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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 May 2011 09:19:00 +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/20/t13058829096iu06y1ut1hv4u8.htm/, Retrieved Sun, 12 May 2024 22:36:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122439, Retrieved Sun, 12 May 2024 22:36:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact83
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] [74be16979710d4c4e7c6647856088456]
- R       [Exponential Smoothing] [Pieter De Bock Oe...] [2011-05-20 09:19:00] [cbef39b832afec63e267b10f62c5e5c1] [Current]
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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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122439&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122439&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122439&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.55298969290894
beta0.0295901195827954
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.55298969290894 \tabularnewline
beta & 0.0295901195827954 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122439&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]0.55298969290894[/C][/ROW]
[ROW][C]beta[/C][C]0.0295901195827954[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122439&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122439&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
alpha0.55298969290894
beta0.0295901195827954
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13170.465207.245518963675-36.7805189636753
14170.102187.558447053807-17.4564470538071
15156.389161.519122348371-5.13012234837052
16124.291122.0429338047452.24806619525545
1799.3694.0255926552435.33440734475697
1886.67580.11954509038556.55545490961448
1985.056130.497241356277-45.4412413562767
20128.23699.996077407737828.2399225922622
21164.257111.17734508374453.0796549162556
22162.401132.5523560892329.8486439107699
23152.779151.164438409331.61456159066989
24156.005150.760033339265.24496666074015
25153.387140.54713232990612.8398676700938
26153.19158.197271180858-5.00727118085806
27148.84146.0155019382552.82449806174472
28144.211115.82971984857628.3812801514235
29145.953105.6644785877240.28852141228
30145.542114.2265475541831.3154524458197
31150.271158.051387579523-7.78038757952336
32147.489184.926952533313-37.4379525333133
33143.824173.432384685125-29.6083846851251
34134.754139.883969831799-5.12996983179946
35131.736127.1466664569234.5893335430769
36126.304130.673137371871-4.36913737187055
37125.511119.0444483461116.46655165388938
38125.495125.593780731207-0.0987807312074693
39130.133120.10898209050810.024017909492
40126.257105.92815564946620.3288443505337
41110.32397.100448071529813.2225519284702
4298.41786.709167380077811.7078326199222
43105.749101.9190189991643.82998100083643
44120.665121.851808429494-1.18680842949372
45124.075134.390873293253-10.3158732932535
46127.245123.2560322335163.98896776648361
47146.731120.85815970984825.8728402901515
48144.979133.45004789658911.5289521034105
49148.21137.01703034618311.1929696538173
50144.67144.883117628552-0.213117628551714
51142.97145.49608199744-2.5260819974396
52142.524130.41218042555312.1118195744474
53146.142115.16013858063330.9818614193666
54146.522115.49925568023831.0227443197616
55148.128139.7714018516338.35659814836694
56148.798161.941704836096-13.1437048360956
