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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 19 Dec 2010 13:58:47 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t1292767000xskov2vo9z0u3pi.htm/, Retrieved Sun, 05 May 2024 07:06:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112389, Retrieved Sun, 05 May 2024 07:06:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-12-19 13:58:47] [c23113896d5051f86859cd73695e1d4c] [Current]
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Dataseries X:
3.65
3.59
3.31
3.89
4.31
4.35
4.11
3.90
3.75
3.75
3.88
3.93
3.97
3.97
4.33
4.16
4.93
3.86
4.06
4.18
4.08
4.38
4.48
4.41
4.37
4.56
4.71
4.94
5.03
5.08
5.05
4.83
4.68
4.69
4.58
4.54
4.75
4.71
4.50
4.62
4.69
5.05
4.93
4.53
4.33
4.33
3.87
3.74
3.31
3.21
2.93
3.19
3.46
3.73
3.60
3.46
3.25
3.19
2.82
1.89
1.98
2.30
2.42
2.47
2.81
3.37
3.14
3.21
3.02
2.96
2.92
3.07




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112389&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112389&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112389&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.997151100012884
beta0.00829700255916443
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.997151100012884 \tabularnewline
beta & 0.00829700255916443 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112389&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]0.997151100012884[/C][/ROW]
[ROW][C]beta[/C][C]0.00829700255916443[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112389&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112389&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
alpha0.997151100012884
beta0.00829700255916443
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33.313.53-0.22
43.893.248806617646860.641193382353144
54.313.831657990865390.478342009134614
64.354.256079436286240.0939205637137581
74.114.29795165366323-0.187951653663235
83.94.0571996867436-0.1571996867436
93.753.84581150704317-0.0958115070431735
103.753.694843934667940.0551560653320622
113.883.694870169426010.185129830573988
123.933.826031533870950.103968466129049
133.973.877122923573620.092877076426376
143.973.917922927808250.052077072191747
154.333.918470015578070.411529984421926
164.164.28085070804473-0.120850708044729
174.934.111367565346840.81863243465316
183.864.88546391695364-1.02546391695364
194.063.812233525512180.247766474487817
204.184.010656082001270.16934391799873
214.084.1322805441043-0.0522805441043008
224.384.03247939399580.347520606004198
234.484.334215565402370.145784434597627
244.414.43599641945058-0.0259964194505775
254.374.366270728050710.00372927194929051
264.564.326216896157740.233783103842263
274.714.51749566880140.192504331198598
284.944.669205926536360.270794073463636
295.034.901223265162160.128776734837839
305.084.992693275316610.087306724683387
315.055.043533739648230.00646626035176734
324.835.01381754377958-0.183817543779579
334.684.79283885363159-0.11283885363159
344.694.641703085394060.0482969146059382
354.584.65164360371996-0.0716436037199601
