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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 02 Jun 2010 11:48:14 +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/2010/Jun/02/t1275479417l96mp1zlr49pc9n.htm/, Retrieved Fri, 26 Apr 2024 07:13:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77270, Retrieved Fri, 26 Apr 2024 07:13:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-06-02 11:48:14] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
127,87
127,94
122,44
120,25
118,13
114,93
112,57
110,81
109,02
106,39
103,75
102,60
101,63
100,00
97,98
96,56
94,32
91,79
89,61
86,83
83,94
81,41
80,47
79,24
78,23
74,60
70,14
65,15
59,92
55,67
52,20
49,97
47,83
44,66
40,91
36,28
32,20
30,10
28,55
27,36
26,33
25,38
24,69
24,01
23,05
22,15
21,26
20,81
20,52
20,32
20,26
20,02
19,76
19,15
18,63
18,73
18,48
18,53
18,37
16,80
16,94
17,21
15,26
14,99
15,80
4,71
4,65
4,50




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77270&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77270&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77270&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.129014448423179
gamma2.56496888259109e-14

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.129014448423179 \tabularnewline
gamma & 2.56496888259109e-14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77270&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]0.129014448423179[/C][/ROW]
[ROW][C]gamma[/C][C]2.56496888259109e-14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77270&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77270&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
beta0.129014448423179
gamma2.56496888259109e-14







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13101.63113.672174302484-12.0421743024838
1410098.3854000541891.61459994581089
1597.9896.66209921815131.31790078184866
1696.5695.4462319886791.113768011321
1794.3293.2761151150311.04388488496906
1891.7990.81847270402910.971527295970887
1989.6187.67654618354451.93345381645551
2086.8387.4766585208546-0.646658520854558
2183.9484.5226792203938-0.582679220393757
2281.4180.77600658545460.63399341454543
2380.4778.30964295497862.16035704502141
2479.2478.77322004010010.466779959899881
2578.2377.70540691220230.524593087797655
2674.676.277301457744-1.67730145774398
2770.1472.1979065027617-2.05790650276172
2865.1567.9223532678424-2.77235326784243
2959.9261.9451427862315-2.02514278623153
3055.6756.2470571238373-0.577057123837342
3152.251.51688323399720.683116766002762
3249.9749.16794650617190.802053493828105
3347.8346.98076516156940.849234838430561
3444.6644.51221239017050.147787609829479
3540.9141.372090749097-0.462090749097008
3636.2838.1410288239702-1.86102882397022
3732.233.265134134704-1.06513413470397
3830.128.80500728766531.29499271233467
3928.5526.77506289332801.77493710667197
4027.3625.62305225421511.73694774578493
4126.3324.40262781571121.92737218428882
4225.3823.53496443876721.84503556123281
4324.6922.64461086264652.04538913735349
4424.0122.69059169630921.31940830369079
4523.0522.15188033876450.898119661235519
