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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 computationThu, 24 May 2012 04:38:02 -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/2012/May/24/t1337848785504aakz2x2seorb.htm/, Retrieved Sun, 05 May 2024 16:17:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167261, Retrieved Sun, 05 May 2024 16:17:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oefening 2] [2012-05-24 08:38:02] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
12693.7
13154
15405.1
13869.4
12827.7
15716.7
13012.5
12837.6
15052.7
15002.6
14839.6
15022.6
14097.8
14776.8
16833.3
15385.5
15172.6
16858.9
14143.5
14731.8
16471.6
15214
17637.4
17972.4
16896.2
16698
19691.6
15930.7
17444.6
17699.4
15189.8
15672.7
17180.8
17664.9
17862.9
16162.3
17463.6
16772.1
19106.9
16721.3
18161.3
18509.9
17802.7
16409.9
17967.7
20286.6
19537.3
18021.9
20194.3
19049.6
20244.7
21473.3
19673.6
21053.2
20159.5
18203.6
21289.5
20432.3
17180.4
15816.8
15076.6
14531.6
15761.3
14345.5
13916.8
15496.8
14285.6
13597.3
16263.1
16773.3
15986.9
16842.6
15911.9
15782.9
18622.8
17422.5
16989.8
18990.5
16849.3
16511.3
18704.5
19111.1
19420.7
18985.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167261&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167261&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167261&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.637629335872465
beta0
gamma0.23707902612391

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.637629335872465 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.23707902612391 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167261&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]0.637629335872465[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.23707902612391[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167261&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167261&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
alpha0.637629335872465
beta0
gamma0.23707902612391







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1314097.813304.300267094793.499732905984
1414776.814491.4978151282285.302184871824
1516833.316720.157864784113.142135216032
1615385.515404.8602829806-19.3602829806332
1715172.615182.5211055944-9.92110559439425
1816858.916751.3006246161107.59937538387
1914143.514575.5021498754-432.002149875447
2014731.814127.3129129479604.487087052104
2116471.616729.0154531348-257.415453134752
221521416520.3894823688-1306.3894823688
2317637.415491.81106466152145.58893533845
2417972.417025.8945195497946.505480450276
2516896.216806.356300333289.8436996667951
261669817501.2226218164-803.222621816356
2719691.619021.0169686861670.583031313876
2815930.718049.7767083519-2119.07670835185
2917444.616489.4076654349955.192334565138
3017699.418683.6680677652-984.268067765166
3115189.815765.305452107-575.505452106985
3215672.715314.6595920399358.040407960134
3317180.817685.1740353942-504.374035394158
3417664.917228.9621611248435.937838875234
3517862.917607.9038932658254.996106734179
3616162.317833.4760583034-1671.17605830343
3717463.615871.23106966821592.36893033176
3816772.117447.4277960577-675.327796057711
3919106.919175.3869929368-68.4869929368288
4016721.317493.2329850356-771.932985035623
