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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 04 Jan 2015 17:37:50 +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/Jan/04/t14203931376ass27kh99tsw26.htm/, Retrieved Tue, 14 May 2024 03:05:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271925, Retrieved Tue, 14 May 2024 03:05:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2015-01-04 17:37:50] [3acc2e190882a8fff3240b97d842d2ea] [Current]
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Dataseries X:
103,1
113,5
115,7
113,1
112,7
121,9
120,3
108,7
102,8
83,4
79,4
77,8
85,7
83,2
82
86,9
95,7
97,9
89,3
91,5
86,8
91
93,8
96,8
95,7
91,4
88,7
88,2
87,7
89,5
95,6
100,5
106,3
112
117,7
125
132,4
138,1
134,7
136,7
134,3
131,6
129,8
131,9
129,8
119,4
116,7
112,8
116
117,5
118,8
118,7
116,3
115,2
131,7
133,7
132,5
126,9
122,2
120,2
117,9
117,2
116,4
112,3
113,6
114,2
108
102,8
102,8
101,6
100,3
101,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271925&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271925&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271925&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.446034343287075
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.446034343287075 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271925&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.446034343287075[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271925&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271925&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
alpha1
beta0.446034343287075
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3115.7123.9-8.2
4113.1122.442518385046-9.34251838504601
5112.7115.675434332525-2.97543433252457
6121.9113.9482884340237.95171156597684
7120.3126.695024880362-6.39502488036189
8108.7122.242624157545-13.5426241575452
9102.8104.602148685051-1.80214868505084
1083.497.8983284798085-14.4983284798085
1179.472.03157605755687.36842394244316
1277.871.31814619178526.48185380821477
1385.772.609275598415113.0907244015849
1483.286.3481882600281-3.14818826002812
158282.4439881769224-0.443988176922403
1686.981.04595420200165.85404579799841
1795.788.55705967508437.14294032491573
1897.9100.543056372047-2.64305637204681
1989.3101.56416245887-12.2641624588702
2091.587.4939248105624.00607518943798
2186.891.4807719268416-4.68077192684164
229184.69298689437626.30701310562375
2393.891.70613134304612.09386865695389
2496.895.44006867437991.35993132562007
2595.799.0466447501184-3.34664475011839
2691.496.4539262567842-5.05392625678419
2788.789.8997015778182-1.19970157781816
2888.286.66459347241561.53540652758443
2987.786.84943751462540.850562485374624
3089.586.72881759421412.77118240578592
3195.689.76486011870755.83513988129251
32100.598.4675329036482.03246709635199
33106.3104.2740830302222.02591696977804
34112110.9777115753911.02228842460896
35117.7117.1336873215110.566312678488529
36125123.0862822251561.91371777484375
37132.4131.2398660760951.16013392390451
38138.1139.157325648969-1.05732564896931
39134.7144.385722097491-9.6857220974907
40136.7136.6655574024750.0344425975246736
41134.3138.680919983843-4.38091998384331
42131.6134.326879215857-2.72687921585657
43129.8130.410597435589-0.610597435588772
44131.9128.3382500093933.56174999060681
45129.8132.026912827406-2.22691282740624
46119.4128.933633226877-9.53363322687653
47116.7114.2813053913872.41869460861318
48112.8112.6601262527520.139873747248402
49116108.8225147477497.17748525225137
50117.5115.2239196686892.27608033131077
