Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 May 2010 10:47:09 +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/May/28/t1275043767hhjzhin6yil5neh.htm/, Retrieved Sun, 28 Apr 2024 13:41:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76625, Retrieved Sun, 28 Apr 2024 13:41:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact194
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-05-28 10:47:09] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
81.28
69.39
67.63
51.25
103.97
133.83
162.37
172.91
163.01
151.50
111.73
88.58
74.29
63.98
61.18
76.48
107.98
124.97
145.57
140.20
143.84
138.80
104.06
74.70
60.18
55.16
35.62
56.18
85.44
114.08
133.64
67.14
95.58
89.37
75.24
69.18
54.49
57.50
62.16
76.67
110.04
127.38
156.47
167.56
153.54
124.08
100.97
79.17
68.13
61.77
54.31
60.30
84.18
104.05
114.66
105.55
96.61
70.94
63.91
58.61
44.53
49.58
57.39
76.76
104.57
125.41
143.11
136.35
135.15
131.70
96.87
70.63
66.29
63.49
62.97
66.43
101.49
127.69
133.21
158.72
148.61
134.31
100.99
75.16
59.74
52.87
52.07
57.38
79.43
101.40
120.19
134.38
135.97
113.83
84.38
70.28
65.96
56.36
49.57
68.33
90.32
117.06
134.69
131.67
129.25
118.77
88.44
76.79
75.28
73.89
76.24
88.58
105.83
115.84
127.76
131.75
119.63
93.38
75.55
51.79




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76625&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76625&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76625&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.74849268925821
beta0
gamma0.105416678642104

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.74849268925821 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.105416678642104 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76625&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]0.74849268925821[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.105416678642104[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76625&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76625&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
alpha0.74849268925821
beta0
gamma0.105416678642104







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1374.2973.94036110992980.349638890070239
1463.9864.6912005135862-0.711200513586213
1561.1862.1791200456466-0.999120045646642
1676.4877.2457571681103-0.765757168110298
17107.98108.403843873499-0.423843873499322
18124.97125.327597717670-0.357597717670401
19145.57150.560664175104-4.99066417510409
20140.2155.995349759207-15.7953497592069
21143.84135.4959705829618.34402941703857
22138.8129.8738282842238.92617171577743
23104.0698.94153926662725.11846073337283
2474.781.0765682372002-6.37656823720023
2560.1864.1470623862881-3.96706238628814
2655.1653.24261328706181.91738671293820
2735.6252.924864229907-17.3048642299070
2856.1850.09589687194596.08410312805406
2985.4477.07443901351758.36556098648252
30114.0896.441063137869417.6389368621306
31133.64131.7676745315781.87232546842216
3267.14141.103337539617-73.963337539617
3395.5880.52966211061215.0503378893880
3489.3783.78936214151265.58063785848745
3575.2463.464087366812211.7759126331878
3669.1856.655976711052812.5240232889472
3754.4955.4764753113273-0.98647531132729
3857.547.72248156231759.77751843768252
3962.1652.61814783501139.54185216498865
4076.6776.2462334895180.423766510482011
41110.04108.2326433203021.80735667969819
42127.38127.2817841204410.098215879559362
43156.47152.6179464904123.85205350958793
44167.56161.1136573854026.44634261459765
45153.54161.200553578699-7.66055357869945
46124.08142.181983996835-18.1019839968354
47100.9793.36598413207647.60401586792356
4879.1777.90194808095741.26805191904263
4968.1365.97224069646072.15775930353934
5061.7759.32677807232772.44322192767229
5154.3158.4775322174813-4.16753221748134
5260.370.3034402120837-10.0034402120837
5384.1888.6959212452881-4.51592124528811