4118161.317055.95424161741105.34575838264
4218509.919179.3368897068-669.43688970682
4317802.716496.83686323841305.86313676159
4416409.917326.0081838349-916.108183834887
4517967.718809.9976644359-842.297664435948
4620286.618219.09841937292067.50158062709
4719537.319622.8282647901-85.5282647901186
4818021.919465.793717715-1443.893717715
4920194.317928.84334697472265.45665302533
5019049.619739.4016273059-689.801627305947
5120244.721510.2658719751-1265.56587197513
5221473.319004.38586769312468.91413230687
5319673.620794.8442450965-1121.24424509652
5421053.221346.0153514538-292.815351453824
5520159.519073.35924790691086.14075209313
5618203.619571.5384983772-1367.93849837718
5721289.520773.7688130463515.73118695369
5820432.321298.7708645051-866.4708645051
5917180.420646.7459718613-3466.34597186133
6015816.818217.3050418109-2400.50504181088
6115076.616389.0633140212-1312.46331402122
6214531.615664.3471923164-1132.7471923164
6315761.317103.3121655261-1342.01216552612
6414345.514869.5187470633-524.018747063312
6513916.814443.1630759151-526.363075915069
6615496.815444.81859443551.981405565024
6714285.613510.4818045504775.118195449571
6813597.313599.5128122432-2.21281224317499
6916263.115834.3968637861428.703136213864
7016773.316185.1616296193588.138370380704
7115986.916237.2817281744-250.381728174409
7216842.615950.0008533402892.59914665979
7315911.916315.0131538107-403.113153810738
7415782.916185.5648698612-402.66486986117
7518622.818072.0736943067550.726305693261
7617422.517115.4200608372307.079939162802
7716989.817218.7958906051-228.995890605132
7818990.518459.7473044123530.752695587689
7916849.316892.8141659434-43.5141659433793
8016511.316393.0802815039118.219718496104
8118704.518741.7758453983-37.2758453982897
8219111.118809.115900813301.984099187033
8319420.718606.7379738357813.962026164267
8418985.119096.3079405485-111.207940548546

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 14097.8 & 13304.300267094 & 793.499732905984 \tabularnewline
14 & 14776.8 & 14491.4978151282 & 285.302184871824 \tabularnewline
15 & 16833.3 & 16720.157864784 & 113.142135216032 \tabularnewline
16 & 15385.5 & 15404.8602829806 & -19.3602829806332 \tabularnewline
17 & 15172.6 & 15182.5211055944 & -9.92110559439425 \tabularnewline
18 & 16858.9 & 16751.3006246161 & 107.59937538387 \tabularnewline
19 & 14143.5 & 14575.5021498754 & -432.002149875447 \tabularnewline
20 & 14731.8 & 14127.3129129479 & 604.487087052104 \tabularnewline
21 & 16471.6 & 16729.0154531348 & -257.415453134752 \tabularnewline
22 & 15214 & 16520.3894823688 & -1306.3894823688 \tabularnewline
23 & 17637.4 & 15491.8110646615 & 2145.58893533845 \tabularnewline
24 & 17972.4 & 17025.8945195497 & 946.505480450276 \tabularnewline
25 & 16896.2 & 16806.3563003332 & 89.8436996667951 \tabularnewline
26 & 16698 & 17501.2226218164 & -803.222621816356 \tabularnewline
27 & 19691.6 & 19021.0169686861 & 670.583031313876 \tabularnewline
28 & 15930.7 & 18049.7767083519 & -2119.07670835185 \tabularnewline
29 & 17444.6 & 16489.4076654349 & 955.192334565138 \tabularnewline
30 & 17699.4 & 18683.6680677652 & -984.268067765166 \tabularnewline
31 & 15189.8 & 15765.305452107 & -575.505452106985 \tabularnewline
32 & 15672.7 & 15314.6595920399 & 358.040407960134 \tabularnewline