51118.8117.7391296645341.06087033546594
52118.7119.512314267926-0.81231426792634
53116.3119.049994206889-2.74999420688911
54115.2115.423402346776-0.223402346776055
55131.7114.22375722774317.476242772257
56133.7138.518761695792-4.81876169579215
57132.5138.369428487353-5.86942848735256
58126.9134.551461806526-7.65146180652582
59122.2125.538647064466-3.33864706446595
60120.2119.34949581360.850504186400443
61117.9117.7288498898440.171150110156418
62117.2115.5051887168311.69481128316929
63116.4115.5611327545150.838867245485346
64112.3115.13529635546-2.83529635545976
65113.6109.7706568075283.82934319247198
66114.2112.7786753836031.42132461639692
67108114.012634975475-6.01263497547545
68102.8105.130793282764-2.33079328276436
69102.898.89117943154863.90882056845138
70101.6100.6346476468250.965352353175149
71100.399.8652279497140.434772050286043
72101.798.75915121564292.94084878435714

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 115.7 & 123.9 & -8.2 \tabularnewline
4 & 113.1 & 122.442518385046 & -9.34251838504601 \tabularnewline
5 & 112.7 & 115.675434332525 & -2.97543433252457 \tabularnewline
6 & 121.9 & 113.948288434023 & 7.95171156597684 \tabularnewline
7 & 120.3 & 126.695024880362 & -6.39502488036189 \tabularnewline
8 & 108.7 & 122.242624157545 & -13.5426241575452 \tabularnewline
9 & 102.8 & 104.602148685051 & -1.80214868505084 \tabularnewline
10 & 83.4 & 97.8983284798085 & -14.4983284798085 \tabularnewline
11 & 79.4 & 72.0315760575568 & 7.36842394244316 \tabularnewline
12 & 77.8 & 71.3181461917852 & 6.48185380821477 \tabularnewline
13 & 85.7 & 72.6092755984151 & 13.0907244015849 \tabularnewline
14 & 83.2 & 86.3481882600281 & -3.14818826002812 \tabularnewline
15 & 82 & 82.4439881769224 & -0.443988176922403 \tabularnewline
16 & 86.9 & 81.0459542020016 & 5.85404579799841 \tabularnewline
17 & 95.7 & 88.5570596750843 & 7.14294032491573 \tabularnewline
18 & 97.9 & 100.543056372047 & -2.64305637204681 \tabularnewline
19 & 89.3 & 101.56416245887 & -12.2641624588702 \tabularnewline
20 & 91.5 & 87.493924810562 & 4.00607518943798 \tabularnewline
21 & 86.8 & 91.4807719268416 & -4.68077192684164 \tabularnewline
22 & 91 & 84.6929868943762 & 6.30701310562375 \tabularnewline
23 & 93.8 & 91.7061313430461 & 2.09386865695389 \tabularnewline
24 & 96.8 & 95.4400686743799 & 1.35993132562007 \tabularnewline
25 & 95.7 & 99.0466447501184 & -3.34664475011839 \tabularnewline
26 & 91.4 & 96.4539262567842 & -5.05392625678419 \tabularnewline
27 & 88.7 & 89.8997015778182 & -1.19970157781816 \tabularnewline
28 & 88.2 & 86.6645934724156 & 1.53540652758443 \tabularnewline
29 & 87.7 & 86.8494375146254 & 0.850562485374624 \tabularnewline
30 & 89.5 & 86.7288175942141 & 2.77118240578592 \tabularnewline
31 & 95.6 & 89.7648601187075 & 5.83513988129251 \tabularnewline
32 & 100.5 & 98.467532903648 & 2.03246709635199 \tabularnewline
33 & 106.3 & 104.274083030222 & 2.02591696977804 \tabularnewline
34 & 112 & 110.977711575391 & 1.02228842460896 \tabularnewline
35 & 117.7 & 117.133687321511 & 0.566312678488529 \tabularnewline
36 & 125 & 123.086282225156 & 1.91371777484375 \tabularnewline
37 & 132.4 & 131.239866076095 & 1.16013392390451 \tabularnewline
38 & 138.1 & 139.157325648969 & -1.05732564896931 \tabularnewline
39 & 134.7 & 144.385722097491 & -9.6857220974907 \tabularnewline
40 & 136.7 & 136.665557402475 & 0.0344425975246736 \tabularnewline
41 & 134.3 & 138.680919983843 & -4.38091998384331 \tabularnewline
42 & 131.6 & 134.326879215857 & -2.72687921585657 \tabularnewline
