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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 May 2011 14:28:47 +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/2011/May/18/t1305728677lrwphkx2ximmsiw.htm/, Retrieved Tue, 14 May 2024 09:26:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121856, Retrieved Tue, 14 May 2024 09:26:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Jonas Cloots, smo...] [2011-05-18 14:28:47] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- R       [Exponential Smoothing] [Pieter De Bock Oe...] [2011-05-20 09:19:00] [bf7e5508c5e5a7a088c466a2b63d5dac]
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Dataseries X:
193.230
199.068
195.076
191.563
191.067
186.665
185.508
184.371
183.046
175.714
175.768
171.029
170.465
170.102
156.389
124.291
99.360
86.675
85.056
128.236
164.257
162.401
152.779
156.005
153.387
153.190
148.840
144.211
145.953
145.542
150.271
147.489
143.824
134.754
131.736
126.304
125.511
125.495
130.133
126.257
110.323
98.417
105.749
120.665
124.075
127.245
146.731
144.979
148.210
144.670
142.970
142.524
146.142
146.522
148.128
148.798
150.181
152.388
155.694
160.662
155.520
158.262
154.338
158.196
160.371
154.856
150.636
145.899
141.242
140.834
141.119
139.104
134.437
129.425
123.155
119.273
120.472
121.523
121.983
123.658
124.794
124.827
120.382
117.395
115.790
114.283
117.271
117.448
118.764
120.550
123.554
125.412
124.182
119.828
115.361
114.226
115.214
115.864
114.276
113.469




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121856&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121856&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121856&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 time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.552989692908948
beta0.0295901195828147
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.552989692908948 \tabularnewline
beta & 0.0295901195828147 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121856&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]0.552989692908948[/C][/ROW]
[ROW][C]beta[/C][C]0.0295901195828147[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121856&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121856&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
alpha0.552989692908948
beta0.0295901195828147
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13170.465207.245518963675-36.7805189636754
14170.102187.558447053806-17.4564470538065
15156.389161.51912234837-5.13012234836955
16124.291122.0429338047432.24806619525653
1799.3694.0255926552425.33440734475802
1886.67580.11954509038466.55545490961539
1985.056130.497241356276-45.4412413562759
20128.23699.996077407736228.2399225922638
21164.257111.17734508374353.0796549162567
22162.401132.5523560892329.8486439107699
23152.779151.1644384093311.61456159066933
24156.005150.760033339265.24496666073952
25153.387140.54713232990712.8398676700929
26153.19158.197271180859-5.00727118085931
27148.84146.0155019382562.82449806174367
28144.211115.82971984857728.3812801514226
29145.953105.66447858772140.2885214122787
30145.542114.22654755418231.3154524458176
31150.271158.051387579526-7.78038757952632
32147.489184.926952533316-37.4379525333157
33143.824173.432384685126-29.6083846851264
34134.754139.8839698318-5.12996983180008
35131.736127.1466664569244.58933354307621
