Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 23 May 2013 06:29:50 -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/2013/May/23/t1369305015u72y71nawy8vnse.htm/, Retrieved Mon, 29 Apr 2024 16:57:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210337, Retrieved Mon, 29 Apr 2024 16:57:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 eigen r...] [2013-05-23 10:29:50] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
-1
-2
-5
-4
-6
-2
-2
-2
-2
2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0
-2
-3
1
-2
-1
1
-3
-4
-9
-9
-7
-14
-12
-16
-20
-12
-12
-10
-10
-13
-16
-14
-17
-24
-25




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=210337&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=210337&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210337&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
alpha0.685421250451419
beta0.0109412799866998
gamma0.819241958975001

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.685421250451419 \tabularnewline
beta & 0.0109412799866998 \tabularnewline
gamma & 0.819241958975001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210337&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]0.685421250451419[/C][/ROW]
[ROW][C]beta[/C][C]0.0109412799866998[/C][/ROW]
[ROW][C]gamma[/C][C]0.819241958975001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210337&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210337&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
alpha0.685421250451419
beta0.0109412799866998
gamma0.819241958975001







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13-1-3.315972222222222.31597222222222
1410.4043430265941280.595656973405872
15-1-1.00834862548320.00834862548320059
1622.30146870976924-0.301468709769238
1722.77166982951722-0.771669829517215
1811.6221313933677-0.622131393367705
19-1-0.387909157562383-0.612090842437617
20-2-0.77065800689697-1.22934199310303
21-2-1.75236988832863-0.24763011167137
22-11.81194734184801-2.81194734184801
23-8-1.56912749509779-6.43087250490221
24-4-15.353918136603611.3539181366036
25-60.025042096006064-6.02504209600606
26-3-2.46830675080823-0.531693249191773
27-3-4.866724135743981.86672413574398
28-7-0.410702088466094-6.58929791153391
29-9-4.46636641914675-4.53363358085325
30-11-8.278983999596-2.721016000404
31-13-11.8638851060551-1.13611489394494
32-11-12.90764465601521.90764465601521
33-9-11.60542869825492.60542869825488
34-17-6.84426644695912-10.1557335530409
35-22-16.3444938690495-5.65550613095055
36-25-25.16150020781460.161500207814605
37-20-22.16393073915482.16393073915477
38-24-17.7982784440531-6.20172155594685
39-24-23.6770840098649-0.322915990135083
40-22-23.12970299846321.12970299846317
41-19-21.53549653632712.53549653632709
42-18-20.15330150458252.15330150458254
43-17-20.06989302056853.06989302056847
44-11-17.49590277456996.49590277456988
45-11-12.88412117461081.88412117461078
46-12-11.9266790637132-0.0733209362868408
47-10-13.30137713829943.30137713829941
48-15-14.3577895975606-0.642210402439424
49-15-11.2788496897074-3.72115031029261