33 & 17180.8 & 17685.1740353942 & -504.374035394158 \tabularnewline
34 & 17664.9 & 17228.9621611248 & 435.937838875234 \tabularnewline
35 & 17862.9 & 17607.9038932658 & 254.996106734179 \tabularnewline
36 & 16162.3 & 17833.4760583034 & -1671.17605830343 \tabularnewline
37 & 17463.6 & 15871.2310696682 & 1592.36893033176 \tabularnewline
38 & 16772.1 & 17447.4277960577 & -675.327796057711 \tabularnewline
39 & 19106.9 & 19175.3869929368 & -68.4869929368288 \tabularnewline
40 & 16721.3 & 17493.2329850356 & -771.932985035623 \tabularnewline
41 & 18161.3 & 17055.9542416174 & 1105.34575838264 \tabularnewline
42 & 18509.9 & 19179.3368897068 & -669.43688970682 \tabularnewline
43 & 17802.7 & 16496.8368632384 & 1305.86313676159 \tabularnewline
44 & 16409.9 & 17326.0081838349 & -916.108183834887 \tabularnewline
45 & 17967.7 & 18809.9976644359 & -842.297664435948 \tabularnewline
46 & 20286.6 & 18219.0984193729 & 2067.50158062709 \tabularnewline
47 & 19537.3 & 19622.8282647901 & -85.5282647901186 \tabularnewline
48 & 18021.9 & 19465.793717715 & -1443.893717715 \tabularnewline
49 & 20194.3 & 17928.8433469747 & 2265.45665302533 \tabularnewline
50 & 19049.6 & 19739.4016273059 & -689.801627305947 \tabularnewline
51 & 20244.7 & 21510.2658719751 & -1265.56587197513 \tabularnewline
52 & 21473.3 & 19004.3858676931 & 2468.91413230687 \tabularnewline
53 & 19673.6 & 20794.8442450965 & -1121.24424509652 \tabularnewline
54 & 21053.2 & 21346.0153514538 & -292.815351453824 \tabularnewline
55 & 20159.5 & 19073.3592479069 & 1086.14075209313 \tabularnewline
56 & 18203.6 & 19571.5384983772 & -1367.93849837718 \tabularnewline
57 & 21289.5 & 20773.7688130463 & 515.73118695369 \tabularnewline
58 & 20432.3 & 21298.7708645051 & -866.4708645051 \tabularnewline
59 & 17180.4 & 20646.7459718613 & -3466.34597186133 \tabularnewline
60 & 15816.8 & 18217.3050418109 & -2400.50504181088 \tabularnewline
61 & 15076.6 & 16389.0633140212 & -1312.46331402122 \tabularnewline
62 & 14531.6 & 15664.3471923164 & -1132.7471923164 \tabularnewline
63 & 15761.3 & 17103.3121655261 & -1342.01216552612 \tabularnewline
64 & 14345.5 & 14869.5187470633 & -524.018747063312 \tabularnewline
65 & 13916.8 & 14443.1630759151 & -526.363075915069 \tabularnewline
66 & 15496.8 & 15444.818594435 & 51.981405565024 \tabularnewline
67 & 14285.6 & 13510.4818045504 & 775.118195449571 \tabularnewline
68 & 13597.3 & 13599.5128122432 & -2.21281224317499 \tabularnewline
69 & 16263.1 & 15834.3968637861 & 428.703136213864 \tabularnewline
70 & 16773.3 & 16185.1616296193 & 588.138370380704 \tabularnewline
71 & 15986.9 & 16237.2817281744 & -250.381728174409 \tabularnewline
72 & 16842.6 & 15950.0008533402 & 892.59914665979 \tabularnewline
73 & 15911.9 & 16315.0131538107 & -403.113153810738 \tabularnewline
74 & 15782.9 & 16185.5648698612 & -402.66486986117 \tabularnewline
75 & 18622.8 & 18072.0736943067 & 550.726305693261 \tabularnewline
76 & 17422.5 & 17115.4200608372 & 307.079939162802 \tabularnewline
77 & 16989.8 & 17218.7958906051 & -228.995890605132 \tabularnewline
78 & 18990.5 & 18459.7473044123 & 530.752695587689 \tabularnewline
79 & 16849.3 & 16892.8141659434 & -43.5141659433793 \tabularnewline
80 & 16511.3 & 16393.0802815039 & 118.219718496104 \tabularnewline
