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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 22:04:27 +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/2016/Apr/25/t1461618314re2ssdt1v83685w.htm/, Retrieved Sun, 05 May 2024 21:36:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294803, Retrieved Sun, 05 May 2024 21:36:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 21:04:27] [9d122f8260d20611f07666190c7f1fd6] [Current]
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Dataseries X:
45564.6
47295.5
46465.5
50679.5
47452.8
49415.4
48165.3
51814
49030.7
50820.8
49729.5
53501.6
50524.9
52095
51290.3
55064
52505.2
54318.3
53039.6
57607.6
54236.4
56586.4
55614
60085.9
56963.5
59152.8
57804.6
62541.5
59449.3
61704.7
60399
65724.7
62679.4
65526.5
64274.8
68769.1
63542.8
66198
64544.9
71041.8
66087.2
69005.8
66897
73702
68485.3
71457
69774.6
76479.7
71204.7
73783.9
71651
78541.6
72714.4
75258
73168.1
79701.6
73944.5
76401.2
73948.1
80583.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294803&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294803&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294803&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.429776854949485
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.429776854949485 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294803&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]0.429776854949485[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294803&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294803&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
alpha0.429776854949485
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
247295.545564.61730.9
346465.546308.5007582321156.999241767931
450679.546375.97539858854303.52460141145
547452.848225.5306669809-772.730666980897
649415.447893.42891120281521.97108879717
748165.348547.5368590701-382.236859070123
85181448383.26030393323430.7396960668
949030.749857.7128206591-827.012820659147
1050820.849502.28185159341318.51814840664
1149729.550068.9504346094-339.450434609389
1253501.649923.06249441173578.53750558827
1350524.951461.0350888822-936.135088882227
145209551058.70589457461036.29410542543
1551290.351504.081116007-213.781116006998
165506451412.20294032193651.79705967808
1752505.252981.6607955441-476.460795544146
1854318.352776.88897332851541.41102667155
1953039.653439.3517565558-399.751756555816
2057607.653267.54770386274340.05229613727
2154236.455132.8017300129-896.401730012898
2256586.454747.54901371671838.85098628332
235561455537.844607322376.1553926777124
2460085.955570.57443247484515.32556752524
2556963.557511.1568539588-547.656853958761
2659152.857275.78661367281877.01338632716
2757804.658082.4835235466-277.883523546618
2862541.557963.05561675454578.44438324553
2959449.359930.7650443469-481.465044346871
3061704.759723.84251181941980.85748818063
316039960575.1692131928-176.169213192778
3265724.760499.45576280795225.24423719214
3362679.462745.1447974112-65.744797411222
3465526.562716.88920515052809.61079484946
3564274.863924.3948961931350.40510380693
3668769.164074.99089966554694.10910033454
3763542.866092.410345597-2549.610345597
386619864996.64682991971201.35317008034