50-15-13.0308627140534-1.96913728594661
51-13-14.38970271831891.38970271831885
52-8-12.17745009460214.17745009460211
53-13-7.99245809288604-5.00754190711396
54-9-11.79598860555972.79598860555974
55-7-10.94809745078943.9480974507894
56-4-6.794892448624692.79489244862469
57-4-5.841810830107611.84181083010761
58-2-5.35156923546283.3515692354628
590-3.417111908050343.41711190805034
60-2-5.317706567402463.31770656740246
61-3-0.195534118597912-2.80446588140209
621-0.7383218831621661.73832188316217
63-21.46682855157308-3.46682855157308
64-11.18952980592264-2.18952980592264
651-1.283639420496852.28363942049685
66-32.0491581229258-5.0491581229258
67-4-2.11439587668134-1.88560412331866
68-9-2.23181447422992-6.76818552577008
69-9-8.12569248221572-0.874307517784276
70-7-9.17501455143582.1750145514358
71-14-8.10589233589473-5.89410766410527
72-12-16.55983247516954.55983247516954
73-16-12.3003671863524-3.69963281364763
74-20-12.4289891735743-7.57101082642573
75-12-18.15893599103586.15893599103585
76-12-11.6499950381095-0.350004961890455
77-10-11.83635609828671.83635609828668
78-10-10.83011949456740.830119494567418
79-13-10.2347052526963-2.76529474730373
80-16-12.3061119366409-3.69388806335913
81-14-14.64350801985670.643508019856728
82-17-13.9248991613344-3.07510083866558
83-24-18.6315045601661-5.36849543983395
84-25-24.1247325067592-0.87526749324082

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & -1 & -3.31597222222222 & 2.31597222222222 \tabularnewline
14 & 1 & 0.404343026594128 & 0.595656973405872 \tabularnewline
15 & -1 & -1.0083486254832 & 0.00834862548320059 \tabularnewline
16 & 2 & 2.30146870976924 & -0.301468709769238 \tabularnewline
17 & 2 & 2.77166982951722 & -0.771669829517215 \tabularnewline
18 & 1 & 1.6221313933677 & -0.622131393367705 \tabularnewline
19 & -1 & -0.387909157562383 & -0.612090842437617 \tabularnewline
20 & -2 & -0.77065800689697 & -1.22934199310303 \tabularnewline
21 & -2 & -1.75236988832863 & -0.24763011167137 \tabularnewline
22 & -1 & 1.81194734184801 & -2.81194734184801 \tabularnewline
23 & -8 & -1.56912749509779 & -6.43087250490221 \tabularnewline
24 & -4 & -15.3539181366036 & 11.3539181366036 \tabularnewline
25 & -6 & 0.025042096006064 & -6.02504209600606 \tabularnewline
26 & -3 & -2.46830675080823 & -0.531693249191773 \tabularnewline
27 & -3 & -4.86672413574398 & 1.86672413574398 \tabularnewline
28 & -7 & -0.410702088466094 & -6.58929791153391 \tabularnewline
29 & -9 & -4.46636641914675 & -4.53363358085325 \tabularnewline
30 & -11 & -8.278983999596 & -2.721016000404 \tabularnewline
31 & -13 & -11.8638851060551 & -1.13611489394494 \tabularnewline
32 & -11 & -12.9076446560152 & 1.90764465601521 \tabularnewline
33 & -9 & -11.6054286982549 & 2.60542869825488 \tabularnewline
34 & -17 & -6.84426644695912 & -10.1557335530409 \tabularnewline
35 & -22 & -16.3444938690495 & -5.65550613095055 \tabularnewline
36 & -25 & -25.1615002078146 & 0.161500207814605 \tabularnewline
37 & -20 & -22.1639307391548 & 2.16393073915477 \tabularnewline
38 & -24 & -17.7982784440531 & -6.20172155594685 \tabularnewline