364.544.5413925685612-0.00139256856119907
374.754.501180909159730.248819090840272
384.714.71252665238087-0.00252665238087246
394.54.67322180734754-0.173221807347544
404.624.462274973494570.157725026505429
414.694.582637055813850.107362944186146
425.054.65366878519880.396331214801197
434.935.01612453638795-0.0861245363879473
444.534.89678646482661-0.366786464826605
454.334.49455148420647-0.164551484206472
464.334.292613942445030.0373860575549729
473.874.29234795109352-0.422347951093518
483.743.83016344845185-0.0901634484518512
493.313.69847113288724-0.388471132887236
503.213.2661070180824-0.0561070180824048
512.933.16469595210753-0.234695952107532
523.192.88326300878990.306736991210103
533.463.144258267642080.315741732357917
543.733.416844860704880.313155139295124
553.63.68944307649045-0.0894430764904457
563.463.55985004330323-0.099850043303228
573.253.4190535958345-0.169053595834499
583.193.20785210769285-0.0178521076928542
592.823.14727365276819-0.327273652768191
601.892.77544750934489-0.885447509344893
611.981.839712060202070.140287939797933
622.31.927950495857350.372049504142652
632.422.250368331770590.169631668229406
642.472.372348424686330.097651575313669
652.812.423361395919840.386638604080162
663.372.765736903160370.60426309683963
673.143.33011620204012-0.190116202040119
683.213.10080640843910.109193591560904
693.023.17085710323558-0.150857103235576
702.962.98034986574422-0.0203498657442234
712.922.919809701805360.000190298194640892
723.072.879752759339040.190247240660955

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3.31 & 3.53 & -0.22 \tabularnewline
4 & 3.89 & 3.24880661764686 & 0.641193382353144 \tabularnewline
5 & 4.31 & 3.83165799086539 & 0.478342009134614 \tabularnewline
6 & 4.35 & 4.25607943628624 & 0.0939205637137581 \tabularnewline
7 & 4.11 & 4.29795165366323 & -0.187951653663235 \tabularnewline
8 & 3.9 & 4.0571996867436 & -0.1571996867436 \tabularnewline
9 & 3.75 & 3.84581150704317 & -0.0958115070431735 \tabularnewline
10 & 3.75 & 3.69484393466794 & 0.0551560653320622 \tabularnewline
11 & 3.88 & 3.69487016942601 & 0.185129830573988 \tabularnewline
12 & 3.93 & 3.82603153387095 & 0.103968466129049 \tabularnewline
13 & 3.97 & 3.87712292357362 & 0.092877076426376 \tabularnewline
14 & 3.97 & 3.91792292780825 & 0.052077072191747 \tabularnewline
15 & 4.33 & 3.91847001557807 & 0.411529984421926 \tabularnewline
16 & 4.16 & 4.28085070804473 & -0.120850708044729 \tabularnewline
17 & 4.93 & 4.11136756534684 & 0.81863243465316 \tabularnewline
18 & 3.86 & 4.88546391695364 & -1.02546391695364 \tabularnewline
19 & 4.06 & 3.81223352551218 & 0.247766474487817 \tabularnewline
20 & 4.18 & 4.01065608200127 & 0.16934391799873 \tabularnewline
21 & 4.08 & 4.1322805441043 & -0.0522805441043008 \tabularnewline
22 & 4.38 & 4.0324793939958 & 0.347520606004198 \tabularnewline
23 & 4.48 & 4.33421556540237 & 0.145784434597627 \tabularnewline
24 & 4.41 & 4.43599641945058 & -0.0259964194505775 \tabularnewline
25 & 4.37 & 4.36627072805071 & 0.00372927194929051 \tabularnewline
26 & 4.56 & 4.32621689615774 & 0.233783103842263 \tabularnewline
