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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 computationSat, 13 Aug 2016 12:45:34 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/13/t1471088781n7zqkf8104tr034.htm/, Retrieved Wed, 01 May 2024 18:35:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296509, Retrieved Wed, 01 May 2024 18:35:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean versus Median] [mean vs median va...] [2016-08-11 11:22:45] [4c392b130fccc63297597dd6ffb6df17]
- RMP   [Mean Plot] [mean en meadian p...] [2016-08-11 22:10:26] [4c392b130fccc63297597dd6ffb6df17]
- RMP     [(Partial) Autocorrelation Function] [autocorrelation a...] [2016-08-11 22:42:14] [4c392b130fccc63297597dd6ffb6df17]
- RMPD        [Exponential Smoothing] [exponentional smo...] [2016-08-13 11:45:34] [d7adcc7732e5b057da1b42af54844e1a] [Current]
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Dataseries X:
2421.21
2378.63
2336.00
2250.79
3113.00
3070.38
2421.21
1990.13
2032.71
2032.71
2075.33
2165.17
1904.92
1644.25
1430.79
1430.79
2250.79
2336.00
1686.83
952.46
1340.96
1340.96
1644.25
1819.29
1776.67
1340.96
1559.04
1473.42
2207.79
2032.71
1340.96
824.25
1298.33
1430.79
1559.04
1729.46
1383.54
1084.92
1213.17
1255.75
2378.63
2378.63
1729.46
1644.25
1904.92
1776.67
2122.58
2553.67
2639.29
2032.71
1861.88
1686.83
2856.96
2942.58
2724.50
2942.58
2899.54
2553.67
2942.58
3373.67
3548.71
3027.79
2681.88
2942.58
4065.42
4411.33
4326.13
4496.50
4453.92
4022.83
4757.21
4932.25
5188.29
4411.33
4108.04
4453.92
5278.13
6012.50
5837.46
5837.46
5923.08
5624.00
6401.42
6401.42
6268.96
5534.17
5666.63
5752.25
6315.79
7050.17
6529.21
6789.92
6571.83
6444.00
7439.08
7221.00
6917.71
6486.63
6917.71
7135.79
7396.04
7741.92
7396.04
7609.50
7349.21
7306.63
8386.88
8476.71
8130.83
7524.29
8041.00
8258.67
8519.33
8907.83
8519.33
8822.63
8690.17
8216.04
9211.08
9211.08




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' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296509&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296509&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296509&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' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.65361082410817
beta0.0529322491866611
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.65361082410817 \tabularnewline
beta & 0.0529322491866611 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296509&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]0.65361082410817[/C][/ROW]
[ROW][C]beta[/C][C]0.0529322491866611[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296509&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296509&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
alpha0.65361082410817
beta0.0529322491866611
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131904.922299.41713141026-394.497131410257
141644.251776.77452130964-132.524521309642
151430.791466.20883186548-35.4188318654815
161430.791416.9337502415613.8562497584396
172250.792209.4835312598441.3064687401638
1823362272.2029061871363.7970938128728
191686.831646.6316742972340.1983257027712
20952.461215.67261060118-263.212610601183
211340.961067.15948413939273.800515860606
221340.961240.10415118778100.85584881222
231644.251344.32796419542299.922035804582
241819.291632.69252170468186.597478295321
251776.671361.37686548707415.293134512931
261340.961493.51819606475-152.558196064748
271559.041237.55331392062321.486686079383
281473.421485.03046383807-11.6104638380698
292207.792315.9688766312-108.178876631205
302032.712329.12725546843-296.417255468427
311340.961487.83303403125-146.873034031248
32824.25850.923081670693-26.6730816706934
331298.331072.63310669722225.69689330278
341430.791182.16913999325248.620860006753
351559.041484.9789510671474.061048932859
361729.461611.70060447514117.759395524858
371383.541397.4644164662-13.9244164661973
381084.921060.3723610543624.547638945641
391213.171098.50253809565114.667461904347