3964544.965512.9606170404-968.060617040384
4071041.865096.91056964835944.88943035169
4166087.267651.8864520473-1564.6864520473
4269005.866979.42042970432026.37957029566
436689767850.3114683599-953.311468359898
447370267440.60026370096261.39973629909
4568485.370131.6049499491-1646.30494994907
467145769424.06118627222032.9388137278
4769774.670297.7712359409-523.17123594087
4876479.770072.92434755826406.77565244182
4971204.772826.4082378316-1621.70823783155
5073783.972129.43557173061654.46442826936
517165172840.486090338-1189.48609033803
5278541.672329.27249942646212.32750057361
5372714.474999.1870745391-2284.78707453913
547525874017.23847141451240.76152858554
5573168.174550.4890589123-1382.38905891226
5679701.673956.37023685645745.22976314362
5773944.576425.5370154224-2481.03701542242
5876401.275359.24472992091041.95527007908
5973948.175807.0529888936-1858.95298889355
6080583.375008.11801982795575.18198017206

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 47295.5 & 45564.6 & 1730.9 \tabularnewline
3 & 46465.5 & 46308.5007582321 & 156.999241767931 \tabularnewline
4 & 50679.5 & 46375.9753985885 & 4303.52460141145 \tabularnewline
5 & 47452.8 & 48225.5306669809 & -772.730666980897 \tabularnewline
6 & 49415.4 & 47893.4289112028 & 1521.97108879717 \tabularnewline
7 & 48165.3 & 48547.5368590701 & -382.236859070123 \tabularnewline
8 & 51814 & 48383.2603039332 & 3430.7396960668 \tabularnewline
9 & 49030.7 & 49857.7128206591 & -827.012820659147 \tabularnewline
10 & 50820.8 & 49502.2818515934 & 1318.51814840664 \tabularnewline
11 & 49729.5 & 50068.9504346094 & -339.450434609389 \tabularnewline
12 & 53501.6 & 49923.0624944117 & 3578.53750558827 \tabularnewline
13 & 50524.9 & 51461.0350888822 & -936.135088882227 \tabularnewline
14 & 52095 & 51058.7058945746 & 1036.29410542543 \tabularnewline
15 & 51290.3 & 51504.081116007 & -213.781116006998 \tabularnewline
16 & 55064 & 51412.2029403219 & 3651.79705967808 \tabularnewline
17 & 52505.2 & 52981.6607955441 & -476.460795544146 \tabularnewline
18 & 54318.3 & 52776.8889733285 & 1541.41102667155 \tabularnewline
19 & 53039.6 & 53439.3517565558 & -399.751756555816 \tabularnewline
20 & 57607.6 & 53267.5477038627 & 4340.05229613727 \tabularnewline
21 & 54236.4 & 55132.8017300129 & -896.401730012898 \tabularnewline
22 & 56586.4 & 54747.5490137167 & 1838.85098628332 \tabularnewline
23 & 55614 & 55537.8446073223 & 76.1553926777124 \tabularnewline
24 & 60085.9 & 55570.5744324748 & 4515.32556752524 \tabularnewline
25 & 56963.5 & 57511.1568539588 & -547.656853958761 \tabularnewline
26 & 59152.8 & 57275.7866136728 & 1877.01338632716 \tabularnewline
27 & 57804.6 & 58082.4835235466 & -277.883523546618 \tabularnewline
28 & 62541.5 & 57963.0556167545 & 4578.44438324553 \tabularnewline
29 & 59449.3 & 59930.7650443469 & -481.465044346871 \tabularnewline
30 & 61704.7 & 59723.8425118194 & 1980.85748818063 \tabularnewline
31 & 60399 & 60575.1692131928 & -176.169213192778 \tabularnewline
32 & 65724.7 & 60499.4557628079 & 5225.24423719214 \tabularnewline
33 & 62679.4 & 62745.1447974112 & -65.744797411222 \tabularnewline
34 & 65526.5 & 62716.8892051505 & 2809.61079484946 \tabularnewline