27 & 4.71 & 4.5174956688014 & 0.192504331198598 \tabularnewline
28 & 4.94 & 4.66920592653636 & 0.270794073463636 \tabularnewline
29 & 5.03 & 4.90122326516216 & 0.128776734837839 \tabularnewline
30 & 5.08 & 4.99269327531661 & 0.087306724683387 \tabularnewline
31 & 5.05 & 5.04353373964823 & 0.00646626035176734 \tabularnewline
32 & 4.83 & 5.01381754377958 & -0.183817543779579 \tabularnewline
33 & 4.68 & 4.79283885363159 & -0.11283885363159 \tabularnewline
34 & 4.69 & 4.64170308539406 & 0.0482969146059382 \tabularnewline
35 & 4.58 & 4.65164360371996 & -0.0716436037199601 \tabularnewline
36 & 4.54 & 4.5413925685612 & -0.00139256856119907 \tabularnewline
37 & 4.75 & 4.50118090915973 & 0.248819090840272 \tabularnewline
38 & 4.71 & 4.71252665238087 & -0.00252665238087246 \tabularnewline
39 & 4.5 & 4.67322180734754 & -0.173221807347544 \tabularnewline
40 & 4.62 & 4.46227497349457 & 0.157725026505429 \tabularnewline
41 & 4.69 & 4.58263705581385 & 0.107362944186146 \tabularnewline
42 & 5.05 & 4.6536687851988 & 0.396331214801197 \tabularnewline
43 & 4.93 & 5.01612453638795 & -0.0861245363879473 \tabularnewline
44 & 4.53 & 4.89678646482661 & -0.366786464826605 \tabularnewline
45 & 4.33 & 4.49455148420647 & -0.164551484206472 \tabularnewline
46 & 4.33 & 4.29261394244503 & 0.0373860575549729 \tabularnewline
47 & 3.87 & 4.29234795109352 & -0.422347951093518 \tabularnewline
48 & 3.74 & 3.83016344845185 & -0.0901634484518512 \tabularnewline
49 & 3.31 & 3.69847113288724 & -0.388471132887236 \tabularnewline
50 & 3.21 & 3.2661070180824 & -0.0561070180824048 \tabularnewline
51 & 2.93 & 3.16469595210753 & -0.234695952107532 \tabularnewline
52 & 3.19 & 2.8832630087899 & 0.306736991210103 \tabularnewline
53 & 3.46 & 3.14425826764208 & 0.315741732357917 \tabularnewline
54 & 3.73 & 3.41684486070488 & 0.313155139295124 \tabularnewline
55 & 3.6 & 3.68944307649045 & -0.0894430764904457 \tabularnewline
56 & 3.46 & 3.55985004330323 & -0.099850043303228 \tabularnewline
57 & 3.25 & 3.4190535958345 & -0.169053595834499 \tabularnewline
58 & 3.19 & 3.20785210769285 & -0.0178521076928542 \tabularnewline
59 & 2.82 & 3.14727365276819 & -0.327273652768191 \tabularnewline
60 & 1.89 & 2.77544750934489 & -0.885447509344893 \tabularnewline
61 & 1.98 & 1.83971206020207 & 0.140287939797933 \tabularnewline
62 & 2.3 & 1.92795049585735 & 0.372049504142652 \tabularnewline
63 & 2.42 & 2.25036833177059 & 0.169631668229406 \tabularnewline
64 & 2.47 & 2.37234842468633 & 0.097651575313669 \tabularnewline
65 & 2.81 & 2.42336139591984 & 0.386638604080162 \tabularnewline
66 & 3.37 & 2.76573690316037 & 0.60426309683963 \tabularnewline
67 & 3.14 & 3.33011620204012 & -0.190116202040119 \tabularnewline
68 & 3.21 & 3.1008064084391 & 0.109193591560904 \tabularnewline
69 & 3.02 & 3.17085710323558 & -0.150857103235576 \tabularnewline
70 & 2.96 & 2.98034986574422 & -0.0203498657442234 \tabularnewline
71 & 2.92 & 2.91980970180536 & 0.000190298194640892 \tabularnewline
