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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Jan 2013 16:14:27 -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/2013/Jan/15/t13582844918a0yptllc2b2e5e.htm/, Retrieved Sun, 28 Apr 2024 16:32:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205550, Retrieved Sun, 28 Apr 2024 16:32:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-15 21:14:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
14
19
16
16
11
13
12
11
6
9
6
15
17
13
12
13
10
14
13
10
11
12
7
11
9
13
12
5
13
11
8
8
8
8
0
3
0
-1
-1
-4
1
-1
0
-1
6
0
-3
-3
4
1
0
-4
-2
3
2
5
6
6
3
4
7
5
6
1
3
6
0
3
4
7
6
6
6
6
2
2
2
3
-1
-4
4
5
3
-1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205550&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205550&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205550&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.709014229144098
beta0.20399768824169
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.709014229144098 \tabularnewline
beta & 0.20399768824169 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205550&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]0.709014229144098[/C][/ROW]
[ROW][C]beta[/C][C]0.20399768824169[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205550&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205550&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
alpha0.709014229144098
beta0.20399768824169
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31624-8
41622.1707880574403-6.17078805744034
51120.7459875109239-9.74598751092395
61315.3766867144603-2.37668671446033
71214.888567578538-2.88856757853805
81113.6197231158555-2.61972311585554
9612.1625836195758-6.16258361957578
1097.302166382376631.69783361762337
1168.26046682199115-2.26046682199115
12156.085328190928778.91467180907123
131713.12291559897993.8770844010201
141317.1495527329696-4.14955273296955
151214.8850099740087-2.88500997400874
161313.0997660761941-0.0997660761940882
171013.2748698412984-3.2748698412984
181410.72511164519483.27488835480524
191313.2928960980648-0.292896098064752
201013.2887069171654-3.2887069171654
211110.68477566816920.315224331830818
221210.68167614036841.3183238596316
23711.5804672067218-4.58046720672182
24117.634425229145323.36557477085468
2599.8090276045998-0.809027604599796
26138.906761955870754.09323804412925
271212.0723071574117-0.0723071574117
28512.273963229525-7.27396322952499
29136.317456535510656.68254346448935
301111.2228564777961-0.222856477796068
31811.1999962519294-3.19999625192943
3288.60346286239931-0.603462862399311
3387.760625375346360.239374624653637
3487.549994150173350.450005849826652
3507.55379107550711-7.55379107550711
3630.7902224220589772.20977757794102
3701.26877905333651-1.26877905333651
38-1-0.902523194329129-0.0974768056708715
39-1-2.257454260215461.25745426021546
40-4-2.46984517748389-1.53015482251611
411-4.880008006229485.88000800622948
42-1-1.185791680706590.185791680706587
430-1.501983353492911.50198335349291
44-1-0.667733639656848-0.332266360343152
456-1.182051169905627.18205116990562
4604.67018157989409-4.67018157989409
47-31.44353037837283-4.44353037837283
48-3-2.26512197120565-0.734878028794351
494-3.450577781204627.45057778120462
5012.2452022331935-1.2452022331935
