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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 26 Nov 2015 14:04:24 +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/26/t14485466848elpk8qtcoaafwi.htm/, Retrieved Mon, 13 May 2024 22:31:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284229, Retrieved Mon, 13 May 2024 22:31:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-26 14:04:24] [88f551c1d3f4ff2d65b8ab6790c1e3d2] [Current]
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Dataseries X:
94.94
95.11
95.53
95.89
95.99
95.42
95.42
95.45
95.99
95.99
95.97
95.97
95.97
96.22
95.8
96.02
96.04
96.15
96.15
95.99
96.08
96.29
96.3
96.44
96.44
96.83
96.7
97.06
97.64
97.61
97.61
97.61
97.55
97.58
97.79
97.79
97.79
97.79
98
98.37
98.68
98.89
98.89
98.89
98.88
98.97
99.05
99.05
99
99.03
99.2
100.3
100.79
100.75
100.75
100.17
99.98
99.93
100.04
100.04
100.49
100.71
100.7
101.27
101.07
101.17
100.71
100.59
100.52
100.65
100.62
100.62




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=284229&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=284229&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284229&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
alpha0.999953214905545
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999953214905545 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284229&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]0.999953214905545[/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=284229&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284229&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
alpha0.999953214905545
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
295.1194.940.170000000000002
395.5395.10999204653390.420007953466055
495.8995.52998034988820.360019650111781
595.9995.88998315644670.100016843553334
695.4295.9899953207025-0.569995320702517
795.4295.4200266672849-2.66672849278393e-05
895.4595.42000000124760.0299999987523591
995.9995.44999859644720.540001403552779
1095.9995.98997473598332.52640166706897e-05
1195.9795.989999998818-0.0199999988180082
1295.9795.9700009357018-9.35701834237079e-07
1395.9795.9700000000438-4.37694325228222e-11
1496.2295.970.25
1595.896.2199883037264-0.419988303726385
1696.0295.80001964919240.219980350807546
1796.0496.01998970819850.0200102918014977
1896.1596.03999906381660.110000936183397
1996.1596.14999485359585.14640419169154e-06
2095.9996.1499999997592-0.159999999759236
2196.0895.99000748561510.0899925143849032
2296.2996.07999578969170.210004210308298
2396.396.28999017493320.0100098250668168
2496.4496.29999953168940.140000468310603
2596.4496.43999345006496.5499351364906e-06
2696.8396.43999999969360.390000000306443
2796.796.8299817538131-0.129981753813141
2897.0696.70000608120860.359993918791361
2997.6497.05998315765050.580016842349494
3097.6197.6399728638572-0.029972863857239
3197.6197.6100014022833-1.40228326017677e-06
3297.6197.6100000000656-6.55973053653724e-11
3397.5597.61-0.0600000000000023
3497.5897.55000280710570.0299971928943279
3597.7997.57999859657850.210001403421501
3697.7997.78999017506459.82493548917773e-06
