C]-0.0340262875225292[/C][/ROW]
[ROW][C]33[/C][C]7.2[/C][C]7.44787058948486[/C][C]-0.247870589484856[/C][/ROW]
[ROW][C]34[/C][C]7.1[/C][C]7.29062617501939[/C][C]-0.190626175019386[/C][/ROW]
[ROW][C]35[/C][C]7.1[/C][C]6.98232820238808[/C][C]0.117671797611916[/C][/ROW]
[ROW][C]36[/C][C]7.2[/C][C]6.99942677511064[/C][C]0.200573224889364[/C][/ROW]
[ROW][C]37[/C][C]7.5[/C][C]7.34015795190824[/C][C]0.159842048091762[/C][/ROW]
[ROW][C]38[/C][C]7.7[/C][C]7.86119326078744[/C][C]-0.161193260787438[/C][/ROW]
[ROW][C]39[/C][C]7.8[/C][C]7.91613815156752[/C][C]-0.116138151567518[/C][/ROW]
[ROW][C]40[/C][C]7.7[/C][C]7.98796015914394[/C][C]-0.287960159143936[/C][/ROW]
[ROW][C]41[/C][C]7.7[/C][C]7.4665799441118[/C][C]0.2334200558882[/C][/ROW]
[ROW][C]42[/C][C]7.8[/C][C]7.23233832294547[/C][C]0.56766167705453[/C][/ROW]
[ROW][C]43[/C][C]8[/C][C]8.18589307909243[/C][C]-0.185893079092429[/C][/ROW]
[ROW][C]44[/C][C]8.1[/C][C]8.19209708543809[/C][C]-0.0920970854380858[/C][/ROW]
[ROW][C]45[/C][C]8.1[/C][C]8.33453167971551[/C][C]-0.234531679715506[/C][/ROW]
[ROW][C]46[/C][C]8[/C][C]8.20289686736101[/C][C]-0.202896867361012[/C][/ROW]
[ROW][C]47[/C][C]8.1[/C][C]7.90389195893274[/C][C]0.196108041067259[/C][/ROW]
[ROW][C]48[/C][C]8.2[/C][C]8.06523253044423[/C][C]0.134767469555774[/C][/ROW]
[ROW][C]49[/C][C]8.4[/C][C]8.35139124264353[/C][C]0.0486087573564706[/C][/ROW]
[ROW][C]50[/C][C]8.5[/C][C]8.66093381834595[/C][C]-0.160933818345953[/C][/ROW]
[ROW][C]51[/C][C]8.5[/C][C]8.63426836561359[/C][C]-0.134268365613588[/C][/ROW]
[ROW][C]52[/C][C]8.5[/C][C]8.57648530828182[/C][C]-0.0764853082818213[/C][/ROW]
[ROW][C]53[/C][C]8.5[/C][C]8.36829018796854[/C][C]0.131709812031463[/C][/ROW]
[ROW][C]54[/C][C]8.5[/C][C]8.05642243797227[/C][C]0.44357756202773[/C][/ROW]
[ROW][C]55[/C][C]8.4[/C][C]8.72827035481302[/C][C]-0.328270354813016[/C][/ROW]
[ROW][C]56[/C][C]8.3[/C][C]8.37499377282246[/C][C]-0.0749937728224559[/C][/ROW]
[ROW][C]57[/C][C]8.2[/C][C]8.3037554311859[/C][C]-0.103755431185899[/C][/ROW]
[ROW][C]58[/C][C]8.1[/C][C]8.18780570993469[/C][C]-0.0878057099346865[/C][/ROW]
[ROW][C]59[/C][C]7.9[/C][C]8.01415345172724[/C][C]-0.114153451727237[/C][/ROW]
[ROW][C]60[/C][C]7.6[/C][C]7.60876392778012[/C][C]-0.00876392778011592[/C][/ROW]
[ROW][C]61[/C][C]7.3[/C][C]7.35901537335677[/C][C]-0.0590153733567655[/C][/ROW]
[ROW][C]62[/C][C]7.1[/C][C]7.06553290292008[/C][C]0.034467097079915[/C][/ROW]
[ROW][C]63[/C][C]7[/C][C]6.9005116121502[/C][C]0.0994883878497959[/C][/ROW]
[ROW][C]64[/C][C]7.1[/C][C]6.9412899937288[/C][C]0.158710006271199[/C][/ROW]
[ROW][C]65[/C][C]7.1[/C][C]7.0440291022596[/C][C]0.055970897740397[/C][/ROW]
[ROW][C]66[/C][C]7.1[/C][C]6.69724596077681[/C][C]0.402754039223193[/C][/ROW]
[ROW][C]67[/C][C]7.3[/C][C]7.2544984885651[/C][C]0.0455015114348969[/C][/ROW]
[ROW][C]68[/C][C]7.3[/C][C]7.56311200388125[/C][C]-0.263112003881254[/C][/ROW]
[ROW][C]69[/C][C]7.3[/C][C]7.45163444716522[/C][C]-0.151634447165219[/C][/ROW]
[ROW][C]70[/C][C]7.2[/C][C]7.38809166288784[/C][C]-0.188091662887843[/C][/ROW]
[ROW][C]71[/C][C]7.2[/C][C]7.12975272212941[/C][C]0.070247277870588[/C][/ROW]