401255.751102.39656603312153.353433966881
412378.632020.39159490652358.238405093476
422378.632302.0229816717176.6070183282864
431729.461798.06887857494-68.6088785749371
441644.251298.38381561885345.866184381146
451904.921908.33116770465-3.41116770464578
461776.671925.45723664367-148.787236643674
472122.581943.698951241178.881048759003
482553.672193.34295864026360.327041359741
492639.292139.7041305913499.585869408698
502032.712217.00659016131-184.296590161314
511861.882208.05737718422-346.177377184215
521686.831966.40166867186-279.571668671858
532856.962699.68718818742157.272811812576
542942.582772.74348647667169.836513523331
552724.52302.98170757379421.518292426207
562942.582307.73345046459634.846549535406
572899.543036.08818922336-136.548189223364
582553.672961.7441956435-408.074195643497
592942.582960.94975266546-18.3697526654641
603373.673174.6309831368199.039016863203
613548.713088.34176479991460.368235200091
623027.792926.29631415639101.493685843606
632681.883081.13112035937-399.25112035937
642942.582859.0832919580483.4967080419583
654065.424024.7794982910340.6405017089664
664411.334065.70751420787345.622485792133
674326.133843.85480443908482.27519556092
684496.54010.14813909159486.351860908411
694453.924417.0404929969736.8795070030337
704022.834410.79528186596-387.965281865956
714757.214607.62758595087149.582414049132
724932.255061.69681393794-129.446813937935
735188.294895.16725832475293.12274167525
744411.334537.6518205943-126.321820594305
754108.044400.40334849102-292.363348491021
764453.924449.407136516654.51286348335452
775278.135579.87109918968-301.741099189677
786012.55522.04922357146490.450776428544
795837.465466.59547993164370.86452006836
805837.465582.02982684304255.430173156965
815923.085694.85581214125228.224187858747
8256245685.69279287713-61.6927928771283
836401.426312.4479833832888.9720166167162
846401.426658.61890440541-257.198904405413
856268.966578.91287826765-309.95287826765
865534.175685.01512770074-150.845127700742
875666.635476.46002990073190.169970099274
885752.255962.6188347804-210.368834780396
896315.796858.04776457266-542.257764572661
907050.176920.60413581405129.565864185947
916529.216578.53900612129-49.329006121292
926789.926355.49791776487434.422082235134
936571.836558.2365027726813.5934972273153
9464446283.28424868908160.71575131092
957439.087090.21123068964348.868769310365
9672217477.94979442168-256.949794421679
976917.717371.74797426465-454.037974264649
986486.636425.4177133086561.2122866913533
996917.716467.55601059731450.153989402688
1007135.796987.86200384758147.927996152417
1017396.048017.87204156591-621.832041565912
1027741.928273.73435251396-531.814352513959
1037396.047427.13899144658-31.098991446579
1047609.57373.93236812307235.567631876934
1057349.217284.4002689700764.809731029929
1067306.637079.13019248745227.49980751255
1078386.887982.43779588641404.442204113589
1088476.718186.12911483016290.580885169837
1098130.838377.95137966831-247.12137966831
1107524.297760.92118863067-236.631188630672
11180417748.38647533972292.613524660278
1128258.678060.85957397609197.81042602391
1138519.338858.38762076955-339.057620769554
1148907.839341.58953750782-433.759537507816
1158519.338747.2526879703-227.9226879703
1168822.638665.6873125161156.942687483899
1178690.178470.81313022177219.35686977823
1188216.048433.45441951389-217.414419513891
1199211.089102.4030627976108.676937202401
1209211.089058.25691913031152.823080869686

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1904.92 & 2299.41713141026 & -394.497131410257 \tabularnewline
14 & 1644.25 & 1776.77452130964 & -132.524521309642 \tabularnewline
15 & 1430.79 & 1466.20883186548 & -35.4188318654815 \tabularnewline
16 & 1430.79 & 1416.93375024156 & 13.8562497584396 \tabularnewline
17 & 2250.79 & 2209.48353125984 & 41.3064687401638 \tabularnewline
18 & 2336 & 2272.20290618713 & 63.7970938128728 \tabularnewline
19 & 1686.83 & 1646.63167429723 & 40.1983257027712 \tabularnewline
20 & 952.46 & 1215.67261060118 & -263.212610601183 \tabularnewline