36126.304130.673137371871-4.36913737187135
37125.511119.0444483461116.46655165388854
38125.495125.593780731209-0.0987807312086346
39130.133120.10898209050910.0240179094909
40126.257105.92815564946720.3288443505326
41110.32397.10044807153113.2225519284691
4298.41786.70916738007911.7078326199209
43105.749101.9190189991653.82998100083454
44120.665121.851808429496-1.1868084294959
45124.075134.390873293255-10.3158732932555
46127.245123.2560322335183.98896776648211
47146.731120.8581597098525.8728402901501
48144.979133.45004789659111.5289521034087
49148.21137.01703034618511.1929696538152
50144.67144.883117628554-0.213117628554159
51142.97145.496081997442-2.52608199744199
52142.524130.41218042555512.1118195744453
53146.142115.16013858063530.9818614193645
54146.522115.49925568024131.0227443197592
55148.128139.7714018516368.35659814836379
56148.798161.941704836099-13.1437048360992
57150.181165.569189583037-15.3881895830371
58152.388159.722069264883-7.33406926488345
59155.694162.357959314038-6.66395931403792
60160.662151.5260349174739.13596508252749
61155.52154.5609441714290.959055828571394
62158.262152.4430977410465.81890225895393
63154.338156.23044388111-1.89244388110993
64158.196148.9232546324269.27274536757426
65160.371141.37290545298118.9980945470185
66154.856135.74387555665419.1121244433456
67150.636143.743154384486.89284561552034
68145.899155.914792482287-10.0157924822865
69141.242160.741487049079-19.4994870490792
70140.834156.626677459884-15.7926774598837
71141.119155.15172300185-14.0327230018497
72139.104147.45423456936-8.35023456936031
73134.437137.024722977956-2.58772297795556
74129.425134.920339864682-5.49533986468185
75123.155128.62123421982-5.46623421982039
76119.273123.887511080068-4.61451108006807
77120.472112.3365265919198.13547340808147
78121.52399.905349345140321.6176506548597
79121.983103.02281040379418.9601895962059
80123.658113.7014838022689.95651619773177
81124.794125.052411468094-0.258411468094167
82124.827133.268604243429-8.44160424342937
83120.382136.799624923598-16.4176249235977
84117.395130.438606619549-13.043606619549
85115.79120.027978352996-4.23797835299553
86114.283115.722650746629-1.43965074662866
87117.271111.7570377096895.51396229031072
88117.448113.7333761905923.71462380940821
89118.764112.8813789243815.8826210756188
90120.55105.58789325232714.9621067476727
91123.554104.08491327636119.4690867236391
92125.412111.27651246046914.1354875395305
93124.182120.6968166208753.48518337912515
94119.828127.711090173143-7.88309017314333
95115.361128.380621834525-13.0196218345246
96114.226125.857508714401-11.631508714401
97115.214120.637692373302-5.42369237330206
98115.864117.38188628516-1.51788628516026
99114.276116.934394197804-2.6583941978038
100113.469113.906504100356-0.437504100355554

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 170.465 & 207.245518963675 & -36.7805189636754 \tabularnewline
14 & 170.102 & 187.558447053806 & -17.4564470538065 \tabularnewline
15 & 156.389 & 161.51912234837 & -5.13012234836955 \tabularnewline
16 & 124.291 & 122.042933804743 & 2.24806619525653 \tabularnewline
17 & 99.36 & 94.025592655242 & 5.33440734475802 \tabularnewline
18 & 86.675 & 80.1195450903846 & 6.55545490961539 \tabularnewline
19 & 85.056 & 130.497241356276 & -45.4412413562759 \tabularnewline
20 & 128.236 & 99.9960774077362 & 28.2399225922638 \tabularnewline