81 & 18704.5 & 18741.7758453983 & -37.2758453982897 \tabularnewline
82 & 19111.1 & 18809.115900813 & 301.984099187033 \tabularnewline
83 & 19420.7 & 18606.7379738357 & 813.962026164267 \tabularnewline
84 & 18985.1 & 19096.3079405485 & -111.207940548546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167261&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]14097.8[/C][C]13304.300267094[/C][C]793.499732905984[/C][/ROW]
[ROW][C]14[/C][C]14776.8[/C][C]14491.4978151282[/C][C]285.302184871824[/C][/ROW]
[ROW][C]15[/C][C]16833.3[/C][C]16720.157864784[/C][C]113.142135216032[/C][/ROW]
[ROW][C]16[/C][C]15385.5[/C][C]15404.8602829806[/C][C]-19.3602829806332[/C][/ROW]
[ROW][C]17[/C][C]15172.6[/C][C]15182.5211055944[/C][C]-9.92110559439425[/C][/ROW]
[ROW][C]18[/C][C]16858.9[/C][C]16751.3006246161[/C][C]107.59937538387[/C][/ROW]
[ROW][C]19[/C][C]14143.5[/C][C]14575.5021498754[/C][C]-432.002149875447[/C][/ROW]
[ROW][C]20[/C][C]14731.8[/C][C]14127.3129129479[/C][C]604.487087052104[/C][/ROW]
[ROW][C]21[/C][C]16471.6[/C][C]16729.0154531348[/C][C]-257.415453134752[/C][/ROW]
[ROW][C]22[/C][C]15214[/C][C]16520.3894823688[/C][C]-1306.3894823688[/C][/ROW]
[ROW][C]23[/C][C]17637.4[/C][C]15491.8110646615[/C][C]2145.58893533845[/C][/ROW]
[ROW][C]24[/C][C]17972.4[/C][C]17025.8945195497[/C][C]946.505480450276[/C][/ROW]
[ROW][C]25[/C][C]16896.2[/C][C]16806.3563003332[/C][C]89.8436996667951[/C][/ROW]
[ROW][C]26[/C][C]16698[/C][C]17501.2226218164[/C][C]-803.222621816356[/C][/ROW]
[ROW][C]27[/C][C]19691.6[/C][C]19021.0169686861[/C][C]670.583031313876[/C][/ROW]
[ROW][C]28[/C][C]15930.7[/C][C]18049.7767083519[/C][C]-2119.07670835185[/C][/ROW]
[ROW][C]29[/C][C]17444.6[/C][C]16489.4076654349[/C][C]955.192334565138[/C][/ROW]
[ROW][C]30[/C][C]17699.4[/C][C]18683.6680677652[/C][C]-984.268067765166[/C][/ROW]
[ROW][C]31[/C][C]15189.8[/C][C]15765.305452107[/C][C]-575.505452106985[/C][/ROW]
[ROW][C]32[/C][C]15672.7[/C][C]15314.6595920399[/C][C]358.040407960134[/C][/ROW]
[ROW][C]33[/C][C]17180.8[/C][C]17685.1740353942[/C][C]-504.374035394158[/C][/ROW]
[ROW][C]34[/C][C]17664.9[/C][C]17228.9621611248[/C][C]435.937838875234[/C][/ROW]
[ROW][C]35[/C][C]17862.9[/C][C]17607.9038932658[/C][C]254.996106734179[/C][/ROW]
[ROW][C]36[/C][C]16162.3[/C][C]17833.4760583034[/C][C]-1671.17605830343[/C][/ROW]
[ROW][C]37[/C][C]17463.6[/C][C]15871.2310696682[/C][C]1592.36893033176[/C][/ROW]
[ROW][C]38[/C][C]16772.1[/C][C]17447.4277960577[/C][C]-675.327796057711[/C][/ROW]
[ROW][C]39[/C][C]19106.9[/C][C]19175.3869929368[/C][C]-68.4869929368288[/C][/ROW]
[ROW][C]40[/C][C]16721.3[/C][C]17493.2329850356[/C][C]-771.932985035623[/C][/ROW]
[ROW][C]41[/C][C]18161.3[/C][C]17055.9542416174[/C][C]1105.34575838264[/C][/ROW]
[ROW][C]42[/C][C]18509.9[/C][C]19179.3368897068[/C][C]-669.43688970682[/C][/ROW]
[ROW][C]43[/C][C]17802.7[/C][C]16496.8368632384[/C][C]1305.86313676159[/C][/ROW]
[ROW][C]44[/C][C]16409.9[/C][C]17326.0081838349[/C][C]-916.108183834887[/C][/ROW]
[ROW][C]45[/C][C]17967.7[/C][C]18809.9976644359[/C][C]-842.297664435948[/C][/ROW]
[ROW][C]46[/C][C]20286.6[/C][C]18219.0984193729[/C][C]2067.50158062709[/C][/ROW]
[ROW][C]47[/C][C]19537.3[/C][C]19622.8282647901[/C][C]-85.5282647901186[/C][/ROW]
[ROW][C]48[/C][C]18021.9[/C][C]19465.793717715[/C][C]-1443.893717715[/C][/ROW]
