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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 29 Nov 2015 13:33:03 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/29/t1448804018c11qdotq5k1svu8.htm/, Retrieved Wed, 15 May 2024 00:09:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284437, Retrieved Wed, 15 May 2024 00:09:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exp smoothing alc...] [2015-11-29 13:33:03] [4bedbbf2e5251222bc39a0f973d05821] [Current]
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Dataseries X:
89,56
89,84
89,97
90,65
91,17
91,35
91,41
91,55
91,63
91,54
91,74
91,87
92,13
92,14
92,05
92
92,51
92,67
92,68
92,77
92,85
92,71
92,73
92,28
92,49
92,46
92,55
92,24
92,41
92,83
92,85
93,04
93,04
92,83
92,96
92,83
93,01
93,21
93,58
94,07
94,57
95,03
95,21
95,89
96,43
96,35
96,71
96,32
97,23
97,88
98,2
98,56
99,31
99,69
99,77
101,06
101,77
101,91
102,52
102,09
102,22
102,74
103,56
104,4
104,76
104,86
104,84
104,96
104,83
104,58
104,8
104,17




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284437&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284437&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284437&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999951664594603
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999951664594603 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284437&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]0.999951664594603[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284437&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284437&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
alpha0.999951664594603
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
289.8489.560.280000000000001
389.9789.83998646608650.130013533913512
490.6589.96999371574310.680006284256876
591.1790.64996713162060.520032868379417
691.3591.16997486400050.180025135999514
791.4191.34999129841210.0600087015879325
891.5591.40999709945510.140002900544914
991.6391.5499932329030.0800067670969611
1091.5491.6299961328405-0.0899961328404686
1191.7491.54000434999960.199995650000417
1291.8791.73999033312920.130009666870819
1392.1391.86999371593010.260006284069945
1492.1492.12998743249090.0100125675091505
1592.0592.1399995160385-0.0899995160385032
169292.0500043501631-0.0500043501630927
1792.5192.00000241698050.509997583019455
1892.6792.50997534906010.160024650939931
1992.6892.66999226514360.0100077348563872
2092.7792.67999951627210.0900004837279056
2192.8592.76999564979010.0800043502098617
2292.7192.8499961329573-0.139996132957293
2392.7392.71000676676980.0199932332301671
2492.2892.729999033619-0.449999033618965
2592.4992.28002175088570.209978249114272
2692.4692.4899898506162-0.0299898506162037
2792.5592.46000144957160.0899985504284189
2892.2492.5499956498836-0.309995649883575
2992.4192.24001498376540.169985016234591
3092.8392.40999178370530.420008216294676
3192.8592.82997969873260.0200203012673938
3293.0492.84999903231060.190000967689386
3393.0493.03999081622629.18377379832691e-06
3492.8393.0399999995561-0.209999999556103
3592.9692.83001015043510.129989849564879
3692.8392.9599937168879-0.129993716887924