4622.1521.09894184286011.05105815713993
4721.2620.33715389791610.922846102083863
4820.8119.86032538139240.94967461860763
4920.5219.55074450371730.969255496282724
5020.3219.25564089035341.06435910964662
5120.2619.13191565938761.12808434061241
5220.0219.34596193469690.674038065303144
5319.7619.00869837199090.751301628009081
5419.1518.77292831050540.377071689494571
5518.6318.06170948918980.568290510810204
5618.7317.97491064484970.755089355150297
5718.4818.15554743030800.324452569692035
5818.5317.77675237410090.753247625899107
5918.3717.91553907378770.454460926212253
6016.818.0712783598503-1.27127835985025
6116.9416.34769168006320.592308319936777
6217.2116.46207711276010.74792288723987
6315.2616.7785493403617-1.51854934036171
6414.9914.72982043844970.260179561550283
6515.814.35454908583811.44545091416191
664.7115.2890253348108-10.5790253348108
674.652.887415748222191.76258425177781
684.53.137812235502011.36218776449799

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 101.63 & 113.672174302484 & -12.0421743024838 \tabularnewline
14 & 100 & 98.385400054189 & 1.61459994581089 \tabularnewline
15 & 97.98 & 96.6620992181513 & 1.31790078184866 \tabularnewline
16 & 96.56 & 95.446231988679 & 1.113768011321 \tabularnewline
17 & 94.32 & 93.276115115031 & 1.04388488496906 \tabularnewline
18 & 91.79 & 90.8184727040291 & 0.971527295970887 \tabularnewline
19 & 89.61 & 87.6765461835445 & 1.93345381645551 \tabularnewline
20 & 86.83 & 87.4766585208546 & -0.646658520854558 \tabularnewline
21 & 83.94 & 84.5226792203938 & -0.582679220393757 \tabularnewline
22 & 81.41 & 80.7760065854546 & 0.63399341454543 \tabularnewline
23 & 80.47 & 78.3096429549786 & 2.16035704502141 \tabularnewline
24 & 79.24 & 78.7732200401001 & 0.466779959899881 \tabularnewline
25 & 78.23 & 77.7054069122023 & 0.524593087797655 \tabularnewline
26 & 74.6 & 76.277301457744 & -1.67730145774398 \tabularnewline
27 & 70.14 & 72.1979065027617 & -2.05790650276172 \tabularnewline
28 & 65.15 & 67.9223532678424 & -2.77235326784243 \tabularnewline
29 & 59.92 & 61.9451427862315 & -2.02514278623153 \tabularnewline
30 & 55.67 & 56.2470571238373 & -0.577057123837342 \tabularnewline
31 & 52.2 & 51.5168832339972 & 0.683116766002762 \tabularnewline
32 & 49.97 & 49.1679465061719 & 0.802053493828105 \tabularnewline
33 & 47.83 & 46.9807651615694 & 0.849234838430561 \tabularnewline
34 & 44.66 & 44.5122123901705 & 0.147787609829479 \tabularnewline
35 & 40.91 & 41.372090749097 & -0.462090749097008 \tabularnewline
36 & 36.28 & 38.1410288239702 & -1.86102882397022 \tabularnewline
37 & 32.2 & 33.265134134704 & -1.06513413470397 \tabularnewline
38 & 30.1 & 28.8050072876653 & 1.29499271233467 \tabularnewline
39 & 28.55 & 26.7750628933280 & 1.77493710667197 \tabularnewline
40 & 27.36 & 25.6230522542151 & 1.73694774578493 \tabularnewline
41 & 26.33 & 24.4026278157112 & 1.92737218428882 \tabularnewline
42 & 25.38 & 23.5349644387672 & 1.84503556123281 \tabularnewline
43 & 24.69 & 22.6446108626465 & 2.04538913735349 \tabularnewline
44 & 24.01 & 22.6905916963092 & 1.31940830369079 \tabularnewline