54104.0598.86613505456245.18386494543761
55114.66123.010550881149-8.35055088114902
56105.55120.756598292350-15.2065982923496
5796.61105.652630103138-9.0426301031379
5870.9489.8723850666105-18.9323850666105
5963.9154.9807824387698.92921756123096
6058.6148.208997429279110.4010025707209
6144.5346.7339612442915-2.2039612442915
6249.5839.446157885526810.1338421144732
6357.3944.743587077254212.6464129227458
6476.7668.68147478940878.0785252105913
65104.57105.953836131095-1.38383613109522
66125.41122.1093661094653.30063389053487
67143.11148.881218725698-5.77121872569847
68136.35149.493664080602-13.1436640806019
69135.15135.362769212441-0.212769212440804
70131.7122.7108945721958.9891054278049
7196.8795.50272022166241.36727977833762
7270.6375.8540139476447-5.22401394764471
7366.2959.80299192209726.48700807790281
7463.4957.14872459848076.34127540151931
7562.9759.03392619194023.93607380805975
7666.4378.3361487778237-11.9061487778237
77101.4998.06567999993673.4243200000633
78127.69117.20654006476710.4834599352330
79133.21149.187182864173-15.9771828641726
80158.72141.65418145544317.0658185445569
81148.61150.160184673231-1.55018467323075
82134.31135.583012920392-1.27301292039161
83100.9999.2140309339171.77596906608306
8475.1678.8518713111839-3.69187131118389
8559.7463.5664037170366-3.82640371703663
8652.8753.6288643023088-0.758864302308758
8752.0750.49856124449841.57143875550164
8857.3864.8213137810088-7.44131378100882
8979.4384.0520226134744-4.62202261347444
90101.493.82539914053787.57460085946222
91120.19117.8605979718832.32940202811672
92134.38124.07467189246310.3053281075366
93135.97127.5837739745028.3862260254984
94113.83121.715057179198-7.88505717919814
9584.3885.3111441316457-0.931144131645723
9670.2866.15563473574614.12436526425391
9765.9657.78385757223818.17614242776192
9856.3656.5526307231324-0.192630723132424
9949.5753.7732891473396-4.20328914733956
10068.3363.23422889150955.09577110849053
10190.3295.3816340095591-5.06163400955913
102117.06107.1265080983029.93349190169766
103134.69135.654762487717-0.96476248771711
104131.67140.328159021533-8.65815902153287
105129.25129.538107198813-0.288107198813236
106118.77117.1483230534721.62167694652797
10788.4487.3376132561331.10238674386690
10876.7969.0823311573937.70766884260705
10975.2862.614302438052512.6656975619475
11073.8963.63105771895110.258942281049
11176.2467.93939058368778.30060941631234
11288.5893.2425600715202-4.66256007152019
113105.83127.476367216397-21.6463672163974
114115.84130.818857639880-14.9788576398797
115127.76141.319582691019-13.5595826910191
116131.75136.178176242322-4.42817624232239
117119.63128.793420868578-9.1634208685779
11893.38110.449148843292-17.0691488432919
11975.5571.94705791838333.6029420816167
12051.7958.5446657421842-6.75466574218419

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 74.29 & 73.9403611099298 & 0.349638890070239 \tabularnewline
14 & 63.98 & 64.6912005135862 & -0.711200513586213 \tabularnewline
15 & 61.18 & 62.1791200456466 & -0.999120045646642 \tabularnewline
16 & 76.48 & 77.2457571681103 & -0.765757168110298 \tabularnewline
17 & 107.98 & 108.403843873499 & -0.423843873499322 \tabularnewline
18 & 124.97 & 125.327597717670 & -0.357597717670401 \tabularnewline
19 & 145.57 & 150.560664175104 & -4.99066417510409 \tabularnewline
20 & 140.2 & 155.995349759207 & -15.7953497592069 \tabularnewline
21 & 143.84 & 135.495970582961 & 8.34402941703857 \tabularnewline
22 & 138.8 & 129.873828284223 & 8.92617171577743 \tabularnewline
23 & 104.06 & 98.9415392666272 & 5.11846073337283 \tabularnewline
24 & 74.7 & 81.0765682372002 & -6.37656823720023 \tabularnewline
25 & 60.18 & 64.1470623862881 & -3.96706238628814 \tabularnewline
26 & 55.16 & 53.2426132870618 & 1.91738671293820 \tabularnewline
27 & 35.62 & 52.924864229907 & -17.3048642299070 \tabularnewline
28 & 56.18 & 50.0958968719459 & 6.08410312805406 \tabularnewline