43 & 129.8 & 130.410597435589 & -0.610597435588772 \tabularnewline
44 & 131.9 & 128.338250009393 & 3.56174999060681 \tabularnewline
45 & 129.8 & 132.026912827406 & -2.22691282740624 \tabularnewline
46 & 119.4 & 128.933633226877 & -9.53363322687653 \tabularnewline
47 & 116.7 & 114.281305391387 & 2.41869460861318 \tabularnewline
48 & 112.8 & 112.660126252752 & 0.139873747248402 \tabularnewline
49 & 116 & 108.822514747749 & 7.17748525225137 \tabularnewline
50 & 117.5 & 115.223919668689 & 2.27608033131077 \tabularnewline
51 & 118.8 & 117.739129664534 & 1.06087033546594 \tabularnewline
52 & 118.7 & 119.512314267926 & -0.81231426792634 \tabularnewline
53 & 116.3 & 119.049994206889 & -2.74999420688911 \tabularnewline
54 & 115.2 & 115.423402346776 & -0.223402346776055 \tabularnewline
55 & 131.7 & 114.223757227743 & 17.476242772257 \tabularnewline
56 & 133.7 & 138.518761695792 & -4.81876169579215 \tabularnewline
57 & 132.5 & 138.369428487353 & -5.86942848735256 \tabularnewline
58 & 126.9 & 134.551461806526 & -7.65146180652582 \tabularnewline
59 & 122.2 & 125.538647064466 & -3.33864706446595 \tabularnewline
60 & 120.2 & 119.3494958136 & 0.850504186400443 \tabularnewline
61 & 117.9 & 117.728849889844 & 0.171150110156418 \tabularnewline
62 & 117.2 & 115.505188716831 & 1.69481128316929 \tabularnewline
63 & 116.4 & 115.561132754515 & 0.838867245485346 \tabularnewline
64 & 112.3 & 115.13529635546 & -2.83529635545976 \tabularnewline
65 & 113.6 & 109.770656807528 & 3.82934319247198 \tabularnewline
66 & 114.2 & 112.778675383603 & 1.42132461639692 \tabularnewline
67 & 108 & 114.012634975475 & -6.01263497547545 \tabularnewline
68 & 102.8 & 105.130793282764 & -2.33079328276436 \tabularnewline
69 & 102.8 & 98.8911794315486 & 3.90882056845138 \tabularnewline
70 & 101.6 & 100.634647646825 & 0.965352353175149 \tabularnewline
71 & 100.3 & 99.865227949714 & 0.434772050286043 \tabularnewline
72 & 101.7 & 98.7591512156429 & 2.94084878435714 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271925&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]115.7[/C][C]123.9[/C][C]-8.2[/C][/ROW]
[ROW][C]4[/C][C]113.1[/C][C]122.442518385046[/C][C]-9.34251838504601[/C][/ROW]
[ROW][C]5[/C][C]112.7[/C][C]115.675434332525[/C][C]-2.97543433252457[/C][/ROW]
[ROW][C]6[/C][C]121.9[/C][C]113.948288434023[/C][C]7.95171156597684[/C][/ROW]
[ROW][C]7[/C][C]120.3[/C][C]126.695024880362[/C][C]-6.39502488036189[/C][/ROW]
[ROW][C]8[/C][C]108.7[/C][C]122.242624157545[/C][C]-13.5426241575452[/C][/ROW]
[ROW][C]9[/C][C]102.8[/C][C]104.602148685051[/C][C]-1.80214868505084[/C][/ROW]
[ROW][C]10[/C][C]83.4[/C][C]97.8983284798085[/C][C]-14.4983284798085[/C][/ROW]
[ROW][C]11[/C][C]79.4[/C][C]72.0315760575568[/C][C]7.36842394244316[/C][/ROW]
[ROW][C]12[/C][C]77.8[/C][C]71.3181461917852[/C][C]6.48185380821477[/C][/ROW]
[ROW][C]13[/C][C]85.7[/C][C]72.6092755984151[/C][C]13.0907244015849[/C][/ROW]
[ROW][C]14[/C][C]83.2[/C][C]86.3481882600281[/C][C]-3.14818826002812[/C][/ROW]
[ROW][C]15[/C][C]82[/C][C]82.4439881769224[/C][C]-0.443988176922403[/C][/ROW]
[ROW][C]16[/C][C]86.9[/C][C]81.0459542020016[/C][C]5.85404579799841[/C][/ROW]
[ROW][C]17[/C][C]95.7[/C][C]88.5570596750843[/C][C]7.14294032491573[/C][/ROW]
[ROW][C]18[/C][C]97.9[/C][C]100.543056372047[/C][C]-2.64305637204681[/C][/ROW]
[ROW][C]19[/C][C]89.3[/C][C]101.56416245887[/C][C]-12.2641624588702[/C][/ROW]
[ROW][C]20[/C][C]91.5[/C][C]87.493924810562[/C][C]4.00607518943798[/C][/ROW]
[ROW][C]21[/C][C]86.8[/C][C]91.4807719268416[/C][C]-4.68077192684164[/C][/ROW]