45 & 23.05 & 22.1518803387645 & 0.898119661235519 \tabularnewline
46 & 22.15 & 21.0989418428601 & 1.05105815713993 \tabularnewline
47 & 21.26 & 20.3371538979161 & 0.922846102083863 \tabularnewline
48 & 20.81 & 19.8603253813924 & 0.94967461860763 \tabularnewline
49 & 20.52 & 19.5507445037173 & 0.969255496282724 \tabularnewline
50 & 20.32 & 19.2556408903534 & 1.06435910964662 \tabularnewline
51 & 20.26 & 19.1319156593876 & 1.12808434061241 \tabularnewline
52 & 20.02 & 19.3459619346969 & 0.674038065303144 \tabularnewline
53 & 19.76 & 19.0086983719909 & 0.751301628009081 \tabularnewline
54 & 19.15 & 18.7729283105054 & 0.377071689494571 \tabularnewline
55 & 18.63 & 18.0617094891898 & 0.568290510810204 \tabularnewline
56 & 18.73 & 17.9749106448497 & 0.755089355150297 \tabularnewline
57 & 18.48 & 18.1555474303080 & 0.324452569692035 \tabularnewline
58 & 18.53 & 17.7767523741009 & 0.753247625899107 \tabularnewline
59 & 18.37 & 17.9155390737877 & 0.454460926212253 \tabularnewline
60 & 16.8 & 18.0712783598503 & -1.27127835985025 \tabularnewline
61 & 16.94 & 16.3476916800632 & 0.592308319936777 \tabularnewline
62 & 17.21 & 16.4620771127601 & 0.74792288723987 \tabularnewline
63 & 15.26 & 16.7785493403617 & -1.51854934036171 \tabularnewline
64 & 14.99 & 14.7298204384497 & 0.260179561550283 \tabularnewline
65 & 15.8 & 14.3545490858381 & 1.44545091416191 \tabularnewline
66 & 4.71 & 15.2890253348108 & -10.5790253348108 \tabularnewline
67 & 4.65 & 2.88741574822219 & 1.76258425177781 \tabularnewline
68 & 4.5 & 3.13781223550201 & 1.36218776449799 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77270&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]101.63[/C][C]113.672174302484[/C][C]-12.0421743024838[/C][/ROW]
[ROW][C]14[/C][C]100[/C][C]98.385400054189[/C][C]1.61459994581089[/C][/ROW]
[ROW][C]15[/C][C]97.98[/C][C]96.6620992181513[/C][C]1.31790078184866[/C][/ROW]
[ROW][C]16[/C][C]96.56[/C][C]95.446231988679[/C][C]1.113768011321[/C][/ROW]
[ROW][C]17[/C][C]94.32[/C][C]93.276115115031[/C][C]1.04388488496906[/C][/ROW]
[ROW][C]18[/C][C]91.79[/C][C]90.8184727040291[/C][C]0.971527295970887[/C][/ROW]
[ROW][C]19[/C][C]89.61[/C][C]87.6765461835445[/C][C]1.93345381645551[/C][/ROW]
[ROW][C]20[/C][C]86.83[/C][C]87.4766585208546[/C][C]-0.646658520854558[/C][/ROW]
[ROW][C]21[/C][C]83.94[/C][C]84.5226792203938[/C][C]-0.582679220393757[/C][/ROW]
[ROW][C]22[/C][C]81.41[/C][C]80.7760065854546[/C][C]0.63399341454543[/C][/ROW]
[ROW][C]23[/C][C]80.47[/C][C]78.3096429549786[/C][C]2.16035704502141[/C][/ROW]
[ROW][C]24[/C][C]79.24[/C][C]78.7732200401001[/C][C]0.466779959899881[/C][/ROW]
[ROW][C]25[/C][C]78.23[/C][C]77.7054069122023[/C][C]0.524593087797655[/C][/ROW]
[ROW][C]26[/C][C]74.6[/C][C]76.277301457744[/C][C]-1.67730145774398[/C][/ROW]
[ROW][C]27[/C][C]70.14[/C][C]72.1979065027617[/C][C]-2.05790650276172[/C][/ROW]
[ROW][C]28[/C][C]65.15[/C][C]67.9223532678424[/C][C]-2.77235326784243[/C][/ROW]
[ROW][C]29[/C][C]59.92[/C][C]61.9451427862315[/C][C]-2.02514278623153[/C][/ROW]
[ROW][C]30[/C][C]55.67[/C][C]56.2470571238373[/C][C]-0.577057123837342[/C][/ROW]