[ROW][C]72[/C][C]7.1[/C][C]7.07049248192508[/C][C]0.0295075180749222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208684&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208684&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
137.98.27147435897436-0.371474358974359
147.97.62290693345970.277093066540303
157.97.816775437353320.0832245626466817
1687.997321549730640.00267845026935554
177.97.892850605261430.0071493947385699
187.47.390286967166590.00971303283341474
197.27.39004275087239-0.190042750872391
2076.838282011239250.161717988760751
216.96.95090597776773-0.0509059777677336
227.16.82272546925180.277274530748199
237.27.2396120976922-0.0396120976921992
247.27.2451570767375-0.045157076737496
257.17.29308563721581-0.193085637215808
266.97.11199422340004-0.211994223400042
276.86.676847989773420.123152010226583
286.86.761733342457290.0382666575427084
296.86.593947628559790.206052371440208
306.96.348988246769430.551011753230567
317.17.37086667218386-0.270866672183859
327.27.23402628752253-0.0340262875225292
337.27.44787058948486-0.247870589484856
347.17.29062617501939-0.190626175019386
357.16.982328202388080.117671797611916
367.26.999426775110640.200573224889364
377.57.340157951908240.159842048091762
387.77.86119326078744-0.161193260787438
397.87.91613815156752-0.116138151567518
407.77.98796015914394-0.287960159143936
417.77.46657994411180.2334200558882
427.87.232338322945470.56766167705453
4388.18589307909243-0.185893079092429
448.18.19209708543809-0.0920970854380858
458.18.33453167971551-0.234531679715506
4688.20289686736101-0.202896867361012
478.17.903891958932740.196108041067259
488.28.065232530444230.134767469555774
498.48.351391242643530.0486087573564706
508.58.66093381834595-0.160933818345953
518.58.63426836561359-0.134268365613588
528.58.57648530828182-0.0764853082818213
538.58.368290187968540.131709812031463
548.58.056422437972270.44357756202773
558.48.72827035481302-0.328270354813016
568.38.37499377282246-0.0749937728224559
578.28.3037554311859-0.103755431185899
588.18.18780570993469-0.0878057099346865
597.98.01415345172724-0.114153451727237
607.67.60876392778012-0.00876392778011592
617.37.35901537335677-0.0590153733567655
627.17.065532902920080.034467097079915
6376.90051161215020.0994883878497959
647.16.94128999372880.158710006271199
657.17.04402910225960.055970897740397
667.16.697245960776810.402754039223193
677.37.25449848856510.0455015114348969
687.37.56311200388125-0.263112003881254
697.37.45163444716522-0.151634447165219
707.27.38809166288784-0.188091662887843
717.27.129752722129410.070247277870588
727.17.070492481925080.0295075180749222







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
737.052658870009136.648336222821217.45698151719704
747.070872330837616.245280606142287.89646405553293
757.099350815337255.752497431969388.44620419870512
767.188105002703945.239296775413839.13691322999404
777.13710186520854.515983823267219.75821990714979
786.716395481006913.3595558113307610.0732351506831
796.48444340531422.3336204117826910.6352663988457
806.300330267034311.3013027276564911.2993578064121
816.236773133541170.33860844459702512.1349378224853