57150.181165.569189583034-15.3881895830336
58152.388159.722069264881-7.33406926488053
59155.694162.357959314036-6.66395931403557
60160.662151.526034917479.13596508252957
61155.52154.5609441714260.959055828573582
62158.262152.4430977410445.81890225895626
63154.338156.230443881107-1.89244388110743
64158.196148.9232546324239.2727453675765
65160.371141.37290545297918.9980945470205
66154.856135.74387555665219.1121244433477
67150.636143.7431543844776.89284561552287
68145.899155.914792482284-10.0157924822835
69141.242160.741487049076-19.4994870490761
70140.834156.626677459881-15.792677459881
71141.119155.151723001848-14.0327230018476
72139.104147.454234569359-8.35023456935872
73134.437137.024722977954-2.58772297795429
74129.425134.920339864681-5.4953398646806
75123.155128.621234219819-5.46623421981917
76119.273123.887511080067-4.6145110800671
77120.472112.3365265919188.13547340808204
78121.52399.9053493451421.6176506548601
79121.983103.02281040379318.9601895962067
80123.658113.7014838022679.95651619773327
81124.794125.052411468092-0.258411468092035
82124.827133.268604243427-8.44160424342707
83120.382136.799624923596-16.4176249235956
84117.395130.438606619547-13.0436066195474
85115.79120.027978352994-4.23797835299443
86114.283115.722650746628-1.43965074662773
87117.271111.7570377096885.51396229031165
88117.448113.7333761905913.71462380940913
89118.764112.881378924385.88262107561951
90120.55105.58789325232714.9621067476732
91123.554104.0849132763619.4690867236396
92125.412111.27651246046814.1354875395316
93124.182120.6968166208733.48518337912689
94119.828127.711090173141-7.88309017314117
95115.361128.380621834522-13.0196218345223
96114.226125.857508714399-11.631508714399
97115.214120.637692373301-5.42369237330057
98115.864117.381886285159-1.51788628515904
99114.276116.934394197803-2.65839419780274
100113.469113.906504100355-0.43750410035463

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 170.465 & 207.245518963675 & -36.7805189636753 \tabularnewline
14 & 170.102 & 187.558447053807 & -17.4564470538071 \tabularnewline
15 & 156.389 & 161.519122348371 & -5.13012234837052 \tabularnewline
16 & 124.291 & 122.042933804745 & 2.24806619525545 \tabularnewline
17 & 99.36 & 94.025592655243 & 5.33440734475697 \tabularnewline
18 & 86.675 & 80.1195450903855 & 6.55545490961448 \tabularnewline
19 & 85.056 & 130.497241356277 & -45.4412413562767 \tabularnewline
20 & 128.236 & 99.9960774077378 & 28.2399225922622 \tabularnewline
21 & 164.257 & 111.177345083744 & 53.0796549162556 \tabularnewline
22 & 162.401 & 132.55235608923 & 29.8486439107699 \tabularnewline
23 & 152.779 & 151.16443840933 & 1.61456159066989 \tabularnewline
24 & 156.005 & 150.76003333926 & 5.24496666074015 \tabularnewline
25 & 153.387 & 140.547132329906 & 12.8398676700938 \tabularnewline
26 & 153.19 & 158.197271180858 & -5.00727118085806 \tabularnewline
27 & 148.84 & 146.015501938255 & 2.82449806174472 \tabularnewline
28 & 144.211 & 115.829719848576 & 28.3812801514235 \tabularnewline
29 & 145.953 & 105.66447858772 & 40.28852141228 \tabularnewline
30 & 145.542 & 114.22654755418 & 31.3154524458197 \tabularnewline
31 & 150.271 & 158.051387579523 & -7.78038757952336 \tabularnewline
32 & 147.489 & 184.926952533313 & -37.4379525333133 \tabularnewline
33 & 143.824 & 173.432384685125 & -29.6083846851251 \tabularnewline
34 & 134.754 & 139.883969831799 & -5.12996983179946 \tabularnewline