35 & 64274.8 & 63924.3948961931 & 350.40510380693 \tabularnewline
36 & 68769.1 & 64074.9908996655 & 4694.10910033454 \tabularnewline
37 & 63542.8 & 66092.410345597 & -2549.610345597 \tabularnewline
38 & 66198 & 64996.6468299197 & 1201.35317008034 \tabularnewline
39 & 64544.9 & 65512.9606170404 & -968.060617040384 \tabularnewline
40 & 71041.8 & 65096.9105696483 & 5944.88943035169 \tabularnewline
41 & 66087.2 & 67651.8864520473 & -1564.6864520473 \tabularnewline
42 & 69005.8 & 66979.4204297043 & 2026.37957029566 \tabularnewline
43 & 66897 & 67850.3114683599 & -953.311468359898 \tabularnewline
44 & 73702 & 67440.6002637009 & 6261.39973629909 \tabularnewline
45 & 68485.3 & 70131.6049499491 & -1646.30494994907 \tabularnewline
46 & 71457 & 69424.0611862722 & 2032.9388137278 \tabularnewline
47 & 69774.6 & 70297.7712359409 & -523.17123594087 \tabularnewline
48 & 76479.7 & 70072.9243475582 & 6406.77565244182 \tabularnewline
49 & 71204.7 & 72826.4082378316 & -1621.70823783155 \tabularnewline
50 & 73783.9 & 72129.4355717306 & 1654.46442826936 \tabularnewline
51 & 71651 & 72840.486090338 & -1189.48609033803 \tabularnewline
52 & 78541.6 & 72329.2724994264 & 6212.32750057361 \tabularnewline
53 & 72714.4 & 74999.1870745391 & -2284.78707453913 \tabularnewline
54 & 75258 & 74017.2384714145 & 1240.76152858554 \tabularnewline
55 & 73168.1 & 74550.4890589123 & -1382.38905891226 \tabularnewline
56 & 79701.6 & 73956.3702368564 & 5745.22976314362 \tabularnewline
57 & 73944.5 & 76425.5370154224 & -2481.03701542242 \tabularnewline
58 & 76401.2 & 75359.2447299209 & 1041.95527007908 \tabularnewline
59 & 73948.1 & 75807.0529888936 & -1858.95298889355 \tabularnewline
60 & 80583.3 & 75008.1180198279 & 5575.18198017206 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294803&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]2[/C][C]47295.5[/C][C]45564.6[/C][C]1730.9[/C][/ROW]
[ROW][C]3[/C][C]46465.5[/C][C]46308.5007582321[/C][C]156.999241767931[/C][/ROW]
[ROW][C]4[/C][C]50679.5[/C][C]46375.9753985885[/C][C]4303.52460141145[/C][/ROW]
[ROW][C]5[/C][C]47452.8[/C][C]48225.5306669809[/C][C]-772.730666980897[/C][/ROW]
[ROW][C]6[/C][C]49415.4[/C][C]47893.4289112028[/C][C]1521.97108879717[/C][/ROW]
[ROW][C]7[/C][C]48165.3[/C][C]48547.5368590701[/C][C]-382.236859070123[/C][/ROW]
[ROW][C]8[/C][C]51814[/C][C]48383.2603039332[/C][C]3430.7396960668[/C][/ROW]
[ROW][C]9[/C][C]49030.7[/C][C]49857.7128206591[/C][C]-827.012820659147[/C][/ROW]
[ROW][C]10[/C][C]50820.8[/C][C]49502.2818515934[/C][C]1318.51814840664[/C][/ROW]
[ROW][C]11[/C][C]49729.5[/C][C]50068.9504346094[/C][C]-339.450434609389[/C][/ROW]
[ROW][C]12[/C][C]53501.6[/C][C]49923.0624944117[/C][C]3578.53750558827[/C][/ROW]
[ROW][C]13[/C][C]50524.9[/C][C]51461.0350888822[/C][C]-936.135088882227[/C][/ROW]
[ROW][C]14[/C][C]52095[/C][C]51058.7058945746[/C][C]1036.29410542543[/C][/ROW]
[ROW][C]15[/C][C]51290.3[/C][C]51504.081116007[/C][C]-213.781116006998[/C][/ROW]
[ROW][C]16[/C][C]55064[/C][C]51412.2029403219[/C][C]3651.79705967808[/C][/ROW]
[ROW][C]17[/C][C]52505.2[/C][C]52981.6607955441[/C][C]-476.460795544146[/C][/ROW]
[ROW][C]18[/C][C]54318.3[/C][C]52776.8889733285[/C][C]1541.41102667155[/C][/ROW]
[ROW][C]19[/C][C]53039.6[/C][C]53439.3517565558[/C][C]-399.751756555816[/C][/ROW]
