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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 01 Dec 2011 10:07:20 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/01/t132275246011qyhdlwg72b0t7.htm/, Retrieved Fri, 29 Mar 2024 01:48:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=149796, Retrieved Fri, 29 Mar 2024 01:48:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Monthly US soldie...] [2010-11-02 12:07:39] [b98453cac15ba1066b407e146608df68]
- RMP   [Classical Decomposition] [Soldiers] [2010-11-30 14:03:31] [b98453cac15ba1066b407e146608df68]
- RMP       [Exponential Smoothing] [] [2011-12-01 15:07:20] [aedc5b8e4f26bdca34b1a0cf88d6dfa2] [Current]
-             [Exponential Smoothing] [ES] [2011-12-22 16:17:00] [b92e58a8a0e3965aa63bc5c13821baa1]
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Dataseries X:
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149796&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]1 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=149796&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149796&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.458869668373879
beta0.0711214003331139
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.458869668373879 \tabularnewline
beta & 0.0711214003331139 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149796&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]0.458869668373879[/C][/ROW]
[ROW][C]beta[/C][C]0.0711214003331139[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149796&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149796&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
alpha0.458869668373879
beta0.0711214003331139
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3472324
43527.79612292221657.20387707778349
53025.12011628371294.87988371628709
64321.536956799664221.4630432003358
78226.263762354519955.7362376454801
84048.5364746640747-8.53647466407467
94741.03779706968155.96220293031854
101940.3867020506924-21.3867020506924
115226.488059354840925.5119406451591
1213634.9423750297094101.057624970291
138081.3603752268598-1.36037522685979
144280.7374651757254-38.7374651757254
155461.6991275159735-7.69912751597347
166656.65207704787469.34792295212543
178159.73247467857721.267525321423
186368.9764916268721-5.97649162687212
1913765.524010039035271.4759899609648
207299.944774330671-27.944774330671
2110787.832375102299319.1676248977007
225897.9639710130011-39.9639710130011
233679.657628804661-43.657628804661
245258.231592560615-6.231592560615
257953.77585830789625.224141692104
267764.577407700551912.4225922994481
275469.9101313006393-15.9101313006393
288461.722593069812222.2774069301878
294871.7851911183916-23.7851911183916
309659.934819579979136.0651804200209
318376.72497169587586.27502830412423
326680.0501149832532-14.0501149832532
336173.5901346381083-12.5901346381083
345367.3892102376778-14.3892102376778
353059.8931462135325-29.8931462135325
367444.3072198498729.69278015013
376957.032505098916511.9674949010835
385962.0147592058819-3.01475920588188
394260.0237233057599-18.0237233057599
406550.557316644719614.4426833552804
417056.460102760919913.5398972390801
4210062.390508396552537.6094916034475
436380.5931236261194-17.5931236261194
4410572.890773545924832.1092264540752
458289.0432235276064-7.04322352760644
468186.9999429770526-5.99994297705263
477585.2395813674112-10.2395813674112
4810281.199604915161320.8003950848387
4912192.081762488072128.9182375119279
5098107.632711515714-9.63271151571374
5176105.1794314399-29.1794314398995
527792.8044705001153-15.8044705001153
536386.0510873910001-23.0510873910001
543775.2201689043062-38.2201689043062
553556.1812864734165-21.1812864734165
562344.2697694857101-21.2697694857101
574031.62350175693228.37649824306778
582932.8543778873243-3.85437788732425
593728.34708657397088.65291342602919
605129.861403630592221.1385963694078