29 & 85.44 & 77.0744390135175 & 8.36556098648252 \tabularnewline
30 & 114.08 & 96.4410631378694 & 17.6389368621306 \tabularnewline
31 & 133.64 & 131.767674531578 & 1.87232546842216 \tabularnewline
32 & 67.14 & 141.103337539617 & -73.963337539617 \tabularnewline
33 & 95.58 & 80.529662110612 & 15.0503378893880 \tabularnewline
34 & 89.37 & 83.7893621415126 & 5.58063785848745 \tabularnewline
35 & 75.24 & 63.4640873668122 & 11.7759126331878 \tabularnewline
36 & 69.18 & 56.6559767110528 & 12.5240232889472 \tabularnewline
37 & 54.49 & 55.4764753113273 & -0.98647531132729 \tabularnewline
38 & 57.5 & 47.7224815623175 & 9.77751843768252 \tabularnewline
39 & 62.16 & 52.6181478350113 & 9.54185216498865 \tabularnewline
40 & 76.67 & 76.246233489518 & 0.423766510482011 \tabularnewline
41 & 110.04 & 108.232643320302 & 1.80735667969819 \tabularnewline
42 & 127.38 & 127.281784120441 & 0.098215879559362 \tabularnewline
43 & 156.47 & 152.617946490412 & 3.85205350958793 \tabularnewline
44 & 167.56 & 161.113657385402 & 6.44634261459765 \tabularnewline
45 & 153.54 & 161.200553578699 & -7.66055357869945 \tabularnewline
46 & 124.08 & 142.181983996835 & -18.1019839968354 \tabularnewline
47 & 100.97 & 93.3659841320764 & 7.60401586792356 \tabularnewline
48 & 79.17 & 77.9019480809574 & 1.26805191904263 \tabularnewline
49 & 68.13 & 65.9722406964607 & 2.15775930353934 \tabularnewline
50 & 61.77 & 59.3267780723277 & 2.44322192767229 \tabularnewline
51 & 54.31 & 58.4775322174813 & -4.16753221748134 \tabularnewline
52 & 60.3 & 70.3034402120837 & -10.0034402120837 \tabularnewline
53 & 84.18 & 88.6959212452881 & -4.51592124528811 \tabularnewline
54 & 104.05 & 98.8661350545624 & 5.18386494543761 \tabularnewline
55 & 114.66 & 123.010550881149 & -8.35055088114902 \tabularnewline
56 & 105.55 & 120.756598292350 & -15.2065982923496 \tabularnewline
57 & 96.61 & 105.652630103138 & -9.0426301031379 \tabularnewline
58 & 70.94 & 89.8723850666105 & -18.9323850666105 \tabularnewline
59 & 63.91 & 54.980782438769 & 8.92921756123096 \tabularnewline
60 & 58.61 & 48.2089974292791 & 10.4010025707209 \tabularnewline
61 & 44.53 & 46.7339612442915 & -2.2039612442915 \tabularnewline
62 & 49.58 & 39.4461578855268 & 10.1338421144732 \tabularnewline
63 & 57.39 & 44.7435870772542 & 12.6464129227458 \tabularnewline
64 & 76.76 & 68.6814747894087 & 8.0785252105913 \tabularnewline
65 & 104.57 & 105.953836131095 & -1.38383613109522 \tabularnewline
66 & 125.41 & 122.109366109465 & 3.30063389053487 \tabularnewline
67 & 143.11 & 148.881218725698 & -5.77121872569847 \tabularnewline
68 & 136.35 & 149.493664080602 & -13.1436640806019 \tabularnewline
69 & 135.15 & 135.362769212441 & -0.212769212440804 \tabularnewline
70 & 131.7 & 122.710894572195 & 8.9891054278049 \tabularnewline
71 & 96.87 & 95.5027202216624 & 1.36727977833762 \tabularnewline
72 & 70.63 & 75.8540139476447 & -5.22401394764471 \tabularnewline
73 & 66.29 & 59.8029919220972 & 6.48700807790281 \tabularnewline
74 & 63.49 & 57.1487245984807 & 6.34127540151931 \tabularnewline
75 & 62.97 & 59.0339261919402 & 3.93607380805975 \tabularnewline
76 & 66.43 & 78.3361487778237 & -11.9061487778237 \tabularnewline
77 & 101.49 & 98.0656799999367 & 3.4243200000633 \tabularnewline
78 & 127.69 & 117.206540064767 & 10.4834599352330 \tabularnewline
79 & 133.21 & 149.187182864173 & -15.9771828641726 \tabularnewline
80 & 158.72 & 141.654181455443 & 17.0658185445569 \tabularnewline
81 & 148.61 & 150.160184673231 & -1.55018467323075 \tabularnewline
82 & 134.31 & 135.583012920392 & -1.27301292039161 \tabularnewline
83 & 100.99 & 99.214030933917 & 1.77596906608306 \tabularnewline
84 & 75.16 & 78.8518713111839 & -3.69187131118389 \tabularnewline
85 & 59.74 & 63.5664037170366 & -3.82640371703663 \tabularnewline
86 & 52.87 & 53.6288643023088 & -0.758864302308758 \tabularnewline