3793.0192.8300062832990.179993716700992
3893.2193.00999129993070.200008700069247
3993.5893.20999033249840.370009667501606
4094.0793.57998211543270.490017884567266
4194.5794.06997631478690.500023685213108
4295.0394.56997583115240.460024168847553
4395.2195.02997776454530.180022235454686
4495.8995.20999129855230.680008701447733
4596.4395.88996713150380.540032868496255
4696.3596.4299738972924-0.0799738972923905
4796.7196.35000386557070.359996134429252
4896.3296.7099825994409-0.389982599440913
4997.2396.3200188499670.909981150032962
5097.8897.22995601569220.650043984307786
5198.297.87996857986050.320031420139514
5298.5698.19998453115160.360015468848431
5399.3198.55998259850640.750017401493636
5499.6999.30996374760480.380036252395158
5599.7799.68998163079370.0800183692063143
56101.0699.76999613227971.29000386772032
57101.77101.059937647140.710062352859907
58101.91101.7699656788480.140034321151674
59102.52101.9099932313840.610006768615676
60102.09102.519970515076-0.429970515075539
61102.22102.0900207827990.129979217200841
62102.74102.2199937174020.520006282598146
63103.56102.7399748652860.820025134714484
64104.4103.5599603637530.840039636247326
65104.76104.3999593963440.360040603656358
66104.86104.7599825972910.100017402708531
67104.84104.859995165618-0.0199951656182833
68104.96104.8400009664740.119999033525559
69104.83104.959994199798-0.129994199798062
70104.58104.830006283322-0.25000628332235
71104.8104.5800120841550.219987915844939
72104.17104.799989366795-0.629989366794902

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 89.84 & 89.56 & 0.280000000000001 \tabularnewline
3 & 89.97 & 89.8399864660865 & 0.130013533913512 \tabularnewline
4 & 90.65 & 89.9699937157431 & 0.680006284256876 \tabularnewline
5 & 91.17 & 90.6499671316206 & 0.520032868379417 \tabularnewline
6 & 91.35 & 91.1699748640005 & 0.180025135999514 \tabularnewline
7 & 91.41 & 91.3499912984121 & 0.0600087015879325 \tabularnewline
8 & 91.55 & 91.4099970994551 & 0.140002900544914 \tabularnewline
9 & 91.63 & 91.549993232903 & 0.0800067670969611 \tabularnewline
10 & 91.54 & 91.6299961328405 & -0.0899961328404686 \tabularnewline
11 & 91.74 & 91.5400043499996 & 0.199995650000417 \tabularnewline
12 & 91.87 & 91.7399903331292 & 0.130009666870819 \tabularnewline
13 & 92.13 & 91.8699937159301 & 0.260006284069945 \tabularnewline
14 & 92.14 & 92.1299874324909 & 0.0100125675091505 \tabularnewline
15 & 92.05 & 92.1399995160385 & -0.0899995160385032 \tabularnewline
16 & 92 & 92.0500043501631 & -0.0500043501630927 \tabularnewline
17 & 92.51 & 92.0000024169805 & 0.509997583019455 \tabularnewline
18 & 92.67 & 92.5099753490601 & 0.160024650939931 \tabularnewline
19 & 92.68 & 92.6699922651436 & 0.0100077348563872 \tabularnewline
20 & 92.77 & 92.6799995162721 & 0.0900004837279056 \tabularnewline
21 & 92.85 & 92.7699956497901 & 0.0800043502098617 \tabularnewline
22 & 92.71 & 92.8499961329573 & -0.139996132957293 \tabularnewline
23 & 92.73 & 92.7100067667698 & 0.0199932332301671 \tabularnewline
24 & 92.28 & 92.729999033619 & -0.449999033618965 \tabularnewline
25 & 92.49 & 92.2800217508857 & 0.209978249114272 \tabularnewline