612037.7948895553043-17.7948895553043
622827.28223541652870.717764583471265
631325.2879013157388-12.2879013157388
642216.92464038620595.07535961379408
652516.69448990338578.3055100966143
661318.2176115890128-5.21761158901281
671613.36510379158162.63489620841841
681312.20186467544550.79813532455454
691610.22183920982815.77816079017186
701710.71556927523166.28443072476838
71911.6467065036014-2.6467065036014
72178.39323928706518.6067607129349
732510.584532378281214.4154676217188
741415.9117202040056-1.91172020400564
75813.6844669110586-5.68446691105861
7679.54049943289231-2.54049943289231
77106.75629291799333.2437070820067
7876.732143179661920.267856820338082
79105.351207647402374.64879235259763
8036.13226599611851-3.13226599611851

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 47 & 23 & 24 \tabularnewline
4 & 35 & 27.7961229222165 & 7.20387707778349 \tabularnewline
5 & 30 & 25.1201162837129 & 4.87988371628709 \tabularnewline
6 & 43 & 21.5369567996642 & 21.4630432003358 \tabularnewline
7 & 82 & 26.2637623545199 & 55.7362376454801 \tabularnewline
8 & 40 & 48.5364746640747 & -8.53647466407467 \tabularnewline
9 & 47 & 41.0377970696815 & 5.96220293031854 \tabularnewline
10 & 19 & 40.3867020506924 & -21.3867020506924 \tabularnewline
11 & 52 & 26.4880593548409 & 25.5119406451591 \tabularnewline
12 & 136 & 34.9423750297094 & 101.057624970291 \tabularnewline
13 & 80 & 81.3603752268598 & -1.36037522685979 \tabularnewline
14 & 42 & 80.7374651757254 & -38.7374651757254 \tabularnewline
15 & 54 & 61.6991275159735 & -7.69912751597347 \tabularnewline
16 & 66 & 56.6520770478746 & 9.34792295212543 \tabularnewline
17 & 81 & 59.732474678577 & 21.267525321423 \tabularnewline
18 & 63 & 68.9764916268721 & -5.97649162687212 \tabularnewline
19 & 137 & 65.5240100390352 & 71.4759899609648 \tabularnewline
20 & 72 & 99.944774330671 & -27.944774330671 \tabularnewline
21 & 107 & 87.8323751022993 & 19.1676248977007 \tabularnewline
22 & 58 & 97.9639710130011 & -39.9639710130011 \tabularnewline
23 & 36 & 79.657628804661 & -43.657628804661 \tabularnewline
24 & 52 & 58.231592560615 & -6.231592560615 \tabularnewline
25 & 79 & 53.775858307896 & 25.224141692104 \tabularnewline
26 & 77 & 64.5774077005519 & 12.4225922994481 \tabularnewline
27 & 54 & 69.9101313006393 & -15.9101313006393 \tabularnewline
28 & 84 & 61.7225930698122 & 22.2774069301878 \tabularnewline
29 & 48 & 71.7851911183916 & -23.7851911183916 \tabularnewline
30 & 96 & 59.9348195799791 & 36.0651804200209 \tabularnewline
31 & 83 & 76.7249716958758 & 6.27502830412423 \tabularnewline
32 & 66 & 80.0501149832532 & -14.0501149832532 \tabularnewline
33 & 61 & 73.5901346381083 & -12.5901346381083 \tabularnewline
34 & 53 & 67.3892102376778 & -14.3892102376778 \tabularnewline
35 & 30 & 59.8931462135325 & -29.8931462135325 \tabularnewline
36 & 74 & 44.30721984987 & 29.69278015013 \tabularnewline
37 & 69 & 57.0325050989165 & 11.9674949010835 \tabularnewline
38 & 59 & 62.0147592058819 & -3.01475920588188 \tabularnewline
39 & 42 & 60.0237233057599 & -18.0237233057599 \tabularnewline
40 & 65 & 50.5573166447196 & 14.4426833552804 \tabularnewline
41 & 70 & 56.4601027609199 & 13.5398972390801 \tabularnewline
42 & 100 & 62.3905083965525 & 37.6094916034475 \tabularnewline
43 & 63 & 80.5931236261194 & -17.5931236261194 \tabularnewline
44 & 105 & 72.8907735459248 & 32.1092264540752 \tabularnewline
45 & 82 & 89.0432235276064 & -7.04322352760644 \tabularnewline
46 & 81 & 86.9999429770526 & -5.99994297705263 \tabularnewline
47 & 75 & 85.2395813674112 & -10.2395813674112 \tabularnewline
48 & 102 & 81.1996049151613 & 20.8003950848387 \tabularnewline
49 & 121 & 92.0817624880721 & 28.9182375119279 \tabularnewline
50 & 98 & 107.632711515714 & -9.63271151571374 \tabularnewline
51 & 76 & 105.1794314399 & -29.1794314398995 \tabularnewline
52 & 77 & 92.8044705001153 & -15.8044705001153 \tabularnewline
53 & 63 & 86.0510873910001 & -23.0510873910001 \tabularnewline