5101.59544784014431-1.59544784014431
52-40.466603118135748-4.46660311813575
53-2-3.343968802984141.34396880298414
543-2.840374582435525.84037458243552
5521.69597111419540.304028885804598
5652.35094284057552.6490571594245
5765.051725359557440.948274640442563
5866.68378472110846-0.68378472110846
5937.05979002150749-4.05979002150749
6044.45496260644831-0.454962606448306
6174.34020457580332.6597954241967
6256.81855984131984-1.81855984131984
6365.858665981143450.141334018856553
6416.30880692119599-5.30880692119599
6532.126869077445240.873130922554759
6662.454300396067263.54569960393274
6705.18946122668055-5.18946122668055
6830.9806792627477982.0193207372522
6942.175095311960781.82490468803922
7073.495616836455023.50438316354498
7166.51377688927098-0.513776889270981
7266.60869300625797-0.608693006257974
7366.5482725548823-0.548272554882297
7466.45139042117654-0.451390421176536
7526.35791122344953-4.35791122344953
7622.8643368357615-0.864336835761498
7721.722741084698870.277258915301133
7831.430654935908981.56934506409102
79-12.28166202772446-3.28166202772446
80-4-0.781414550235204-3.2185854497648
814-4.265296329256678.26529632925667
8251.588527323390543.41147267660946
8334.49434701360445-1.49434701360445
84-13.70573247481147-4.70573247481147

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 16 & 24 & -8 \tabularnewline
4 & 16 & 22.1707880574403 & -6.17078805744034 \tabularnewline
5 & 11 & 20.7459875109239 & -9.74598751092395 \tabularnewline
6 & 13 & 15.3766867144603 & -2.37668671446033 \tabularnewline
7 & 12 & 14.888567578538 & -2.88856757853805 \tabularnewline
8 & 11 & 13.6197231158555 & -2.61972311585554 \tabularnewline
9 & 6 & 12.1625836195758 & -6.16258361957578 \tabularnewline
10 & 9 & 7.30216638237663 & 1.69783361762337 \tabularnewline
11 & 6 & 8.26046682199115 & -2.26046682199115 \tabularnewline
12 & 15 & 6.08532819092877 & 8.91467180907123 \tabularnewline
13 & 17 & 13.1229155989799 & 3.8770844010201 \tabularnewline
14 & 13 & 17.1495527329696 & -4.14955273296955 \tabularnewline
15 & 12 & 14.8850099740087 & -2.88500997400874 \tabularnewline
16 & 13 & 13.0997660761941 & -0.0997660761940882 \tabularnewline
17 & 10 & 13.2748698412984 & -3.2748698412984 \tabularnewline
18 & 14 & 10.7251116451948 & 3.27488835480524 \tabularnewline
19 & 13 & 13.2928960980648 & -0.292896098064752 \tabularnewline
20 & 10 & 13.2887069171654 & -3.2887069171654 \tabularnewline
21 & 11 & 10.6847756681692 & 0.315224331830818 \tabularnewline
22 & 12 & 10.6816761403684 & 1.3183238596316 \tabularnewline
23 & 7 & 11.5804672067218 & -4.58046720672182 \tabularnewline
24 & 11 & 7.63442522914532 & 3.36557477085468 \tabularnewline
25 & 9 & 9.8090276045998 & -0.809027604599796 \tabularnewline
26 & 13 & 8.90676195587075 & 4.09323804412925 \tabularnewline
27 & 12 & 12.0723071574117 & -0.0723071574117 \tabularnewline
28 & 5 & 12.273963229525 & -7.27396322952499 \tabularnewline
29 & 13 & 6.31745653551065 & 6.68254346448935 \tabularnewline
30 & 11 & 11.2228564777961 & -0.222856477796068 \tabularnewline
31 & 8 & 11.1999962519294 & -3.19999625192943 \tabularnewline
32 & 8 & 8.60346286239931 & -0.603462862399311 \tabularnewline
33 & 8 & 7.76062537534636 & 0.239374624653637 \tabularnewline
34 & 8 & 7.54999415017335 & 0.450005849826652 \tabularnewline