87 & 52.07 & 50.4985612444984 & 1.57143875550164 \tabularnewline
88 & 57.38 & 64.8213137810088 & -7.44131378100882 \tabularnewline
89 & 79.43 & 84.0520226134744 & -4.62202261347444 \tabularnewline
90 & 101.4 & 93.8253991405378 & 7.57460085946222 \tabularnewline
91 & 120.19 & 117.860597971883 & 2.32940202811672 \tabularnewline
92 & 134.38 & 124.074671892463 & 10.3053281075366 \tabularnewline
93 & 135.97 & 127.583773974502 & 8.3862260254984 \tabularnewline
94 & 113.83 & 121.715057179198 & -7.88505717919814 \tabularnewline
95 & 84.38 & 85.3111441316457 & -0.931144131645723 \tabularnewline
96 & 70.28 & 66.1556347357461 & 4.12436526425391 \tabularnewline
97 & 65.96 & 57.7838575722381 & 8.17614242776192 \tabularnewline
98 & 56.36 & 56.5526307231324 & -0.192630723132424 \tabularnewline
99 & 49.57 & 53.7732891473396 & -4.20328914733956 \tabularnewline
100 & 68.33 & 63.2342288915095 & 5.09577110849053 \tabularnewline
101 & 90.32 & 95.3816340095591 & -5.06163400955913 \tabularnewline
102 & 117.06 & 107.126508098302 & 9.93349190169766 \tabularnewline
103 & 134.69 & 135.654762487717 & -0.96476248771711 \tabularnewline
104 & 131.67 & 140.328159021533 & -8.65815902153287 \tabularnewline
105 & 129.25 & 129.538107198813 & -0.288107198813236 \tabularnewline
106 & 118.77 & 117.148323053472 & 1.62167694652797 \tabularnewline
107 & 88.44 & 87.337613256133 & 1.10238674386690 \tabularnewline
108 & 76.79 & 69.082331157393 & 7.70766884260705 \tabularnewline
109 & 75.28 & 62.6143024380525 & 12.6656975619475 \tabularnewline
110 & 73.89 & 63.631057718951 & 10.258942281049 \tabularnewline
111 & 76.24 & 67.9393905836877 & 8.30060941631234 \tabularnewline
112 & 88.58 & 93.2425600715202 & -4.66256007152019 \tabularnewline
113 & 105.83 & 127.476367216397 & -21.6463672163974 \tabularnewline
114 & 115.84 & 130.818857639880 & -14.9788576398797 \tabularnewline
115 & 127.76 & 141.319582691019 & -13.5595826910191 \tabularnewline
116 & 131.75 & 136.178176242322 & -4.42817624232239 \tabularnewline
117 & 119.63 & 128.793420868578 & -9.1634208685779 \tabularnewline
118 & 93.38 & 110.449148843292 & -17.0691488432919 \tabularnewline
119 & 75.55 & 71.9470579183833 & 3.6029420816167 \tabularnewline
120 & 51.79 & 58.5446657421842 & -6.75466574218419 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76625&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]74.29[/C][C]73.9403611099298[/C][C]0.349638890070239[/C][/ROW]
[ROW][C]14[/C][C]63.98[/C][C]64.6912005135862[/C][C]-0.711200513586213[/C][/ROW]
[ROW][C]15[/C][C]61.18[/C][C]62.1791200456466[/C][C]-0.999120045646642[/C][/ROW]
[ROW][C]16[/C][C]76.48[/C][C]77.2457571681103[/C][C]-0.765757168110298[/C][/ROW]
[ROW][C]17[/C][C]107.98[/C][C]108.403843873499[/C][C]-0.423843873499322[/C][/ROW]
[ROW][C]18[/C][C]124.97[/C][C]125.327597717670[/C][C]-0.357597717670401[/C][/ROW]
[ROW][C]19[/C][C]145.57[/C][C]150.560664175104[/C][C]-4.99066417510409[/C][/ROW]
[ROW][C]20[/C][C]140.2[/C][C]155.995349759207[/C][C]-15.7953497592069[/C][/ROW]
[ROW][C]21[/C][C]143.84[/C][C]135.495970582961[/C][C]8.34402941703857[/C][/ROW]
[ROW][C]22[/C][C]138.8[/C][C]129.873828284223[/C][C]8.92617171577743[/C][/ROW]
[ROW][C]23[/C][C]104.06[/C][C]98.9415392666272[/C][C]5.11846073337283[/C][/ROW]
[ROW][C]24[/C][C]74.7[/C][C]81.0765682372002[/C][C]-6.37656823720023[/C][/ROW]
[ROW][C]25[/C][C]60.18[/C][C]64.1470623862881[/C][C]-3.96706238628814[/C][/ROW]
[ROW][C]26[/C][C]55.16[/C][C]53.2426132870618[/C][C]1.91738671293820[/C][/ROW]
[ROW][C]27[/C][C]35.62[/C][C]52.924864229907[/C][C]-17.3048642299070[/C][/ROW]
[ROW][C]28[/C][C]56.18[/C][C]50.0958968719459[/C][C]6.08410312805406[/C][/ROW]
[ROW][C]29[/C][C]85.44[/C][C]77.0744390135175[/C][C]8.36556098648252[/C][/ROW]
[ROW][C]30[/C][C]114.08[/C][C]96.4410631378694[/C][C]17.6389368621306[/C][/ROW]
[ROW][C]31[/C][C]133.64[/C][C]131.767674531578[/C][C]1.87232546842216[/C][/ROW]