54 & 37 & 75.2201689043062 & -38.2201689043062 \tabularnewline
55 & 35 & 56.1812864734165 & -21.1812864734165 \tabularnewline
56 & 23 & 44.2697694857101 & -21.2697694857101 \tabularnewline
57 & 40 & 31.6235017569322 & 8.37649824306778 \tabularnewline
58 & 29 & 32.8543778873243 & -3.85437788732425 \tabularnewline
59 & 37 & 28.3470865739708 & 8.65291342602919 \tabularnewline
60 & 51 & 29.8614036305922 & 21.1385963694078 \tabularnewline
61 & 20 & 37.7948895553043 & -17.7948895553043 \tabularnewline
62 & 28 & 27.2822354165287 & 0.717764583471265 \tabularnewline
63 & 13 & 25.2879013157388 & -12.2879013157388 \tabularnewline
64 & 22 & 16.9246403862059 & 5.07535961379408 \tabularnewline
65 & 25 & 16.6944899033857 & 8.3055100966143 \tabularnewline
66 & 13 & 18.2176115890128 & -5.21761158901281 \tabularnewline
67 & 16 & 13.3651037915816 & 2.63489620841841 \tabularnewline
68 & 13 & 12.2018646754455 & 0.79813532455454 \tabularnewline
69 & 16 & 10.2218392098281 & 5.77816079017186 \tabularnewline
70 & 17 & 10.7155692752316 & 6.28443072476838 \tabularnewline
71 & 9 & 11.6467065036014 & -2.6467065036014 \tabularnewline
72 & 17 & 8.3932392870651 & 8.6067607129349 \tabularnewline
73 & 25 & 10.5845323782812 & 14.4154676217188 \tabularnewline
74 & 14 & 15.9117202040056 & -1.91172020400564 \tabularnewline
75 & 8 & 13.6844669110586 & -5.68446691105861 \tabularnewline
76 & 7 & 9.54049943289231 & -2.54049943289231 \tabularnewline
77 & 10 & 6.7562929179933 & 3.2437070820067 \tabularnewline
78 & 7 & 6.73214317966192 & 0.267856820338082 \tabularnewline
79 & 10 & 5.35120764740237 & 4.64879235259763 \tabularnewline
80 & 3 & 6.13226599611851 & -3.13226599611851 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149796&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]47[/C][C]23[/C][C]24[/C][/ROW]
[ROW][C]4[/C][C]35[/C][C]27.7961229222165[/C][C]7.20387707778349[/C][/ROW]
[ROW][C]5[/C][C]30[/C][C]25.1201162837129[/C][C]4.87988371628709[/C][/ROW]
[ROW][C]6[/C][C]43[/C][C]21.5369567996642[/C][C]21.4630432003358[/C][/ROW]
[ROW][C]7[/C][C]82[/C][C]26.2637623545199[/C][C]55.7362376454801[/C][/ROW]
[ROW][C]8[/C][C]40[/C][C]48.5364746640747[/C][C]-8.53647466407467[/C][/ROW]
[ROW][C]9[/C][C]47[/C][C]41.0377970696815[/C][C]5.96220293031854[/C][/ROW]
[ROW][C]10[/C][C]19[/C][C]40.3867020506924[/C][C]-21.3867020506924[/C][/ROW]
[ROW][C]11[/C][C]52[/C][C]26.4880593548409[/C][C]25.5119406451591[/C][/ROW]
[ROW][C]12[/C][C]136[/C][C]34.9423750297094[/C][C]101.057624970291[/C][/ROW]
[ROW][C]13[/C][C]80[/C][C]81.3603752268598[/C][C]-1.36037522685979[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]80.7374651757254[/C][C]-38.7374651757254[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]61.6991275159735[/C][C]-7.69912751597347[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]56.6520770478746[/C][C]9.34792295212543[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]59.732474678577[/C][C]21.267525321423[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]68.9764916268721[/C][C]-5.97649162687212[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]65.5240100390352[/C][C]71.4759899609648[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]99.944774330671[/C][C]-27.944774330671[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]87.8323751022993[/C][C]19.1676248977007[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]97.9639710130011[/C][C]-39.9639710130011[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]79.657628804661[/C][C]-43.657628804661[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]58.231592560615[/C][C]-6.231592560615[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]53.775858307896[/C][C]25.224141692104[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]64.5774077005519[/C][C]12.4225922994481[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]69.9101313006393[/C][C]-15.9101313006393