35 & 131.736 & 127.146666456923 & 4.5893335430769 \tabularnewline
36 & 126.304 & 130.673137371871 & -4.36913737187055 \tabularnewline
37 & 125.511 & 119.044448346111 & 6.46655165388938 \tabularnewline
38 & 125.495 & 125.593780731207 & -0.0987807312074693 \tabularnewline
39 & 130.133 & 120.108982090508 & 10.024017909492 \tabularnewline
40 & 126.257 & 105.928155649466 & 20.3288443505337 \tabularnewline
41 & 110.323 & 97.1004480715298 & 13.2225519284702 \tabularnewline
42 & 98.417 & 86.7091673800778 & 11.7078326199222 \tabularnewline
43 & 105.749 & 101.919018999164 & 3.82998100083643 \tabularnewline
44 & 120.665 & 121.851808429494 & -1.18680842949372 \tabularnewline
45 & 124.075 & 134.390873293253 & -10.3158732932535 \tabularnewline
46 & 127.245 & 123.256032233516 & 3.98896776648361 \tabularnewline
47 & 146.731 & 120.858159709848 & 25.8728402901515 \tabularnewline
48 & 144.979 & 133.450047896589 & 11.5289521034105 \tabularnewline
49 & 148.21 & 137.017030346183 & 11.1929696538173 \tabularnewline
50 & 144.67 & 144.883117628552 & -0.213117628551714 \tabularnewline
51 & 142.97 & 145.49608199744 & -2.5260819974396 \tabularnewline
52 & 142.524 & 130.412180425553 & 12.1118195744474 \tabularnewline
53 & 146.142 & 115.160138580633 & 30.9818614193666 \tabularnewline
54 & 146.522 & 115.499255680238 & 31.0227443197616 \tabularnewline
55 & 148.128 & 139.771401851633 & 8.35659814836694 \tabularnewline
56 & 148.798 & 161.941704836096 & -13.1437048360956 \tabularnewline
57 & 150.181 & 165.569189583034 & -15.3881895830336 \tabularnewline
58 & 152.388 & 159.722069264881 & -7.33406926488053 \tabularnewline
59 & 155.694 & 162.357959314036 & -6.66395931403557 \tabularnewline
60 & 160.662 & 151.52603491747 & 9.13596508252957 \tabularnewline
61 & 155.52 & 154.560944171426 & 0.959055828573582 \tabularnewline
62 & 158.262 & 152.443097741044 & 5.81890225895626 \tabularnewline
63 & 154.338 & 156.230443881107 & -1.89244388110743 \tabularnewline
64 & 158.196 & 148.923254632423 & 9.2727453675765 \tabularnewline
65 & 160.371 & 141.372905452979 & 18.9980945470205 \tabularnewline
66 & 154.856 & 135.743875556652 & 19.1121244433477 \tabularnewline
67 & 150.636 & 143.743154384477 & 6.89284561552287 \tabularnewline
68 & 145.899 & 155.914792482284 & -10.0157924822835 \tabularnewline
69 & 141.242 & 160.741487049076 & -19.4994870490761 \tabularnewline
70 & 140.834 & 156.626677459881 & -15.792677459881 \tabularnewline
71 & 141.119 & 155.151723001848 & -14.0327230018476 \tabularnewline
72 & 139.104 & 147.454234569359 & -8.35023456935872 \tabularnewline
73 & 134.437 & 137.024722977954 & -2.58772297795429 \tabularnewline
74 & 129.425 & 134.920339864681 & -5.4953398646806 \tabularnewline
75 & 123.155 & 128.621234219819 & -5.46623421981917 \tabularnewline
76 & 119.273 & 123.887511080067 & -4.6145110800671 \tabularnewline
77 & 120.472 & 112.336526591918 & 8.13547340808204 \tabularnewline
78 & 121.523 & 99.90534934514 & 21.6176506548601 \tabularnewline
79 & 121.983 & 103.022810403793 & 18.9601895962067 \tabularnewline
80 & 123.658 & 113.701483802267 & 9.95651619773327 \tabularnewline
81 & 124.794 & 125.052411468092 & -0.258411468092035 \tabularnewline
82 & 124.827 & 133.268604243427 & -8.44160424342707 \tabularnewline
83 & 120.382 & 136.799624923596 & -16.4176249235956 \tabularnewline
84 & 117.395 & 130.438606619547 & -13.0436066195474 \tabularnewline