3797.7997.78999999954044.59650095763209e-10
3897.7997.791.4210854715202e-14
399897.790.209999999999994
4098.3797.99999017513020.37000982486984
4198.6898.36998268905540.310017310944602
4298.8998.67998549581080.210014504189175
4398.8998.88999017445169.82554841755245e-06
4498.8998.88999999954034.59692728327354e-10
4598.8898.89-0.00999999999997669
4698.9798.88000046785090.0899995321490508
4799.0598.96999578936340.0800042106366163
4899.0599.04999625699553.7430045409792e-06
499999.0499999998249-0.049999999824891
5099.0399.00000233925470.0299976607452805
5199.299.02999859655660.170001403443393
52100.399.19999204646831.10000795353172
53100.79100.2999485360240.490051463976016
54100.75100.789977072896-0.0399770728959794
55100.75100.750001870331-1.87033113263624e-06
56100.17100.750000000087-0.580000000087495
5799.98100.170027135355-0.190027135354782
5899.9399.9800088904375-0.050008890437482
59100.0499.93000233967070.109997660329327
60100.04100.0399948537495.14625092762344e-06
61100.49100.0399999997590.450000000240749
62100.71100.4899789467070.220021053292513
63100.7100.709989706294-0.00998970629423468
64101.27100.7000004673690.569999532630632
65101.07101.269973332518-0.199973332518027
66101.17101.0700093557710.0999906442287539
67100.71101.169995321928-0.459995321928275
68100.59100.710021520925-0.120021520924567
69100.52100.590005615218-0.0700056152181929
70100.65100.5200032752190.129996724780696
71100.62100.649993918091-0.0299939180909519
72100.62100.620001403268-1.40326828557136e-06

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 95.11 & 94.94 & 0.170000000000002 \tabularnewline
3 & 95.53 & 95.1099920465339 & 0.420007953466055 \tabularnewline
4 & 95.89 & 95.5299803498882 & 0.360019650111781 \tabularnewline
5 & 95.99 & 95.8899831564467 & 0.100016843553334 \tabularnewline
6 & 95.42 & 95.9899953207025 & -0.569995320702517 \tabularnewline
7 & 95.42 & 95.4200266672849 & -2.66672849278393e-05 \tabularnewline
8 & 95.45 & 95.4200000012476 & 0.0299999987523591 \tabularnewline
9 & 95.99 & 95.4499985964472 & 0.540001403552779 \tabularnewline
10 & 95.99 & 95.9899747359833 & 2.52640166706897e-05 \tabularnewline
11 & 95.97 & 95.989999998818 & -0.0199999988180082 \tabularnewline
12 & 95.97 & 95.9700009357018 & -9.35701834237079e-07 \tabularnewline
13 & 95.97 & 95.9700000000438 & -4.37694325228222e-11 \tabularnewline
14 & 96.22 & 95.97 & 0.25 \tabularnewline
15 & 95.8 & 96.2199883037264 & -0.419988303726385 \tabularnewline
16 & 96.02 & 95.8000196491924 & 0.219980350807546 \tabularnewline
17 & 96.04 & 96.0199897081985 & 0.0200102918014977 \tabularnewline
18 & 96.15 & 96.0399990638166 & 0.110000936183397 \tabularnewline
19 & 96.15 & 96.1499948535958 & 5.14640419169154e-06 \tabularnewline
20 & 95.99 & 96.1499999997592 & -0.159999999759236 \tabularnewline
21 & 96.08 & 95.9900074856151 & 0.0899925143849032 \tabularnewline
22 & 96.29 & 96.0799957896917 & 0.210004210308298 \tabularnewline
23 & 96.3 & 96.2899901749332 & 0.0100098250668168 \tabularnewline
24 & 96.44 & 96.2999995316894 & 0.140000468310603 \tabularnewline
25 & 96.44 & 96.4399934500649 & 6.5499351364906e-06 \tabularnewline