21 & 1340.96 & 1067.15948413939 & 273.800515860606 \tabularnewline
22 & 1340.96 & 1240.10415118778 & 100.85584881222 \tabularnewline
23 & 1644.25 & 1344.32796419542 & 299.922035804582 \tabularnewline
24 & 1819.29 & 1632.69252170468 & 186.597478295321 \tabularnewline
25 & 1776.67 & 1361.37686548707 & 415.293134512931 \tabularnewline
26 & 1340.96 & 1493.51819606475 & -152.558196064748 \tabularnewline
27 & 1559.04 & 1237.55331392062 & 321.486686079383 \tabularnewline
28 & 1473.42 & 1485.03046383807 & -11.6104638380698 \tabularnewline
29 & 2207.79 & 2315.9688766312 & -108.178876631205 \tabularnewline
30 & 2032.71 & 2329.12725546843 & -296.417255468427 \tabularnewline
31 & 1340.96 & 1487.83303403125 & -146.873034031248 \tabularnewline
32 & 824.25 & 850.923081670693 & -26.6730816706934 \tabularnewline
33 & 1298.33 & 1072.63310669722 & 225.69689330278 \tabularnewline
34 & 1430.79 & 1182.16913999325 & 248.620860006753 \tabularnewline
35 & 1559.04 & 1484.97895106714 & 74.061048932859 \tabularnewline
36 & 1729.46 & 1611.70060447514 & 117.759395524858 \tabularnewline
37 & 1383.54 & 1397.4644164662 & -13.9244164661973 \tabularnewline
38 & 1084.92 & 1060.37236105436 & 24.547638945641 \tabularnewline
39 & 1213.17 & 1098.50253809565 & 114.667461904347 \tabularnewline
40 & 1255.75 & 1102.39656603312 & 153.353433966881 \tabularnewline
41 & 2378.63 & 2020.39159490652 & 358.238405093476 \tabularnewline
42 & 2378.63 & 2302.02298167171 & 76.6070183282864 \tabularnewline
43 & 1729.46 & 1798.06887857494 & -68.6088785749371 \tabularnewline
44 & 1644.25 & 1298.38381561885 & 345.866184381146 \tabularnewline
45 & 1904.92 & 1908.33116770465 & -3.41116770464578 \tabularnewline
46 & 1776.67 & 1925.45723664367 & -148.787236643674 \tabularnewline
47 & 2122.58 & 1943.698951241 & 178.881048759003 \tabularnewline
48 & 2553.67 & 2193.34295864026 & 360.327041359741 \tabularnewline
49 & 2639.29 & 2139.7041305913 & 499.585869408698 \tabularnewline
50 & 2032.71 & 2217.00659016131 & -184.296590161314 \tabularnewline
51 & 1861.88 & 2208.05737718422 & -346.177377184215 \tabularnewline
52 & 1686.83 & 1966.40166867186 & -279.571668671858 \tabularnewline
53 & 2856.96 & 2699.68718818742 & 157.272811812576 \tabularnewline
54 & 2942.58 & 2772.74348647667 & 169.836513523331 \tabularnewline
55 & 2724.5 & 2302.98170757379 & 421.518292426207 \tabularnewline
56 & 2942.58 & 2307.73345046459 & 634.846549535406 \tabularnewline
57 & 2899.54 & 3036.08818922336 & -136.548189223364 \tabularnewline
58 & 2553.67 & 2961.7441956435 & -408.074195643497 \tabularnewline
59 & 2942.58 & 2960.94975266546 & -18.3697526654641 \tabularnewline
60 & 3373.67 & 3174.6309831368 & 199.039016863203 \tabularnewline
61 & 3548.71 & 3088.34176479991 & 460.368235200091 \tabularnewline
62 & 3027.79 & 2926.29631415639 & 101.493685843606 \tabularnewline
63 & 2681.88 & 3081.13112035937 & -399.25112035937 \tabularnewline
64 & 2942.58 & 2859.08329195804 & 83.4967080419583 \tabularnewline
65 & 4065.42 & 4024.77949829103 & 40.6405017089664 \tabularnewline
66 & 4411.33 & 4065.70751420787 & 345.622485792133 \tabularnewline
67 & 4326.13 & 3843.85480443908 & 482.27519556092 \tabularnewline
68 & 4496.5 & 4010.14813909159 & 486.351860908411 \tabularnewline
69 & 4453.92 & 4417.04049299697 & 36.8795070030337 \tabularnewline
70 & 4022.83 & 4410.79528186596 & -387.965281865956 \tabularnewline
71 & 4757.21 & 4607.62758595087 & 149.582414049132 \tabularnewline
72 & 4932.25 & 5061.69681393794 & -129.446813937935 \tabularnewline
73 & 5188.29 & 4895.16725832475 & 293.12274167525 \tabularnewline
74 & 4411.33 & 4537.6518205943 & -126.321820594305 \tabularnewline
75 & 4108.04 & 4400.40334849102 & -292.363348491021 \tabularnewline
76 & 4453.92 & 4449.40713651665 & 4.51286348335452 \tabularnewline
77 & 5278.13 & 5579.87109918968 & -301.741099189677 \tabularnewline
78 & 6012.5 & 5522.04922357146 & 490.450776428544 \tabularnewline
79 & 5837.46 & 5466.59547993164 & 370.86452006836 \tabularnewline
80 & 5837.46 & 5582.02982684304 & 255.430173156965 \tabularnewline