21 & 164.257 & 111.177345083743 & 53.0796549162567 \tabularnewline
22 & 162.401 & 132.55235608923 & 29.8486439107699 \tabularnewline
23 & 152.779 & 151.164438409331 & 1.61456159066933 \tabularnewline
24 & 156.005 & 150.76003333926 & 5.24496666073952 \tabularnewline
25 & 153.387 & 140.547132329907 & 12.8398676700929 \tabularnewline
26 & 153.19 & 158.197271180859 & -5.00727118085931 \tabularnewline
27 & 148.84 & 146.015501938256 & 2.82449806174367 \tabularnewline
28 & 144.211 & 115.829719848577 & 28.3812801514226 \tabularnewline
29 & 145.953 & 105.664478587721 & 40.2885214122787 \tabularnewline
30 & 145.542 & 114.226547554182 & 31.3154524458176 \tabularnewline
31 & 150.271 & 158.051387579526 & -7.78038757952632 \tabularnewline
32 & 147.489 & 184.926952533316 & -37.4379525333157 \tabularnewline
33 & 143.824 & 173.432384685126 & -29.6083846851264 \tabularnewline
34 & 134.754 & 139.8839698318 & -5.12996983180008 \tabularnewline
35 & 131.736 & 127.146666456924 & 4.58933354307621 \tabularnewline
36 & 126.304 & 130.673137371871 & -4.36913737187135 \tabularnewline
37 & 125.511 & 119.044448346111 & 6.46655165388854 \tabularnewline
38 & 125.495 & 125.593780731209 & -0.0987807312086346 \tabularnewline
39 & 130.133 & 120.108982090509 & 10.0240179094909 \tabularnewline
40 & 126.257 & 105.928155649467 & 20.3288443505326 \tabularnewline
41 & 110.323 & 97.100448071531 & 13.2225519284691 \tabularnewline
42 & 98.417 & 86.709167380079 & 11.7078326199209 \tabularnewline
43 & 105.749 & 101.919018999165 & 3.82998100083454 \tabularnewline
44 & 120.665 & 121.851808429496 & -1.1868084294959 \tabularnewline
45 & 124.075 & 134.390873293255 & -10.3158732932555 \tabularnewline
46 & 127.245 & 123.256032233518 & 3.98896776648211 \tabularnewline
47 & 146.731 & 120.85815970985 & 25.8728402901501 \tabularnewline
48 & 144.979 & 133.450047896591 & 11.5289521034087 \tabularnewline
49 & 148.21 & 137.017030346185 & 11.1929696538152 \tabularnewline
50 & 144.67 & 144.883117628554 & -0.213117628554159 \tabularnewline
51 & 142.97 & 145.496081997442 & -2.52608199744199 \tabularnewline
52 & 142.524 & 130.412180425555 & 12.1118195744453 \tabularnewline
53 & 146.142 & 115.160138580635 & 30.9818614193645 \tabularnewline
54 & 146.522 & 115.499255680241 & 31.0227443197592 \tabularnewline
55 & 148.128 & 139.771401851636 & 8.35659814836379 \tabularnewline
56 & 148.798 & 161.941704836099 & -13.1437048360992 \tabularnewline
57 & 150.181 & 165.569189583037 & -15.3881895830371 \tabularnewline
58 & 152.388 & 159.722069264883 & -7.33406926488345 \tabularnewline
59 & 155.694 & 162.357959314038 & -6.66395931403792 \tabularnewline
60 & 160.662 & 151.526034917473 & 9.13596508252749 \tabularnewline
61 & 155.52 & 154.560944171429 & 0.959055828571394 \tabularnewline
62 & 158.262 & 152.443097741046 & 5.81890225895393 \tabularnewline
63 & 154.338 & 156.23044388111 & -1.89244388110993 \tabularnewline
64 & 158.196 & 148.923254632426 & 9.27274536757426 \tabularnewline
65 & 160.371 & 141.372905452981 & 18.9980945470185 \tabularnewline
66 & 154.856 & 135.743875556654 & 19.1121244433456 \tabularnewline
67 & 150.636 & 143.74315438448 & 6.89284561552034 \tabularnewline
68 & 145.899 & 155.914792482287 & -10.0157924822865 \tabularnewline
69 & 141.242 & 160.741487049079 & -19.4994870490792 \tabularnewline
70 & 140.834 & 156.626677459884 & -15.7926774598837 \tabularnewline