39 & -24 & -23.6770840098649 & -0.322915990135083 \tabularnewline
40 & -22 & -23.1297029984632 & 1.12970299846317 \tabularnewline
41 & -19 & -21.5354965363271 & 2.53549653632709 \tabularnewline
42 & -18 & -20.1533015045825 & 2.15330150458254 \tabularnewline
43 & -17 & -20.0698930205685 & 3.06989302056847 \tabularnewline
44 & -11 & -17.4959027745699 & 6.49590277456988 \tabularnewline
45 & -11 & -12.8841211746108 & 1.88412117461078 \tabularnewline
46 & -12 & -11.9266790637132 & -0.0733209362868408 \tabularnewline
47 & -10 & -13.3013771382994 & 3.30137713829941 \tabularnewline
48 & -15 & -14.3577895975606 & -0.642210402439424 \tabularnewline
49 & -15 & -11.2788496897074 & -3.72115031029261 \tabularnewline
50 & -15 & -13.0308627140534 & -1.96913728594661 \tabularnewline
51 & -13 & -14.3897027183189 & 1.38970271831885 \tabularnewline
52 & -8 & -12.1774500946021 & 4.17745009460211 \tabularnewline
53 & -13 & -7.99245809288604 & -5.00754190711396 \tabularnewline
54 & -9 & -11.7959886055597 & 2.79598860555974 \tabularnewline
55 & -7 & -10.9480974507894 & 3.9480974507894 \tabularnewline
56 & -4 & -6.79489244862469 & 2.79489244862469 \tabularnewline
57 & -4 & -5.84181083010761 & 1.84181083010761 \tabularnewline
58 & -2 & -5.3515692354628 & 3.3515692354628 \tabularnewline
59 & 0 & -3.41711190805034 & 3.41711190805034 \tabularnewline
60 & -2 & -5.31770656740246 & 3.31770656740246 \tabularnewline
61 & -3 & -0.195534118597912 & -2.80446588140209 \tabularnewline
62 & 1 & -0.738321883162166 & 1.73832188316217 \tabularnewline
63 & -2 & 1.46682855157308 & -3.46682855157308 \tabularnewline
64 & -1 & 1.18952980592264 & -2.18952980592264 \tabularnewline
65 & 1 & -1.28363942049685 & 2.28363942049685 \tabularnewline
66 & -3 & 2.0491581229258 & -5.0491581229258 \tabularnewline
67 & -4 & -2.11439587668134 & -1.88560412331866 \tabularnewline
68 & -9 & -2.23181447422992 & -6.76818552577008 \tabularnewline
69 & -9 & -8.12569248221572 & -0.874307517784276 \tabularnewline
70 & -7 & -9.1750145514358 & 2.1750145514358 \tabularnewline
71 & -14 & -8.10589233589473 & -5.89410766410527 \tabularnewline
72 & -12 & -16.5598324751695 & 4.55983247516954 \tabularnewline
73 & -16 & -12.3003671863524 & -3.69963281364763 \tabularnewline
74 & -20 & -12.4289891735743 & -7.57101082642573 \tabularnewline
75 & -12 & -18.1589359910358 & 6.15893599103585 \tabularnewline
76 & -12 & -11.6499950381095 & -0.350004961890455 \tabularnewline
77 & -10 & -11.8363560982867 & 1.83635609828668 \tabularnewline
78 & -10 & -10.8301194945674 & 0.830119494567418 \tabularnewline
79 & -13 & -10.2347052526963 & -2.76529474730373 \tabularnewline
80 & -16 & -12.3061119366409 & -3.69388806335913 \tabularnewline
81 & -14 & -14.6435080198567 & 0.643508019856728 \tabularnewline
82 & -17 & -13.9248991613344 & -3.07510083866558 \tabularnewline
83 & -24 & -18.6315045601661 & -5.36849543983395 \tabularnewline
84 & -25 & -24.1247325067592 & -0.87526749324082 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210337&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]-1[/C][C]-3.31597222222222[/C][C]2.31597222222222[/C][/ROW]