81 & 5923.08 & 5694.85581214125 & 228.224187858747 \tabularnewline
82 & 5624 & 5685.69279287713 & -61.6927928771283 \tabularnewline
83 & 6401.42 & 6312.44798338328 & 88.9720166167162 \tabularnewline
84 & 6401.42 & 6658.61890440541 & -257.198904405413 \tabularnewline
85 & 6268.96 & 6578.91287826765 & -309.95287826765 \tabularnewline
86 & 5534.17 & 5685.01512770074 & -150.845127700742 \tabularnewline
87 & 5666.63 & 5476.46002990073 & 190.169970099274 \tabularnewline
88 & 5752.25 & 5962.6188347804 & -210.368834780396 \tabularnewline
89 & 6315.79 & 6858.04776457266 & -542.257764572661 \tabularnewline
90 & 7050.17 & 6920.60413581405 & 129.565864185947 \tabularnewline
91 & 6529.21 & 6578.53900612129 & -49.329006121292 \tabularnewline
92 & 6789.92 & 6355.49791776487 & 434.422082235134 \tabularnewline
93 & 6571.83 & 6558.23650277268 & 13.5934972273153 \tabularnewline
94 & 6444 & 6283.28424868908 & 160.71575131092 \tabularnewline
95 & 7439.08 & 7090.21123068964 & 348.868769310365 \tabularnewline
96 & 7221 & 7477.94979442168 & -256.949794421679 \tabularnewline
97 & 6917.71 & 7371.74797426465 & -454.037974264649 \tabularnewline
98 & 6486.63 & 6425.41771330865 & 61.2122866913533 \tabularnewline
99 & 6917.71 & 6467.55601059731 & 450.153989402688 \tabularnewline
100 & 7135.79 & 6987.86200384758 & 147.927996152417 \tabularnewline
101 & 7396.04 & 8017.87204156591 & -621.832041565912 \tabularnewline
102 & 7741.92 & 8273.73435251396 & -531.814352513959 \tabularnewline
103 & 7396.04 & 7427.13899144658 & -31.098991446579 \tabularnewline
104 & 7609.5 & 7373.93236812307 & 235.567631876934 \tabularnewline
105 & 7349.21 & 7284.40026897007 & 64.809731029929 \tabularnewline
106 & 7306.63 & 7079.13019248745 & 227.49980751255 \tabularnewline
107 & 8386.88 & 7982.43779588641 & 404.442204113589 \tabularnewline
108 & 8476.71 & 8186.12911483016 & 290.580885169837 \tabularnewline
109 & 8130.83 & 8377.95137966831 & -247.12137966831 \tabularnewline
110 & 7524.29 & 7760.92118863067 & -236.631188630672 \tabularnewline
111 & 8041 & 7748.38647533972 & 292.613524660278 \tabularnewline
112 & 8258.67 & 8060.85957397609 & 197.81042602391 \tabularnewline
113 & 8519.33 & 8858.38762076955 & -339.057620769554 \tabularnewline
114 & 8907.83 & 9341.58953750782 & -433.759537507816 \tabularnewline
115 & 8519.33 & 8747.2526879703 & -227.9226879703 \tabularnewline
116 & 8822.63 & 8665.6873125161 & 156.942687483899 \tabularnewline
117 & 8690.17 & 8470.81313022177 & 219.35686977823 \tabularnewline
118 & 8216.04 & 8433.45441951389 & -217.414419513891 \tabularnewline
119 & 9211.08 & 9102.4030627976 & 108.676937202401 \tabularnewline
120 & 9211.08 & 9058.25691913031 & 152.823080869686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296509&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]1904.92[/C][C]2299.41713141026[/C][C]-394.497131410257[/C][/ROW]
[ROW][C]14[/C][C]1644.25[/C][C]1776.77452130964[/C][C]-132.524521309642[/C][/ROW]
[ROW][C]15[/C][C]1430.79[/C][C]1466.20883186548[/C][C]-35.4188318654815[/C][/ROW]
[ROW][C]16[/C][C]1430.79[/C][C]1416.93375024156[/C][C]13.8562497584396[/C][/ROW]
[ROW][C]17[/C][C]2250.79[/C][C]2209.48353125984[/C][C]41.3064687401638[/C][/ROW]
[ROW][C]18[/C][C]2336[/C][C]2272.20290618713[/C][C]63.7970938128728[/C][/ROW]
[ROW][C]19[/C][C]1686.83[/C][C]1646.63167429723[/C][C]40.1983257027712[/C][/ROW]
[ROW][C]20[/C][C]952.46[/C][C]1215.67261060118[/C][C]-263.212610601183[/C][/ROW]
[ROW][C]21[/C][C]1340.96[/C][C]1067.15948413939[/C][C]273.800515860606[/C][/ROW]
[ROW][C]22[/C][C]1340.96[/C][C]1240.10415118778[/C][C]100.85584881222[/C][/ROW]
[ROW][C]23[/C][C]1644.25[/C][C]1344.32796419542[/C][C]299.922035804582[/C][/ROW]
[ROW][C]24[/C][C]1819.29[/C][C]1632.69252170468[/C][C]186.597478295321[/C][/ROW]
[ROW][C]25[/C][C]1776.67[/C][C]1361.37686548707[/C][C]415.293134512931[/C][/ROW]
[ROW][C]26[/C][C]1340.96[/C][C]1493.51819606475[/C][C]-152.558196064748[/C][/ROW]
[ROW][C]27[/C][C]1559.04[/C][C]1237.55331392062[/C][C]321.486686079383[/C][/ROW]