[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]61.7225930698122[/C][C]22.2774069301878[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]71.7851911183916[/C][C]-23.7851911183916[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]59.9348195799791[/C][C]36.0651804200209[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]76.7249716958758[/C][C]6.27502830412423[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]80.0501149832532[/C][C]-14.0501149832532[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]73.5901346381083[/C][C]-12.5901346381083[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]67.3892102376778[/C][C]-14.3892102376778[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]59.8931462135325[/C][C]-29.8931462135325[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]44.30721984987[/C][C]29.69278015013[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]57.0325050989165[/C][C]11.9674949010835[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]62.0147592058819[/C][C]-3.01475920588188[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]60.0237233057599[/C][C]-18.0237233057599[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]50.5573166447196[/C][C]14.4426833552804[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]56.4601027609199[/C][C]13.5398972390801[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]62.3905083965525[/C][C]37.6094916034475[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]80.5931236261194[/C][C]-17.5931236261194[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]72.8907735459248[/C][C]32.1092264540752[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]89.0432235276064[/C][C]-7.04322352760644[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]86.9999429770526[/C][C]-5.99994297705263[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]85.2395813674112[/C][C]-10.2395813674112[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]81.1996049151613[/C][C]20.8003950848387[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]92.0817624880721[/C][C]28.9182375119279[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]107.632711515714[/C][C]-9.63271151571374[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]105.1794314399[/C][C]-29.1794314398995[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]92.8044705001153[/C][C]-15.8044705001153[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]86.0510873910001[/C][C]-23.0510873910001[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]75.2201689043062[/C][C]-38.2201689043062[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]56.1812864734165[/C][C]-21.1812864734165[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]44.2697694857101[/C][C]-21.2697694857101[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]31.6235017569322[/C][C]8.37649824306778[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]32.8543778873243[/C][C]-3.85437788732425[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]28.3470865739708[/C][C]8.65291342602919[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]29.8614036305922[/C][C]21.1385963694078[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]37.7948895553043[/C][C]-17.7948895553043[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]27.2822354165287[/C][C]0.717764583471265[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]25.2879013157388[/C][C]-12.2879013157388[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]16.9246403862059[/C][C]5.07535961379408[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]16.6944899033857[/C][C]8.3055100966143[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]18.2176115890128[/C][C]-5.21761158901281[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]13.3651037915816[/C][C]2.63489620841841[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]12.2018646754455[/C][C]0.79813532455454[