[ROW][C]20[/C][C]57607.6[/C][C]53267.5477038627[/C][C]4340.05229613727[/C][/ROW]
[ROW][C]21[/C][C]54236.4[/C][C]55132.8017300129[/C][C]-896.401730012898[/C][/ROW]
[ROW][C]22[/C][C]56586.4[/C][C]54747.5490137167[/C][C]1838.85098628332[/C][/ROW]
[ROW][C]23[/C][C]55614[/C][C]55537.8446073223[/C][C]76.1553926777124[/C][/ROW]
[ROW][C]24[/C][C]60085.9[/C][C]55570.5744324748[/C][C]4515.32556752524[/C][/ROW]
[ROW][C]25[/C][C]56963.5[/C][C]57511.1568539588[/C][C]-547.656853958761[/C][/ROW]
[ROW][C]26[/C][C]59152.8[/C][C]57275.7866136728[/C][C]1877.01338632716[/C][/ROW]
[ROW][C]27[/C][C]57804.6[/C][C]58082.4835235466[/C][C]-277.883523546618[/C][/ROW]
[ROW][C]28[/C][C]62541.5[/C][C]57963.0556167545[/C][C]4578.44438324553[/C][/ROW]
[ROW][C]29[/C][C]59449.3[/C][C]59930.7650443469[/C][C]-481.465044346871[/C][/ROW]
[ROW][C]30[/C][C]61704.7[/C][C]59723.8425118194[/C][C]1980.85748818063[/C][/ROW]
[ROW][C]31[/C][C]60399[/C][C]60575.1692131928[/C][C]-176.169213192778[/C][/ROW]
[ROW][C]32[/C][C]65724.7[/C][C]60499.4557628079[/C][C]5225.24423719214[/C][/ROW]
[ROW][C]33[/C][C]62679.4[/C][C]62745.1447974112[/C][C]-65.744797411222[/C][/ROW]
[ROW][C]34[/C][C]65526.5[/C][C]62716.8892051505[/C][C]2809.61079484946[/C][/ROW]
[ROW][C]35[/C][C]64274.8[/C][C]63924.3948961931[/C][C]350.40510380693[/C][/ROW]
[ROW][C]36[/C][C]68769.1[/C][C]64074.9908996655[/C][C]4694.10910033454[/C][/ROW]
[ROW][C]37[/C][C]63542.8[/C][C]66092.410345597[/C][C]-2549.610345597[/C][/ROW]
[ROW][C]38[/C][C]66198[/C][C]64996.6468299197[/C][C]1201.35317008034[/C][/ROW]
[ROW][C]39[/C][C]64544.9[/C][C]65512.9606170404[/C][C]-968.060617040384[/C][/ROW]
[ROW][C]40[/C][C]71041.8[/C][C]65096.9105696483[/C][C]5944.88943035169[/C][/ROW]
[ROW][C]41[/C][C]66087.2[/C][C]67651.8864520473[/C][C]-1564.6864520473[/C][/ROW]
[ROW][C]42[/C][C]69005.8[/C][C]66979.4204297043[/C][C]2026.37957029566[/C][/ROW]
[ROW][C]43[/C][C]66897[/C][C]67850.3114683599[/C][C]-953.311468359898[/C][/ROW]
[ROW][C]44[/C][C]73702[/C][C]67440.6002637009[/C][C]6261.39973629909[/C][/ROW]
[ROW][C]45[/C][C]68485.3[/C][C]70131.6049499491[/C][C]-1646.30494994907[/C][/ROW]
[ROW][C]46[/C][C]71457[/C][C]69424.0611862722[/C][C]2032.9388137278[/C][/ROW]
[ROW][C]47[/C][C]69774.6[/C][C]70297.7712359409[/C][C]-523.17123594087[/C][/ROW]
[ROW][C]48[/C][C]76479.7[/C][C]70072.9243475582[/C][C]6406.77565244182[/C][/ROW]
[ROW][C]49[/C][C]71204.7[/C][C]72826.4082378316[/C][C]-1621.70823783155[/C][/ROW]
[ROW][C]50[/C][C]73783.9[/C][C]72129.4355717306[/C][C]1654.46442826936[/C][/ROW]
[ROW][C]51[/C][C]71651[/C][C]72840.486090338[/C][C]-1189.48609033803[/C][/ROW]
[ROW][C]52[/C][C]78541.6[/C][C]72329.2724994264[/C][C]6212.32750057361[/C][/ROW]
[ROW][C]53[/C][C]72714.4[/C][C]74999.1870745391[/C][C]-2284.78707453913[/C][/ROW]
[ROW][C]54[/C][C]75258[/C][C]74017.2384714145[/C][C]1240.76152858554[/C][/ROW]
[ROW][C]55[/C][C]73168.1[/C][C]74550.4890589123[/C][C]-1382.38905891226[/C][/ROW]
[ROW][C]56[/C][C]79701.6[/C][C]73956.3702368564[/C][C]5745.22976314362[/C][/ROW]
[ROW][C]57[/C][C]73944.5[/C][C]76425.5370154224[/C][C]-2481.03701542242[/C][/ROW]
[ROW][C]58[/C][C]76401.2[/C][C]75359.2447299209[/C][C]1041.95527007908[/C][/ROW]