[ROW][C]28[/C][C]1473.42[/C][C]1485.03046383807[/C][C]-11.6104638380698[/C][/ROW]
[ROW][C]29[/C][C]2207.79[/C][C]2315.9688766312[/C][C]-108.178876631205[/C][/ROW]
[ROW][C]30[/C][C]2032.71[/C][C]2329.12725546843[/C][C]-296.417255468427[/C][/ROW]
[ROW][C]31[/C][C]1340.96[/C][C]1487.83303403125[/C][C]-146.873034031248[/C][/ROW]
[ROW][C]32[/C][C]824.25[/C][C]850.923081670693[/C][C]-26.6730816706934[/C][/ROW]
[ROW][C]33[/C][C]1298.33[/C][C]1072.63310669722[/C][C]225.69689330278[/C][/ROW]
[ROW][C]34[/C][C]1430.79[/C][C]1182.16913999325[/C][C]248.620860006753[/C][/ROW]
[ROW][C]35[/C][C]1559.04[/C][C]1484.97895106714[/C][C]74.061048932859[/C][/ROW]
[ROW][C]36[/C][C]1729.46[/C][C]1611.70060447514[/C][C]117.759395524858[/C][/ROW]
[ROW][C]37[/C][C]1383.54[/C][C]1397.4644164662[/C][C]-13.9244164661973[/C][/ROW]
[ROW][C]38[/C][C]1084.92[/C][C]1060.37236105436[/C][C]24.547638945641[/C][/ROW]
[ROW][C]39[/C][C]1213.17[/C][C]1098.50253809565[/C][C]114.667461904347[/C][/ROW]
[ROW][C]40[/C][C]1255.75[/C][C]1102.39656603312[/C][C]153.353433966881[/C][/ROW]
[ROW][C]41[/C][C]2378.63[/C][C]2020.39159490652[/C][C]358.238405093476[/C][/ROW]
[ROW][C]42[/C][C]2378.63[/C][C]2302.02298167171[/C][C]76.6070183282864[/C][/ROW]
[ROW][C]43[/C][C]1729.46[/C][C]1798.06887857494[/C][C]-68.6088785749371[/C][/ROW]
[ROW][C]44[/C][C]1644.25[/C][C]1298.38381561885[/C][C]345.866184381146[/C][/ROW]
[ROW][C]45[/C][C]1904.92[/C][C]1908.33116770465[/C][C]-3.41116770464578[/C][/ROW]
[ROW][C]46[/C][C]1776.67[/C][C]1925.45723664367[/C][C]-148.787236643674[/C][/ROW]
[ROW][C]47[/C][C]2122.58[/C][C]1943.698951241[/C][C]178.881048759003[/C][/ROW]
[ROW][C]48[/C][C]2553.67[/C][C]2193.34295864026[/C][C]360.327041359741[/C][/ROW]
[ROW][C]49[/C][C]2639.29[/C][C]2139.7041305913[/C][C]499.585869408698[/C][/ROW]
[ROW][C]50[/C][C]2032.71[/C][C]2217.00659016131[/C][C]-184.296590161314[/C][/ROW]
[ROW][C]51[/C][C]1861.88[/C][C]2208.05737718422[/C][C]-346.177377184215[/C][/ROW]
[ROW][C]52[/C][C]1686.83[/C][C]1966.40166867186[/C][C]-279.571668671858[/C][/ROW]
[ROW][C]53[/C][C]2856.96[/C][C]2699.68718818742[/C][C]157.272811812576[/C][/ROW]
[ROW][C]54[/C][C]2942.58[/C][C]2772.74348647667[/C][C]169.836513523331[/C][/ROW]
[ROW][C]55[/C][C]2724.5[/C][C]2302.98170757379[/C][C]421.518292426207[/C][/ROW]
[ROW][C]56[/C][C]2942.58[/C][C]2307.73345046459[/C][C]634.846549535406[/C][/ROW]
[ROW][C]57[/C][C]2899.54[/C][C]3036.08818922336[/C][C]-136.548189223364[/C][/ROW]
[ROW][C]58[/C][C]2553.67[/C][C]2961.7441956435[/C][C]-408.074195643497[/C][/ROW]
[ROW][C]59[/C][C]2942.58[/C][C]2960.94975266546[/C][C]-18.3697526654641[/C][/ROW]
[ROW][C]60[/C][C]3373.67[/C][C]3174.6309831368[/C][C]199.039016863203[/C][/ROW]
[ROW][C]61[/C][C]3548.71[/C][C]3088.34176479991[/C][C]460.368235200091[/C][/ROW]
[ROW][C]62[/C][C]3027.79[/C][C]2926.29631415639[/C][C]101.493685843606[/C][/ROW]
[ROW][C]63[/C][C]2681.88[/C][C]3081.13112035937[/C][C]-399.25112035937[/C][/ROW]
[ROW][C]64[/C][C]2942.58[/C][C]2859.08329195804[/C][C]83.4967080419583[/C][/ROW]
[ROW][C]65[/C][C]4065.42[/C][C]4024.77949829103[/C][C]40.6405017089664[/C][/ROW]
[ROW][C]66[/C][C]4411.33[/C][C]4065.70751420787[/C][C]345.622485792133[/C][/ROW]
[ROW][C]67[/C][C]4326.13[/C][C]3843.85480443908[/C][C]482.27519556092[/C][/ROW]
[ROW][C]68[/C][C]4496.5[/C][C]4010.14813909159[/C][C]486.351860908411[/C][/ROW]
[ROW][C]69[/C][C]4453.92[/C][C]4417.04049299697[/C][C]36.8795070030337[/C][/ROW]
[ROW][C]70[/C][C]4022.83[/C][C]4410.79528186596[/C][C]-387.965281865956[/C][/ROW]
[ROW][C]71[/C][C]4757.21[/C][C]4607.62758595087[/C][C]149.582414049132[/C][/ROW]
[ROW][C]72[/C][C]4932.25[/C][C]5061.69681393794[/C][C]-129.446813937935[/C][/ROW]
[ROW][C]73[/C][C]5188.29[/C][C]4895.16725832475[/C][C]293.12274167525[/C][/ROW]
[ROW][C]74[/C][C]4411.33[/C][C]4537.6518205943[/C][C]-126.321820594305[/C][/ROW]
[ROW][C]75[/C][C]4108.04[/C][C]4400.40334849102[/C][C]-292.363348491021[/C][/ROW]
[ROW][C]76[/C][C]4453.92[/C][C]4449.40713651665[/C][C]4.51286348335452[/C][/ROW]