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]10.2218392098281[/C][C]5.77816079017186[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]10.7155692752316[/C][C]6.28443072476838[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]11.6467065036014[/C][C]-2.6467065036014[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]8.3932392870651[/C][C]8.6067607129349[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]10.5845323782812[/C][C]14.4154676217188[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]15.9117202040056[/C][C]-1.91172020400564[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]13.6844669110586[/C][C]-5.68446691105861[/C][/ROW]
[ROW][C]76[/C][C]7[/C][C]9.54049943289231[/C][C]-2.54049943289231[/C][/ROW]
[ROW][C]77[/C][C]10[/C][C]6.7562929179933[/C][C]3.2437070820067[/C][/ROW]
[ROW][C]78[/C][C]7[/C][C]6.73214317966192[/C][C]0.267856820338082[/C][/ROW]
[ROW][C]79[/C][C]10[/C][C]5.35120764740237[/C][C]4.64879235259763[/C][/ROW]
[ROW][C]80[/C][C]3[/C][C]6.13226599611851[/C][C]-3.13226599611851[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149796&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149796&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
3472324
43527.79612292221657.20387707778349
53025.12011628371294.87988371628709
64321.536956799664221.4630432003358
78226.263762354519955.7362376454801
84048.5364746640747-8.53647466407467
94741.03779706968155.96220293031854
101940.3867020506924-21.3867020506924
115226.488059354840925.5119406451591
1213634.9423750297094101.057624970291
138081.3603752268598-1.36037522685979
144280.7374651757254-38.7374651757254
155461.6991275159735-7.69912751597347
166656.65207704787469.34792295212543
178159.73247467857721.267525321423
186368.9764916268721-5.97649162687212
1913765.524010039035271.4759899609648
207299.944774330671-27.944774330671
2110787.832375102299319.1676248977007
225897.9639710130011-39.9639710130011
233679.657628804661-43.657628804661
245258.231592560615-6.231592560615
257953.77585830789625.224141692104
267764.577407700551912.4225922994481
275469.9101313006393-15.9101313006393
288461.722593069812222.2774069301878
294871.7851911183916-23.7851911183916
309659.934819579979136.0651804200209
318376.72497169587586.27502830412423
326680.0501149832532-14.0501149832532
336173.5901346381083-12.5901346381083
345367.3892102376778-14.3892102376778
353059.8931462135325-29.8931462135325
367444.3072198498729.69278015013
376957.032505098916511.9674949010835
385962.0147592058819-3.01475920588188
394260.0237233057599-18.0237233057599
406550.557316644719614.4426833552804
417056.460102760919913.5398972390801
4210062.390508396552537.6094916034475
436380.5931236261194-17.5931236261194
4410572.890773545924832.1092264540752
458289.0432235276064-7.04322352760644
468186.9999429770526-5.99994297705263
477585.2395813674112-10.2395813674112
4810281.199604915161320.8003950848387
4912192.081762488072128.9182375119279
5098107.632711515714-9.63271151571374
5176105.1794314399-29.1794314398995
527792.8044705001153-15.8044705001153
536386.0510873910001-23.0510873910001
543775.2201689043062-38.2201689043062
553556.1812864734165-21.1812864734165
562344.2697694857101-21.2697694857101
574031.62350175693228.37649824306778
582932.8543778873243-3.85437788732425
593728.34708657397088.65291342602919
605129.861403630592221.1385963694078
612037.7948895553043-17.7948895553043
622827.28223541652870.717764583471265
631325.2879013157388-12.2879013157388
642216.92464038620595.07535961379408
652516.69448990338578.3055100966143
661318.2176115890128-5.21761158901281
671613.36510379158162.63489620841841
681312.20186467544550.79813532455454
691610.22183920982815.77816079017186
701710.71556927523166.28443072476838
71911.6467065036014-2.6467065036014
72178.39323928706518.6067607129349
732510.584532378281214.4154676217188
741415.9117202040056-1.91172020400564
75813.6844669110586-5.68446691105861