[ROW][C]14[/C][C]1[/C][C]0.404343026594128[/C][C]0.595656973405872[/C][/ROW]
[ROW][C]15[/C][C]-1[/C][C]-1.0083486254832[/C][C]0.00834862548320059[/C][/ROW]
[ROW][C]16[/C][C]2[/C][C]2.30146870976924[/C][C]-0.301468709769238[/C][/ROW]
[ROW][C]17[/C][C]2[/C][C]2.77166982951722[/C][C]-0.771669829517215[/C][/ROW]
[ROW][C]18[/C][C]1[/C][C]1.6221313933677[/C][C]-0.622131393367705[/C][/ROW]
[ROW][C]19[/C][C]-1[/C][C]-0.387909157562383[/C][C]-0.612090842437617[/C][/ROW]
[ROW][C]20[/C][C]-2[/C][C]-0.77065800689697[/C][C]-1.22934199310303[/C][/ROW]
[ROW][C]21[/C][C]-2[/C][C]-1.75236988832863[/C][C]-0.24763011167137[/C][/ROW]
[ROW][C]22[/C][C]-1[/C][C]1.81194734184801[/C][C]-2.81194734184801[/C][/ROW]
[ROW][C]23[/C][C]-8[/C][C]-1.56912749509779[/C][C]-6.43087250490221[/C][/ROW]
[ROW][C]24[/C][C]-4[/C][C]-15.3539181366036[/C][C]11.3539181366036[/C][/ROW]
[ROW][C]25[/C][C]-6[/C][C]0.025042096006064[/C][C]-6.02504209600606[/C][/ROW]
[ROW][C]26[/C][C]-3[/C][C]-2.46830675080823[/C][C]-0.531693249191773[/C][/ROW]
[ROW][C]27[/C][C]-3[/C][C]-4.86672413574398[/C][C]1.86672413574398[/C][/ROW]
[ROW][C]28[/C][C]-7[/C][C]-0.410702088466094[/C][C]-6.58929791153391[/C][/ROW]
[ROW][C]29[/C][C]-9[/C][C]-4.46636641914675[/C][C]-4.53363358085325[/C][/ROW]
[ROW][C]30[/C][C]-11[/C][C]-8.278983999596[/C][C]-2.721016000404[/C][/ROW]
[ROW][C]31[/C][C]-13[/C][C]-11.8638851060551[/C][C]-1.13611489394494[/C][/ROW]
[ROW][C]32[/C][C]-11[/C][C]-12.9076446560152[/C][C]1.90764465601521[/C][/ROW]
[ROW][C]33[/C][C]-9[/C][C]-11.6054286982549[/C][C]2.60542869825488[/C][/ROW]
[ROW][C]34[/C][C]-17[/C][C]-6.84426644695912[/C][C]-10.1557335530409[/C][/ROW]
[ROW][C]35[/C][C]-22[/C][C]-16.3444938690495[/C][C]-5.65550613095055[/C][/ROW]
[ROW][C]36[/C][C]-25[/C][C]-25.1615002078146[/C][C]0.161500207814605[/C][/ROW]
[ROW][C]37[/C][C]-20[/C][C]-22.1639307391548[/C][C]2.16393073915477[/C][/ROW]
[ROW][C]38[/C][C]-24[/C][C]-17.7982784440531[/C][C]-6.20172155594685[/C][/ROW]
[ROW][C]39[/C][C]-24[/C][C]-23.6770840098649[/C][C]-0.322915990135083[/C][/ROW]
[ROW][C]40[/C][C]-22[/C][C]-23.1297029984632[/C][C]1.12970299846317[/C][/ROW]
[ROW][C]41[/C][C]-19[/C][C]-21.5354965363271[/C][C]2.53549653632709[/C][/ROW]
[ROW][C]42[/C][C]-18[/C][C]-20.1533015045825[/C][C]2.15330150458254[/C][/ROW]
[ROW][C]43[/C][C]-17[/C][C]-20.0698930205685[/C][C]3.06989302056847[/C][/ROW]
[ROW][C]44[/C][C]-11[/C][C]-17.4959027745699[/C][C]6.49590277456988[/C][/ROW]
[ROW][C]45[/C][C]-11[/C][C]-12.8841211746108[/C][C]1.88412117461078[/C][/ROW]
[ROW][C]46[/C][C]-12[/C][C]-11.9266790637132[/C][C]-0.0733209362868408[/C][/ROW]
[ROW][C]47[/C][C]-10[/C][C]-13.3013771382994[/C][C]3.30137713829941[/C][/ROW]
[ROW][C]48[/C][C]-15[/C][C]-14.3577895975606[/C][C]-0.642210402439424[/C][/ROW]
[ROW][C]49[/C][C]-15[/C][C]-11.2788496897074[/C][C]-3.72115031029261[/C][/ROW]
[ROW][C]50[/C][C]-15[/C][C]-13.0308627140534[/C][C]-1.96913728594661[/C][/ROW]
[ROW][C]51[/C][C]-13[/C][C]-14.3897027183189[/C][C]1.38970271831885[/C][/ROW]
[ROW][C]52[/C][C]-8[/C][C]-12.1774500946021[/C][C]4.17745009460211[/C][/ROW]