72 & 3.07 & 2.87975275933904 & 0.190247240660955 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112389&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]3.31[/C][C]3.53[/C][C]-0.22[/C][/ROW]
[ROW][C]4[/C][C]3.89[/C][C]3.24880661764686[/C][C]0.641193382353144[/C][/ROW]
[ROW][C]5[/C][C]4.31[/C][C]3.83165799086539[/C][C]0.478342009134614[/C][/ROW]
[ROW][C]6[/C][C]4.35[/C][C]4.25607943628624[/C][C]0.0939205637137581[/C][/ROW]
[ROW][C]7[/C][C]4.11[/C][C]4.29795165366323[/C][C]-0.187951653663235[/C][/ROW]
[ROW][C]8[/C][C]3.9[/C][C]4.0571996867436[/C][C]-0.1571996867436[/C][/ROW]
[ROW][C]9[/C][C]3.75[/C][C]3.84581150704317[/C][C]-0.0958115070431735[/C][/ROW]
[ROW][C]10[/C][C]3.75[/C][C]3.69484393466794[/C][C]0.0551560653320622[/C][/ROW]
[ROW][C]11[/C][C]3.88[/C][C]3.69487016942601[/C][C]0.185129830573988[/C][/ROW]
[ROW][C]12[/C][C]3.93[/C][C]3.82603153387095[/C][C]0.103968466129049[/C][/ROW]
[ROW][C]13[/C][C]3.97[/C][C]3.87712292357362[/C][C]0.092877076426376[/C][/ROW]
[ROW][C]14[/C][C]3.97[/C][C]3.91792292780825[/C][C]0.052077072191747[/C][/ROW]
[ROW][C]15[/C][C]4.33[/C][C]3.91847001557807[/C][C]0.411529984421926[/C][/ROW]
[ROW][C]16[/C][C]4.16[/C][C]4.28085070804473[/C][C]-0.120850708044729[/C][/ROW]
[ROW][C]17[/C][C]4.93[/C][C]4.11136756534684[/C][C]0.81863243465316[/C][/ROW]
[ROW][C]18[/C][C]3.86[/C][C]4.88546391695364[/C][C]-1.02546391695364[/C][/ROW]
[ROW][C]19[/C][C]4.06[/C][C]3.81223352551218[/C][C]0.247766474487817[/C][/ROW]
[ROW][C]20[/C][C]4.18[/C][C]4.01065608200127[/C][C]0.16934391799873[/C][/ROW]
[ROW][C]21[/C][C]4.08[/C][C]4.1322805441043[/C][C]-0.0522805441043008[/C][/ROW]
[ROW][C]22[/C][C]4.38[/C][C]4.0324793939958[/C][C]0.347520606004198[/C][/ROW]
[ROW][C]23[/C][C]4.48[/C][C]4.33421556540237[/C][C]0.145784434597627[/C][/ROW]
[ROW][C]24[/C][C]4.41[/C][C]4.43599641945058[/C][C]-0.0259964194505775[/C][/ROW]
[ROW][C]25[/C][C]4.37[/C][C]4.36627072805071[/C][C]0.00372927194929051[/C][/ROW]
[ROW][C]26[/C][C]4.56[/C][C]4.32621689615774[/C][C]0.233783103842263[/C][/ROW]
[ROW][C]27[/C][C]4.71[/C][C]4.5174956688014[/C][C]0.192504331198598[/C][/ROW]
[ROW][C]28[/C][C]4.94[/C][C]4.66920592653636[/C][C]0.270794073463636[/C][/ROW]
[ROW][C]29[/C][C]5.03[/C][C]4.90122326516216[/C][C]0.128776734837839[/C][/ROW]
[ROW][C]30[/C][C]5.08[/C][C]4.99269327531661[/C][C]0.087306724683387[/C][/ROW]
[ROW][C]31[/C][C]5.05[/C][C]5.04353373964823[/C][C]0.00646626035176734[/C][/ROW]
[ROW][C]32[/C][C]4.83[/C][C]5.01381754377958[/C][C]-0.183817543779579[/C][/ROW]
[ROW][C]33[/C][C]4.68[/C][C]4.79283885363159[/C][C]-0.11283885363159[/C][/ROW]
[ROW][C]34[/C][C]4.69[/C][C]4.64170308539406[/C][C]0.0482969146059382[/C][/ROW]
[ROW][C]35[/C][C]4.58[/C][C]4.65164360371996[/C][C]-0.0716436037199601[/C][/ROW]
[ROW][C]36[/C][C]4.54[/C][C]4.5413925685612[/C][C]-0.00139256856119907[/C][/ROW]
[ROW][C]37[/C][C]4.75[/C][C]4.50118090915973[/C][C]0.248819090840272[/C][/ROW]
[ROW][C]38[/C][C]4.71[/C][C]4.71252665238087[/C][C]-0.00252665238087246[/C][/ROW]
[ROW][C]39[/C][C]4.5[/C][C]4.67322180734754[/C][C]-0.173221807347544[/C][/ROW]
[ROW][C]40[/C][C]4.62[/C][C]4.46227497349457[/C][C]0.157725026505429[/C][/ROW]