26 & 92.46 & 92.4899898506162 & -0.0299898506162037 \tabularnewline
27 & 92.55 & 92.4600014495716 & 0.0899985504284189 \tabularnewline
28 & 92.24 & 92.5499956498836 & -0.309995649883575 \tabularnewline
29 & 92.41 & 92.2400149837654 & 0.169985016234591 \tabularnewline
30 & 92.83 & 92.4099917837053 & 0.420008216294676 \tabularnewline
31 & 92.85 & 92.8299796987326 & 0.0200203012673938 \tabularnewline
32 & 93.04 & 92.8499990323106 & 0.190000967689386 \tabularnewline
33 & 93.04 & 93.0399908162262 & 9.18377379832691e-06 \tabularnewline
34 & 92.83 & 93.0399999995561 & -0.209999999556103 \tabularnewline
35 & 92.96 & 92.8300101504351 & 0.129989849564879 \tabularnewline
36 & 92.83 & 92.9599937168879 & -0.129993716887924 \tabularnewline
37 & 93.01 & 92.830006283299 & 0.179993716700992 \tabularnewline
38 & 93.21 & 93.0099912999307 & 0.200008700069247 \tabularnewline
39 & 93.58 & 93.2099903324984 & 0.370009667501606 \tabularnewline
40 & 94.07 & 93.5799821154327 & 0.490017884567266 \tabularnewline
41 & 94.57 & 94.0699763147869 & 0.500023685213108 \tabularnewline
42 & 95.03 & 94.5699758311524 & 0.460024168847553 \tabularnewline
43 & 95.21 & 95.0299777645453 & 0.180022235454686 \tabularnewline
44 & 95.89 & 95.2099912985523 & 0.680008701447733 \tabularnewline
45 & 96.43 & 95.8899671315038 & 0.540032868496255 \tabularnewline
46 & 96.35 & 96.4299738972924 & -0.0799738972923905 \tabularnewline
47 & 96.71 & 96.3500038655707 & 0.359996134429252 \tabularnewline
48 & 96.32 & 96.7099825994409 & -0.389982599440913 \tabularnewline
49 & 97.23 & 96.320018849967 & 0.909981150032962 \tabularnewline
50 & 97.88 & 97.2299560156922 & 0.650043984307786 \tabularnewline
51 & 98.2 & 97.8799685798605 & 0.320031420139514 \tabularnewline
52 & 98.56 & 98.1999845311516 & 0.360015468848431 \tabularnewline
53 & 99.31 & 98.5599825985064 & 0.750017401493636 \tabularnewline
54 & 99.69 & 99.3099637476048 & 0.380036252395158 \tabularnewline
55 & 99.77 & 99.6899816307937 & 0.0800183692063143 \tabularnewline
56 & 101.06 & 99.7699961322797 & 1.29000386772032 \tabularnewline
57 & 101.77 & 101.05993764714 & 0.710062352859907 \tabularnewline
58 & 101.91 & 101.769965678848 & 0.140034321151674 \tabularnewline
59 & 102.52 & 101.909993231384 & 0.610006768615676 \tabularnewline
60 & 102.09 & 102.519970515076 & -0.429970515075539 \tabularnewline
61 & 102.22 & 102.090020782799 & 0.129979217200841 \tabularnewline
62 & 102.74 & 102.219993717402 & 0.520006282598146 \tabularnewline
63 & 103.56 & 102.739974865286 & 0.820025134714484 \tabularnewline
64 & 104.4 & 103.559960363753 & 0.840039636247326 \tabularnewline
65 & 104.76 & 104.399959396344 & 0.360040603656358 \tabularnewline
66 & 104.86 & 104.759982597291 & 0.100017402708531 \tabularnewline
67 & 104.84 & 104.859995165618 & -0.0199951656182833 \tabularnewline
68 & 104.96 & 104.840000966474 & 0.119999033525559 \tabularnewline
69 & 104.83 & 104.959994199798 & -0.129994199798062 \tabularnewline
70 & 104.58 & 104.830006283322 & -0.25000628332235 \tabularnewline
71 & 104.8 & 104.580012084155 & 0.219987915844939 \tabularnewline