[ROW][C]53[/C][C]-13[/C][C]-7.99245809288604[/C][C]-5.00754190711396[/C][/ROW]
[ROW][C]54[/C][C]-9[/C][C]-11.7959886055597[/C][C]2.79598860555974[/C][/ROW]
[ROW][C]55[/C][C]-7[/C][C]-10.9480974507894[/C][C]3.9480974507894[/C][/ROW]
[ROW][C]56[/C][C]-4[/C][C]-6.79489244862469[/C][C]2.79489244862469[/C][/ROW]
[ROW][C]57[/C][C]-4[/C][C]-5.84181083010761[/C][C]1.84181083010761[/C][/ROW]
[ROW][C]58[/C][C]-2[/C][C]-5.3515692354628[/C][C]3.3515692354628[/C][/ROW]
[ROW][C]59[/C][C]0[/C][C]-3.41711190805034[/C][C]3.41711190805034[/C][/ROW]
[ROW][C]60[/C][C]-2[/C][C]-5.31770656740246[/C][C]3.31770656740246[/C][/ROW]
[ROW][C]61[/C][C]-3[/C][C]-0.195534118597912[/C][C]-2.80446588140209[/C][/ROW]
[ROW][C]62[/C][C]1[/C][C]-0.738321883162166[/C][C]1.73832188316217[/C][/ROW]
[ROW][C]63[/C][C]-2[/C][C]1.46682855157308[/C][C]-3.46682855157308[/C][/ROW]
[ROW][C]64[/C][C]-1[/C][C]1.18952980592264[/C][C]-2.18952980592264[/C][/ROW]
[ROW][C]65[/C][C]1[/C][C]-1.28363942049685[/C][C]2.28363942049685[/C][/ROW]
[ROW][C]66[/C][C]-3[/C][C]2.0491581229258[/C][C]-5.0491581229258[/C][/ROW]
[ROW][C]67[/C][C]-4[/C][C]-2.11439587668134[/C][C]-1.88560412331866[/C][/ROW]
[ROW][C]68[/C][C]-9[/C][C]-2.23181447422992[/C][C]-6.76818552577008[/C][/ROW]
[ROW][C]69[/C][C]-9[/C][C]-8.12569248221572[/C][C]-0.874307517784276[/C][/ROW]
[ROW][C]70[/C][C]-7[/C][C]-9.1750145514358[/C][C]2.1750145514358[/C][/ROW]
[ROW][C]71[/C][C]-14[/C][C]-8.10589233589473[/C][C]-5.89410766410527[/C][/ROW]
[ROW][C]72[/C][C]-12[/C][C]-16.5598324751695[/C][C]4.55983247516954[/C][/ROW]
[ROW][C]73[/C][C]-16[/C][C]-12.3003671863524[/C][C]-3.69963281364763[/C][/ROW]
[ROW][C]74[/C][C]-20[/C][C]-12.4289891735743[/C][C]-7.57101082642573[/C][/ROW]
[ROW][C]75[/C][C]-12[/C][C]-18.1589359910358[/C][C]6.15893599103585[/C][/ROW]
[ROW][C]76[/C][C]-12[/C][C]-11.6499950381095[/C][C]-0.350004961890455[/C][/ROW]
[ROW][C]77[/C][C]-10[/C][C]-11.8363560982867[/C][C]1.83635609828668[/C][/ROW]
[ROW][C]78[/C][C]-10[/C][C]-10.8301194945674[/C][C]0.830119494567418[/C][/ROW]
[ROW][C]79[/C][C]-13[/C][C]-10.2347052526963[/C][C]-2.76529474730373[/C][/ROW]
[ROW][C]80[/C][C]-16[/C][C]-12.3061119366409[/C][C]-3.69388806335913[/C][/ROW]
[ROW][C]81[/C][C]-14[/C][C]-14.6435080198567[/C][C]0.643508019856728[/C][/ROW]
[ROW][C]82[/C][C]-17[/C][C]-13.9248991613344[/C][C]-3.07510083866558[/C][/ROW]
[ROW][C]83[/C][C]-24[/C][C]-18.6315045601661[/C][C]-5.36849543983395[/C][/ROW]
[ROW][C]84[/C][C]-25[/C][C]-24.1247325067592[/C][C]-0.87526749324082[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210337&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210337&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
13-1-3.315972222222222.31597222222222
1410.4043430265941280.595656973405872
15-1-1.00834862548320.00834862548320059
1622.30146870976924-0.301468709769238
1722.77166982951722-0.771669829517215
1811.6221313933677-0.622131393367705
19-1-0.387909157562383-0.612090842437617
20-2-0.77065800689697-1.22934199310303
21-2-1.75236988832863-0.24763011167137
22-11.81194734184801-2.81194734184801
23-8-1.56912749509779-6.43087250490221