[ROW][C]49[/C][C]20194.3[/C][C]17928.8433469747[/C][C]2265.45665302533[/C][/ROW]
[ROW][C]50[/C][C]19049.6[/C][C]19739.4016273059[/C][C]-689.801627305947[/C][/ROW]
[ROW][C]51[/C][C]20244.7[/C][C]21510.2658719751[/C][C]-1265.56587197513[/C][/ROW]
[ROW][C]52[/C][C]21473.3[/C][C]19004.3858676931[/C][C]2468.91413230687[/C][/ROW]
[ROW][C]53[/C][C]19673.6[/C][C]20794.8442450965[/C][C]-1121.24424509652[/C][/ROW]
[ROW][C]54[/C][C]21053.2[/C][C]21346.0153514538[/C][C]-292.815351453824[/C][/ROW]
[ROW][C]55[/C][C]20159.5[/C][C]19073.3592479069[/C][C]1086.14075209313[/C][/ROW]
[ROW][C]56[/C][C]18203.6[/C][C]19571.5384983772[/C][C]-1367.93849837718[/C][/ROW]
[ROW][C]57[/C][C]21289.5[/C][C]20773.7688130463[/C][C]515.73118695369[/C][/ROW]
[ROW][C]58[/C][C]20432.3[/C][C]21298.7708645051[/C][C]-866.4708645051[/C][/ROW]
[ROW][C]59[/C][C]17180.4[/C][C]20646.7459718613[/C][C]-3466.34597186133[/C][/ROW]
[ROW][C]60[/C][C]15816.8[/C][C]18217.3050418109[/C][C]-2400.50504181088[/C][/ROW]
[ROW][C]61[/C][C]15076.6[/C][C]16389.0633140212[/C][C]-1312.46331402122[/C][/ROW]
[ROW][C]62[/C][C]14531.6[/C][C]15664.3471923164[/C][C]-1132.7471923164[/C][/ROW]
[ROW][C]63[/C][C]15761.3[/C][C]17103.3121655261[/C][C]-1342.01216552612[/C][/ROW]
[ROW][C]64[/C][C]14345.5[/C][C]14869.5187470633[/C][C]-524.018747063312[/C][/ROW]
[ROW][C]65[/C][C]13916.8[/C][C]14443.1630759151[/C][C]-526.363075915069[/C][/ROW]
[ROW][C]66[/C][C]15496.8[/C][C]15444.818594435[/C][C]51.981405565024[/C][/ROW]
[ROW][C]67[/C][C]14285.6[/C][C]13510.4818045504[/C][C]775.118195449571[/C][/ROW]
[ROW][C]68[/C][C]13597.3[/C][C]13599.5128122432[/C][C]-2.21281224317499[/C][/ROW]
[ROW][C]69[/C][C]16263.1[/C][C]15834.3968637861[/C][C]428.703136213864[/C][/ROW]
[ROW][C]70[/C][C]16773.3[/C][C]16185.1616296193[/C][C]588.138370380704[/C][/ROW]
[ROW][C]71[/C][C]15986.9[/C][C]16237.2817281744[/C][C]-250.381728174409[/C][/ROW]
[ROW][C]72[/C][C]16842.6[/C][C]15950.0008533402[/C][C]892.59914665979[/C][/ROW]
[ROW][C]73[/C][C]15911.9[/C][C]16315.0131538107[/C][C]-403.113153810738[/C][/ROW]
[ROW][C]74[/C][C]15782.9[/C][C]16185.5648698612[/C][C]-402.66486986117[/C][/ROW]
[ROW][C]75[/C][C]18622.8[/C][C]18072.0736943067[/C][C]550.726305693261[/C][/ROW]
[ROW][C]76[/C][C]17422.5[/C][C]17115.4200608372[/C][C]307.079939162802[/C][/ROW]
[ROW][C]77[/C][C]16989.8[/C][C]17218.7958906051[/C][C]-228.995890605132[/C][/ROW]
[ROW][C]78[/C][C]18990.5[/C][C]18459.7473044123[/C][C]530.752695587689[/C][/ROW]
[ROW][C]79[/C][C]16849.3[/C][C]16892.8141659434[/C][C]-43.5141659433793[/C][/ROW]
[ROW][C]80[/C][C]16511.3[/C][C]16393.0802815039[/C][C]118.219718496104[/C][/ROW]
[ROW][C]81[/C][C]18704.5[/C][C]18741.7758453983[/C][C]-37.2758453982897[/C][/ROW]
[ROW][C]82[/C][C]19111.1[/C][C]18809.115900813[/C][C]301.984099187033[/C][/ROW]
[ROW][C]83[/C][C]19420.7[/C][C]18606.7379738357[/C][C]813.962026164267[/C][/ROW]
[ROW][C]84[/C][C]18985.1[/C][C]19096.3079405485[/C][C]-111.207940548546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167261&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167261&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
1314097.813304.300267094793.499732905984
1414776.814491.4978151282285.302184871824
1516833.316720.157864784113.142135216032
1615385.515404.8602829806-19.3602829806332