72 & 104.17 & 104.799989366795 & -0.629989366794902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284437&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]89.84[/C][C]89.56[/C][C]0.280000000000001[/C][/ROW]
[ROW][C]3[/C][C]89.97[/C][C]89.8399864660865[/C][C]0.130013533913512[/C][/ROW]
[ROW][C]4[/C][C]90.65[/C][C]89.9699937157431[/C][C]0.680006284256876[/C][/ROW]
[ROW][C]5[/C][C]91.17[/C][C]90.6499671316206[/C][C]0.520032868379417[/C][/ROW]
[ROW][C]6[/C][C]91.35[/C][C]91.1699748640005[/C][C]0.180025135999514[/C][/ROW]
[ROW][C]7[/C][C]91.41[/C][C]91.3499912984121[/C][C]0.0600087015879325[/C][/ROW]
[ROW][C]8[/C][C]91.55[/C][C]91.4099970994551[/C][C]0.140002900544914[/C][/ROW]
[ROW][C]9[/C][C]91.63[/C][C]91.549993232903[/C][C]0.0800067670969611[/C][/ROW]
[ROW][C]10[/C][C]91.54[/C][C]91.6299961328405[/C][C]-0.0899961328404686[/C][/ROW]
[ROW][C]11[/C][C]91.74[/C][C]91.5400043499996[/C][C]0.199995650000417[/C][/ROW]
[ROW][C]12[/C][C]91.87[/C][C]91.7399903331292[/C][C]0.130009666870819[/C][/ROW]
[ROW][C]13[/C][C]92.13[/C][C]91.8699937159301[/C][C]0.260006284069945[/C][/ROW]
[ROW][C]14[/C][C]92.14[/C][C]92.1299874324909[/C][C]0.0100125675091505[/C][/ROW]
[ROW][C]15[/C][C]92.05[/C][C]92.1399995160385[/C][C]-0.0899995160385032[/C][/ROW]
[ROW][C]16[/C][C]92[/C][C]92.0500043501631[/C][C]-0.0500043501630927[/C][/ROW]
[ROW][C]17[/C][C]92.51[/C][C]92.0000024169805[/C][C]0.509997583019455[/C][/ROW]
[ROW][C]18[/C][C]92.67[/C][C]92.5099753490601[/C][C]0.160024650939931[/C][/ROW]
[ROW][C]19[/C][C]92.68[/C][C]92.6699922651436[/C][C]0.0100077348563872[/C][/ROW]
[ROW][C]20[/C][C]92.77[/C][C]92.6799995162721[/C][C]0.0900004837279056[/C][/ROW]
[ROW][C]21[/C][C]92.85[/C][C]92.7699956497901[/C][C]0.0800043502098617[/C][/ROW]
[ROW][C]22[/C][C]92.71[/C][C]92.8499961329573[/C][C]-0.139996132957293[/C][/ROW]
[ROW][C]23[/C][C]92.73[/C][C]92.7100067667698[/C][C]0.0199932332301671[/C][/ROW]
[ROW][C]24[/C][C]92.28[/C][C]92.729999033619[/C][C]-0.449999033618965[/C][/ROW]
[ROW][C]25[/C][C]92.49[/C][C]92.2800217508857[/C][C]0.209978249114272[/C][/ROW]
[ROW][C]26[/C][C]92.46[/C][C]92.4899898506162[/C][C]-0.0299898506162037[/C][/ROW]
[ROW][C]27[/C][C]92.55[/C][C]92.4600014495716[/C][C]0.0899985504284189[/C][/ROW]
[ROW][C]28[/C][C]92.24[/C][C]92.5499956498836[/C][C]-0.309995649883575[/C][/ROW]
[ROW][C]29[/C][C]92.41[/C][C]92.2400149837654[/C][C]0.169985016234591[/C][/ROW]
[ROW][C]30[/C][C]92.83[/C][C]92.4099917837053[/C][C]0.420008216294676[/C][/ROW]
[ROW][C]31[/C][C]92.85[/C][C]92.8299796987326[/C][C]0.0200203012673938[/C][/ROW]
[ROW][C]32[/C][C]93.04[/C][C]92.8499990323106[/C][C]0.190000967689386[/C][/ROW]
[ROW][C]33[/C][C]93.04[/C][C]93.0399908162262[/C][C]9.18377379832691e-06[/C][/ROW]
[ROW][C]34[/C][C]92.83[/C][C]93.0399999995561[/C][C]-0.209999999556103[/C][/ROW]
[ROW][C]35[/C][C]92.96[/C][C]92.8300101504351[/C][C]0.129989849564879[/C][/ROW]
[ROW][C]36[/C][C]92.83[/C][C]92.9599937168879[/C][C]-0.129993716887924[/C][/ROW]
[ROW][C]37[/C][C]93.01[/C][C]92.830006283299[/C][C]0.179993716700992[/C][/ROW]
[ROW][C]38[/C][C]93.21[/C][C]93.0099912999307[/C][C]0.200008700069247[/C][/ROW]
[ROW][C]39[/C][C]93.58[/C][C]93.2099903324984[/C][C]0.370009667501606[/C][/ROW]