85 & 115.79 & 120.027978352994 & -4.23797835299443 \tabularnewline
86 & 114.283 & 115.722650746628 & -1.43965074662773 \tabularnewline
87 & 117.271 & 111.757037709688 & 5.51396229031165 \tabularnewline
88 & 117.448 & 113.733376190591 & 3.71462380940913 \tabularnewline
89 & 118.764 & 112.88137892438 & 5.88262107561951 \tabularnewline
90 & 120.55 & 105.587893252327 & 14.9621067476732 \tabularnewline
91 & 123.554 & 104.08491327636 & 19.4690867236396 \tabularnewline
92 & 125.412 & 111.276512460468 & 14.1354875395316 \tabularnewline
93 & 124.182 & 120.696816620873 & 3.48518337912689 \tabularnewline
94 & 119.828 & 127.711090173141 & -7.88309017314117 \tabularnewline
95 & 115.361 & 128.380621834522 & -13.0196218345223 \tabularnewline
96 & 114.226 & 125.857508714399 & -11.631508714399 \tabularnewline
97 & 115.214 & 120.637692373301 & -5.42369237330057 \tabularnewline
98 & 115.864 & 117.381886285159 & -1.51788628515904 \tabularnewline
99 & 114.276 & 116.934394197803 & -2.65839419780274 \tabularnewline
100 & 113.469 & 113.906504100355 & -0.43750410035463 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122439&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]-36.7805189636753[/C][/ROW]
[ROW][C]14[/C][C]170.102[/C][C]187.558447053807[/C][C]-17.4564470538071[/C][/ROW]
[ROW][C]15[/C][C]156.389[/C][C]161.519122348371[/C][C]-5.13012234837052[/C][/ROW]
[ROW][C]16[/C][C]124.291[/C][C]122.042933804745[/C][C]2.24806619525545[/C][/ROW]
[ROW][C]17[/C][C]99.36[/C][C]94.025592655243[/C][C]5.33440734475697[/C][/ROW]
[ROW][C]18[/C][C]86.675[/C][C]80.1195450903855[/C][C]6.55545490961448[/C][/ROW]
[ROW][C]19[/C][C]85.056[/C][C]130.497241356277[/C][C]-45.4412413562767[/C][/ROW]
[ROW][C]20[/C][C]128.236[/C][C]99.9960774077378[/C][C]28.2399225922622[/C][/ROW]
[ROW][C]21[/C][C]164.257[/C][C]111.177345083744[/C][C]53.0796549162556[/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]151.16443840933[/C][C]1.61456159066989[/C][/ROW]
[ROW][C]24[/C][C]156.005[/C][C]150.76003333926[/C][C]5.24496666074015[/C][/ROW]
[ROW][C]25[/C][C]153.387[/C][C]140.547132329906[/C][C]12.8398676700938[/C][/ROW]
[ROW][C]26[/C][C]153.19[/C][C]158.197271180858[/C][C]-5.00727118085806[/C][/ROW]
[ROW][C]27[/C][C]148.84[/C][C]146.015501938255[/C][C]2.82449806174472[/C][/ROW]
[ROW][C]28[/C][C]144.211[/C][C]115.829719848576[/C][C]28.3812801514235[/C][/ROW]
[ROW][C]29[/C][C]145.953[/C][C]105.66447858772[/C][C]40.28852141228[/C][/ROW]
[ROW][C]30[/C][C]145.542[/C][C]114.22654755418[/C][C]31.3154524458197[/C][/ROW]
[ROW][C]31[/C][C]150.271[/C][C]158.051387579523[/C][C]-7.78038757952336[/C][/ROW]
[ROW][C]32[/C][C]147.489[/C][C]184.926952533313[/C][C]-37.4379525333133[/C][/ROW]
[ROW][C]33[/C][C]143.824[/C][C]173.432384685125[/C][C]-29.6083846851251[/C][/ROW]
[ROW][C]34[/C][C]134.754[/C][C]139.883969831799[/C][C]-5.12996983179946[/C][/ROW]
[ROW][C]35[/C][C]131.736[/C][C]127.146666456923[/C][C]4.5893335430769[/C][/ROW]
[ROW][C]36[/C][C]126.304[/C][C]130.673137371871[/C][C]-4.36913737187055[/C][/ROW]
[ROW][C]37[/C][C]125.511[/C][C]119.044448346111[/C][C]6.46655165388938[/C][/ROW]
[ROW][C]38[/C][C]125.495[/C][C]125.593780731207[/C][C]-0.0987807312074693[/C][/ROW]
[ROW][C]39[/C][C]130.133[/C][C]120.108982090508[/C][C]10.024017909492[/C][/ROW]
[ROW][C]40[/C][C]126.257[/C][C]105.928155649466[/C][C]20.3288443505337[/C][/ROW]
[ROW][C]41[/C][C]110.323[/C][C]97.1004480715298[/C][C]13.2225519284702[/C][/ROW]