[ROW][C]22[/C][C]91[/C][C]84.6929868943762[/C][C]6.30701310562375[/C][/ROW]
[ROW][C]23[/C][C]93.8[/C][C]91.7061313430461[/C][C]2.09386865695389[/C][/ROW]
[ROW][C]24[/C][C]96.8[/C][C]95.4400686743799[/C][C]1.35993132562007[/C][/ROW]
[ROW][C]25[/C][C]95.7[/C][C]99.0466447501184[/C][C]-3.34664475011839[/C][/ROW]
[ROW][C]26[/C][C]91.4[/C][C]96.4539262567842[/C][C]-5.05392625678419[/C][/ROW]
[ROW][C]27[/C][C]88.7[/C][C]89.8997015778182[/C][C]-1.19970157781816[/C][/ROW]
[ROW][C]28[/C][C]88.2[/C][C]86.6645934724156[/C][C]1.53540652758443[/C][/ROW]
[ROW][C]29[/C][C]87.7[/C][C]86.8494375146254[/C][C]0.850562485374624[/C][/ROW]
[ROW][C]30[/C][C]89.5[/C][C]86.7288175942141[/C][C]2.77118240578592[/C][/ROW]
[ROW][C]31[/C][C]95.6[/C][C]89.7648601187075[/C][C]5.83513988129251[/C][/ROW]
[ROW][C]32[/C][C]100.5[/C][C]98.467532903648[/C][C]2.03246709635199[/C][/ROW]
[ROW][C]33[/C][C]106.3[/C][C]104.274083030222[/C][C]2.02591696977804[/C][/ROW]
[ROW][C]34[/C][C]112[/C][C]110.977711575391[/C][C]1.02228842460896[/C][/ROW]
[ROW][C]35[/C][C]117.7[/C][C]117.133687321511[/C][C]0.566312678488529[/C][/ROW]
[ROW][C]36[/C][C]125[/C][C]123.086282225156[/C][C]1.91371777484375[/C][/ROW]
[ROW][C]37[/C][C]132.4[/C][C]131.239866076095[/C][C]1.16013392390451[/C][/ROW]
[ROW][C]38[/C][C]138.1[/C][C]139.157325648969[/C][C]-1.05732564896931[/C][/ROW]
[ROW][C]39[/C][C]134.7[/C][C]144.385722097491[/C][C]-9.6857220974907[/C][/ROW]
[ROW][C]40[/C][C]136.7[/C][C]136.665557402475[/C][C]0.0344425975246736[/C][/ROW]
[ROW][C]41[/C][C]134.3[/C][C]138.680919983843[/C][C]-4.38091998384331[/C][/ROW]
[ROW][C]42[/C][C]131.6[/C][C]134.326879215857[/C][C]-2.72687921585657[/C][/ROW]
[ROW][C]43[/C][C]129.8[/C][C]130.410597435589[/C][C]-0.610597435588772[/C][/ROW]
[ROW][C]44[/C][C]131.9[/C][C]128.338250009393[/C][C]3.56174999060681[/C][/ROW]
[ROW][C]45[/C][C]129.8[/C][C]132.026912827406[/C][C]-2.22691282740624[/C][/ROW]
[ROW][C]46[/C][C]119.4[/C][C]128.933633226877[/C][C]-9.53363322687653[/C][/ROW]
[ROW][C]47[/C][C]116.7[/C][C]114.281305391387[/C][C]2.41869460861318[/C][/ROW]
[ROW][C]48[/C][C]112.8[/C][C]112.660126252752[/C][C]0.139873747248402[/C][/ROW]
[ROW][C]49[/C][C]116[/C][C]108.822514747749[/C][C]7.17748525225137[/C][/ROW]
[ROW][C]50[/C][C]117.5[/C][C]115.223919668689[/C][C]2.27608033131077[/C][/ROW]
[ROW][C]51[/C][C]118.8[/C][C]117.739129664534[/C][C]1.06087033546594[/C][/ROW]
[ROW][C]52[/C][C]118.7[/C][C]119.512314267926[/C][C]-0.81231426792634[/C][/ROW]
[ROW][C]53[/C][C]116.3[/C][C]119.049994206889[/C][C]-2.74999420688911[/C][/ROW]
[ROW][C]54[/C][C]115.2[/C][C]115.423402346776[/C][C]-0.223402346776055[/C][/ROW]
[ROW][C]55[/C][C]131.7[/C][C]114.223757227743[/C][C]17.476242772257[/C][/ROW]
[ROW][C]56[/C][C]133.7[/C][C]138.518761695792[/C][C]-4.81876169579215[/C][/ROW]
[ROW][C]57[/C][C]132.5[/C][C]138.369428487353[/C][C]-5.86942848735256[/C][/ROW]
[ROW][C]58[/C][C]126.9[/C][C]134.551461806526[/C][C]-7.65146180652582[/C][/ROW]
[ROW][C]59[/C][C]122.2[/C][C]125.538647064466[/C][C]-3.33864706446595[/C][/ROW]
[ROW][C]60[/C][C]120.2[/C][C]119.3494958136[/C][C]0.850504186400443[/C][/ROW]
[ROW][C]61[/C][C]117.9[/C][C]117.728849889844[/C][C]0.171150110156418[/C][/ROW]
[ROW][C]62[/C][C]117.2[/C][C]115.505188716831[/C][C]1.69481128316929[/C][/ROW]
[ROW][C]63[/C][C]116.4[/C][C]115.561132754515[/C][C]0.838867245485346[/C][/ROW]
[ROW][C]64[/C][C]112.3[/C][C]115.13529635546[/C][C]-2.83529635545976[/C][/ROW]
[ROW][C]65[/C][C]113.6[/C][C]109.770656807528[/C][C]3.82934319247198[/C][/ROW]
[ROW][C]66[/C][C]114.2[/C][C]112.778675383603[/C][C]1.42132461639692[/C][/ROW]