[ROW][C]40[/C][C]94.07[/C][C]93.5799821154327[/C][C]0.490017884567266[/C][/ROW]
[ROW][C]41[/C][C]94.57[/C][C]94.0699763147869[/C][C]0.500023685213108[/C][/ROW]
[ROW][C]42[/C][C]95.03[/C][C]94.5699758311524[/C][C]0.460024168847553[/C][/ROW]
[ROW][C]43[/C][C]95.21[/C][C]95.0299777645453[/C][C]0.180022235454686[/C][/ROW]
[ROW][C]44[/C][C]95.89[/C][C]95.2099912985523[/C][C]0.680008701447733[/C][/ROW]
[ROW][C]45[/C][C]96.43[/C][C]95.8899671315038[/C][C]0.540032868496255[/C][/ROW]
[ROW][C]46[/C][C]96.35[/C][C]96.4299738972924[/C][C]-0.0799738972923905[/C][/ROW]
[ROW][C]47[/C][C]96.71[/C][C]96.3500038655707[/C][C]0.359996134429252[/C][/ROW]
[ROW][C]48[/C][C]96.32[/C][C]96.7099825994409[/C][C]-0.389982599440913[/C][/ROW]
[ROW][C]49[/C][C]97.23[/C][C]96.320018849967[/C][C]0.909981150032962[/C][/ROW]
[ROW][C]50[/C][C]97.88[/C][C]97.2299560156922[/C][C]0.650043984307786[/C][/ROW]
[ROW][C]51[/C][C]98.2[/C][C]97.8799685798605[/C][C]0.320031420139514[/C][/ROW]
[ROW][C]52[/C][C]98.56[/C][C]98.1999845311516[/C][C]0.360015468848431[/C][/ROW]
[ROW][C]53[/C][C]99.31[/C][C]98.5599825985064[/C][C]0.750017401493636[/C][/ROW]
[ROW][C]54[/C][C]99.69[/C][C]99.3099637476048[/C][C]0.380036252395158[/C][/ROW]
[ROW][C]55[/C][C]99.77[/C][C]99.6899816307937[/C][C]0.0800183692063143[/C][/ROW]
[ROW][C]56[/C][C]101.06[/C][C]99.7699961322797[/C][C]1.29000386772032[/C][/ROW]
[ROW][C]57[/C][C]101.77[/C][C]101.05993764714[/C][C]0.710062352859907[/C][/ROW]
[ROW][C]58[/C][C]101.91[/C][C]101.769965678848[/C][C]0.140034321151674[/C][/ROW]
[ROW][C]59[/C][C]102.52[/C][C]101.909993231384[/C][C]0.610006768615676[/C][/ROW]
[ROW][C]60[/C][C]102.09[/C][C]102.519970515076[/C][C]-0.429970515075539[/C][/ROW]
[ROW][C]61[/C][C]102.22[/C][C]102.090020782799[/C][C]0.129979217200841[/C][/ROW]
[ROW][C]62[/C][C]102.74[/C][C]102.219993717402[/C][C]0.520006282598146[/C][/ROW]
[ROW][C]63[/C][C]103.56[/C][C]102.739974865286[/C][C]0.820025134714484[/C][/ROW]
[ROW][C]64[/C][C]104.4[/C][C]103.559960363753[/C][C]0.840039636247326[/C][/ROW]
[ROW][C]65[/C][C]104.76[/C][C]104.399959396344[/C][C]0.360040603656358[/C][/ROW]
[ROW][C]66[/C][C]104.86[/C][C]104.759982597291[/C][C]0.100017402708531[/C][/ROW]
[ROW][C]67[/C][C]104.84[/C][C]104.859995165618[/C][C]-0.0199951656182833[/C][/ROW]
[ROW][C]68[/C][C]104.96[/C][C]104.840000966474[/C][C]0.119999033525559[/C][/ROW]
[ROW][C]69[/C][C]104.83[/C][C]104.959994199798[/C][C]-0.129994199798062[/C][/ROW]
[ROW][C]70[/C][C]104.58[/C][C]104.830006283322[/C][C]-0.25000628332235[/C][/ROW]
[ROW][C]71[/C][C]104.8[/C][C]104.580012084155[/C][C]0.219987915844939[/C][/ROW]
[ROW][C]72[/C][C]104.17[/C][C]104.799989366795[/C][C]-0.629989366794902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284437&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284437&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
289.8489.560.280000000000001
389.9789.83998646608650.130013533913512
490.6589.96999371574310.680006284256876
591.1790.64996713162060.520032868379417
691.3591.16997486400050.180025135999514
791.4191.34999129841210.0600087015879325
891.5591.40999709945510.140002900544914
991.6391.5499932329030.0800067670969611