26 & 96.83 & 96.4399999996936 & 0.390000000306443 \tabularnewline
27 & 96.7 & 96.8299817538131 & -0.129981753813141 \tabularnewline
28 & 97.06 & 96.7000060812086 & 0.359993918791361 \tabularnewline
29 & 97.64 & 97.0599831576505 & 0.580016842349494 \tabularnewline
30 & 97.61 & 97.6399728638572 & -0.029972863857239 \tabularnewline
31 & 97.61 & 97.6100014022833 & -1.40228326017677e-06 \tabularnewline
32 & 97.61 & 97.6100000000656 & -6.55973053653724e-11 \tabularnewline
33 & 97.55 & 97.61 & -0.0600000000000023 \tabularnewline
34 & 97.58 & 97.5500028071057 & 0.0299971928943279 \tabularnewline
35 & 97.79 & 97.5799985965785 & 0.210001403421501 \tabularnewline
36 & 97.79 & 97.7899901750645 & 9.82493548917773e-06 \tabularnewline
37 & 97.79 & 97.7899999995404 & 4.59650095763209e-10 \tabularnewline
38 & 97.79 & 97.79 & 1.4210854715202e-14 \tabularnewline
39 & 98 & 97.79 & 0.209999999999994 \tabularnewline
40 & 98.37 & 97.9999901751302 & 0.37000982486984 \tabularnewline
41 & 98.68 & 98.3699826890554 & 0.310017310944602 \tabularnewline
42 & 98.89 & 98.6799854958108 & 0.210014504189175 \tabularnewline
43 & 98.89 & 98.8899901744516 & 9.82554841755245e-06 \tabularnewline
44 & 98.89 & 98.8899999995403 & 4.59692728327354e-10 \tabularnewline
45 & 98.88 & 98.89 & -0.00999999999997669 \tabularnewline
46 & 98.97 & 98.8800004678509 & 0.0899995321490508 \tabularnewline
47 & 99.05 & 98.9699957893634 & 0.0800042106366163 \tabularnewline
48 & 99.05 & 99.0499962569955 & 3.7430045409792e-06 \tabularnewline
49 & 99 & 99.0499999998249 & -0.049999999824891 \tabularnewline
50 & 99.03 & 99.0000023392547 & 0.0299976607452805 \tabularnewline
51 & 99.2 & 99.0299985965566 & 0.170001403443393 \tabularnewline
52 & 100.3 & 99.1999920464683 & 1.10000795353172 \tabularnewline
53 & 100.79 & 100.299948536024 & 0.490051463976016 \tabularnewline
54 & 100.75 & 100.789977072896 & -0.0399770728959794 \tabularnewline
55 & 100.75 & 100.750001870331 & -1.87033113263624e-06 \tabularnewline
56 & 100.17 & 100.750000000087 & -0.580000000087495 \tabularnewline
57 & 99.98 & 100.170027135355 & -0.190027135354782 \tabularnewline
58 & 99.93 & 99.9800088904375 & -0.050008890437482 \tabularnewline
59 & 100.04 & 99.9300023396707 & 0.109997660329327 \tabularnewline
60 & 100.04 & 100.039994853749 & 5.14625092762344e-06 \tabularnewline
61 & 100.49 & 100.039999999759 & 0.450000000240749 \tabularnewline
62 & 100.71 & 100.489978946707 & 0.220021053292513 \tabularnewline
63 & 100.7 & 100.709989706294 & -0.00998970629423468 \tabularnewline
64 & 101.27 & 100.700000467369 & 0.569999532630632 \tabularnewline
65 & 101.07 & 101.269973332518 & -0.199973332518027 \tabularnewline
66 & 101.17 & 101.070009355771 & 0.0999906442287539 \tabularnewline
67 & 100.71 & 101.169995321928 & -0.459995321928275 \tabularnewline
68 & 100.59 & 100.710021520925 & -0.120021520924567 \tabularnewline
69 & 100.52 & 100.590005615218 & -0.0700056152181929 \tabularnewline
70 & 100.65 & 100.520003275219 & 0.129996724780696 \tabularnewline
71 & 100.62 & 100.649993918091 & -0.0299939180909519 \tabularnewline