[ROW][C]32[/C][C]67.14[/C][C]141.103337539617[/C][C]-73.963337539617[/C][/ROW]
[ROW][C]33[/C][C]95.58[/C][C]80.529662110612[/C][C]15.0503378893880[/C][/ROW]
[ROW][C]34[/C][C]89.37[/C][C]83.7893621415126[/C][C]5.58063785848745[/C][/ROW]
[ROW][C]35[/C][C]75.24[/C][C]63.4640873668122[/C][C]11.7759126331878[/C][/ROW]
[ROW][C]36[/C][C]69.18[/C][C]56.6559767110528[/C][C]12.5240232889472[/C][/ROW]
[ROW][C]37[/C][C]54.49[/C][C]55.4764753113273[/C][C]-0.98647531132729[/C][/ROW]
[ROW][C]38[/C][C]57.5[/C][C]47.7224815623175[/C][C]9.77751843768252[/C][/ROW]
[ROW][C]39[/C][C]62.16[/C][C]52.6181478350113[/C][C]9.54185216498865[/C][/ROW]
[ROW][C]40[/C][C]76.67[/C][C]76.246233489518[/C][C]0.423766510482011[/C][/ROW]
[ROW][C]41[/C][C]110.04[/C][C]108.232643320302[/C][C]1.80735667969819[/C][/ROW]
[ROW][C]42[/C][C]127.38[/C][C]127.281784120441[/C][C]0.098215879559362[/C][/ROW]
[ROW][C]43[/C][C]156.47[/C][C]152.617946490412[/C][C]3.85205350958793[/C][/ROW]
[ROW][C]44[/C][C]167.56[/C][C]161.113657385402[/C][C]6.44634261459765[/C][/ROW]
[ROW][C]45[/C][C]153.54[/C][C]161.200553578699[/C][C]-7.66055357869945[/C][/ROW]
[ROW][C]46[/C][C]124.08[/C][C]142.181983996835[/C][C]-18.1019839968354[/C][/ROW]
[ROW][C]47[/C][C]100.97[/C][C]93.3659841320764[/C][C]7.60401586792356[/C][/ROW]
[ROW][C]48[/C][C]79.17[/C][C]77.9019480809574[/C][C]1.26805191904263[/C][/ROW]
[ROW][C]49[/C][C]68.13[/C][C]65.9722406964607[/C][C]2.15775930353934[/C][/ROW]
[ROW][C]50[/C][C]61.77[/C][C]59.3267780723277[/C][C]2.44322192767229[/C][/ROW]
[ROW][C]51[/C][C]54.31[/C][C]58.4775322174813[/C][C]-4.16753221748134[/C][/ROW]
[ROW][C]52[/C][C]60.3[/C][C]70.3034402120837[/C][C]-10.0034402120837[/C][/ROW]
[ROW][C]53[/C][C]84.18[/C][C]88.6959212452881[/C][C]-4.51592124528811[/C][/ROW]
[ROW][C]54[/C][C]104.05[/C][C]98.8661350545624[/C][C]5.18386494543761[/C][/ROW]
[ROW][C]55[/C][C]114.66[/C][C]123.010550881149[/C][C]-8.35055088114902[/C][/ROW]
[ROW][C]56[/C][C]105.55[/C][C]120.756598292350[/C][C]-15.2065982923496[/C][/ROW]
[ROW][C]57[/C][C]96.61[/C][C]105.652630103138[/C][C]-9.0426301031379[/C][/ROW]
[ROW][C]58[/C][C]70.94[/C][C]89.8723850666105[/C][C]-18.9323850666105[/C][/ROW]
[ROW][C]59[/C][C]63.91[/C][C]54.980782438769[/C][C]8.92921756123096[/C][/ROW]
[ROW][C]60[/C][C]58.61[/C][C]48.2089974292791[/C][C]10.4010025707209[/C][/ROW]
[ROW][C]61[/C][C]44.53[/C][C]46.7339612442915[/C][C]-2.2039612442915[/C][/ROW]
[ROW][C]62[/C][C]49.58[/C][C]39.4461578855268[/C][C]10.1338421144732[/C][/ROW]
[ROW][C]63[/C][C]57.39[/C][C]44.7435870772542[/C][C]12.6464129227458[/C][/ROW]
[ROW][C]64[/C][C]76.76[/C][C]68.6814747894087[/C][C]8.0785252105913[/C][/ROW]
[ROW][C]65[/C][C]104.57[/C][C]105.953836131095[/C][C]-1.38383613109522[/C][/ROW]
[ROW][C]66[/C][C]125.41[/C][C]122.109366109465[/C][C]3.30063389053487[/C][/ROW]
[ROW][C]67[/C][C]143.11[/C][C]148.881218725698[/C][C]-5.77121872569847[/C][/ROW]
[ROW][C]68[/C][C]136.35[/C][C]149.493664080602[/C][C]-13.1436640806019[/C][/ROW]
[ROW][C]69[/C][C]135.15[/C][C]135.362769212441[/C][C]-0.212769212440804[/C][/ROW]
[ROW][C]70[/C][C]131.7[/C][C]122.710894572195[/C][C]8.9891054278049[/C][/ROW]
[ROW][C]71[/C][C]96.87[/C][C]95.5027202216624[/C][C]1.36727977833762[/C][/ROW]
[ROW][C]72[/C][C]70.63[/C][C]75.8540139476447[/C][C]-5.22401394764471[/C][/ROW]
[ROW][C]73[/C][C]66.29[/C][C]59.8029919220972[/C][C]6.48700807790281[/C][/ROW]
[ROW][C]74[/C][C]63.49[/C][C]57.1487245984807[/C][C]6.34127540151931[/C][/ROW]
[ROW][C]75[/C][C]62.97[/C][C]59.0339261919402[/C][C]3.93607380805975[/C][/ROW]
[ROW][C]76[/C][C]66.43[/C][C]78.3361487778237[/C][C]-11.9061487778237[/C][/ROW]
[ROW][C]77[/C][C]101.49[/C][C]98.0656799999367[/C][C]3.4243200000633[/C][/ROW]
[ROW][C]78[/C][C]127.69[/C][C]117.206540064767[/C][C]10.4834599352330[/C][/ROW]
[ROW][C]79[/C][C]133.21[/C][C]149.187182864173[/C][C]-15.9771828641726[/C][/ROW]