[ROW][C]77[/C][C]5278.13[/C][C]5579.87109918968[/C][C]-301.741099189677[/C][/ROW]
[ROW][C]78[/C][C]6012.5[/C][C]5522.04922357146[/C][C]490.450776428544[/C][/ROW]
[ROW][C]79[/C][C]5837.46[/C][C]5466.59547993164[/C][C]370.86452006836[/C][/ROW]
[ROW][C]80[/C][C]5837.46[/C][C]5582.02982684304[/C][C]255.430173156965[/C][/ROW]
[ROW][C]81[/C][C]5923.08[/C][C]5694.85581214125[/C][C]228.224187858747[/C][/ROW]
[ROW][C]82[/C][C]5624[/C][C]5685.69279287713[/C][C]-61.6927928771283[/C][/ROW]
[ROW][C]83[/C][C]6401.42[/C][C]6312.44798338328[/C][C]88.9720166167162[/C][/ROW]
[ROW][C]84[/C][C]6401.42[/C][C]6658.61890440541[/C][C]-257.198904405413[/C][/ROW]
[ROW][C]85[/C][C]6268.96[/C][C]6578.91287826765[/C][C]-309.95287826765[/C][/ROW]
[ROW][C]86[/C][C]5534.17[/C][C]5685.01512770074[/C][C]-150.845127700742[/C][/ROW]
[ROW][C]87[/C][C]5666.63[/C][C]5476.46002990073[/C][C]190.169970099274[/C][/ROW]
[ROW][C]88[/C][C]5752.25[/C][C]5962.6188347804[/C][C]-210.368834780396[/C][/ROW]
[ROW][C]89[/C][C]6315.79[/C][C]6858.04776457266[/C][C]-542.257764572661[/C][/ROW]
[ROW][C]90[/C][C]7050.17[/C][C]6920.60413581405[/C][C]129.565864185947[/C][/ROW]
[ROW][C]91[/C][C]6529.21[/C][C]6578.53900612129[/C][C]-49.329006121292[/C][/ROW]
[ROW][C]92[/C][C]6789.92[/C][C]6355.49791776487[/C][C]434.422082235134[/C][/ROW]
[ROW][C]93[/C][C]6571.83[/C][C]6558.23650277268[/C][C]13.5934972273153[/C][/ROW]
[ROW][C]94[/C][C]6444[/C][C]6283.28424868908[/C][C]160.71575131092[/C][/ROW]
[ROW][C]95[/C][C]7439.08[/C][C]7090.21123068964[/C][C]348.868769310365[/C][/ROW]
[ROW][C]96[/C][C]7221[/C][C]7477.94979442168[/C][C]-256.949794421679[/C][/ROW]
[ROW][C]97[/C][C]6917.71[/C][C]7371.74797426465[/C][C]-454.037974264649[/C][/ROW]
[ROW][C]98[/C][C]6486.63[/C][C]6425.41771330865[/C][C]61.2122866913533[/C][/ROW]
[ROW][C]99[/C][C]6917.71[/C][C]6467.55601059731[/C][C]450.153989402688[/C][/ROW]
[ROW][C]100[/C][C]7135.79[/C][C]6987.86200384758[/C][C]147.927996152417[/C][/ROW]
[ROW][C]101[/C][C]7396.04[/C][C]8017.87204156591[/C][C]-621.832041565912[/C][/ROW]
[ROW][C]102[/C][C]7741.92[/C][C]8273.73435251396[/C][C]-531.814352513959[/C][/ROW]
[ROW][C]103[/C][C]7396.04[/C][C]7427.13899144658[/C][C]-31.098991446579[/C][/ROW]
[ROW][C]104[/C][C]7609.5[/C][C]7373.93236812307[/C][C]235.567631876934[/C][/ROW]
[ROW][C]105[/C][C]7349.21[/C][C]7284.40026897007[/C][C]64.809731029929[/C][/ROW]
[ROW][C]106[/C][C]7306.63[/C][C]7079.13019248745[/C][C]227.49980751255[/C][/ROW]
[ROW][C]107[/C][C]8386.88[/C][C]7982.43779588641[/C][C]404.442204113589[/C][/ROW]
[ROW][C]108[/C][C]8476.71[/C][C]8186.12911483016[/C][C]290.580885169837[/C][/ROW]
[ROW][C]109[/C][C]8130.83[/C][C]8377.95137966831[/C][C]-247.12137966831[/C][/ROW]
[ROW][C]110[/C][C]7524.29[/C][C]7760.92118863067[/C][C]-236.631188630672[/C][/ROW]
[ROW][C]111[/C][C]8041[/C][C]7748.38647533972[/C][C]292.613524660278[/C][/ROW]
[ROW][C]112[/C][C]8258.67[/C][C]8060.85957397609[/C][C]197.81042602391[/C][/ROW]
[ROW][C]113[/C][C]8519.33[/C][C]8858.38762076955[/C][C]-339.057620769554[/C][/ROW]
[ROW][C]114[/C][C]8907.83[/C][C]9341.58953750782[/C][C]-433.759537507816[/C][/ROW]
[ROW][C]115[/C][C]8519.33[/C][C]8747.2526879703[/C][C]-227.9226879703[/C][/ROW]
[ROW][C]116[/C][C]8822.63[/C][C]8665.6873125161[/C][C]156.942687483899[/C][/ROW]
[ROW][C]117[/C][C]8690.17[/C][C]8470.81313022177[/C][C]219.35686977823[/C][/ROW]
[ROW][C]118[/C][C]8216.04[/C][C]8433.45441951389[/C][C]-217.414419513891[/C][/ROW]
[ROW][C]119[/C][C]9211.08[/C][C]9102.4030627976[/C][C]108.676937202401[/C][/ROW]
[ROW][C]120[/C][C]9211.08[/C][C]9058.25691913031[/C][C]152.823080869686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296509&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296509&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
131904.922299.41713141026-394.497131410257
141644.251776.77452130964-132.524521309642
151430.791466.20883186548-35.4188318654815
161430.791416.9337502415613.8562497584396
172250.792209.4835312598441.3064687401638
1823362272.2029061871363.7970938128728