71 & 141.119 & 155.15172300185 & -14.0327230018497 \tabularnewline
72 & 139.104 & 147.45423456936 & -8.35023456936031 \tabularnewline
73 & 134.437 & 137.024722977956 & -2.58772297795556 \tabularnewline
74 & 129.425 & 134.920339864682 & -5.49533986468185 \tabularnewline
75 & 123.155 & 128.62123421982 & -5.46623421982039 \tabularnewline
76 & 119.273 & 123.887511080068 & -4.61451108006807 \tabularnewline
77 & 120.472 & 112.336526591919 & 8.13547340808147 \tabularnewline
78 & 121.523 & 99.9053493451403 & 21.6176506548597 \tabularnewline
79 & 121.983 & 103.022810403794 & 18.9601895962059 \tabularnewline
80 & 123.658 & 113.701483802268 & 9.95651619773177 \tabularnewline
81 & 124.794 & 125.052411468094 & -0.258411468094167 \tabularnewline
82 & 124.827 & 133.268604243429 & -8.44160424342937 \tabularnewline
83 & 120.382 & 136.799624923598 & -16.4176249235977 \tabularnewline
84 & 117.395 & 130.438606619549 & -13.043606619549 \tabularnewline
85 & 115.79 & 120.027978352996 & -4.23797835299553 \tabularnewline
86 & 114.283 & 115.722650746629 & -1.43965074662866 \tabularnewline
87 & 117.271 & 111.757037709689 & 5.51396229031072 \tabularnewline
88 & 117.448 & 113.733376190592 & 3.71462380940821 \tabularnewline
89 & 118.764 & 112.881378924381 & 5.8826210756188 \tabularnewline
90 & 120.55 & 105.587893252327 & 14.9621067476727 \tabularnewline
91 & 123.554 & 104.084913276361 & 19.4690867236391 \tabularnewline
92 & 125.412 & 111.276512460469 & 14.1354875395305 \tabularnewline
93 & 124.182 & 120.696816620875 & 3.48518337912515 \tabularnewline
94 & 119.828 & 127.711090173143 & -7.88309017314333 \tabularnewline
95 & 115.361 & 128.380621834525 & -13.0196218345246 \tabularnewline
96 & 114.226 & 125.857508714401 & -11.631508714401 \tabularnewline
97 & 115.214 & 120.637692373302 & -5.42369237330206 \tabularnewline
98 & 115.864 & 117.38188628516 & -1.51788628516026 \tabularnewline
99 & 114.276 & 116.934394197804 & -2.6583941978038 \tabularnewline
100 & 113.469 & 113.906504100356 & -0.437504100355554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121856&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]170.465[/C][C]207.245518963675[/C][C]-36.7805189636754[/C][/ROW]
[ROW][C]14[/C][C]170.102[/C][C]187.558447053806[/C][C]-17.4564470538065[/C][/ROW]
[ROW][C]15[/C][C]156.389[/C][C]161.51912234837[/C][C]-5.13012234836955[/C][/ROW]
[ROW][C]16[/C][C]124.291[/C][C]122.042933804743[/C][C]2.24806619525653[/C][/ROW]
[ROW][C]17[/C][C]99.36[/C][C]94.025592655242[/C][C]5.33440734475802[/C][/ROW]
[ROW][C]18[/C][C]86.675[/C][C]80.1195450903846[/C][C]6.55545490961539[/C][/ROW]
[ROW][C]19[/C][C]85.056[/C][C]130.497241356276[/C][C]-45.4412413562759[/C][/ROW]
[ROW][C]20[/C][C]128.236[/C][C]99.9960774077362[/C][C]28.2399225922638[/C][/ROW]
[ROW][C]21[/C][C]164.257[/C][C]111.177345083743[/C][C]53.0796549162567[/C][/ROW]
[ROW][C]22[/C][C]162.401[/C][C]132.55235608923[/C][C]29.8486439107699[/C][/ROW]
[ROW][C]23[/C][C]152.779[/C][C]151.164438409331[/C][C]1.61456159066933[/C][/ROW]
[ROW][C]24[/C][C]156.005[/C][C]150.76003333926[/C][C]5.24496666073952[/C][/ROW]
[ROW][C]25[/C][C]153.387[/C][C]140.547132329907[/C][C]12.8398676700929[/C][/ROW]
[ROW][C]26[/C][C]153.19[/C][C]158.197271180859[/C][C]-5.00727118085931[/C][/ROW]
[ROW][C]27[/C][C]148.84[/C][C]146.015501938256[/C][C]2.82449806174367[/C][/ROW]
[ROW][C]28[/C][C]144.211[/C][C]115.829719848577[/C][C]28.3812801514226[/C][/ROW]