826.23621039375419-0.60927587688366913.0816966643921
836.25593189191611-1.5827174032572614.0945811870895
846.15366005761131-2.7219643065735215.0292844217961

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 7.05265887000913 & 6.64833622282121 & 7.45698151719704 \tabularnewline
74 & 7.07087233083761 & 6.24528060614228 & 7.89646405553293 \tabularnewline
75 & 7.09935081533725 & 5.75249743196938 & 8.44620419870512 \tabularnewline
76 & 7.18810500270394 & 5.23929677541383 & 9.13691322999404 \tabularnewline
77 & 7.1371018652085 & 4.51598382326721 & 9.75821990714979 \tabularnewline
78 & 6.71639548100691 & 3.35955581133076 & 10.0732351506831 \tabularnewline
79 & 6.4844434053142 & 2.33362041178269 & 10.6352663988457 \tabularnewline
80 & 6.30033026703431 & 1.30130272765649 & 11.2993578064121 \tabularnewline
81 & 6.23677313354117 & 0.338608444597025 & 12.1349378224853 \tabularnewline
82 & 6.23621039375419 & -0.609275876883669 & 13.0816966643921 \tabularnewline
83 & 6.25593189191611 & -1.58271740325726 & 14.0945811870895 \tabularnewline
84 & 6.15366005761131 & -2.72196430657352 & 15.0292844217961 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208684&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]7.05265887000913[/C][C]6.64833622282121[/C][C]7.45698151719704[/C][/ROW]
[ROW][C]74[/C][C]7.07087233083761[/C][C]6.24528060614228[/C][C]7.89646405553293[/C][/ROW]
[ROW][C]75[/C][C]7.09935081533725[/C][C]5.75249743196938[/C][C]8.44620419870512[/C][/ROW]
[ROW][C]76[/C][C]7.18810500270394[/C][C]5.23929677541383[/C][C]9.13691322999404[/C][/ROW]
[ROW][C]77[/C][C]7.1371018652085[/C][C]4.51598382326721[/C][C]9.75821990714979[/C][/ROW]
[ROW][C]78[/C][C]6.71639548100691[/C][C]3.35955581133076[/C][C]10.0732351506831[/C][/ROW]
[ROW][C]79[/C][C]6.4844434053142[/C][C]2.33362041178269[/C][C]10.6352663988457[/C][/ROW]
[ROW][C]80[/C][C]6.30033026703431[/C][C]1.30130272765649[/C][C]11.2993578064121[/C][/ROW]
[ROW][C]81[/C][C]6.23677313354117[/C][C]0.338608444597025[/C][C]12.1349378224853[/C][/ROW]
[ROW][C]82[/C][C]6.23621039375419[/C][C]-0.609275876883669[/C][C]13.0816966643921[/C][/ROW]
[ROW][C]83[/C][C]6.25593189191611[/C][C]-1.58271740325726[/C][C]14.0945811870895[/C][/ROW]
[ROW][C]84[/C][C]6.15366005761131[/C][C]-2.72196430657352[/C][C]15.0292844217961[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208684&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208684&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
737.052658870009136.648336222821217.45698151719704
747.070872330837616.245280606142287.89646405553293
757.099350815337255.752497431969388.44620419870512
767.188105002703945.239296775413839.13691322999404
777.13710186520854.515983823267219.75821990714979
786.716395481006913.3595558113307610.0732351506831
796.48444340531422.3336204117826910.6352663988457
806.300330267034311.3013027276564911.2993578064121
816.236773133541170.33860844459702512.1349378224853
826.23621039375419-0.60927587688366913.0816966643921
836.25593189191611-1.5827174032572614.0945811870895
846.15366005761131-2.7219643065735215.0292844217961



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')