[ROW][C]67[/C][C]108[/C][C]114.012634975475[/C][C]-6.01263497547545[/C][/ROW]
[ROW][C]68[/C][C]102.8[/C][C]105.130793282764[/C][C]-2.33079328276436[/C][/ROW]
[ROW][C]69[/C][C]102.8[/C][C]98.8911794315486[/C][C]3.90882056845138[/C][/ROW]
[ROW][C]70[/C][C]101.6[/C][C]100.634647646825[/C][C]0.965352353175149[/C][/ROW]
[ROW][C]71[/C][C]100.3[/C][C]99.865227949714[/C][C]0.434772050286043[/C][/ROW]
[ROW][C]72[/C][C]101.7[/C][C]98.7591512156429[/C][C]2.94084878435714[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271925&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271925&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
3115.7123.9-8.2
4113.1122.442518385046-9.34251838504601
5112.7115.675434332525-2.97543433252457
6121.9113.9482884340237.95171156597684
7120.3126.695024880362-6.39502488036189
8108.7122.242624157545-13.5426241575452
9102.8104.602148685051-1.80214868505084
1083.497.8983284798085-14.4983284798085
1179.472.03157605755687.36842394244316
1277.871.31814619178526.48185380821477
1385.772.609275598415113.0907244015849
1483.286.3481882600281-3.14818826002812
158282.4439881769224-0.443988176922403
1686.981.04595420200165.85404579799841
1795.788.55705967508437.14294032491573
1897.9100.543056372047-2.64305637204681
1989.3101.56416245887-12.2641624588702
2091.587.4939248105624.00607518943798
2186.891.4807719268416-4.68077192684164
229184.69298689437626.30701310562375
2393.891.70613134304612.09386865695389
2496.895.44006867437991.35993132562007
2595.799.0466447501184-3.34664475011839
2691.496.4539262567842-5.05392625678419
2788.789.8997015778182-1.19970157781816
2888.286.66459347241561.53540652758443
2987.786.84943751462540.850562485374624
3089.586.72881759421412.77118240578592
3195.689.76486011870755.83513988129251
32100.598.4675329036482.03246709635199
33106.3104.2740830302222.02591696977804
34112110.9777115753911.02228842460896
35117.7117.1336873215110.566312678488529
36125123.0862822251561.91371777484375
37132.4131.2398660760951.16013392390451
38138.1139.157325648969-1.05732564896931
39134.7144.385722097491-9.6857220974907
40136.7136.6655574024750.0344425975246736
41134.3138.680919983843-4.38091998384331
42131.6134.326879215857-2.72687921585657
43129.8130.410597435589-0.610597435588772
44131.9128.3382500093933.56174999060681
45129.8132.026912827406-2.22691282740624
46119.4128.933633226877-9.53363322687653
47116.7114.2813053913872.41869460861318
48112.8112.6601262527520.139873747248402
49116108.8225147477497.17748525225137
50117.5115.2239196686892.27608033131077
51118.8117.7391296645341.06087033546594
52118.7119.512314267926-0.81231426792634
53116.3119.049994206889-2.74999420688911
54115.2115.423402346776-0.223402346776055
55131.7114.22375722774317.476242772257
56133.7138.518761695792-4.81876169579215
57132.5138.369428487353-5.86942848735256
58126.9134.551461806526-7.65146180652582
59122.2125.538647064466-3.33864706446595
60120.2119.34949581360.850504186400443
61117.9117.7288498898440.171150110156418
62117.2115.5051887168311.69481128316929
63116.4115.5611327545150.838867245485346
64112.3115.13529635546-2.83529635545976
65113.6109.7706568075283.82934319247198
66114.2112.7786753836031.42132461639692
67108114.012634975475-6.01263497547545
68102.8105.130793282764-2.33079328276436
69102.898.89117943154863.90882056845138
70101.6100.6346476468250.965352353175149
71100.399.8652279497140.434772050286043
72101.798.75915121564292.94084878435714







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73101.4708707718890.4309913263211112.510750217439