1715172.615182.5211055944-9.92110559439425
1816858.916751.3006246161107.59937538387
1914143.514575.5021498754-432.002149875447
2014731.814127.3129129479604.487087052104
2116471.616729.0154531348-257.415453134752
221521416520.3894823688-1306.3894823688
2317637.415491.81106466152145.58893533845
2417972.417025.8945195497946.505480450276
2516896.216806.356300333289.8436996667951
261669817501.2226218164-803.222621816356
2719691.619021.0169686861670.583031313876
2815930.718049.7767083519-2119.07670835185
2917444.616489.4076654349955.192334565138
3017699.418683.6680677652-984.268067765166
3115189.815765.305452107-575.505452106985
3215672.715314.6595920399358.040407960134
3317180.817685.1740353942-504.374035394158
3417664.917228.9621611248435.937838875234
3517862.917607.9038932658254.996106734179
3616162.317833.4760583034-1671.17605830343
3717463.615871.23106966821592.36893033176
3816772.117447.4277960577-675.327796057711
3919106.919175.3869929368-68.4869929368288
4016721.317493.2329850356-771.932985035623
4118161.317055.95424161741105.34575838264
4218509.919179.3368897068-669.43688970682
4317802.716496.83686323841305.86313676159
4416409.917326.0081838349-916.108183834887
4517967.718809.9976644359-842.297664435948
4620286.618219.09841937292067.50158062709
4719537.319622.8282647901-85.5282647901186
4818021.919465.793717715-1443.893717715
4920194.317928.84334697472265.45665302533
5019049.619739.4016273059-689.801627305947
5120244.721510.2658719751-1265.56587197513
5221473.319004.38586769312468.91413230687
5319673.620794.8442450965-1121.24424509652
5421053.221346.0153514538-292.815351453824
5520159.519073.35924790691086.14075209313
5618203.619571.5384983772-1367.93849837718
5721289.520773.7688130463515.73118695369
5820432.321298.7708645051-866.4708645051
5917180.420646.7459718613-3466.34597186133
6015816.818217.3050418109-2400.50504181088
6115076.616389.0633140212-1312.46331402122
6214531.615664.3471923164-1132.7471923164
6315761.317103.3121655261-1342.01216552612
6414345.514869.5187470633-524.018747063312
6513916.814443.1630759151-526.363075915069
6615496.815444.81859443551.981405565024
6714285.613510.4818045504775.118195449571
6813597.313599.5128122432-2.21281224317499
6916263.115834.3968637861428.703136213864
7016773.316185.1616296193588.138370380704
7115986.916237.2817281744-250.381728174409
7216842.615950.0008533402892.59914665979
7315911.916315.0131538107-403.113153810738
7415782.916185.5648698612-402.66486986117
7518622.818072.0736943067550.726305693261
7617422.517115.4200608372307.079939162802
7716989.817218.7958906051-228.995890605132
7818990.518459.7473044123530.752695587689
7916849.316892.8141659434-43.5141659433793
8016511.316393.0802815039118.219718496104
8118704.518741.7758453983-37.2758453982897
8219111.118809.115900813301.984099187033
8319420.718606.7379738357813.962026164267
8418985.119096.3079405485-111.207940548546







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8518709.948123609416632.168638455820787.727608763
8618837.575124496816373.350405342621301.7998436509
8721062.741179964718264.949310640723860.5330492886
8819733.996520639116638.374576405522829.6184648726
8919595.514638663916228.303463346122962.7258139817
9021047.750918985217429.277901709724666.2239362606