[ROW][C]41[/C][C]4.69[/C][C]4.58263705581385[/C][C]0.107362944186146[/C][/ROW]
[ROW][C]42[/C][C]5.05[/C][C]4.6536687851988[/C][C]0.396331214801197[/C][/ROW]
[ROW][C]43[/C][C]4.93[/C][C]5.01612453638795[/C][C]-0.0861245363879473[/C][/ROW]
[ROW][C]44[/C][C]4.53[/C][C]4.89678646482661[/C][C]-0.366786464826605[/C][/ROW]
[ROW][C]45[/C][C]4.33[/C][C]4.49455148420647[/C][C]-0.164551484206472[/C][/ROW]
[ROW][C]46[/C][C]4.33[/C][C]4.29261394244503[/C][C]0.0373860575549729[/C][/ROW]
[ROW][C]47[/C][C]3.87[/C][C]4.29234795109352[/C][C]-0.422347951093518[/C][/ROW]
[ROW][C]48[/C][C]3.74[/C][C]3.83016344845185[/C][C]-0.0901634484518512[/C][/ROW]
[ROW][C]49[/C][C]3.31[/C][C]3.69847113288724[/C][C]-0.388471132887236[/C][/ROW]
[ROW][C]50[/C][C]3.21[/C][C]3.2661070180824[/C][C]-0.0561070180824048[/C][/ROW]
[ROW][C]51[/C][C]2.93[/C][C]3.16469595210753[/C][C]-0.234695952107532[/C][/ROW]
[ROW][C]52[/C][C]3.19[/C][C]2.8832630087899[/C][C]0.306736991210103[/C][/ROW]
[ROW][C]53[/C][C]3.46[/C][C]3.14425826764208[/C][C]0.315741732357917[/C][/ROW]
[ROW][C]54[/C][C]3.73[/C][C]3.41684486070488[/C][C]0.313155139295124[/C][/ROW]
[ROW][C]55[/C][C]3.6[/C][C]3.68944307649045[/C][C]-0.0894430764904457[/C][/ROW]
[ROW][C]56[/C][C]3.46[/C][C]3.55985004330323[/C][C]-0.099850043303228[/C][/ROW]
[ROW][C]57[/C][C]3.25[/C][C]3.4190535958345[/C][C]-0.169053595834499[/C][/ROW]
[ROW][C]58[/C][C]3.19[/C][C]3.20785210769285[/C][C]-0.0178521076928542[/C][/ROW]
[ROW][C]59[/C][C]2.82[/C][C]3.14727365276819[/C][C]-0.327273652768191[/C][/ROW]
[ROW][C]60[/C][C]1.89[/C][C]2.77544750934489[/C][C]-0.885447509344893[/C][/ROW]
[ROW][C]61[/C][C]1.98[/C][C]1.83971206020207[/C][C]0.140287939797933[/C][/ROW]
[ROW][C]62[/C][C]2.3[/C][C]1.92795049585735[/C][C]0.372049504142652[/C][/ROW]
[ROW][C]63[/C][C]2.42[/C][C]2.25036833177059[/C][C]0.169631668229406[/C][/ROW]
[ROW][C]64[/C][C]2.47[/C][C]2.37234842468633[/C][C]0.097651575313669[/C][/ROW]
[ROW][C]65[/C][C]2.81[/C][C]2.42336139591984[/C][C]0.386638604080162[/C][/ROW]
[ROW][C]66[/C][C]3.37[/C][C]2.76573690316037[/C][C]0.60426309683963[/C][/ROW]
[ROW][C]67[/C][C]3.14[/C][C]3.33011620204012[/C][C]-0.190116202040119[/C][/ROW]
[ROW][C]68[/C][C]3.21[/C][C]3.1008064084391[/C][C]0.109193591560904[/C][/ROW]
[ROW][C]69[/C][C]3.02[/C][C]3.17085710323558[/C][C]-0.150857103235576[/C][/ROW]
[ROW][C]70[/C][C]2.96[/C][C]2.98034986574422[/C][C]-0.0203498657442234[/C][/ROW]
[ROW][C]71[/C][C]2.92[/C][C]2.91980970180536[/C][C]0.000190298194640892[/C][/ROW]
[ROW][C]72[/C][C]3.07[/C][C]2.87975275933904[/C][C]0.190247240660955[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112389&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112389&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
33.313.53-0.22
43.893.248806617646860.641193382353144
54.313.831657990865390.478342009134614
64.354.256079436286240.0939205637137581
74.114.29795165366323-0.187951653663235
83.94.0571996867436-0.1571996867436
93.753.84581150704317-0.0958115070431735
103.753.694843934667940.0551560653320622
113.883.694870169426010.185129830573988