[ROW][C]29[/C][C]145.953[/C][C]105.664478587721[/C][C]40.2885214122787[/C][/ROW]
[ROW][C]30[/C][C]145.542[/C][C]114.226547554182[/C][C]31.3154524458176[/C][/ROW]
[ROW][C]31[/C][C]150.271[/C][C]158.051387579526[/C][C]-7.78038757952632[/C][/ROW]
[ROW][C]32[/C][C]147.489[/C][C]184.926952533316[/C][C]-37.4379525333157[/C][/ROW]
[ROW][C]33[/C][C]143.824[/C][C]173.432384685126[/C][C]-29.6083846851264[/C][/ROW]
[ROW][C]34[/C][C]134.754[/C][C]139.8839698318[/C][C]-5.12996983180008[/C][/ROW]
[ROW][C]35[/C][C]131.736[/C][C]127.146666456924[/C][C]4.58933354307621[/C][/ROW]
[ROW][C]36[/C][C]126.304[/C][C]130.673137371871[/C][C]-4.36913737187135[/C][/ROW]
[ROW][C]37[/C][C]125.511[/C][C]119.044448346111[/C][C]6.46655165388854[/C][/ROW]
[ROW][C]38[/C][C]125.495[/C][C]125.593780731209[/C][C]-0.0987807312086346[/C][/ROW]
[ROW][C]39[/C][C]130.133[/C][C]120.108982090509[/C][C]10.0240179094909[/C][/ROW]
[ROW][C]40[/C][C]126.257[/C][C]105.928155649467[/C][C]20.3288443505326[/C][/ROW]
[ROW][C]41[/C][C]110.323[/C][C]97.100448071531[/C][C]13.2225519284691[/C][/ROW]
[ROW][C]42[/C][C]98.417[/C][C]86.709167380079[/C][C]11.7078326199209[/C][/ROW]
[ROW][C]43[/C][C]105.749[/C][C]101.919018999165[/C][C]3.82998100083454[/C][/ROW]
[ROW][C]44[/C][C]120.665[/C][C]121.851808429496[/C][C]-1.1868084294959[/C][/ROW]
[ROW][C]45[/C][C]124.075[/C][C]134.390873293255[/C][C]-10.3158732932555[/C][/ROW]
[ROW][C]46[/C][C]127.245[/C][C]123.256032233518[/C][C]3.98896776648211[/C][/ROW]
[ROW][C]47[/C][C]146.731[/C][C]120.85815970985[/C][C]25.8728402901501[/C][/ROW]
[ROW][C]48[/C][C]144.979[/C][C]133.450047896591[/C][C]11.5289521034087[/C][/ROW]
[ROW][C]49[/C][C]148.21[/C][C]137.017030346185[/C][C]11.1929696538152[/C][/ROW]
[ROW][C]50[/C][C]144.67[/C][C]144.883117628554[/C][C]-0.213117628554159[/C][/ROW]
[ROW][C]51[/C][C]142.97[/C][C]145.496081997442[/C][C]-2.52608199744199[/C][/ROW]
[ROW][C]52[/C][C]142.524[/C][C]130.412180425555[/C][C]12.1118195744453[/C][/ROW]
[ROW][C]53[/C][C]146.142[/C][C]115.160138580635[/C][C]30.9818614193645[/C][/ROW]
[ROW][C]54[/C][C]146.522[/C][C]115.499255680241[/C][C]31.0227443197592[/C][/ROW]
[ROW][C]55[/C][C]148.128[/C][C]139.771401851636[/C][C]8.35659814836379[/C][/ROW]
[ROW][C]56[/C][C]148.798[/C][C]161.941704836099[/C][C]-13.1437048360992[/C][/ROW]
[ROW][C]57[/C][C]150.181[/C][C]165.569189583037[/C][C]-15.3881895830371[/C][/ROW]
[ROW][C]58[/C][C]152.388[/C][C]159.722069264883[/C][C]-7.33406926488345[/C][/ROW]
[ROW][C]59[/C][C]155.694[/C][C]162.357959314038[/C][C]-6.66395931403792[/C][/ROW]
[ROW][C]60[/C][C]160.662[/C][C]151.526034917473[/C][C]9.13596508252749[/C][/ROW]
[ROW][C]61[/C][C]155.52[/C][C]154.560944171429[/C][C]0.959055828571394[/C][/ROW]
[ROW][C]62[/C][C]158.262[/C][C]152.443097741046[/C][C]5.81890225895393[/C][/ROW]
[ROW][C]63[/C][C]154.338[/C][C]156.23044388111[/C][C]-1.89244388110993[/C][/ROW]
[ROW][C]64[/C][C]158.196[/C][C]148.923254632426[/C][C]9.27274536757426[/C][/ROW]
[ROW][C]65[/C][C]160.371[/C][C]141.372905452981[/C][C]18.9980945470185[/C][/ROW]
[ROW][C]66[/C][C]154.856[/C][C]135.743875556654[/C][C]19.1121244433456[/C][/ROW]
[ROW][C]67[/C][C]150.636[/C][C]143.74315438448[/C][C]6.89284561552034[/C][/ROW]
[ROW][C]68[/C][C]145.899[/C][C]155.914792482287[/C][C]-10.0157924822865[/C][/ROW]
[ROW][C]69[/C][C]141.242[/C][C]160.741487049079[/C][C]-19.4994870490792[/C][/ROW]