9119093.058747612315239.67285280322946.4446424216
9218634.965408219514560.187042236922709.7437742022
9320894.921912345316610.175174270225179.6686504204
9421015.176126396516530.280309656625500.0719431363
9520664.228550389915987.742009772525340.7150910072
9620555.310651175415694.779585320525415.8417170303

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 18709.9481236094 & 16632.1686384558 & 20787.727608763 \tabularnewline
86 & 18837.5751244968 & 16373.3504053426 & 21301.7998436509 \tabularnewline
87 & 21062.7411799647 & 18264.9493106407 & 23860.5330492886 \tabularnewline
88 & 19733.9965206391 & 16638.3745764055 & 22829.6184648726 \tabularnewline
89 & 19595.5146386639 & 16228.3034633461 & 22962.7258139817 \tabularnewline
90 & 21047.7509189852 & 17429.2779017097 & 24666.2239362606 \tabularnewline
91 & 19093.0587476123 & 15239.672852803 & 22946.4446424216 \tabularnewline
92 & 18634.9654082195 & 14560.1870422369 & 22709.7437742022 \tabularnewline
93 & 20894.9219123453 & 16610.1751742702 & 25179.6686504204 \tabularnewline
94 & 21015.1761263965 & 16530.2803096566 & 25500.0719431363 \tabularnewline
95 & 20664.2285503899 & 15987.7420097725 & 25340.7150910072 \tabularnewline
96 & 20555.3106511754 & 15694.7795853205 & 25415.8417170303 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167261&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]85[/C][C]18709.9481236094[/C][C]16632.1686384558[/C][C]20787.727608763[/C][/ROW]
[ROW][C]86[/C][C]18837.5751244968[/C][C]16373.3504053426[/C][C]21301.7998436509[/C][/ROW]
[ROW][C]87[/C][C]21062.7411799647[/C][C]18264.9493106407[/C][C]23860.5330492886[/C][/ROW]
[ROW][C]88[/C][C]19733.9965206391[/C][C]16638.3745764055[/C][C]22829.6184648726[/C][/ROW]
[ROW][C]89[/C][C]19595.5146386639[/C][C]16228.3034633461[/C][C]22962.7258139817[/C][/ROW]
[ROW][C]90[/C][C]21047.7509189852[/C][C]17429.2779017097[/C][C]24666.2239362606[/C][/ROW]
[ROW][C]91[/C][C]19093.0587476123[/C][C]15239.672852803[/C][C]22946.4446424216[/C][/ROW]
[ROW][C]92[/C][C]18634.9654082195[/C][C]14560.1870422369[/C][C]22709.7437742022[/C][/ROW]
[ROW][C]93[/C][C]20894.9219123453[/C][C]16610.1751742702[/C][C]25179.6686504204[/C][/ROW]
[ROW][C]94[/C][C]21015.1761263965[/C][C]16530.2803096566[/C][C]25500.0719431363[/C][/ROW]
[ROW][C]95[/C][C]20664.2285503899[/C][C]15987.7420097725[/C][C]25340.7150910072[/C][/ROW]
[ROW][C]96[/C][C]20555.3106511754[/C][C]15694.7795853205[/C][C]25415.8417170303[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167261&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167261&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
8518709.948123609416632.168638455820787.727608763
8618837.575124496816373.350405342621301.7998436509
8721062.741179964718264.949310640723860.5330492886
8819733.996520639116638.374576405522829.6184648726
8919595.514638663916228.303463346122962.7258139817
9021047.750918985217429.277901709724666.2239362606
9119093.058747612315239.67285280322946.4446424216
9218634.965408219514560.187042236922709.7437742022
9320894.921912345316610.175174270225179.6686504204
9421015.176126396516530.280309656625500.0719431363
9520664.228550389915987.742009772525340.7150910072
9620555.310651175415694.779585320525415.8417170303



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')