7679.54049943289231-2.54049943289231
77106.75629291799333.2437070820067
7876.732143179661920.267856820338082
79105.351207647402374.64879235259763
8036.13226599611851-3.13226599611851







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
813.24060975985528-43.515313575419649.9965330951302
821.78625538248973-50.312040395105853.8845511600853
830.331901005124177-57.242482346980957.9062843572292
84-1.12245337224137-64.308723237674662.0638164931919
85-2.57680774960693-71.511373916108366.3577584168945
86-4.03116212697248-78.850113628458170.7877893745131
87-5.48551650433803-86.324026630380975.3529936217048
88-6.93987088170358-93.931817667892480.0520759044852
89-8.39422525906913-101.67195308719184.8835025690531
90-9.84857963643468-109.54275486755989.8455955946895
91-11.3029340138002-117.54246408899894.9365960613978
92-12.7572883911658-125.669284130188100.154707347857

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 3.24060975985528 & -43.5153135754196 & 49.9965330951302 \tabularnewline
82 & 1.78625538248973 & -50.3120403951058 & 53.8845511600853 \tabularnewline
83 & 0.331901005124177 & -57.2424823469809 & 57.9062843572292 \tabularnewline
84 & -1.12245337224137 & -64.3087232376746 & 62.0638164931919 \tabularnewline
85 & -2.57680774960693 & -71.5113739161083 & 66.3577584168945 \tabularnewline
86 & -4.03116212697248 & -78.8501136284581 & 70.7877893745131 \tabularnewline
87 & -5.48551650433803 & -86.3240266303809 & 75.3529936217048 \tabularnewline
88 & -6.93987088170358 & -93.9318176678924 & 80.0520759044852 \tabularnewline
89 & -8.39422525906913 & -101.671953087191 & 84.8835025690531 \tabularnewline
90 & -9.84857963643468 & -109.542754867559 & 89.8455955946895 \tabularnewline
91 & -11.3029340138002 & -117.542464088998 & 94.9365960613978 \tabularnewline
92 & -12.7572883911658 & -125.669284130188 & 100.154707347857 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149796&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]81[/C][C]3.24060975985528[/C][C]-43.5153135754196[/C][C]49.9965330951302[/C][/ROW]
[ROW][C]82[/C][C]1.78625538248973[/C][C]-50.3120403951058[/C][C]53.8845511600853[/C][/ROW]
[ROW][C]83[/C][C]0.331901005124177[/C][C]-57.2424823469809[/C][C]57.9062843572292[/C][/ROW]
[ROW][C]84[/C][C]-1.12245337224137[/C][C]-64.3087232376746[/C][C]62.0638164931919[/C][/ROW]
[ROW][C]85[/C][C]-2.57680774960693[/C][C]-71.5113739161083[/C][C]66.3577584168945[/C][/ROW]
[ROW][C]86[/C][C]-4.03116212697248[/C][C]-78.8501136284581[/C][C]70.7877893745131[/C][/ROW]
[ROW][C]87[/C][C]-5.48551650433803[/C][C]-86.3240266303809[/C][C]75.3529936217048[/C][/ROW]
[ROW][C]88[/C][C]-6.93987088170358[/C][C]-93.9318176678924[/C][C]80.0520759044852[/C][/ROW]
[ROW][C]89[/C][C]-8.39422525906913[/C][C]-101.671953087191[/C][C]84.8835025690531[/C][/ROW]
[ROW][C]90[/C][C]-9.84857963643468[/C][C]-109.542754867559[/C][C]89.8455955946895[/C][/ROW]
[ROW][C]91[/C][C]-11.3029340138002[/C][C]-117.542464088998[/C][C]94.9365960613978[/C][/ROW]
[ROW][C]92[/C][C]-12.7572883911658[/C][C]-125.669284130188[/C][C]100.154707347857[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149796&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149796&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
813.24060975985528-43.515313575419649.9965330951302
821.78625538248973-50.312040395105853.8845511600853
830.331901005124177-57.242482346980957.9062843572292
84-1.12245337224137-64.308723237674662.0638164931919
85-2.57680774960693-71.511373916108366.3577584168945
86-4.03116212697248-78.850113628458170.7877893745131
87-5.48551650433803-86.324026630380975.3529936217048
88-6.93987088170358-93.931817667892480.0520759044852
89-8.39422525906913-101.67195308719184.8835025690531
90-9.84857963643468-109.54275486755989.8455955946895
91-11.3029340138002-117.54246408899894.9365960613978
92-12.7572883911658-125.669284130188100.154707347857



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')