[ROW][C]31[/C][C]52.2[/C][C]51.5168832339972[/C][C]0.683116766002762[/C][/ROW]
[ROW][C]32[/C][C]49.97[/C][C]49.1679465061719[/C][C]0.802053493828105[/C][/ROW]
[ROW][C]33[/C][C]47.83[/C][C]46.9807651615694[/C][C]0.849234838430561[/C][/ROW]
[ROW][C]34[/C][C]44.66[/C][C]44.5122123901705[/C][C]0.147787609829479[/C][/ROW]
[ROW][C]35[/C][C]40.91[/C][C]41.372090749097[/C][C]-0.462090749097008[/C][/ROW]
[ROW][C]36[/C][C]36.28[/C][C]38.1410288239702[/C][C]-1.86102882397022[/C][/ROW]
[ROW][C]37[/C][C]32.2[/C][C]33.265134134704[/C][C]-1.06513413470397[/C][/ROW]
[ROW][C]38[/C][C]30.1[/C][C]28.8050072876653[/C][C]1.29499271233467[/C][/ROW]
[ROW][C]39[/C][C]28.55[/C][C]26.7750628933280[/C][C]1.77493710667197[/C][/ROW]
[ROW][C]40[/C][C]27.36[/C][C]25.6230522542151[/C][C]1.73694774578493[/C][/ROW]
[ROW][C]41[/C][C]26.33[/C][C]24.4026278157112[/C][C]1.92737218428882[/C][/ROW]
[ROW][C]42[/C][C]25.38[/C][C]23.5349644387672[/C][C]1.84503556123281[/C][/ROW]
[ROW][C]43[/C][C]24.69[/C][C]22.6446108626465[/C][C]2.04538913735349[/C][/ROW]
[ROW][C]44[/C][C]24.01[/C][C]22.6905916963092[/C][C]1.31940830369079[/C][/ROW]
[ROW][C]45[/C][C]23.05[/C][C]22.1518803387645[/C][C]0.898119661235519[/C][/ROW]
[ROW][C]46[/C][C]22.15[/C][C]21.0989418428601[/C][C]1.05105815713993[/C][/ROW]
[ROW][C]47[/C][C]21.26[/C][C]20.3371538979161[/C][C]0.922846102083863[/C][/ROW]
[ROW][C]48[/C][C]20.81[/C][C]19.8603253813924[/C][C]0.94967461860763[/C][/ROW]
[ROW][C]49[/C][C]20.52[/C][C]19.5507445037173[/C][C]0.969255496282724[/C][/ROW]
[ROW][C]50[/C][C]20.32[/C][C]19.2556408903534[/C][C]1.06435910964662[/C][/ROW]
[ROW][C]51[/C][C]20.26[/C][C]19.1319156593876[/C][C]1.12808434061241[/C][/ROW]
[ROW][C]52[/C][C]20.02[/C][C]19.3459619346969[/C][C]0.674038065303144[/C][/ROW]
[ROW][C]53[/C][C]19.76[/C][C]19.0086983719909[/C][C]0.751301628009081[/C][/ROW]
[ROW][C]54[/C][C]19.15[/C][C]18.7729283105054[/C][C]0.377071689494571[/C][/ROW]
[ROW][C]55[/C][C]18.63[/C][C]18.0617094891898[/C][C]0.568290510810204[/C][/ROW]
[ROW][C]56[/C][C]18.73[/C][C]17.9749106448497[/C][C]0.755089355150297[/C][/ROW]
[ROW][C]57[/C][C]18.48[/C][C]18.1555474303080[/C][C]0.324452569692035[/C][/ROW]
[ROW][C]58[/C][C]18.53[/C][C]17.7767523741009[/C][C]0.753247625899107[/C][/ROW]
[ROW][C]59[/C][C]18.37[/C][C]17.9155390737877[/C][C]0.454460926212253[/C][/ROW]
[ROW][C]60[/C][C]16.8[/C][C]18.0712783598503[/C][C]-1.27127835985025[/C][/ROW]
[ROW][C]61[/C][C]16.94[/C][C]16.3476916800632[/C][C]0.592308319936777[/C][/ROW]
[ROW][C]62[/C][C]17.21[/C][C]16.4620771127601[/C][C]0.74792288723987[/C][/ROW]
[ROW][C]63[/C][C]15.26[/C][C]16.7785493403617[/C][C]-1.51854934036171[/C][/ROW]
[ROW][C]64[/C][C]14.99[/C][C]14.7298204384497[/C][C]0.260179561550283[/C][/ROW]
[ROW][C]65[/C][C]15.8[/C][C]14.3545490858381[/C][C]1.44545091416191[/C][/ROW]
[ROW][C]66[/C][C]4.71[/C][C]15.2890253348108[/C][C]-10.5790253348108[/C][/ROW]
[ROW][C]67[/C][C]4.65[/C][C]2.88741574822219[/C][C]1.76258425177781[/C][/ROW]