191686.831646.6316742972340.1983257027712
20952.461215.67261060118-263.212610601183
211340.961067.15948413939273.800515860606
221340.961240.10415118778100.85584881222
231644.251344.32796419542299.922035804582
241819.291632.69252170468186.597478295321
251776.671361.37686548707415.293134512931
261340.961493.51819606475-152.558196064748
271559.041237.55331392062321.486686079383
281473.421485.03046383807-11.6104638380698
292207.792315.9688766312-108.178876631205
302032.712329.12725546843-296.417255468427
311340.961487.83303403125-146.873034031248
32824.25850.923081670693-26.6730816706934
331298.331072.63310669722225.69689330278
341430.791182.16913999325248.620860006753
351559.041484.9789510671474.061048932859
361729.461611.70060447514117.759395524858
371383.541397.4644164662-13.9244164661973
381084.921060.3723610543624.547638945641
391213.171098.50253809565114.667461904347
401255.751102.39656603312153.353433966881
412378.632020.39159490652358.238405093476
422378.632302.0229816717176.6070183282864
431729.461798.06887857494-68.6088785749371
441644.251298.38381561885345.866184381146
451904.921908.33116770465-3.41116770464578
461776.671925.45723664367-148.787236643674
472122.581943.698951241178.881048759003
482553.672193.34295864026360.327041359741
492639.292139.7041305913499.585869408698
502032.712217.00659016131-184.296590161314
511861.882208.05737718422-346.177377184215
521686.831966.40166867186-279.571668671858
532856.962699.68718818742157.272811812576
542942.582772.74348647667169.836513523331
552724.52302.98170757379421.518292426207
562942.582307.73345046459634.846549535406
572899.543036.08818922336-136.548189223364
582553.672961.7441956435-408.074195643497
592942.582960.94975266546-18.3697526654641
603373.673174.6309831368199.039016863203
613548.713088.34176479991460.368235200091
623027.792926.29631415639101.493685843606
632681.883081.13112035937-399.25112035937
642942.582859.0832919580483.4967080419583
654065.424024.7794982910340.6405017089664
664411.334065.70751420787345.622485792133
674326.133843.85480443908482.27519556092
684496.54010.14813909159486.351860908411
694453.924417.0404929969736.8795070030337
704022.834410.79528186596-387.965281865956
714757.214607.62758595087149.582414049132
724932.255061.69681393794-129.446813937935
735188.294895.16725832475293.12274167525
744411.334537.6518205943-126.321820594305
754108.044400.40334849102-292.363348491021
764453.924449.407136516654.51286348335452
775278.135579.87109918968-301.741099189677
786012.55522.04922357146490.450776428544
795837.465466.59547993164370.86452006836
805837.465582.02982684304255.430173156965
815923.085694.85581214125228.224187858747
8256245685.69279287713-61.6927928771283
836401.426312.4479833832888.9720166167162
846401.426658.61890440541-257.198904405413
856268.966578.91287826765-309.95287826765
865534.175685.01512770074-150.845127700742
875666.635476.46002990073190.169970099274
885752.255962.6188347804-210.368834780396
896315.796858.04776457266-542.257764572661
907050.176920.60413581405129.565864185947
916529.216578.53900612129-49.329006121292
926789.926355.49791776487434.422082235134
936571.836558.2365027726813.5934972273153
9464446283.28424868908160.71575131092
957439.087090.21123068964348.868769310365
9672217477.94979442168-256.949794421679
976917.717371.74797426465-454.037974264649
986486.636425.4177133086561.2122866913533
996917.716467.55601059731450.153989402688
1007135.796987.86200384758147.927996152417
1017396.048017.87204156591-621.832041565912
1027741.928273.73435251396-531.814352513959
1037396.047427.13899144658-31.098991446579
1047609.57373.93236812307235.567631876934
1057349.217284.4002689700764.809731029929
1067306.637079.13019248745227.49980751255
1078386.887982.43779588641404.442204113589
1088476.718186.12911483016290.580885169837
1098130.838377.95137966831-247.12137966831
1107524.297760.92118863067-236.631188630672
11180417748.38647533972292.613524660278
1128258.678060.85957397609197.81042602391