35 & 0 & 7.55379107550711 & -7.55379107550711 \tabularnewline
36 & 3 & 0.790222422058977 & 2.20977757794102 \tabularnewline
37 & 0 & 1.26877905333651 & -1.26877905333651 \tabularnewline
38 & -1 & -0.902523194329129 & -0.0974768056708715 \tabularnewline
39 & -1 & -2.25745426021546 & 1.25745426021546 \tabularnewline
40 & -4 & -2.46984517748389 & -1.53015482251611 \tabularnewline
41 & 1 & -4.88000800622948 & 5.88000800622948 \tabularnewline
42 & -1 & -1.18579168070659 & 0.185791680706587 \tabularnewline
43 & 0 & -1.50198335349291 & 1.50198335349291 \tabularnewline
44 & -1 & -0.667733639656848 & -0.332266360343152 \tabularnewline
45 & 6 & -1.18205116990562 & 7.18205116990562 \tabularnewline
46 & 0 & 4.67018157989409 & -4.67018157989409 \tabularnewline
47 & -3 & 1.44353037837283 & -4.44353037837283 \tabularnewline
48 & -3 & -2.26512197120565 & -0.734878028794351 \tabularnewline
49 & 4 & -3.45057778120462 & 7.45057778120462 \tabularnewline
50 & 1 & 2.2452022331935 & -1.2452022331935 \tabularnewline
51 & 0 & 1.59544784014431 & -1.59544784014431 \tabularnewline
52 & -4 & 0.466603118135748 & -4.46660311813575 \tabularnewline
53 & -2 & -3.34396880298414 & 1.34396880298414 \tabularnewline
54 & 3 & -2.84037458243552 & 5.84037458243552 \tabularnewline
55 & 2 & 1.6959711141954 & 0.304028885804598 \tabularnewline
56 & 5 & 2.3509428405755 & 2.6490571594245 \tabularnewline
57 & 6 & 5.05172535955744 & 0.948274640442563 \tabularnewline
58 & 6 & 6.68378472110846 & -0.68378472110846 \tabularnewline
59 & 3 & 7.05979002150749 & -4.05979002150749 \tabularnewline
60 & 4 & 4.45496260644831 & -0.454962606448306 \tabularnewline
61 & 7 & 4.3402045758033 & 2.6597954241967 \tabularnewline
62 & 5 & 6.81855984131984 & -1.81855984131984 \tabularnewline
63 & 6 & 5.85866598114345 & 0.141334018856553 \tabularnewline
64 & 1 & 6.30880692119599 & -5.30880692119599 \tabularnewline
65 & 3 & 2.12686907744524 & 0.873130922554759 \tabularnewline
66 & 6 & 2.45430039606726 & 3.54569960393274 \tabularnewline
67 & 0 & 5.18946122668055 & -5.18946122668055 \tabularnewline
68 & 3 & 0.980679262747798 & 2.0193207372522 \tabularnewline
69 & 4 & 2.17509531196078 & 1.82490468803922 \tabularnewline
70 & 7 & 3.49561683645502 & 3.50438316354498 \tabularnewline
71 & 6 & 6.51377688927098 & -0.513776889270981 \tabularnewline
72 & 6 & 6.60869300625797 & -0.608693006257974 \tabularnewline
73 & 6 & 6.5482725548823 & -0.548272554882297 \tabularnewline
74 & 6 & 6.45139042117654 & -0.451390421176536 \tabularnewline
75 & 2 & 6.35791122344953 & -4.35791122344953 \tabularnewline
76 & 2 & 2.8643368357615 & -0.864336835761498 \tabularnewline
77 & 2 & 1.72274108469887 & 0.277258915301133 \tabularnewline
78 & 3 & 1.43065493590898 & 1.56934506409102 \tabularnewline
79 & -1 & 2.28166202772446 & -3.28166202772446 \tabularnewline
80 & -4 & -0.781414550235204 & -3.2185854497648 \tabularnewline
81 & 4 & -4.26529632925667 & 8.26529632925667 \tabularnewline
82 & 5 & 1.58852732339054 & 3.41147267660946 \tabularnewline
83 & 3 & 4.49434701360445 & -1.49434701360445 \tabularnewline
84 & -1 & 3.70573247481147 & -4.70573247481147 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205550&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]16[/C][C]24[/C][C]-8[/C][/ROW]
[ROW][C]4[/C][C]16[/C][C]22.1707880574403[/C][C]-6.17078805744034[/C][/ROW]