24-4-15.353918136603611.3539181366036
25-60.025042096006064-6.02504209600606
26-3-2.46830675080823-0.531693249191773
27-3-4.866724135743981.86672413574398
28-7-0.410702088466094-6.58929791153391
29-9-4.46636641914675-4.53363358085325
30-11-8.278983999596-2.721016000404
31-13-11.8638851060551-1.13611489394494
32-11-12.90764465601521.90764465601521
33-9-11.60542869825492.60542869825488
34-17-6.84426644695912-10.1557335530409
35-22-16.3444938690495-5.65550613095055
36-25-25.16150020781460.161500207814605
37-20-22.16393073915482.16393073915477
38-24-17.7982784440531-6.20172155594685
39-24-23.6770840098649-0.322915990135083
40-22-23.12970299846321.12970299846317
41-19-21.53549653632712.53549653632709
42-18-20.15330150458252.15330150458254
43-17-20.06989302056853.06989302056847
44-11-17.49590277456996.49590277456988
45-11-12.88412117461081.88412117461078
46-12-11.9266790637132-0.0733209362868408
47-10-13.30137713829943.30137713829941
48-15-14.3577895975606-0.642210402439424
49-15-11.2788496897074-3.72115031029261
50-15-13.0308627140534-1.96913728594661
51-13-14.38970271831891.38970271831885
52-8-12.17745009460214.17745009460211
53-13-7.99245809288604-5.00754190711396
54-9-11.79598860555972.79598860555974
55-7-10.94809745078943.9480974507894
56-4-6.794892448624692.79489244862469
57-4-5.841810830107611.84181083010761
58-2-5.35156923546283.3515692354628
590-3.417111908050343.41711190805034
60-2-5.317706567402463.31770656740246
61-3-0.195534118597912-2.80446588140209
621-0.7383218831621661.73832188316217
63-21.46682855157308-3.46682855157308
64-11.18952980592264-2.18952980592264
651-1.283639420496852.28363942049685
66-32.0491581229258-5.0491581229258
67-4-2.11439587668134-1.88560412331866
68-9-2.23181447422992-6.76818552577008
69-9-8.12569248221572-0.874307517784276
70-7-9.17501455143582.1750145514358
71-14-8.10589233589473-5.89410766410527
72-12-16.55983247516954.55983247516954
73-16-12.3003671863524-3.69963281364763
74-20-12.4289891735743-7.57101082642573
75-12-18.15893599103586.15893599103585
76-12-11.6499950381095-0.350004961890455
77-10-11.83635609828671.83635609828668
78-10-10.83011949456740.830119494567418
79-13-10.2347052526963-2.76529474730373
80-16-12.3061119366409-3.69388806335913
81-14-14.64350801985670.643508019856728
82-17-13.9248991613344-3.07510083866558
83-24-18.6315045601661-5.36849543983395
84-25-24.1247325067592-0.87526749324082







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85-25.853659812623-33.2998706301959-18.40744899505
86-24.5509086670329-33.6100405047317-15.4917768293342
87-21.603034677773-32.0562184340711-11.1498509214749
88-21.0891459193564-32.7962307473476-9.38206109136519
89-20.5656484856629-33.4277812750959-7.70351569622997
90-21.1846871167731-35.1278274184507-7.24154681509553
91-22.1983503365941-37.1647185188625-7.23198215432564
92-22.7064404266679-38.6495813291852-6.7632995241507
93-21.459210123719-38.3409189810245-4.57750126641349
94-22.2099065050455-39.9982023633565-4.42161064673462
95-25.4466415665914-44.1143705472976-6.77891258588513
96-26.1087753920129-45.6326130748399-6.58493770918582