[ROW][C]59[/C][C]73948.1[/C][C]75807.0529888936[/C][C]-1858.95298889355[/C][/ROW]
[ROW][C]60[/C][C]80583.3[/C][C]75008.1180198279[/C][C]5575.18198017206[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294803&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294803&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
247295.545564.61730.9
346465.546308.5007582321156.999241767931
450679.546375.97539858854303.52460141145
547452.848225.5306669809-772.730666980897
649415.447893.42891120281521.97108879717
748165.348547.5368590701-382.236859070123
85181448383.26030393323430.7396960668
949030.749857.7128206591-827.012820659147
1050820.849502.28185159341318.51814840664
1149729.550068.9504346094-339.450434609389
1253501.649923.06249441173578.53750558827
1350524.951461.0350888822-936.135088882227
145209551058.70589457461036.29410542543
1551290.351504.081116007-213.781116006998
165506451412.20294032193651.79705967808
1752505.252981.6607955441-476.460795544146
1854318.352776.88897332851541.41102667155
1953039.653439.3517565558-399.751756555816
2057607.653267.54770386274340.05229613727
2154236.455132.8017300129-896.401730012898
2256586.454747.54901371671838.85098628332
235561455537.844607322376.1553926777124
2460085.955570.57443247484515.32556752524
2556963.557511.1568539588-547.656853958761
2659152.857275.78661367281877.01338632716
2757804.658082.4835235466-277.883523546618
2862541.557963.05561675454578.44438324553
2959449.359930.7650443469-481.465044346871
3061704.759723.84251181941980.85748818063
316039960575.1692131928-176.169213192778
3265724.760499.45576280795225.24423719214
3362679.462745.1447974112-65.744797411222
3465526.562716.88920515052809.61079484946
3564274.863924.3948961931350.40510380693
3668769.164074.99089966554694.10910033454
3763542.866092.410345597-2549.610345597
386619864996.64682991971201.35317008034
3964544.965512.9606170404-968.060617040384
4071041.865096.91056964835944.88943035169
4166087.267651.8864520473-1564.6864520473
4269005.866979.42042970432026.37957029566
436689767850.3114683599-953.311468359898
447370267440.60026370096261.39973629909
4568485.370131.6049499491-1646.30494994907
467145769424.06118627222032.9388137278
4769774.670297.7712359409-523.17123594087
4876479.770072.92434755826406.77565244182
4971204.772826.4082378316-1621.70823783155
5073783.972129.43557173061654.46442826936
517165172840.486090338-1189.48609033803
5278541.672329.27249942646212.32750057361
5372714.474999.1870745391-2284.78707453913
547525874017.23847141451240.76152858554
5573168.174550.4890589123-1382.38905891226
5679701.673956.37023685645745.22976314362
5773944.576425.5370154224-2481.03701542242
5876401.275359.24472992091041.95527007908
5973948.175807.0529888936-1858.95298889355
6080583.375008.11801982795575.18198017206







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6177404.202197037372423.88611783282384.5182762427
6277404.202197037371983.41206676282824.9923273127
6377404.202197037371576.133646978183232.2707470966
6477404.202197037371195.514701931183612.8896921436
6577404.202197037370836.91829883583971.4860952397
6677404.202197037370496.913641657184311.4907524176
6777404.202197037370172.877797248184635.5265968265