[ROW][C]42[/C][C]98.417[/C][C]86.7091673800778[/C][C]11.7078326199222[/C][/ROW]
[ROW][C]43[/C][C]105.749[/C][C]101.919018999164[/C][C]3.82998100083643[/C][/ROW]
[ROW][C]44[/C][C]120.665[/C][C]121.851808429494[/C][C]-1.18680842949372[/C][/ROW]
[ROW][C]45[/C][C]124.075[/C][C]134.390873293253[/C][C]-10.3158732932535[/C][/ROW]
[ROW][C]46[/C][C]127.245[/C][C]123.256032233516[/C][C]3.98896776648361[/C][/ROW]
[ROW][C]47[/C][C]146.731[/C][C]120.858159709848[/C][C]25.8728402901515[/C][/ROW]
[ROW][C]48[/C][C]144.979[/C][C]133.450047896589[/C][C]11.5289521034105[/C][/ROW]
[ROW][C]49[/C][C]148.21[/C][C]137.017030346183[/C][C]11.1929696538173[/C][/ROW]
[ROW][C]50[/C][C]144.67[/C][C]144.883117628552[/C][C]-0.213117628551714[/C][/ROW]
[ROW][C]51[/C][C]142.97[/C][C]145.49608199744[/C][C]-2.5260819974396[/C][/ROW]
[ROW][C]52[/C][C]142.524[/C][C]130.412180425553[/C][C]12.1118195744474[/C][/ROW]
[ROW][C]53[/C][C]146.142[/C][C]115.160138580633[/C][C]30.9818614193666[/C][/ROW]
[ROW][C]54[/C][C]146.522[/C][C]115.499255680238[/C][C]31.0227443197616[/C][/ROW]
[ROW][C]55[/C][C]148.128[/C][C]139.771401851633[/C][C]8.35659814836694[/C][/ROW]
[ROW][C]56[/C][C]148.798[/C][C]161.941704836096[/C][C]-13.1437048360956[/C][/ROW]
[ROW][C]57[/C][C]150.181[/C][C]165.569189583034[/C][C]-15.3881895830336[/C][/ROW]
[ROW][C]58[/C][C]152.388[/C][C]159.722069264881[/C][C]-7.33406926488053[/C][/ROW]
[ROW][C]59[/C][C]155.694[/C][C]162.357959314036[/C][C]-6.66395931403557[/C][/ROW]
[ROW][C]60[/C][C]160.662[/C][C]151.52603491747[/C][C]9.13596508252957[/C][/ROW]
[ROW][C]61[/C][C]155.52[/C][C]154.560944171426[/C][C]0.959055828573582[/C][/ROW]
[ROW][C]62[/C][C]158.262[/C][C]152.443097741044[/C][C]5.81890225895626[/C][/ROW]
[ROW][C]63[/C][C]154.338[/C][C]156.230443881107[/C][C]-1.89244388110743[/C][/ROW]
[ROW][C]64[/C][C]158.196[/C][C]148.923254632423[/C][C]9.2727453675765[/C][/ROW]
[ROW][C]65[/C][C]160.371[/C][C]141.372905452979[/C][C]18.9980945470205[/C][/ROW]
[ROW][C]66[/C][C]154.856[/C][C]135.743875556652[/C][C]19.1121244433477[/C][/ROW]
[ROW][C]67[/C][C]150.636[/C][C]143.743154384477[/C][C]6.89284561552287[/C][/ROW]
[ROW][C]68[/C][C]145.899[/C][C]155.914792482284[/C][C]-10.0157924822835[/C][/ROW]
[ROW][C]69[/C][C]141.242[/C][C]160.741487049076[/C][C]-19.4994870490761[/C][/ROW]
[ROW][C]70[/C][C]140.834[/C][C]156.626677459881[/C][C]-15.792677459881[/C][/ROW]
[ROW][C]71[/C][C]141.119[/C][C]155.151723001848[/C][C]-14.0327230018476[/C][/ROW]
[ROW][C]72[/C][C]139.104[/C][C]147.454234569359[/C][C]-8.35023456935872[/C][/ROW]
[ROW][C]73[/C][C]134.437[/C][C]137.024722977954[/C][C]-2.58772297795429[/C][/ROW]
[ROW][C]74[/C][C]129.425[/C][C]134.920339864681[/C][C]-5.4953398646806[/C][/ROW]
[ROW][C]75[/C][C]123.155[/C][C]128.621234219819[/C][C]-5.46623421981917[/C][/ROW]
[ROW][C]76[/C][C]119.273[/C][C]123.887511080067[/C][C]-4.6145110800671[/C][/ROW]
[ROW][C]77[/C][C]120.472[/C][C]112.336526591918[/C][C]8.13547340808204[/C][/ROW]
[ROW][C]78[/C][C]121.523[/C][C]99.90534934514[/C][C]21.6176506548601[/C][/ROW]
[ROW][C]79[/C][C]121.983[/C][C]103.022810403793[/C][C]18.9601895962067[/C][/ROW]
[ROW][C]80[/C][C]123.658[/C][C]113.701483802267[/C][C]9.95651619773327[/C][/ROW]
[ROW][C]81[/C][C]124.794[/C][C]125.052411468092[/C][C]-0.258411468092035[/C][/ROW]
[ROW][C]82[/C][C]124.827[/C][C]133.268604243427[/C][C]-8.44160424342707[/C][/ROW]