72 & 100.62 & 100.620001403268 & -1.40326828557136e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284229&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]95.11[/C][C]94.94[/C][C]0.170000000000002[/C][/ROW]
[ROW][C]3[/C][C]95.53[/C][C]95.1099920465339[/C][C]0.420007953466055[/C][/ROW]
[ROW][C]4[/C][C]95.89[/C][C]95.5299803498882[/C][C]0.360019650111781[/C][/ROW]
[ROW][C]5[/C][C]95.99[/C][C]95.8899831564467[/C][C]0.100016843553334[/C][/ROW]
[ROW][C]6[/C][C]95.42[/C][C]95.9899953207025[/C][C]-0.569995320702517[/C][/ROW]
[ROW][C]7[/C][C]95.42[/C][C]95.4200266672849[/C][C]-2.66672849278393e-05[/C][/ROW]
[ROW][C]8[/C][C]95.45[/C][C]95.4200000012476[/C][C]0.0299999987523591[/C][/ROW]
[ROW][C]9[/C][C]95.99[/C][C]95.4499985964472[/C][C]0.540001403552779[/C][/ROW]
[ROW][C]10[/C][C]95.99[/C][C]95.9899747359833[/C][C]2.52640166706897e-05[/C][/ROW]
[ROW][C]11[/C][C]95.97[/C][C]95.989999998818[/C][C]-0.0199999988180082[/C][/ROW]
[ROW][C]12[/C][C]95.97[/C][C]95.9700009357018[/C][C]-9.35701834237079e-07[/C][/ROW]
[ROW][C]13[/C][C]95.97[/C][C]95.9700000000438[/C][C]-4.37694325228222e-11[/C][/ROW]
[ROW][C]14[/C][C]96.22[/C][C]95.97[/C][C]0.25[/C][/ROW]
[ROW][C]15[/C][C]95.8[/C][C]96.2199883037264[/C][C]-0.419988303726385[/C][/ROW]
[ROW][C]16[/C][C]96.02[/C][C]95.8000196491924[/C][C]0.219980350807546[/C][/ROW]
[ROW][C]17[/C][C]96.04[/C][C]96.0199897081985[/C][C]0.0200102918014977[/C][/ROW]
[ROW][C]18[/C][C]96.15[/C][C]96.0399990638166[/C][C]0.110000936183397[/C][/ROW]
[ROW][C]19[/C][C]96.15[/C][C]96.1499948535958[/C][C]5.14640419169154e-06[/C][/ROW]
[ROW][C]20[/C][C]95.99[/C][C]96.1499999997592[/C][C]-0.159999999759236[/C][/ROW]
[ROW][C]21[/C][C]96.08[/C][C]95.9900074856151[/C][C]0.0899925143849032[/C][/ROW]
[ROW][C]22[/C][C]96.29[/C][C]96.0799957896917[/C][C]0.210004210308298[/C][/ROW]
[ROW][C]23[/C][C]96.3[/C][C]96.2899901749332[/C][C]0.0100098250668168[/C][/ROW]
[ROW][C]24[/C][C]96.44[/C][C]96.2999995316894[/C][C]0.140000468310603[/C][/ROW]
[ROW][C]25[/C][C]96.44[/C][C]96.4399934500649[/C][C]6.5499351364906e-06[/C][/ROW]
[ROW][C]26[/C][C]96.83[/C][C]96.4399999996936[/C][C]0.390000000306443[/C][/ROW]
[ROW][C]27[/C][C]96.7[/C][C]96.8299817538131[/C][C]-0.129981753813141[/C][/ROW]
[ROW][C]28[/C][C]97.06[/C][C]96.7000060812086[/C][C]0.359993918791361[/C][/ROW]
[ROW][C]29[/C][C]97.64[/C][C]97.0599831576505[/C][C]0.580016842349494[/C][/ROW]
[ROW][C]30[/C][C]97.61[/C][C]97.6399728638572[/C][C]-0.029972863857239[/C][/ROW]
[ROW][C]31[/C][C]97.61[/C][C]97.6100014022833[/C][C]-1.40228326017677e-06[/C][/ROW]
[ROW][C]32[/C][C]97.61[/C][C]97.6100000000656[/C][C]-6.55973053653724e-11[/C][/ROW]
[ROW][C]33[/C][C]97.55[/C][C]97.61[/C][C]-0.0600000000000023[/C][/ROW]
[ROW][C]34[/C][C]97.58[/C][C]97.5500028071057[/C][C]0.0299971928943279[/C][/ROW]
[ROW][C]35[/C][C]97.79[/C][C]97.5799985965785[/C][C]0.210001403421501[/C][/ROW]
[ROW][C]36[/C][C]97.79[/C][C]97.7899901750645[/C][C]9.82493548917773e-06[/C][/ROW]
[ROW][C]37[/C][C]97.79[/C][C]97.7899999995404[/C][C]4.59650095763209e-10[/C][/ROW]
[ROW][C]38[/C][C]97.79[/C][C]97.79[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]39[/C][C]98[/C][C]97.79[/C][C]0.209999999999994[/C][/ROW]