[ROW][C]68[/C][C]4.5[/C][C]3.13781223550201[/C][C]1.36218776449799[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77270&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77270&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
13101.63113.672174302484-12.0421743024838
1410098.3854000541891.61459994581089
1597.9896.66209921815131.31790078184866
1696.5695.4462319886791.113768011321
1794.3293.2761151150311.04388488496906
1891.7990.81847270402910.971527295970887
1989.6187.67654618354451.93345381645551
2086.8387.4766585208546-0.646658520854558
2183.9484.5226792203938-0.582679220393757
2281.4180.77600658545460.63399341454543
2380.4778.30964295497862.16035704502141
2479.2478.77322004010010.466779959899881
2578.2377.70540691220230.524593087797655
2674.676.277301457744-1.67730145774398
2770.1472.1979065027617-2.05790650276172
2865.1567.9223532678424-2.77235326784243
2959.9261.9451427862315-2.02514278623153
3055.6756.2470571238373-0.577057123837342
3152.251.51688323399720.683116766002762
3249.9749.16794650617190.802053493828105
3347.8346.98076516156940.849234838430561
3444.6644.51221239017050.147787609829479
3540.9141.372090749097-0.462090749097008
3636.2838.1410288239702-1.86102882397022
3732.233.265134134704-1.06513413470397
3830.128.80500728766531.29499271233467
3928.5526.77506289332801.77493710667197
4027.3625.62305225421511.73694774578493
4126.3324.40262781571121.92737218428882
4225.3823.53496443876721.84503556123281
4324.6922.64461086264652.04538913735349
4424.0122.69059169630921.31940830369079
4523.0522.15188033876450.898119661235519
4622.1521.09894184286011.05105815713993
4721.2620.33715389791610.922846102083863
4820.8119.86032538139240.94967461860763
4920.5219.55074450371730.969255496282724
5020.3219.25564089035341.06435910964662
5120.2619.13191565938761.12808434061241
5220.0219.34596193469690.674038065303144
5319.7619.00869837199090.751301628009081
5419.1518.77292831050540.377071689494571
5518.6318.06170948918980.568290510810204
5618.7317.97491064484970.755089355150297
5718.4818.15554743030800.324452569692035
5818.5317.77675237410090.753247625899107
5918.3717.91553907378770.454460926212253
6016.818.0712783598503-1.27127835985025
6116.9416.34769168006320.592308319936777
6217.2116.46207711276010.74792288723987
6315.2616.7785493403617-1.51854934036171
6414.9914.72982043844970.260179561550283
6515.814.35454908583811.44545091416191
664.7115.2890253348108-10.5790253348108
674.652.887415748222191.76258425177781
684.53.137812235502011.36218776449799







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
693.15453720120978-1.738566077837348.04764048025691
701.78273530557923-5.57285980821699.13833041937534
710.426634442942795-9.114558499711619.9678273855972
72-0.924958824678932-12.695102450222410.8451848008645
73-2.30107192827578-16.329330729142711.7271868725911
74-3.68076902624497-19.924915598638212.5633775461482
75-5.05472174846452-23.508315847271913.3988723503428
76-6.47285116523605-27.310561483360114.3648591528880
77-7.83840903211632-30.929448154604415.2526300903717
78-9.16146505824447-34.450681251689016.1277511352
79-10.3769578920506-37.661565307671916.9076495235708