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & -25.853659812623 & -33.2998706301959 & -18.40744899505 \tabularnewline
86 & -24.5509086670329 & -33.6100405047317 & -15.4917768293342 \tabularnewline
87 & -21.603034677773 & -32.0562184340711 & -11.1498509214749 \tabularnewline
88 & -21.0891459193564 & -32.7962307473476 & -9.38206109136519 \tabularnewline
89 & -20.5656484856629 & -33.4277812750959 & -7.70351569622997 \tabularnewline
90 & -21.1846871167731 & -35.1278274184507 & -7.24154681509553 \tabularnewline
91 & -22.1983503365941 & -37.1647185188625 & -7.23198215432564 \tabularnewline
92 & -22.7064404266679 & -38.6495813291852 & -6.7632995241507 \tabularnewline
93 & -21.459210123719 & -38.3409189810245 & -4.57750126641349 \tabularnewline
94 & -22.2099065050455 & -39.9982023633565 & -4.42161064673462 \tabularnewline
95 & -25.4466415665914 & -44.1143705472976 & -6.77891258588513 \tabularnewline
96 & -26.1087753920129 & -45.6326130748399 & -6.58493770918582 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210337&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]-25.853659812623[/C][C]-33.2998706301959[/C][C]-18.40744899505[/C][/ROW]
[ROW][C]86[/C][C]-24.5509086670329[/C][C]-33.6100405047317[/C][C]-15.4917768293342[/C][/ROW]
[ROW][C]87[/C][C]-21.603034677773[/C][C]-32.0562184340711[/C][C]-11.1498509214749[/C][/ROW]
[ROW][C]88[/C][C]-21.0891459193564[/C][C]-32.7962307473476[/C][C]-9.38206109136519[/C][/ROW]
[ROW][C]89[/C][C]-20.5656484856629[/C][C]-33.4277812750959[/C][C]-7.70351569622997[/C][/ROW]
[ROW][C]90[/C][C]-21.1846871167731[/C][C]-35.1278274184507[/C][C]-7.24154681509553[/C][/ROW]
[ROW][C]91[/C][C]-22.1983503365941[/C][C]-37.1647185188625[/C][C]-7.23198215432564[/C][/ROW]
[ROW][C]92[/C][C]-22.7064404266679[/C][C]-38.6495813291852[/C][C]-6.7632995241507[/C][/ROW]
[ROW][C]93[/C][C]-21.459210123719[/C][C]-38.3409189810245[/C][C]-4.57750126641349[/C][/ROW]
[ROW][C]94[/C][C]-22.2099065050455[/C][C]-39.9982023633565[/C][C]-4.42161064673462[/C][/ROW]
[ROW][C]95[/C][C]-25.4466415665914[/C][C]-44.1143705472976[/C][C]-6.77891258588513[/C][/ROW]
[ROW][C]96[/C][C]-26.1087753920129[/C][C]-45.6326130748399[/C][C]-6.58493770918582[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210337&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210337&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
85-25.853659812623-33.2998706301959-18.40744899505
86-24.5509086670329-33.6100405047317-15.4917768293342
87-21.603034677773-32.0562184340711-11.1498509214749
88-21.0891459193564-32.7962307473476-9.38206109136519
89-20.5656484856629-33.4277812750959-7.70351569622997
90-21.1846871167731-35.1278274184507-7.24154681509553
91-22.1983503365941-37.1647185188625-7.23198215432564
92-22.7064404266679-38.6495813291852-6.7632995241507
93-21.459210123719-38.3409189810245-4.57750126641349
94-22.2099065050455-39.9982023633565-4.42161064673462
95-25.4466415665914-44.1143705472976-6.77891258588513
96-26.1087753920129-45.6326130748399-6.58493770918582



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')