[ROW][C]5[/C][C]11[/C][C]20.7459875109239[/C][C]-9.74598751092395[/C][/ROW]
[ROW][C]6[/C][C]13[/C][C]15.3766867144603[/C][C]-2.37668671446033[/C][/ROW]
[ROW][C]7[/C][C]12[/C][C]14.888567578538[/C][C]-2.88856757853805[/C][/ROW]
[ROW][C]8[/C][C]11[/C][C]13.6197231158555[/C][C]-2.61972311585554[/C][/ROW]
[ROW][C]9[/C][C]6[/C][C]12.1625836195758[/C][C]-6.16258361957578[/C][/ROW]
[ROW][C]10[/C][C]9[/C][C]7.30216638237663[/C][C]1.69783361762337[/C][/ROW]
[ROW][C]11[/C][C]6[/C][C]8.26046682199115[/C][C]-2.26046682199115[/C][/ROW]
[ROW][C]12[/C][C]15[/C][C]6.08532819092877[/C][C]8.91467180907123[/C][/ROW]
[ROW][C]13[/C][C]17[/C][C]13.1229155989799[/C][C]3.8770844010201[/C][/ROW]
[ROW][C]14[/C][C]13[/C][C]17.1495527329696[/C][C]-4.14955273296955[/C][/ROW]
[ROW][C]15[/C][C]12[/C][C]14.8850099740087[/C][C]-2.88500997400874[/C][/ROW]
[ROW][C]16[/C][C]13[/C][C]13.0997660761941[/C][C]-0.0997660761940882[/C][/ROW]
[ROW][C]17[/C][C]10[/C][C]13.2748698412984[/C][C]-3.2748698412984[/C][/ROW]
[ROW][C]18[/C][C]14[/C][C]10.7251116451948[/C][C]3.27488835480524[/C][/ROW]
[ROW][C]19[/C][C]13[/C][C]13.2928960980648[/C][C]-0.292896098064752[/C][/ROW]
[ROW][C]20[/C][C]10[/C][C]13.2887069171654[/C][C]-3.2887069171654[/C][/ROW]
[ROW][C]21[/C][C]11[/C][C]10.6847756681692[/C][C]0.315224331830818[/C][/ROW]
[ROW][C]22[/C][C]12[/C][C]10.6816761403684[/C][C]1.3183238596316[/C][/ROW]
[ROW][C]23[/C][C]7[/C][C]11.5804672067218[/C][C]-4.58046720672182[/C][/ROW]
[ROW][C]24[/C][C]11[/C][C]7.63442522914532[/C][C]3.36557477085468[/C][/ROW]
[ROW][C]25[/C][C]9[/C][C]9.8090276045998[/C][C]-0.809027604599796[/C][/ROW]
[ROW][C]26[/C][C]13[/C][C]8.90676195587075[/C][C]4.09323804412925[/C][/ROW]
[ROW][C]27[/C][C]12[/C][C]12.0723071574117[/C][C]-0.0723071574117[/C][/ROW]
[ROW][C]28[/C][C]5[/C][C]12.273963229525[/C][C]-7.27396322952499[/C][/ROW]
[ROW][C]29[/C][C]13[/C][C]6.31745653551065[/C][C]6.68254346448935[/C][/ROW]
[ROW][C]30[/C][C]11[/C][C]11.2228564777961[/C][C]-0.222856477796068[/C][/ROW]
[ROW][C]31[/C][C]8[/C][C]11.1999962519294[/C][C]-3.19999625192943[/C][/ROW]
[ROW][C]32[/C][C]8[/C][C]8.60346286239931[/C][C]-0.603462862399311[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]7.76062537534636[/C][C]0.239374624653637[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.54999415017335[/C][C]0.450005849826652[/C][/ROW]
[ROW][C]35[/C][C]0[/C][C]7.55379107550711[/C][C]-7.55379107550711[/C][/ROW]
[ROW][C]36[/C][C]3[/C][C]0.790222422058977[/C][C]2.20977757794102[/C][/ROW]
[ROW][C]37[/C][C]0[/C][C]1.26877905333651[/C][C]-1.26877905333651[/C][/ROW]
[ROW][C]38[/C][C]-1[/C][C]-0.902523194329129[/C][C]-0.0974768056708715[/C][/ROW]
[ROW][C]39[/C][C]-1[/C][C]-2.25745426021546[/C][C]1.25745426021546[/C][/ROW]
[ROW][C]40[/C][C]-4[/C][C]-2.46984517748389[/C][C]-1.53015482251611[/C][/ROW]
[ROW][C]41[/C][C]1[/C][C]-4.88000800622948[/C][C]5.88000800622948[/C][/ROW]
[ROW][C]42[/C][C]-1[/C][C]-1.18579168070659[/C][C]0.185791680706587[/C][/ROW]
[ROW][C]43[/C][C]0[/C][C]-1.50198335349291[/C][C]1.50198335349291[/C][/ROW]
[ROW][C]44[/C][C]-1[/C][C]-0.667733639656848[/C][C]-0.332266360343152[/C][/ROW]
[ROW][C]45[/C][C]6[/C][C]-1.18205116990562[/C][C]7.18205116990562[/C][/ROW]
[ROW][C]46[/C][C]0[/C][C]4.67018157989409[/C][C]-4.67018157989409[/C][/ROW]