[ROW][C]80[/C][C]158.72[/C][C]141.654181455443[/C][C]17.0658185445569[/C][/ROW]
[ROW][C]81[/C][C]148.61[/C][C]150.160184673231[/C][C]-1.55018467323075[/C][/ROW]
[ROW][C]82[/C][C]134.31[/C][C]135.583012920392[/C][C]-1.27301292039161[/C][/ROW]
[ROW][C]83[/C][C]100.99[/C][C]99.214030933917[/C][C]1.77596906608306[/C][/ROW]
[ROW][C]84[/C][C]75.16[/C][C]78.8518713111839[/C][C]-3.69187131118389[/C][/ROW]
[ROW][C]85[/C][C]59.74[/C][C]63.5664037170366[/C][C]-3.82640371703663[/C][/ROW]
[ROW][C]86[/C][C]52.87[/C][C]53.6288643023088[/C][C]-0.758864302308758[/C][/ROW]
[ROW][C]87[/C][C]52.07[/C][C]50.4985612444984[/C][C]1.57143875550164[/C][/ROW]
[ROW][C]88[/C][C]57.38[/C][C]64.8213137810088[/C][C]-7.44131378100882[/C][/ROW]
[ROW][C]89[/C][C]79.43[/C][C]84.0520226134744[/C][C]-4.62202261347444[/C][/ROW]
[ROW][C]90[/C][C]101.4[/C][C]93.8253991405378[/C][C]7.57460085946222[/C][/ROW]
[ROW][C]91[/C][C]120.19[/C][C]117.860597971883[/C][C]2.32940202811672[/C][/ROW]
[ROW][C]92[/C][C]134.38[/C][C]124.074671892463[/C][C]10.3053281075366[/C][/ROW]
[ROW][C]93[/C][C]135.97[/C][C]127.583773974502[/C][C]8.3862260254984[/C][/ROW]
[ROW][C]94[/C][C]113.83[/C][C]121.715057179198[/C][C]-7.88505717919814[/C][/ROW]
[ROW][C]95[/C][C]84.38[/C][C]85.3111441316457[/C][C]-0.931144131645723[/C][/ROW]
[ROW][C]96[/C][C]70.28[/C][C]66.1556347357461[/C][C]4.12436526425391[/C][/ROW]
[ROW][C]97[/C][C]65.96[/C][C]57.7838575722381[/C][C]8.17614242776192[/C][/ROW]
[ROW][C]98[/C][C]56.36[/C][C]56.5526307231324[/C][C]-0.192630723132424[/C][/ROW]
[ROW][C]99[/C][C]49.57[/C][C]53.7732891473396[/C][C]-4.20328914733956[/C][/ROW]
[ROW][C]100[/C][C]68.33[/C][C]63.2342288915095[/C][C]5.09577110849053[/C][/ROW]
[ROW][C]101[/C][C]90.32[/C][C]95.3816340095591[/C][C]-5.06163400955913[/C][/ROW]
[ROW][C]102[/C][C]117.06[/C][C]107.126508098302[/C][C]9.93349190169766[/C][/ROW]
[ROW][C]103[/C][C]134.69[/C][C]135.654762487717[/C][C]-0.96476248771711[/C][/ROW]
[ROW][C]104[/C][C]131.67[/C][C]140.328159021533[/C][C]-8.65815902153287[/C][/ROW]
[ROW][C]105[/C][C]129.25[/C][C]129.538107198813[/C][C]-0.288107198813236[/C][/ROW]
[ROW][C]106[/C][C]118.77[/C][C]117.148323053472[/C][C]1.62167694652797[/C][/ROW]
[ROW][C]107[/C][C]88.44[/C][C]87.337613256133[/C][C]1.10238674386690[/C][/ROW]
[ROW][C]108[/C][C]76.79[/C][C]69.082331157393[/C][C]7.70766884260705[/C][/ROW]
[ROW][C]109[/C][C]75.28[/C][C]62.6143024380525[/C][C]12.6656975619475[/C][/ROW]
[ROW][C]110[/C][C]73.89[/C][C]63.631057718951[/C][C]10.258942281049[/C][/ROW]
[ROW][C]111[/C][C]76.24[/C][C]67.9393905836877[/C][C]8.30060941631234[/C][/ROW]
[ROW][C]112[/C][C]88.58[/C][C]93.2425600715202[/C][C]-4.66256007152019[/C][/ROW]
[ROW][C]113[/C][C]105.83[/C][C]127.476367216397[/C][C]-21.6463672163974[/C][/ROW]
[ROW][C]114[/C][C]115.84[/C][C]130.818857639880[/C][C]-14.9788576398797[/C][/ROW]
[ROW][C]115[/C][C]127.76[/C][C]141.319582691019[/C][C]-13.5595826910191[/C][/ROW]
[ROW][C]116[/C][C]131.75[/C][C]136.178176242322[/C][C]-4.42817624232239[/C][/ROW]
[ROW][C]117[/C][C]119.63[/C][C]128.793420868578[/C][C]-9.1634208685779[/C][/ROW]
[ROW][C]118[/C][C]93.38[/C][C]110.449148843292[/C][C]-17.0691488432919[/C][/ROW]
[ROW][C]119[/C][C]75.55[/C][C]71.9470579183833[/C][C]3.6029420816167[/C][/ROW]
[ROW][C]120[/C][C]51.79[/C][C]58.5446657421842[/C][C]-6.75466574218419[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76625&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76625&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
1374.2973.94036110992980.349638890070239
1463.9864.6912005135862-0.711200513586213
1561.1862.1791200456466-0.999120045646642
1676.4877.2457571681103-0.765757168110298
17107.98108.403843873499-0.423843873499322
18124.97125.327597717670-0.357597717670401
19145.57150.560664175104-4.99066417510409
20140.2155.995349759207-15.7953497592069
21143.84135.4959705829618.34402941703857
22138.8129.8738282842238.92617171577743