[ROW][C]70[/C][C]140.834[/C][C]156.626677459884[/C][C]-15.7926774598837[/C][/ROW]
[ROW][C]71[/C][C]141.119[/C][C]155.15172300185[/C][C]-14.0327230018497[/C][/ROW]
[ROW][C]72[/C][C]139.104[/C][C]147.45423456936[/C][C]-8.35023456936031[/C][/ROW]
[ROW][C]73[/C][C]134.437[/C][C]137.024722977956[/C][C]-2.58772297795556[/C][/ROW]
[ROW][C]74[/C][C]129.425[/C][C]134.920339864682[/C][C]-5.49533986468185[/C][/ROW]
[ROW][C]75[/C][C]123.155[/C][C]128.62123421982[/C][C]-5.46623421982039[/C][/ROW]
[ROW][C]76[/C][C]119.273[/C][C]123.887511080068[/C][C]-4.61451108006807[/C][/ROW]
[ROW][C]77[/C][C]120.472[/C][C]112.336526591919[/C][C]8.13547340808147[/C][/ROW]
[ROW][C]78[/C][C]121.523[/C][C]99.9053493451403[/C][C]21.6176506548597[/C][/ROW]
[ROW][C]79[/C][C]121.983[/C][C]103.022810403794[/C][C]18.9601895962059[/C][/ROW]
[ROW][C]80[/C][C]123.658[/C][C]113.701483802268[/C][C]9.95651619773177[/C][/ROW]
[ROW][C]81[/C][C]124.794[/C][C]125.052411468094[/C][C]-0.258411468094167[/C][/ROW]
[ROW][C]82[/C][C]124.827[/C][C]133.268604243429[/C][C]-8.44160424342937[/C][/ROW]
[ROW][C]83[/C][C]120.382[/C][C]136.799624923598[/C][C]-16.4176249235977[/C][/ROW]
[ROW][C]84[/C][C]117.395[/C][C]130.438606619549[/C][C]-13.043606619549[/C][/ROW]
[ROW][C]85[/C][C]115.79[/C][C]120.027978352996[/C][C]-4.23797835299553[/C][/ROW]
[ROW][C]86[/C][C]114.283[/C][C]115.722650746629[/C][C]-1.43965074662866[/C][/ROW]
[ROW][C]87[/C][C]117.271[/C][C]111.757037709689[/C][C]5.51396229031072[/C][/ROW]
[ROW][C]88[/C][C]117.448[/C][C]113.733376190592[/C][C]3.71462380940821[/C][/ROW]
[ROW][C]89[/C][C]118.764[/C][C]112.881378924381[/C][C]5.8826210756188[/C][/ROW]
[ROW][C]90[/C][C]120.55[/C][C]105.587893252327[/C][C]14.9621067476727[/C][/ROW]
[ROW][C]91[/C][C]123.554[/C][C]104.084913276361[/C][C]19.4690867236391[/C][/ROW]
[ROW][C]92[/C][C]125.412[/C][C]111.276512460469[/C][C]14.1354875395305[/C][/ROW]
[ROW][C]93[/C][C]124.182[/C][C]120.696816620875[/C][C]3.48518337912515[/C][/ROW]
[ROW][C]94[/C][C]119.828[/C][C]127.711090173143[/C][C]-7.88309017314333[/C][/ROW]
[ROW][C]95[/C][C]115.361[/C][C]128.380621834525[/C][C]-13.0196218345246[/C][/ROW]
[ROW][C]96[/C][C]114.226[/C][C]125.857508714401[/C][C]-11.631508714401[/C][/ROW]
[ROW][C]97[/C][C]115.214[/C][C]120.637692373302[/C][C]-5.42369237330206[/C][/ROW]
[ROW][C]98[/C][C]115.864[/C][C]117.38188628516[/C][C]-1.51788628516026[/C][/ROW]
[ROW][C]99[/C][C]114.276[/C][C]116.934394197804[/C][C]-2.6583941978038[/C][/ROW]
[ROW][C]100[/C][C]113.469[/C][C]113.906504100356[/C][C]-0.437504100355554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121856&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121856&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
13170.465207.245518963675-36.7805189636754
14170.102187.558447053806-17.4564470538065
15156.389161.51912234837-5.13012234836955
16124.291122.0429338047432.24806619525653
1799.3694.0255926552425.33440734475802
1886.67580.11954509038466.55545490961539
1985.056130.497241356276-45.4412413562759
20128.23699.996077407736228.2399225922638
21164.257111.17734508374353.0796549162567
22162.401132.5523560892329.8486439107699
23152.779151.1644384093311.61456159066933
24156.005150.760033339265.24496666073952
25153.387140.54713232990712.8398676700929
26153.19158.197271180859-5.00727118085931
27148.84146.0155019382562.82449806174367
28144.211115.82971984857728.3812801514226