1138519.338858.38762076955-339.057620769554
1148907.839341.58953750782-433.759537507816
1158519.338747.2526879703-227.9226879703
1168822.638665.6873125161156.942687483899
1178690.178470.81313022177219.35686977823
1188216.048433.45441951389-217.414419513891
1199211.089102.4030627976108.676937202401
1209211.089058.25691913031152.823080869686







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1218953.93717395928424.263869408419483.61047850999
1228490.763787412527847.776580627679133.75099419738
1238813.107078426388064.770880049439561.44327680334
1248888.251124123728039.163975863549737.3382723839
1259350.444271010658403.3804245055910297.5081175157
12610014.10602310588970.7357530193411057.4762931923
1279781.237400539818642.512068679310919.9627324003
1289996.502064732058762.8801069312211230.1240225329
1299729.782383356198401.3711506451311058.1936160672
1309399.282034733337975.9314773004410822.6325921662
13110332.3367521728813.7038222402311850.9696821038
13210237.73716637978623.3315403275611852.1427924319

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 8953.9371739592 & 8424.26386940841 & 9483.61047850999 \tabularnewline
122 & 8490.76378741252 & 7847.77658062767 & 9133.75099419738 \tabularnewline
123 & 8813.10707842638 & 8064.77088004943 & 9561.44327680334 \tabularnewline
124 & 8888.25112412372 & 8039.16397586354 & 9737.3382723839 \tabularnewline
125 & 9350.44427101065 & 8403.38042450559 & 10297.5081175157 \tabularnewline
126 & 10014.1060231058 & 8970.73575301934 & 11057.4762931923 \tabularnewline
127 & 9781.23740053981 & 8642.5120686793 & 10919.9627324003 \tabularnewline
128 & 9996.50206473205 & 8762.88010693122 & 11230.1240225329 \tabularnewline
129 & 9729.78238335619 & 8401.37115064513 & 11058.1936160672 \tabularnewline
130 & 9399.28203473333 & 7975.93147730044 & 10822.6325921662 \tabularnewline
131 & 10332.336752172 & 8813.70382224023 & 11850.9696821038 \tabularnewline
132 & 10237.7371663797 & 8623.33154032756 & 11852.1427924319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296509&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]121[/C][C]8953.9371739592[/C][C]8424.26386940841[/C][C]9483.61047850999[/C][/ROW]
[ROW][C]122[/C][C]8490.76378741252[/C][C]7847.77658062767[/C][C]9133.75099419738[/C][/ROW]
[ROW][C]123[/C][C]8813.10707842638[/C][C]8064.77088004943[/C][C]9561.44327680334[/C][/ROW]
[ROW][C]124[/C][C]8888.25112412372[/C][C]8039.16397586354[/C][C]9737.3382723839[/C][/ROW]
[ROW][C]125[/C][C]9350.44427101065[/C][C]8403.38042450559[/C][C]10297.5081175157[/C][/ROW]
[ROW][C]126[/C][C]10014.1060231058[/C][C]8970.73575301934[/C][C]11057.4762931923[/C][/ROW]
[ROW][C]127[/C][C]9781.23740053981[/C][C]8642.5120686793[/C][C]10919.9627324003[/C][/ROW]
[ROW][C]128[/C][C]9996.50206473205[/C][C]8762.88010693122[/C][C]11230.1240225329[/C][/ROW]
[ROW][C]129[/C][C]9729.78238335619[/C][C]8401.37115064513[/C][C]11058.1936160672[/C][/ROW]
[ROW][C]130[/C][C]9399.28203473333[/C][C]7975.93147730044[/C][C]10822.6325921662[/C][/ROW]
[ROW][C]131[/C][C]10332.336752172[/C][C]8813.70382224023[/C][C]11850.9696821038[/C][/ROW]
[ROW][C]132[/C][C]10237.7371663797[/C][C]8623.33154032756[/C][C]11852.1427924319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296509&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296509&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
1218953.93717395928424.263869408419483.61047850999
1228490.763787412527847.776580627679133.75099419738
1238813.107078426388064.770880049439561.44327680334
1248888.251124123728039.163975863549737.3382723839
1259350.444271010658403.3804245055910297.5081175157
12610014.10602310588970.7357530193411057.4762931923
1279781.237400539818642.512068679310919.9627324003
1289996.502064732058762.8801069312211230.1240225329
1299729.782383356198401.3711506451311058.1936160672
1309399.282034733337975.9314773004410822.6325921662
13110332.3367521728813.7038222402311850.9696821038
13210237.73716637978623.3315403275611852.1427924319



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