[ROW][C]40[/C][C]98.37[/C][C]97.9999901751302[/C][C]0.37000982486984[/C][/ROW]
[ROW][C]41[/C][C]98.68[/C][C]98.3699826890554[/C][C]0.310017310944602[/C][/ROW]
[ROW][C]42[/C][C]98.89[/C][C]98.6799854958108[/C][C]0.210014504189175[/C][/ROW]
[ROW][C]43[/C][C]98.89[/C][C]98.8899901744516[/C][C]9.82554841755245e-06[/C][/ROW]
[ROW][C]44[/C][C]98.89[/C][C]98.8899999995403[/C][C]4.59692728327354e-10[/C][/ROW]
[ROW][C]45[/C][C]98.88[/C][C]98.89[/C][C]-0.00999999999997669[/C][/ROW]
[ROW][C]46[/C][C]98.97[/C][C]98.8800004678509[/C][C]0.0899995321490508[/C][/ROW]
[ROW][C]47[/C][C]99.05[/C][C]98.9699957893634[/C][C]0.0800042106366163[/C][/ROW]
[ROW][C]48[/C][C]99.05[/C][C]99.0499962569955[/C][C]3.7430045409792e-06[/C][/ROW]
[ROW][C]49[/C][C]99[/C][C]99.0499999998249[/C][C]-0.049999999824891[/C][/ROW]
[ROW][C]50[/C][C]99.03[/C][C]99.0000023392547[/C][C]0.0299976607452805[/C][/ROW]
[ROW][C]51[/C][C]99.2[/C][C]99.0299985965566[/C][C]0.170001403443393[/C][/ROW]
[ROW][C]52[/C][C]100.3[/C][C]99.1999920464683[/C][C]1.10000795353172[/C][/ROW]
[ROW][C]53[/C][C]100.79[/C][C]100.299948536024[/C][C]0.490051463976016[/C][/ROW]
[ROW][C]54[/C][C]100.75[/C][C]100.789977072896[/C][C]-0.0399770728959794[/C][/ROW]
[ROW][C]55[/C][C]100.75[/C][C]100.750001870331[/C][C]-1.87033113263624e-06[/C][/ROW]
[ROW][C]56[/C][C]100.17[/C][C]100.750000000087[/C][C]-0.580000000087495[/C][/ROW]
[ROW][C]57[/C][C]99.98[/C][C]100.170027135355[/C][C]-0.190027135354782[/C][/ROW]
[ROW][C]58[/C][C]99.93[/C][C]99.9800088904375[/C][C]-0.050008890437482[/C][/ROW]
[ROW][C]59[/C][C]100.04[/C][C]99.9300023396707[/C][C]0.109997660329327[/C][/ROW]
[ROW][C]60[/C][C]100.04[/C][C]100.039994853749[/C][C]5.14625092762344e-06[/C][/ROW]
[ROW][C]61[/C][C]100.49[/C][C]100.039999999759[/C][C]0.450000000240749[/C][/ROW]
[ROW][C]62[/C][C]100.71[/C][C]100.489978946707[/C][C]0.220021053292513[/C][/ROW]
[ROW][C]63[/C][C]100.7[/C][C]100.709989706294[/C][C]-0.00998970629423468[/C][/ROW]
[ROW][C]64[/C][C]101.27[/C][C]100.700000467369[/C][C]0.569999532630632[/C][/ROW]
[ROW][C]65[/C][C]101.07[/C][C]101.269973332518[/C][C]-0.199973332518027[/C][/ROW]
[ROW][C]66[/C][C]101.17[/C][C]101.070009355771[/C][C]0.0999906442287539[/C][/ROW]
[ROW][C]67[/C][C]100.71[/C][C]101.169995321928[/C][C]-0.459995321928275[/C][/ROW]
[ROW][C]68[/C][C]100.59[/C][C]100.710021520925[/C][C]-0.120021520924567[/C][/ROW]
[ROW][C]69[/C][C]100.52[/C][C]100.590005615218[/C][C]-0.0700056152181929[/C][/ROW]
[ROW][C]70[/C][C]100.65[/C][C]100.520003275219[/C][C]0.129996724780696[/C][/ROW]
[ROW][C]71[/C][C]100.62[/C][C]100.649993918091[/C][C]-0.0299939180909519[/C][/ROW]
[ROW][C]72[/C][C]100.62[/C][C]100.620001403268[/C][C]-1.40326828557136e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284229&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284229&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
295.1194.940.170000000000002
395.5395.10999204653390.420007953466055
495.8995.52998034988820.360019650111781
595.9995.88998315644670.100016843553334
695.4295.9899953207025-0.569995320702517
795.4295.4200266672849-2.66672849278393e-05
895.4595.42000000124760.0299999987523591
995.9995.44999859644720.540001403552779