6877404.202197037369862.752073706684945.6523203681
6977404.202197037369564.885431503285243.5189625715
7077404.202197037369277.929697417185530.4746966576
7177404.202197037369000.767058608385807.6373354664
7277404.202197037368732.458455811986075.9459382628

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 77404.2021970373 & 72423.886117832 & 82384.5182762427 \tabularnewline
62 & 77404.2021970373 & 71983.412066762 & 82824.9923273127 \tabularnewline
63 & 77404.2021970373 & 71576.1336469781 & 83232.2707470966 \tabularnewline
64 & 77404.2021970373 & 71195.5147019311 & 83612.8896921436 \tabularnewline
65 & 77404.2021970373 & 70836.918298835 & 83971.4860952397 \tabularnewline
66 & 77404.2021970373 & 70496.9136416571 & 84311.4907524176 \tabularnewline
67 & 77404.2021970373 & 70172.8777972481 & 84635.5265968265 \tabularnewline
68 & 77404.2021970373 & 69862.7520737066 & 84945.6523203681 \tabularnewline
69 & 77404.2021970373 & 69564.8854315032 & 85243.5189625715 \tabularnewline
70 & 77404.2021970373 & 69277.9296974171 & 85530.4746966576 \tabularnewline
71 & 77404.2021970373 & 69000.7670586083 & 85807.6373354664 \tabularnewline
72 & 77404.2021970373 & 68732.4584558119 & 86075.9459382628 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294803&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]77404.2021970373[/C][C]72423.886117832[/C][C]82384.5182762427[/C][/ROW]
[ROW][C]62[/C][C]77404.2021970373[/C][C]71983.412066762[/C][C]82824.9923273127[/C][/ROW]
[ROW][C]63[/C][C]77404.2021970373[/C][C]71576.1336469781[/C][C]83232.2707470966[/C][/ROW]
[ROW][C]64[/C][C]77404.2021970373[/C][C]71195.5147019311[/C][C]83612.8896921436[/C][/ROW]
[ROW][C]65[/C][C]77404.2021970373[/C][C]70836.918298835[/C][C]83971.4860952397[/C][/ROW]
[ROW][C]66[/C][C]77404.2021970373[/C][C]70496.9136416571[/C][C]84311.4907524176[/C][/ROW]
[ROW][C]67[/C][C]77404.2021970373[/C][C]70172.8777972481[/C][C]84635.5265968265[/C][/ROW]
[ROW][C]68[/C][C]77404.2021970373[/C][C]69862.7520737066[/C][C]84945.6523203681[/C][/ROW]
[ROW][C]69[/C][C]77404.2021970373[/C][C]69564.8854315032[/C][C]85243.5189625715[/C][/ROW]
[ROW][C]70[/C][C]77404.2021970373[/C][C]69277.9296974171[/C][C]85530.4746966576[/C][/ROW]
[ROW][C]71[/C][C]77404.2021970373[/C][C]69000.7670586083[/C][C]85807.6373354664[/C][/ROW]
[ROW][C]72[/C][C]77404.2021970373[/C][C]68732.4584558119[/C][C]86075.9459382628[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294803&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294803&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
6177404.202197037372423.88611783282384.5182762427
6277404.202197037371983.41206676282824.9923273127
6377404.202197037371576.133646978183232.2707470966
6477404.202197037371195.514701931183612.8896921436
6577404.202197037370836.91829883583971.4860952397
6677404.202197037370496.913641657184311.4907524176
6777404.202197037370172.877797248184635.5265968265
6877404.202197037369862.752073706684945.6523203681
6977404.202197037369564.885431503285243.5189625715
7077404.202197037369277.929697417185530.4746966576
7177404.202197037369000.767058608385807.6373354664
7277404.202197037368732.458455811986075.9459382628



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