29145.953105.66447858772140.2885214122787
30145.542114.22654755418231.3154524458176
31150.271158.051387579526-7.78038757952632
32147.489184.926952533316-37.4379525333157
33143.824173.432384685126-29.6083846851264
34134.754139.8839698318-5.12996983180008
35131.736127.1466664569244.58933354307621
36126.304130.673137371871-4.36913737187135
37125.511119.0444483461116.46655165388854
38125.495125.593780731209-0.0987807312086346
39130.133120.10898209050910.0240179094909
40126.257105.92815564946720.3288443505326
41110.32397.10044807153113.2225519284691
4298.41786.70916738007911.7078326199209
43105.749101.9190189991653.82998100083454
44120.665121.851808429496-1.1868084294959
45124.075134.390873293255-10.3158732932555
46127.245123.2560322335183.98896776648211
47146.731120.8581597098525.8728402901501
48144.979133.45004789659111.5289521034087
49148.21137.01703034618511.1929696538152
50144.67144.883117628554-0.213117628554159
51142.97145.496081997442-2.52608199744199
52142.524130.41218042555512.1118195744453
53146.142115.16013858063530.9818614193645
54146.522115.49925568024131.0227443197592
55148.128139.7714018516368.35659814836379
56148.798161.941704836099-13.1437048360992
57150.181165.569189583037-15.3881895830371
58152.388159.722069264883-7.33406926488345
59155.694162.357959314038-6.66395931403792
60160.662151.5260349174739.13596508252749
61155.52154.5609441714290.959055828571394
62158.262152.4430977410465.81890225895393
63154.338156.23044388111-1.89244388110993
64158.196148.9232546324269.27274536757426
65160.371141.37290545298118.9980945470185
66154.856135.74387555665419.1121244433456
67150.636143.743154384486.89284561552034
68145.899155.914792482287-10.0157924822865
69141.242160.741487049079-19.4994870490792
70140.834156.626677459884-15.7926774598837
71141.119155.15172300185-14.0327230018497
72139.104147.45423456936-8.35023456936031
73134.437137.024722977956-2.58772297795556
74129.425134.920339864682-5.49533986468185
75123.155128.62123421982-5.46623421982039
76119.273123.887511080068-4.61451108006807
77120.472112.3365265919198.13547340808147
78121.52399.905349345140321.6176506548597
79121.983103.02281040379418.9601895962059
80123.658113.7014838022689.95651619773177
81124.794125.052411468094-0.258411468094167
82124.827133.268604243429-8.44160424342937
83120.382136.799624923598-16.4176249235977
84117.395130.438606619549-13.043606619549
85115.79120.027978352996-4.23797835299553
86114.283115.722650746629-1.43965074662866
87117.271111.7570377096895.51396229031072
88117.448113.7333761905923.71462380940821
89118.764112.8813789243815.8826210756188
90120.55105.58789325232714.9621067476727
91123.554104.08491327636119.4690867236391
92125.412111.27651246046914.1354875395305
93124.182120.6968166208753.48518337912515
94119.828127.711090173143-7.88309017314333
95115.361128.380621834525-13.0196218345246
96114.226125.857508714401-11.631508714401
97115.214120.637692373302-5.42369237330206
98115.864117.38188628516-1.51788628516026
99114.276116.934394197804-2.6583941978038
100113.469113.906504100356-0.437504100355554







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
101111.97892179512179.9180345773319144.039809012909
102105.64615524257568.7529674352971142.539343049853
10397.794249798522156.3968842244165139.191615372628
10491.427196457038545.7505652645833137.103827649494
10587.630352119798437.8358139991373137.42489024046