23104.0698.94153926662725.11846073337283
2474.781.0765682372002-6.37656823720023
2560.1864.1470623862881-3.96706238628814
2655.1653.24261328706181.91738671293820
2735.6252.924864229907-17.3048642299070
2856.1850.09589687194596.08410312805406
2985.4477.07443901351758.36556098648252
30114.0896.441063137869417.6389368621306
31133.64131.7676745315781.87232546842216
3267.14141.103337539617-73.963337539617
3395.5880.52966211061215.0503378893880
3489.3783.78936214151265.58063785848745
3575.2463.464087366812211.7759126331878
3669.1856.655976711052812.5240232889472
3754.4955.4764753113273-0.98647531132729
3857.547.72248156231759.77751843768252
3962.1652.61814783501139.54185216498865
4076.6776.2462334895180.423766510482011
41110.04108.2326433203021.80735667969819
42127.38127.2817841204410.098215879559362
43156.47152.6179464904123.85205350958793
44167.56161.1136573854026.44634261459765
45153.54161.200553578699-7.66055357869945
46124.08142.181983996835-18.1019839968354
47100.9793.36598413207647.60401586792356
4879.1777.90194808095741.26805191904263
4968.1365.97224069646072.15775930353934
5061.7759.32677807232772.44322192767229
5154.3158.4775322174813-4.16753221748134
5260.370.3034402120837-10.0034402120837
5384.1888.6959212452881-4.51592124528811
54104.0598.86613505456245.18386494543761
55114.66123.010550881149-8.35055088114902
56105.55120.756598292350-15.2065982923496
5796.61105.652630103138-9.0426301031379
5870.9489.8723850666105-18.9323850666105
5963.9154.9807824387698.92921756123096
6058.6148.208997429279110.4010025707209
6144.5346.7339612442915-2.2039612442915
6249.5839.446157885526810.1338421144732
6357.3944.743587077254212.6464129227458
6476.7668.68147478940878.0785252105913
65104.57105.953836131095-1.38383613109522
66125.41122.1093661094653.30063389053487
67143.11148.881218725698-5.77121872569847
68136.35149.493664080602-13.1436640806019
69135.15135.362769212441-0.212769212440804
70131.7122.7108945721958.9891054278049
7196.8795.50272022166241.36727977833762
7270.6375.8540139476447-5.22401394764471
7366.2959.80299192209726.48700807790281
7463.4957.14872459848076.34127540151931
7562.9759.03392619194023.93607380805975
7666.4378.3361487778237-11.9061487778237
77101.4998.06567999993673.4243200000633
78127.69117.20654006476710.4834599352330
79133.21149.187182864173-15.9771828641726
80158.72141.65418145544317.0658185445569
81148.61150.160184673231-1.55018467323075
82134.31135.583012920392-1.27301292039161
83100.9999.2140309339171.77596906608306
8475.1678.8518713111839-3.69187131118389
8559.7463.5664037170366-3.82640371703663
8652.8753.6288643023088-0.758864302308758
8752.0750.49856124449841.57143875550164
8857.3864.8213137810088-7.44131378100882
8979.4384.0520226134744-4.62202261347444
90101.493.82539914053787.57460085946222
91120.19117.8605979718832.32940202811672
92134.38124.07467189246310.3053281075366
93135.97127.5837739745028.3862260254984
94113.83121.715057179198-7.88505717919814
9584.3885.3111441316457-0.931144131645723
9670.2866.15563473574614.12436526425391
9765.9657.78385757223818.17614242776192
9856.3656.5526307231324-0.192630723132424
9949.5753.7732891473396-4.20328914733956
10068.3363.23422889150955.09577110849053
10190.3295.3816340095591-5.06163400955913
102117.06107.1265080983029.93349190169766
103134.69135.654762487717-0.96476248771711
104131.67140.328159021533-8.65815902153287
105129.25129.538107198813-0.288107198813236
106118.77117.1483230534721.62167694652797
10788.4487.3376132561331.10238674386690
10876.7969.0823311573937.70766884260705
10975.2862.614302438052512.6656975619475
11073.8963.63105771895110.258942281049
11176.2467.93939058368778.30060941631234
11288.5893.2425600715202-4.66256007152019
113105.83127.476367216397-21.6463672163974
114115.84130.818857639880-14.9788576398797
115127.76141.319582691019-13.5595826910191
116131.75136.178176242322-4.42817624232239