1091.5491.6299961328405-0.0899961328404686
1191.7491.54000434999960.199995650000417
1291.8791.73999033312920.130009666870819
1392.1391.86999371593010.260006284069945
1492.1492.12998743249090.0100125675091505
1592.0592.1399995160385-0.0899995160385032
169292.0500043501631-0.0500043501630927
1792.5192.00000241698050.509997583019455
1892.6792.50997534906010.160024650939931
1992.6892.66999226514360.0100077348563872
2092.7792.67999951627210.0900004837279056
2192.8592.76999564979010.0800043502098617
2292.7192.8499961329573-0.139996132957293
2392.7392.71000676676980.0199932332301671
2492.2892.729999033619-0.449999033618965
2592.4992.28002175088570.209978249114272
2692.4692.4899898506162-0.0299898506162037
2792.5592.46000144957160.0899985504284189
2892.2492.5499956498836-0.309995649883575
2992.4192.24001498376540.169985016234591
3092.8392.40999178370530.420008216294676
3192.8592.82997969873260.0200203012673938
3293.0492.84999903231060.190000967689386
3393.0493.03999081622629.18377379832691e-06
3492.8393.0399999995561-0.209999999556103
3592.9692.83001015043510.129989849564879
3692.8392.9599937168879-0.129993716887924
3793.0192.8300062832990.179993716700992
3893.2193.00999129993070.200008700069247
3993.5893.20999033249840.370009667501606
4094.0793.57998211543270.490017884567266
4194.5794.06997631478690.500023685213108
4295.0394.56997583115240.460024168847553
4395.2195.02997776454530.180022235454686
4495.8995.20999129855230.680008701447733
4596.4395.88996713150380.540032868496255
4696.3596.4299738972924-0.0799738972923905
4796.7196.35000386557070.359996134429252
4896.3296.7099825994409-0.389982599440913
4997.2396.3200188499670.909981150032962
5097.8897.22995601569220.650043984307786
5198.297.87996857986050.320031420139514
5298.5698.19998453115160.360015468848431
5399.3198.55998259850640.750017401493636
5499.6999.30996374760480.380036252395158
5599.7799.68998163079370.0800183692063143
56101.0699.76999613227971.29000386772032
57101.77101.059937647140.710062352859907
58101.91101.7699656788480.140034321151674
59102.52101.9099932313840.610006768615676
60102.09102.519970515076-0.429970515075539
61102.22102.0900207827990.129979217200841
62102.74102.2199937174020.520006282598146
63103.56102.7399748652860.820025134714484
64104.4103.5599603637530.840039636247326
65104.76104.3999593963440.360040603656358
66104.86104.7599825972910.100017402708531
67104.84104.859995165618-0.0199951656182833
68104.96104.8400009664740.119999033525559
69104.83104.959994199798-0.129994199798062
70104.58104.830006283322-0.25000628332235
71104.8104.5800120841550.219987915844939
72104.17104.799989366795-0.629989366794902







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73104.170030450791103.495558943461104.844501958122
74104.170030450791103.216206749696105.123854151887
75104.170030450791103.001849175757105.338211725826
76104.170030450791102.821136337115105.518924564468
77104.170030450791102.661924629411105.678136272172
78104.170030450791102.517985957731105.822074943852
79104.170030450791102.385620507527105.954440394056
80104.170030450791102.262417627342106.077643274241
81104.170030450791102.146702864176106.193358037407