10686.939017718966733.1457422714544140.732293166479
10789.104123634171531.4017281424934146.80651912585
10894.046657778881832.5032068585045155.590108699259
10997.86966021080632.5369988634746163.202321558137
11099.283540180691730.200997188216168.366083173167
11199.114946491503226.3119924844305171.917900498576
11298.542722856386722.0409308872323175.044514825541

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
101 & 111.978921795121 & 79.9180345773319 & 144.039809012909 \tabularnewline
102 & 105.646155242575 & 68.7529674352971 & 142.539343049853 \tabularnewline
103 & 97.7942497985221 & 56.3968842244165 & 139.191615372628 \tabularnewline
104 & 91.4271964570385 & 45.7505652645833 & 137.103827649494 \tabularnewline
105 & 87.6303521197984 & 37.8358139991373 & 137.42489024046 \tabularnewline
106 & 86.9390177189667 & 33.1457422714544 & 140.732293166479 \tabularnewline
107 & 89.1041236341715 & 31.4017281424934 & 146.80651912585 \tabularnewline
108 & 94.0466577788818 & 32.5032068585045 & 155.590108699259 \tabularnewline
109 & 97.869660210806 & 32.5369988634746 & 163.202321558137 \tabularnewline
110 & 99.2835401806917 & 30.200997188216 & 168.366083173167 \tabularnewline
111 & 99.1149464915032 & 26.3119924844305 & 171.917900498576 \tabularnewline
112 & 98.5427228563867 & 22.0409308872323 & 175.044514825541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121856&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]101[/C][C]111.978921795121[/C][C]79.9180345773319[/C][C]144.039809012909[/C][/ROW]
[ROW][C]102[/C][C]105.646155242575[/C][C]68.7529674352971[/C][C]142.539343049853[/C][/ROW]
[ROW][C]103[/C][C]97.7942497985221[/C][C]56.3968842244165[/C][C]139.191615372628[/C][/ROW]
[ROW][C]104[/C][C]91.4271964570385[/C][C]45.7505652645833[/C][C]137.103827649494[/C][/ROW]
[ROW][C]105[/C][C]87.6303521197984[/C][C]37.8358139991373[/C][C]137.42489024046[/C][/ROW]
[ROW][C]106[/C][C]86.9390177189667[/C][C]33.1457422714544[/C][C]140.732293166479[/C][/ROW]
[ROW][C]107[/C][C]89.1041236341715[/C][C]31.4017281424934[/C][C]146.80651912585[/C][/ROW]
[ROW][C]108[/C][C]94.0466577788818[/C][C]32.5032068585045[/C][C]155.590108699259[/C][/ROW]
[ROW][C]109[/C][C]97.869660210806[/C][C]32.5369988634746[/C][C]163.202321558137[/C][/ROW]
[ROW][C]110[/C][C]99.2835401806917[/C][C]30.200997188216[/C][C]168.366083173167[/C][/ROW]
[ROW][C]111[/C][C]99.1149464915032[/C][C]26.3119924844305[/C][C]171.917900498576[/C][/ROW]
[ROW][C]112[/C][C]98.5427228563867[/C][C]22.0409308872323[/C][C]175.044514825541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121856&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121856&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
101111.97892179512179.9180345773319144.039809012909
102105.64615524257568.7529674352971142.539343049853
10397.794249798522156.3968842244165139.191615372628
10491.427196457038545.7505652645833137.103827649494
10587.630352119798437.8358139991373137.42489024046
10686.939017718966733.1457422714544140.732293166479
10789.104123634171531.4017281424934146.80651912585
10894.046657778881832.5032068585045155.590108699259
10997.86966021080632.5369988634746163.202321558137
11099.283540180691730.200997188216168.366083173167
11199.114946491503226.3119924844305171.917900498576
11298.542722856386722.0409308872323175.044514825541



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')