80-11.7782884699307-41.420930881268217.8643539414067

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
69 & 3.15453720120978 & -1.73856607783734 & 8.04764048025691 \tabularnewline
70 & 1.78273530557923 & -5.5728598082169 & 9.13833041937534 \tabularnewline
71 & 0.426634442942795 & -9.11455849971161 & 9.9678273855972 \tabularnewline
72 & -0.924958824678932 & -12.6951024502224 & 10.8451848008645 \tabularnewline
73 & -2.30107192827578 & -16.3293307291427 & 11.7271868725911 \tabularnewline
74 & -3.68076902624497 & -19.9249155986382 & 12.5633775461482 \tabularnewline
75 & -5.05472174846452 & -23.5083158472719 & 13.3988723503428 \tabularnewline
76 & -6.47285116523605 & -27.3105614833601 & 14.3648591528880 \tabularnewline
77 & -7.83840903211632 & -30.9294481546044 & 15.2526300903717 \tabularnewline
78 & -9.16146505824447 & -34.4506812516890 & 16.1277511352 \tabularnewline
79 & -10.3769578920506 & -37.6615653076719 & 16.9076495235708 \tabularnewline
80 & -11.7782884699307 & -41.4209308812682 & 17.8643539414067 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77270&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]69[/C][C]3.15453720120978[/C][C]-1.73856607783734[/C][C]8.04764048025691[/C][/ROW]
[ROW][C]70[/C][C]1.78273530557923[/C][C]-5.5728598082169[/C][C]9.13833041937534[/C][/ROW]
[ROW][C]71[/C][C]0.426634442942795[/C][C]-9.11455849971161[/C][C]9.9678273855972[/C][/ROW]
[ROW][C]72[/C][C]-0.924958824678932[/C][C]-12.6951024502224[/C][C]10.8451848008645[/C][/ROW]
[ROW][C]73[/C][C]-2.30107192827578[/C][C]-16.3293307291427[/C][C]11.7271868725911[/C][/ROW]
[ROW][C]74[/C][C]-3.68076902624497[/C][C]-19.9249155986382[/C][C]12.5633775461482[/C][/ROW]
[ROW][C]75[/C][C]-5.05472174846452[/C][C]-23.5083158472719[/C][C]13.3988723503428[/C][/ROW]
[ROW][C]76[/C][C]-6.47285116523605[/C][C]-27.3105614833601[/C][C]14.3648591528880[/C][/ROW]
[ROW][C]77[/C][C]-7.83840903211632[/C][C]-30.9294481546044[/C][C]15.2526300903717[/C][/ROW]
[ROW][C]78[/C][C]-9.16146505824447[/C][C]-34.4506812516890[/C][C]16.1277511352[/C][/ROW]
[ROW][C]79[/C][C]-10.3769578920506[/C][C]-37.6615653076719[/C][C]16.9076495235708[/C][/ROW]
[ROW][C]80[/C][C]-11.7782884699307[/C][C]-41.4209308812682[/C][C]17.8643539414067[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77270&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77270&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
693.15453720120978-1.738566077837348.04764048025691
701.78273530557923-5.57285980821699.13833041937534
710.426634442942795-9.114558499711619.9678273855972
72-0.924958824678932-12.695102450222410.8451848008645
73-2.30107192827578-16.329330729142711.7271868725911
74-3.68076902624497-19.924915598638212.5633775461482
75-5.05472174846452-23.508315847271913.3988723503428
76-6.47285116523605-27.310561483360114.3648591528880
77-7.83840903211632-30.929448154604415.2526300903717
78-9.16146505824447-34.450681251689016.1277511352
79-10.3769578920506-37.661565307671916.9076495235708
80-11.7782884699307-41.420930881268217.8643539414067



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