82104.170030450791102.037257054171106.302803847411
83104.170030450791101.933159824246106.406901077336
84104.170030450791101.833696134288106.506364767294

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 104.170030450791 & 103.495558943461 & 104.844501958122 \tabularnewline
74 & 104.170030450791 & 103.216206749696 & 105.123854151887 \tabularnewline
75 & 104.170030450791 & 103.001849175757 & 105.338211725826 \tabularnewline
76 & 104.170030450791 & 102.821136337115 & 105.518924564468 \tabularnewline
77 & 104.170030450791 & 102.661924629411 & 105.678136272172 \tabularnewline
78 & 104.170030450791 & 102.517985957731 & 105.822074943852 \tabularnewline
79 & 104.170030450791 & 102.385620507527 & 105.954440394056 \tabularnewline
80 & 104.170030450791 & 102.262417627342 & 106.077643274241 \tabularnewline
81 & 104.170030450791 & 102.146702864176 & 106.193358037407 \tabularnewline
82 & 104.170030450791 & 102.037257054171 & 106.302803847411 \tabularnewline
83 & 104.170030450791 & 101.933159824246 & 106.406901077336 \tabularnewline
84 & 104.170030450791 & 101.833696134288 & 106.506364767294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284437&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]73[/C][C]104.170030450791[/C][C]103.495558943461[/C][C]104.844501958122[/C][/ROW]
[ROW][C]74[/C][C]104.170030450791[/C][C]103.216206749696[/C][C]105.123854151887[/C][/ROW]
[ROW][C]75[/C][C]104.170030450791[/C][C]103.001849175757[/C][C]105.338211725826[/C][/ROW]
[ROW][C]76[/C][C]104.170030450791[/C][C]102.821136337115[/C][C]105.518924564468[/C][/ROW]
[ROW][C]77[/C][C]104.170030450791[/C][C]102.661924629411[/C][C]105.678136272172[/C][/ROW]
[ROW][C]78[/C][C]104.170030450791[/C][C]102.517985957731[/C][C]105.822074943852[/C][/ROW]
[ROW][C]79[/C][C]104.170030450791[/C][C]102.385620507527[/C][C]105.954440394056[/C][/ROW]
[ROW][C]80[/C][C]104.170030450791[/C][C]102.262417627342[/C][C]106.077643274241[/C][/ROW]
[ROW][C]81[/C][C]104.170030450791[/C][C]102.146702864176[/C][C]106.193358037407[/C][/ROW]
[ROW][C]82[/C][C]104.170030450791[/C][C]102.037257054171[/C][C]106.302803847411[/C][/ROW]
[ROW][C]83[/C][C]104.170030450791[/C][C]101.933159824246[/C][C]106.406901077336[/C][/ROW]
[ROW][C]84[/C][C]104.170030450791[/C][C]101.833696134288[/C][C]106.506364767294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284437&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284437&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
73104.170030450791103.495558943461104.844501958122
74104.170030450791103.216206749696105.123854151887
75104.170030450791103.001849175757105.338211725826
76104.170030450791102.821136337115105.518924564468
77104.170030450791102.661924629411105.678136272172
78104.170030450791102.517985957731105.822074943852
79104.170030450791102.385620507527105.954440394056
80104.170030450791102.262417627342106.077643274241
81104.170030450791102.146702864176106.193358037407
82104.170030450791102.037257054171106.302803847411
83104.170030450791101.933159824246106.406901077336
84104.170030450791101.833696134288106.506364767294



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')