117119.63128.793420868578-9.1634208685779
11893.38110.449148843292-17.0691488432919
11975.5571.94705791838333.6029420816167
12051.7958.5446657421842-6.75466574218419







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12144.696266258678227.892350333664561.5001821836918
12239.257686568195817.124858382917561.3905147534741
12337.191799198220810.470279804783363.9133185916583
12446.31482945158929.1185847735512883.5110741296271
12565.18946179065310.0085767818953120.370346799411
12676.43542643074239.09730288897072143.773549972514
12790.00400913352488.252607843439171.755410423611
12893.28684716308656.08784036517878180.485853960994
12990.0241878130593.37882098114349176.669554644974
13081.08584154202050.474262489647515161.697420594394
13159.967722270763-2.55556753736494122.491012078891
13246.7077712362005-5.6286310289546799.0441735013557

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 44.6962662586782 & 27.8923503336645 & 61.5001821836918 \tabularnewline
122 & 39.2576865681958 & 17.1248583829175 & 61.3905147534741 \tabularnewline
123 & 37.1917991982208 & 10.4702798047833 & 63.9133185916583 \tabularnewline
124 & 46.3148294515892 & 9.11858477355128 & 83.5110741296271 \tabularnewline
125 & 65.189461790653 & 10.0085767818953 & 120.370346799411 \tabularnewline
126 & 76.4354264307423 & 9.09730288897072 & 143.773549972514 \tabularnewline
127 & 90.0040091335248 & 8.252607843439 & 171.755410423611 \tabularnewline
128 & 93.2868471630865 & 6.08784036517878 & 180.485853960994 \tabularnewline
129 & 90.024187813059 & 3.37882098114349 & 176.669554644974 \tabularnewline
130 & 81.0858415420205 & 0.474262489647515 & 161.697420594394 \tabularnewline
131 & 59.967722270763 & -2.55556753736494 & 122.491012078891 \tabularnewline
132 & 46.7077712362005 & -5.62863102895467 & 99.0441735013557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76625&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]44.6962662586782[/C][C]27.8923503336645[/C][C]61.5001821836918[/C][/ROW]
[ROW][C]122[/C][C]39.2576865681958[/C][C]17.1248583829175[/C][C]61.3905147534741[/C][/ROW]
[ROW][C]123[/C][C]37.1917991982208[/C][C]10.4702798047833[/C][C]63.9133185916583[/C][/ROW]
[ROW][C]124[/C][C]46.3148294515892[/C][C]9.11858477355128[/C][C]83.5110741296271[/C][/ROW]
[ROW][C]125[/C][C]65.189461790653[/C][C]10.0085767818953[/C][C]120.370346799411[/C][/ROW]
[ROW][C]126[/C][C]76.4354264307423[/C][C]9.09730288897072[/C][C]143.773549972514[/C][/ROW]
[ROW][C]127[/C][C]90.0040091335248[/C][C]8.252607843439[/C][C]171.755410423611[/C][/ROW]
[ROW][C]128[/C][C]93.2868471630865[/C][C]6.08784036517878[/C][C]180.485853960994[/C][/ROW]
[ROW][C]129[/C][C]90.024187813059[/C][C]3.37882098114349[/C][C]176.669554644974[/C][/ROW]
[ROW][C]130[/C][C]81.0858415420205[/C][C]0.474262489647515[/C][C]161.697420594394[/C][/ROW]
[ROW][C]131[/C][C]59.967722270763[/C][C]-2.55556753736494[/C][C]122.491012078891[/C][/ROW]
[ROW][C]132[/C][C]46.7077712362005[/C][C]-5.62863102895467[/C][C]99.0441735013557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76625&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76625&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
12144.696266258678227.892350333664561.5001821836918
12239.257686568195817.124858382917561.3905147534741
12337.191799198220810.470279804783363.9133185916583
12446.31482945158929.1185847735512883.5110741296271
12565.18946179065310.0085767818953120.370346799411
12676.43542643074239.09730288897072143.773549972514
12790.00400913352488.252607843439171.755410423611
12893.28684716308656.08784036517878180.485853960994
12990.0241878130593.37882098114349176.669554644974
13081.08584154202050.474262489647515161.697420594394
13159.967722270763-2.55556753736494122.491012078891
13246.7077712362005-5.6286310289546799.0441735013557



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')