[ROW][C]47[/C][C]-3[/C][C]1.44353037837283[/C][C]-4.44353037837283[/C][/ROW]
[ROW][C]48[/C][C]-3[/C][C]-2.26512197120565[/C][C]-0.734878028794351[/C][/ROW]
[ROW][C]49[/C][C]4[/C][C]-3.45057778120462[/C][C]7.45057778120462[/C][/ROW]
[ROW][C]50[/C][C]1[/C][C]2.2452022331935[/C][C]-1.2452022331935[/C][/ROW]
[ROW][C]51[/C][C]0[/C][C]1.59544784014431[/C][C]-1.59544784014431[/C][/ROW]
[ROW][C]52[/C][C]-4[/C][C]0.466603118135748[/C][C]-4.46660311813575[/C][/ROW]
[ROW][C]53[/C][C]-2[/C][C]-3.34396880298414[/C][C]1.34396880298414[/C][/ROW]
[ROW][C]54[/C][C]3[/C][C]-2.84037458243552[/C][C]5.84037458243552[/C][/ROW]
[ROW][C]55[/C][C]2[/C][C]1.6959711141954[/C][C]0.304028885804598[/C][/ROW]
[ROW][C]56[/C][C]5[/C][C]2.3509428405755[/C][C]2.6490571594245[/C][/ROW]
[ROW][C]57[/C][C]6[/C][C]5.05172535955744[/C][C]0.948274640442563[/C][/ROW]
[ROW][C]58[/C][C]6[/C][C]6.68378472110846[/C][C]-0.68378472110846[/C][/ROW]
[ROW][C]59[/C][C]3[/C][C]7.05979002150749[/C][C]-4.05979002150749[/C][/ROW]
[ROW][C]60[/C][C]4[/C][C]4.45496260644831[/C][C]-0.454962606448306[/C][/ROW]
[ROW][C]61[/C][C]7[/C][C]4.3402045758033[/C][C]2.6597954241967[/C][/ROW]
[ROW][C]62[/C][C]5[/C][C]6.81855984131984[/C][C]-1.81855984131984[/C][/ROW]
[ROW][C]63[/C][C]6[/C][C]5.85866598114345[/C][C]0.141334018856553[/C][/ROW]
[ROW][C]64[/C][C]1[/C][C]6.30880692119599[/C][C]-5.30880692119599[/C][/ROW]
[ROW][C]65[/C][C]3[/C][C]2.12686907744524[/C][C]0.873130922554759[/C][/ROW]
[ROW][C]66[/C][C]6[/C][C]2.45430039606726[/C][C]3.54569960393274[/C][/ROW]
[ROW][C]67[/C][C]0[/C][C]5.18946122668055[/C][C]-5.18946122668055[/C][/ROW]
[ROW][C]68[/C][C]3[/C][C]0.980679262747798[/C][C]2.0193207372522[/C][/ROW]
[ROW][C]69[/C][C]4[/C][C]2.17509531196078[/C][C]1.82490468803922[/C][/ROW]
[ROW][C]70[/C][C]7[/C][C]3.49561683645502[/C][C]3.50438316354498[/C][/ROW]
[ROW][C]71[/C][C]6[/C][C]6.51377688927098[/C][C]-0.513776889270981[/C][/ROW]
[ROW][C]72[/C][C]6[/C][C]6.60869300625797[/C][C]-0.608693006257974[/C][/ROW]
[ROW][C]73[/C][C]6[/C][C]6.5482725548823[/C][C]-0.548272554882297[/C][/ROW]
[ROW][C]74[/C][C]6[/C][C]6.45139042117654[/C][C]-0.451390421176536[/C][/ROW]
[ROW][C]75[/C][C]2[/C][C]6.35791122344953[/C][C]-4.35791122344953[/C][/ROW]
[ROW][C]76[/C][C]2[/C][C]2.8643368357615[/C][C]-0.864336835761498[/C][/ROW]
[ROW][C]77[/C][C]2[/C][C]1.72274108469887[/C][C]0.277258915301133[/C][/ROW]
[ROW][C]78[/C][C]3[/C][C]1.43065493590898[/C][C]1.56934506409102[/C][/ROW]
[ROW][C]79[/C][C]-1[/C][C]2.28166202772446[/C][C]-3.28166202772446[/C][/ROW]
[ROW][C]80[/C][C]-4[/C][C]-0.781414550235204[/C][C]-3.2185854497648[/C][/ROW]
[ROW][C]81[/C][C]4[/C][C]-4.26529632925667[/C][C]8.26529632925667[/C][/ROW]
[ROW][C]82[/C][C]5[/C][C]1.58852732339054[/C][C]3.41147267660946[/C][/ROW]
[ROW][C]83[/C][C]3[/C][C]4.49434701360445[/C][C]-1.49434701360445[/C][/ROW]
[ROW][C]84[/C][C]-1[/C][C]3.70573247481147[/C][C]-4.70573247481147[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205550&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205550&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
31624-8
41622.1707880574403-6.17078805744034
51120.7459875109239-9.74598751092395
61315.3766867144603-2.37668671446033
71214.888567578538-2.88856757853805
81113.6197231158555-2.61972311585554
9612.1625836195758-6.16258361957578