74101.2417415437681.8322164255088120.651266662012
75101.01261231564172.4986334494827129.526591181798
76100.78348308752162.3214794487025139.245486726339
77100.55435385940151.3196031840562149.789104534746
78100.32522463128139.5325716986989161.117877563863
79100.09609540316127.0010992487351173.191091557588
8099.866966175041613.7626636105648185.971268739518
8199.6378369469218-0.149230510883143199.424904404727
8299.408707718802-14.7048191187525213.522234556356
8399.1795784906822-29.8776191229892228.236776104354
8498.9504492625624-45.6439606810603243.544859206185

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 101.47087077188 & 90.4309913263211 & 112.510750217439 \tabularnewline
74 & 101.24174154376 & 81.8322164255088 & 120.651266662012 \tabularnewline
75 & 101.012612315641 & 72.4986334494827 & 129.526591181798 \tabularnewline
76 & 100.783483087521 & 62.3214794487025 & 139.245486726339 \tabularnewline
77 & 100.554353859401 & 51.3196031840562 & 149.789104534746 \tabularnewline
78 & 100.325224631281 & 39.5325716986989 & 161.117877563863 \tabularnewline
79 & 100.096095403161 & 27.0010992487351 & 173.191091557588 \tabularnewline
80 & 99.8669661750416 & 13.7626636105648 & 185.971268739518 \tabularnewline
81 & 99.6378369469218 & -0.149230510883143 & 199.424904404727 \tabularnewline
82 & 99.408707718802 & -14.7048191187525 & 213.522234556356 \tabularnewline
83 & 99.1795784906822 & -29.8776191229892 & 228.236776104354 \tabularnewline
84 & 98.9504492625624 & -45.6439606810603 & 243.544859206185 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271925&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]101.47087077188[/C][C]90.4309913263211[/C][C]112.510750217439[/C][/ROW]
[ROW][C]74[/C][C]101.24174154376[/C][C]81.8322164255088[/C][C]120.651266662012[/C][/ROW]
[ROW][C]75[/C][C]101.012612315641[/C][C]72.4986334494827[/C][C]129.526591181798[/C][/ROW]
[ROW][C]76[/C][C]100.783483087521[/C][C]62.3214794487025[/C][C]139.245486726339[/C][/ROW]
[ROW][C]77[/C][C]100.554353859401[/C][C]51.3196031840562[/C][C]149.789104534746[/C][/ROW]
[ROW][C]78[/C][C]100.325224631281[/C][C]39.5325716986989[/C][C]161.117877563863[/C][/ROW]
[ROW][C]79[/C][C]100.096095403161[/C][C]27.0010992487351[/C][C]173.191091557588[/C][/ROW]
[ROW][C]80[/C][C]99.8669661750416[/C][C]13.7626636105648[/C][C]185.971268739518[/C][/ROW]
[ROW][C]81[/C][C]99.6378369469218[/C][C]-0.149230510883143[/C][C]199.424904404727[/C][/ROW]
[ROW][C]82[/C][C]99.408707718802[/C][C]-14.7048191187525[/C][C]213.522234556356[/C][/ROW]
[ROW][C]83[/C][C]99.1795784906822[/C][C]-29.8776191229892[/C][C]228.236776104354[/C][/ROW]
[ROW][C]84[/C][C]98.9504492625624[/C][C]-45.6439606810603[/C][C]243.544859206185[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271925&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271925&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
73101.4708707718890.4309913263211112.510750217439
74101.2417415437681.8322164255088120.651266662012
75101.01261231564172.4986334494827129.526591181798
76100.78348308752162.3214794487025139.245486726339
77100.55435385940151.3196031840562149.789104534746
78100.32522463128139.5325716986989161.117877563863
79100.09609540316127.0010992487351173.191091557588
8099.866966175041613.7626636105648185.971268739518
8199.6378369469218-0.149230510883143199.424904404727
8299.408707718802-14.7048191187525213.522234556356
8399.1795784906822-29.8776191229892228.236776104354
8498.9504492625624-45.6439606810603243.544859206185



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