1095.9995.98997473598332.52640166706897e-05
1195.9795.989999998818-0.0199999988180082
1295.9795.9700009357018-9.35701834237079e-07
1395.9795.9700000000438-4.37694325228222e-11
1496.2295.970.25
1595.896.2199883037264-0.419988303726385
1696.0295.80001964919240.219980350807546
1796.0496.01998970819850.0200102918014977
1896.1596.03999906381660.110000936183397
1996.1596.14999485359585.14640419169154e-06
2095.9996.1499999997592-0.159999999759236
2196.0895.99000748561510.0899925143849032
2296.2996.07999578969170.210004210308298
2396.396.28999017493320.0100098250668168
2496.4496.29999953168940.140000468310603
2596.4496.43999345006496.5499351364906e-06
2696.8396.43999999969360.390000000306443
2796.796.8299817538131-0.129981753813141
2897.0696.70000608120860.359993918791361
2997.6497.05998315765050.580016842349494
3097.6197.6399728638572-0.029972863857239
3197.6197.6100014022833-1.40228326017677e-06
3297.6197.6100000000656-6.55973053653724e-11
3397.5597.61-0.0600000000000023
3497.5897.55000280710570.0299971928943279
3597.7997.57999859657850.210001403421501
3697.7997.78999017506459.82493548917773e-06
3797.7997.78999999954044.59650095763209e-10
3897.7997.791.4210854715202e-14
399897.790.209999999999994
4098.3797.99999017513020.37000982486984
4198.6898.36998268905540.310017310944602
4298.8998.67998549581080.210014504189175
4398.8998.88999017445169.82554841755245e-06
4498.8998.88999999954034.59692728327354e-10
4598.8898.89-0.00999999999997669
4698.9798.88000046785090.0899995321490508
4799.0598.96999578936340.0800042106366163
4899.0599.04999625699553.7430045409792e-06
499999.0499999998249-0.049999999824891
5099.0399.00000233925470.0299976607452805
5199.299.02999859655660.170001403443393
52100.399.19999204646831.10000795353172
53100.79100.2999485360240.490051463976016
54100.75100.789977072896-0.0399770728959794
55100.75100.750001870331-1.87033113263624e-06
56100.17100.750000000087-0.580000000087495
5799.98100.170027135355-0.190027135354782
5899.9399.9800088904375-0.050008890437482
59100.0499.93000233967070.109997660329327
60100.04100.0399948537495.14625092762344e-06
61100.49100.0399999997590.450000000240749
62100.71100.4899789467070.220021053292513
63100.7100.709989706294-0.00998970629423468
64101.27100.7000004673690.569999532630632
65101.07101.269973332518-0.199973332518027
66101.17101.0700093557710.0999906442287539
67100.71101.169995321928-0.459995321928275
68100.59100.710021520925-0.120021520924567
69100.52100.590005615218-0.0700056152181929
70100.65100.5200032752190.129996724780696
71100.62100.649993918091-0.0299939180909519
72100.62100.620001403268-1.40326828557136e-06







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73100.620000000066100.113668361197101.126331638935
74100.62000000006699.903955679615101.336044320516
75100.62000000006699.7430352292912101.49696477084
76100.62000000006699.6073722552802101.632627744851
77100.62000000006699.4878504119638101.752149588167
78100.62000000006699.3797941985275101.860205801604
79100.62000000006699.2804261236039101.959573876527
80100.62000000006699.1879364851234102.052063515008
81100.62000000006699.1010682533573102.138931746774