1097.302166382376631.69783361762337
1168.26046682199115-2.26046682199115
12156.085328190928778.91467180907123
131713.12291559897993.8770844010201
141317.1495527329696-4.14955273296955
151214.8850099740087-2.88500997400874
161313.0997660761941-0.0997660761940882
171013.2748698412984-3.2748698412984
181410.72511164519483.27488835480524
191313.2928960980648-0.292896098064752
201013.2887069171654-3.2887069171654
211110.68477566816920.315224331830818
221210.68167614036841.3183238596316
23711.5804672067218-4.58046720672182
24117.634425229145323.36557477085468
2599.8090276045998-0.809027604599796
26138.906761955870754.09323804412925
271212.0723071574117-0.0723071574117
28512.273963229525-7.27396322952499
29136.317456535510656.68254346448935
301111.2228564777961-0.222856477796068
31811.1999962519294-3.19999625192943
3288.60346286239931-0.603462862399311
3387.760625375346360.239374624653637
3487.549994150173350.450005849826652
3507.55379107550711-7.55379107550711
3630.7902224220589772.20977757794102
3701.26877905333651-1.26877905333651
38-1-0.902523194329129-0.0974768056708715
39-1-2.257454260215461.25745426021546
40-4-2.46984517748389-1.53015482251611
411-4.880008006229485.88000800622948
42-1-1.185791680706590.185791680706587
430-1.501983353492911.50198335349291
44-1-0.667733639656848-0.332266360343152
456-1.182051169905627.18205116990562
4604.67018157989409-4.67018157989409
47-31.44353037837283-4.44353037837283
48-3-2.26512197120565-0.734878028794351
494-3.450577781204627.45057778120462
5012.2452022331935-1.2452022331935
5101.59544784014431-1.59544784014431
52-40.466603118135748-4.46660311813575
53-2-3.343968802984141.34396880298414
543-2.840374582435525.84037458243552
5521.69597111419540.304028885804598
5652.35094284057552.6490571594245
5765.051725359557440.948274640442563
5866.68378472110846-0.68378472110846
5937.05979002150749-4.05979002150749
6044.45496260644831-0.454962606448306
6174.34020457580332.6597954241967
6256.81855984131984-1.81855984131984
6365.858665981143450.141334018856553
6416.30880692119599-5.30880692119599
6532.126869077445240.873130922554759
6662.454300396067263.54569960393274
6705.18946122668055-5.18946122668055
6830.9806792627477982.0193207372522
6942.175095311960781.82490468803922
7073.495616836455023.50438316354498
7166.51377688927098-0.513776889270981
7266.60869300625797-0.608693006257974
7366.5482725548823-0.548272554882297
7466.45139042117654-0.451390421176536
7526.35791122344953-4.35791122344953
7622.8643368357615-0.864336835761498
7721.722741084698870.277258915301133
7831.430654935908981.56934506409102
79-12.28166202772446-3.28166202772446
80-4-0.781414550235204-3.2185854497648
814-4.265296329256678.26529632925667
8251.588527323390543.41147267660946
8334.49434701360445-1.49434701360445
84-13.70573247481147-4.70573247481147







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85-0.0404243199911367-7.410919550775377.33007091079309
86-0.450149831606938-10.14093815141379.24063848819984
87-0.85987534322274-13.027447550457211.3076968640117
88-1.26960085483854-16.068669177480313.5294674678032
89-1.67932636645434-19.259773614846315.9011208819376
90-2.08905187807014-22.595193346381718.4170895902414
91-2.49877738968595-26.069404840122721.0718500607508