123.933.826031533870950.103968466129049
133.973.877122923573620.092877076426376
143.973.917922927808250.052077072191747
154.333.918470015578070.411529984421926
164.164.28085070804473-0.120850708044729
174.934.111367565346840.81863243465316
183.864.88546391695364-1.02546391695364
194.063.812233525512180.247766474487817
204.184.010656082001270.16934391799873
214.084.1322805441043-0.0522805441043008
224.384.03247939399580.347520606004198
234.484.334215565402370.145784434597627
244.414.43599641945058-0.0259964194505775
254.374.366270728050710.00372927194929051
264.564.326216896157740.233783103842263
274.714.51749566880140.192504331198598
284.944.669205926536360.270794073463636
295.034.901223265162160.128776734837839
305.084.992693275316610.087306724683387
315.055.043533739648230.00646626035176734
324.835.01381754377958-0.183817543779579
334.684.79283885363159-0.11283885363159
344.694.641703085394060.0482969146059382
354.584.65164360371996-0.0716436037199601
364.544.5413925685612-0.00139256856119907
374.754.501180909159730.248819090840272
384.714.71252665238087-0.00252665238087246
394.54.67322180734754-0.173221807347544
404.624.462274973494570.157725026505429
414.694.582637055813850.107362944186146
425.054.65366878519880.396331214801197
434.935.01612453638795-0.0861245363879473
444.534.89678646482661-0.366786464826605
454.334.49455148420647-0.164551484206472
464.334.292613942445030.0373860575549729
473.874.29234795109352-0.422347951093518
483.743.83016344845185-0.0901634484518512
493.313.69847113288724-0.388471132887236
503.213.2661070180824-0.0561070180824048
512.933.16469595210753-0.234695952107532
523.192.88326300878990.306736991210103
533.463.144258267642080.315741732357917
543.733.416844860704880.313155139295124
553.63.68944307649045-0.0894430764904457
563.463.55985004330323-0.099850043303228
573.253.4190535958345-0.169053595834499
583.193.20785210769285-0.0178521076928542
592.823.14727365276819-0.327273652768191
601.892.77544750934489-0.885447509344893
611.981.839712060202070.140287939797933
622.31.927950495857350.372049504142652
632.422.250368331770590.169631668229406
642.472.372348424686330.097651575313669
652.812.423361395919840.386638604080162
663.372.765736903160370.60426309683963
673.143.33011620204012-0.190116202040119
683.213.10080640843910.109193591560904
693.023.17085710323558-0.150857103235576
702.962.98034986574422-0.0203498657442234
712.922.919809701805360.000190298194640892
723.072.879752759339040.190247240660955







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
733.030785291023842.452092576713153.60947800533453
742.992112577409142.171494812544453.81273034227383
752.953439863794451.944709963728453.96216976386044
762.914767150179761.745451714440264.08408258591925
772.876094436565061.563559830635964.18862904249417
782.837421722950371.393840285472354.28100316042838
792.798749009335671.233218665425664.36427935324568
802.760076295720981.079699370798294.44045322064367
812.721403582106280.9319016212815664.510905542931
822.682730868491590.7888240396092764.5766376973739