82100.62000000006699.0189061891075102.221093811024
83100.62000000006698.9407593586392102.299240641492
84100.62000000006698.8660909738764102.373909026255

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 100.620000000066 & 100.113668361197 & 101.126331638935 \tabularnewline
74 & 100.620000000066 & 99.903955679615 & 101.336044320516 \tabularnewline
75 & 100.620000000066 & 99.7430352292912 & 101.49696477084 \tabularnewline
76 & 100.620000000066 & 99.6073722552802 & 101.632627744851 \tabularnewline
77 & 100.620000000066 & 99.4878504119638 & 101.752149588167 \tabularnewline
78 & 100.620000000066 & 99.3797941985275 & 101.860205801604 \tabularnewline
79 & 100.620000000066 & 99.2804261236039 & 101.959573876527 \tabularnewline
80 & 100.620000000066 & 99.1879364851234 & 102.052063515008 \tabularnewline
81 & 100.620000000066 & 99.1010682533573 & 102.138931746774 \tabularnewline
82 & 100.620000000066 & 99.0189061891075 & 102.221093811024 \tabularnewline
83 & 100.620000000066 & 98.9407593586392 & 102.299240641492 \tabularnewline
84 & 100.620000000066 & 98.8660909738764 & 102.373909026255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284229&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]100.620000000066[/C][C]100.113668361197[/C][C]101.126331638935[/C][/ROW]
[ROW][C]74[/C][C]100.620000000066[/C][C]99.903955679615[/C][C]101.336044320516[/C][/ROW]
[ROW][C]75[/C][C]100.620000000066[/C][C]99.7430352292912[/C][C]101.49696477084[/C][/ROW]
[ROW][C]76[/C][C]100.620000000066[/C][C]99.6073722552802[/C][C]101.632627744851[/C][/ROW]
[ROW][C]77[/C][C]100.620000000066[/C][C]99.4878504119638[/C][C]101.752149588167[/C][/ROW]
[ROW][C]78[/C][C]100.620000000066[/C][C]99.3797941985275[/C][C]101.860205801604[/C][/ROW]
[ROW][C]79[/C][C]100.620000000066[/C][C]99.2804261236039[/C][C]101.959573876527[/C][/ROW]
[ROW][C]80[/C][C]100.620000000066[/C][C]99.1879364851234[/C][C]102.052063515008[/C][/ROW]
[ROW][C]81[/C][C]100.620000000066[/C][C]99.1010682533573[/C][C]102.138931746774[/C][/ROW]
[ROW][C]82[/C][C]100.620000000066[/C][C]99.0189061891075[/C][C]102.221093811024[/C][/ROW]
[ROW][C]83[/C][C]100.620000000066[/C][C]98.9407593586392[/C][C]102.299240641492[/C][/ROW]
[ROW][C]84[/C][C]100.620000000066[/C][C]98.8660909738764[/C][C]102.373909026255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284229&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284229&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
73100.620000000066100.113668361197101.126331638935
74100.62000000006699.903955679615101.336044320516
75100.62000000006699.7430352292912101.49696477084
76100.62000000006699.6073722552802101.632627744851
77100.62000000006699.4878504119638101.752149588167
78100.62000000006699.3797941985275101.860205801604
79100.62000000006699.2804261236039101.959573876527
80100.62000000006699.1879364851234102.052063515008
81100.62000000006699.1010682533573102.138931746774
82100.62000000006699.0189061891075102.221093811024
83100.62000000006698.9407593586392102.299240641492
84100.62000000006698.8660909738764102.373909026255



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')