92-2.90850290130175-29.677196644449823.8601908418463
93-3.31822841291755-33.413746594770326.7772897689352
94-3.72795392453335-37.274625085185829.818717236119
95-4.13767943614915-41.255770395800132.9804115235018
96-4.54740494776495-45.353455038560136.2586451430302

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & -0.0404243199911367 & -7.41091955077537 & 7.33007091079309 \tabularnewline
86 & -0.450149831606938 & -10.1409381514137 & 9.24063848819984 \tabularnewline
87 & -0.85987534322274 & -13.0274475504572 & 11.3076968640117 \tabularnewline
88 & -1.26960085483854 & -16.0686691774803 & 13.5294674678032 \tabularnewline
89 & -1.67932636645434 & -19.2597736148463 & 15.9011208819376 \tabularnewline
90 & -2.08905187807014 & -22.5951933463817 & 18.4170895902414 \tabularnewline
91 & -2.49877738968595 & -26.0694048401227 & 21.0718500607508 \tabularnewline
92 & -2.90850290130175 & -29.6771966444498 & 23.8601908418463 \tabularnewline
93 & -3.31822841291755 & -33.4137465947703 & 26.7772897689352 \tabularnewline
94 & -3.72795392453335 & -37.2746250851858 & 29.818717236119 \tabularnewline
95 & -4.13767943614915 & -41.2557703958001 & 32.9804115235018 \tabularnewline
96 & -4.54740494776495 & -45.3534550385601 & 36.2586451430302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205550&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]-0.0404243199911367[/C][C]-7.41091955077537[/C][C]7.33007091079309[/C][/ROW]
[ROW][C]86[/C][C]-0.450149831606938[/C][C]-10.1409381514137[/C][C]9.24063848819984[/C][/ROW]
[ROW][C]87[/C][C]-0.85987534322274[/C][C]-13.0274475504572[/C][C]11.3076968640117[/C][/ROW]
[ROW][C]88[/C][C]-1.26960085483854[/C][C]-16.0686691774803[/C][C]13.5294674678032[/C][/ROW]
[ROW][C]89[/C][C]-1.67932636645434[/C][C]-19.2597736148463[/C][C]15.9011208819376[/C][/ROW]
[ROW][C]90[/C][C]-2.08905187807014[/C][C]-22.5951933463817[/C][C]18.4170895902414[/C][/ROW]
[ROW][C]91[/C][C]-2.49877738968595[/C][C]-26.0694048401227[/C][C]21.0718500607508[/C][/ROW]
[ROW][C]92[/C][C]-2.90850290130175[/C][C]-29.6771966444498[/C][C]23.8601908418463[/C][/ROW]
[ROW][C]93[/C][C]-3.31822841291755[/C][C]-33.4137465947703[/C][C]26.7772897689352[/C][/ROW]
[ROW][C]94[/C][C]-3.72795392453335[/C][C]-37.2746250851858[/C][C]29.818717236119[/C][/ROW]
[ROW][C]95[/C][C]-4.13767943614915[/C][C]-41.2557703958001[/C][C]32.9804115235018[/C][/ROW]
[ROW][C]96[/C][C]-4.54740494776495[/C][C]-45.3534550385601[/C][C]36.2586451430302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205550&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205550&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
85-0.0404243199911367-7.410919550775377.33007091079309
86-0.450149831606938-10.14093815141379.24063848819984
87-0.85987534322274-13.027447550457211.3076968640117
88-1.26960085483854-16.068669177480313.5294674678032
89-1.67932636645434-19.259773614846315.9011208819376
90-2.08905187807014-22.595193346381718.4170895902414
91-2.49877738968595-26.069404840122721.0718500607508
92-2.90850290130175-29.677196644449823.8601908418463
93-3.31822841291755-33.413746594770326.7772897689352
94-3.72795392453335-37.274625085185829.818717236119
95-4.13767943614915-41.255770395800132.9804115235018
96-4.54740494776495-45.353455038560136.2586451430302



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')