832.64405815487690.6497136809399654.63840262881383
842.60538544126220.513987935923224.69678294660118

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 3.03078529102384 & 2.45209257671315 & 3.60947800533453 \tabularnewline
74 & 2.99211257740914 & 2.17149481254445 & 3.81273034227383 \tabularnewline
75 & 2.95343986379445 & 1.94470996372845 & 3.96216976386044 \tabularnewline
76 & 2.91476715017976 & 1.74545171444026 & 4.08408258591925 \tabularnewline
77 & 2.87609443656506 & 1.56355983063596 & 4.18862904249417 \tabularnewline
78 & 2.83742172295037 & 1.39384028547235 & 4.28100316042838 \tabularnewline
79 & 2.79874900933567 & 1.23321866542566 & 4.36427935324568 \tabularnewline
80 & 2.76007629572098 & 1.07969937079829 & 4.44045322064367 \tabularnewline
81 & 2.72140358210628 & 0.931901621281566 & 4.510905542931 \tabularnewline
82 & 2.68273086849159 & 0.788824039609276 & 4.5766376973739 \tabularnewline
83 & 2.6440581548769 & 0.649713680939965 & 4.63840262881383 \tabularnewline
84 & 2.6053854412622 & 0.51398793592322 & 4.69678294660118 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112389&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]3.03078529102384[/C][C]2.45209257671315[/C][C]3.60947800533453[/C][/ROW]
[ROW][C]74[/C][C]2.99211257740914[/C][C]2.17149481254445[/C][C]3.81273034227383[/C][/ROW]
[ROW][C]75[/C][C]2.95343986379445[/C][C]1.94470996372845[/C][C]3.96216976386044[/C][/ROW]
[ROW][C]76[/C][C]2.91476715017976[/C][C]1.74545171444026[/C][C]4.08408258591925[/C][/ROW]
[ROW][C]77[/C][C]2.87609443656506[/C][C]1.56355983063596[/C][C]4.18862904249417[/C][/ROW]
[ROW][C]78[/C][C]2.83742172295037[/C][C]1.39384028547235[/C][C]4.28100316042838[/C][/ROW]
[ROW][C]79[/C][C]2.79874900933567[/C][C]1.23321866542566[/C][C]4.36427935324568[/C][/ROW]
[ROW][C]80[/C][C]2.76007629572098[/C][C]1.07969937079829[/C][C]4.44045322064367[/C][/ROW]
[ROW][C]81[/C][C]2.72140358210628[/C][C]0.931901621281566[/C][C]4.510905542931[/C][/ROW]
[ROW][C]82[/C][C]2.68273086849159[/C][C]0.788824039609276[/C][C]4.5766376973739[/C][/ROW]
[ROW][C]83[/C][C]2.6440581548769[/C][C]0.649713680939965[/C][C]4.63840262881383[/C][/ROW]
[ROW][C]84[/C][C]2.6053854412622[/C][C]0.51398793592322[/C][C]4.69678294660118[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112389&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112389&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
733.030785291023842.452092576713153.60947800533453
742.992112577409142.171494812544453.81273034227383
752.953439863794451.944709963728453.96216976386044
762.914767150179761.745451714440264.08408258591925
772.876094436565061.563559830635964.18862904249417
782.837421722950371.393840285472354.28100316042838
792.798749009335671.233218665425664.36427935324568
802.760076295720981.079699370798294.44045322064367
812.721403582106280.9319016212815664.510905542931
822.682730868491590.7888240396092764.5766376973739
832.64405815487690.6497136809399654.63840262881383
842.60538544126220.513987935923224.69678294660118



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')