[ROW][C]83[/C][C]120.382[/C][C]136.799624923596[/C][C]-16.4176249235956[/C][/ROW]
[ROW][C]84[/C][C]117.395[/C][C]130.438606619547[/C][C]-13.0436066195474[/C][/ROW]
[ROW][C]85[/C][C]115.79[/C][C]120.027978352994[/C][C]-4.23797835299443[/C][/ROW]
[ROW][C]86[/C][C]114.283[/C][C]115.722650746628[/C][C]-1.43965074662773[/C][/ROW]
[ROW][C]87[/C][C]117.271[/C][C]111.757037709688[/C][C]5.51396229031165[/C][/ROW]
[ROW][C]88[/C][C]117.448[/C][C]113.733376190591[/C][C]3.71462380940913[/C][/ROW]
[ROW][C]89[/C][C]118.764[/C][C]112.88137892438[/C][C]5.88262107561951[/C][/ROW]
[ROW][C]90[/C][C]120.55[/C][C]105.587893252327[/C][C]14.9621067476732[/C][/ROW]
[ROW][C]91[/C][C]123.554[/C][C]104.08491327636[/C][C]19.4690867236396[/C][/ROW]
[ROW][C]92[/C][C]125.412[/C][C]111.276512460468[/C][C]14.1354875395316[/C][/ROW]
[ROW][C]93[/C][C]124.182[/C][C]120.696816620873[/C][C]3.48518337912689[/C][/ROW]
[ROW][C]94[/C][C]119.828[/C][C]127.711090173141[/C][C]-7.88309017314117[/C][/ROW]
[ROW][C]95[/C][C]115.361[/C][C]128.380621834522[/C][C]-13.0196218345223[/C][/ROW]
[ROW][C]96[/C][C]114.226[/C][C]125.857508714399[/C][C]-11.631508714399[/C][/ROW]
[ROW][C]97[/C][C]115.214[/C][C]120.637692373301[/C][C]-5.42369237330057[/C][/ROW]
[ROW][C]98[/C][C]115.864[/C][C]117.381886285159[/C][C]-1.51788628515904[/C][/ROW]
[ROW][C]99[/C][C]114.276[/C][C]116.934394197803[/C][C]-2.65839419780274[/C][/ROW]
[ROW][C]100[/C][C]113.469[/C][C]113.906504100355[/C][C]-0.43750410035463[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122439&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122439&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
13170.465207.245518963675-36.7805189636753
14170.102187.558447053807-17.4564470538071
15156.389161.519122348371-5.13012234837052
16124.291122.0429338047452.24806619525545
1799.3694.0255926552435.33440734475697
1886.67580.11954509038556.55545490961448
1985.056130.497241356277-45.4412413562767
20128.23699.996077407737828.2399225922622
21164.257111.17734508374453.0796549162556
22162.401132.5523560892329.8486439107699
23152.779151.164438409331.61456159066989
24156.005150.760033339265.24496666074015
25153.387140.54713232990612.8398676700938
26153.19158.197271180858-5.00727118085806
27148.84146.0155019382552.82449806174472
28144.211115.82971984857628.3812801514235
29145.953105.6644785877240.28852141228
30145.542114.2265475541831.3154524458197
31150.271158.051387579523-7.78038757952336
32147.489184.926952533313-37.4379525333133
33143.824173.432384685125-29.6083846851251
34134.754139.883969831799-5.12996983179946
35131.736127.1466664569234.5893335430769
36126.304130.673137371871-4.36913737187055
37125.511119.0444483461116.46655165388938
38125.495125.593780731207-0.0987807312074693
39130.133120.10898209050810.024017909492
40126.257105.92815564946620.3288443505337
41110.32397.100448071529813.2225519284702
4298.41786.709167380077811.7078326199222
43105.749101.9190189991643.82998100083643
44120.665121.851808429494-1.18680842949372
45124.075134.390873293253-10.3158732932535
46127.245123.2560322335163.98896776648361
47146.731120.85815970984825.8728402901515
48144.979133.45004789658911.5289521034105
49148.21137.01703034618311.1929696538173
50144.67144.883117628552-0.213117628551714
51142.97145.49608199744-2.5260819974396
52142.524130.41218042555312.1118195744474
53146.142115.16013858063330.9818614193666
54146.522115.49925568023831.0227443197616
55148.128139.7714018516338.35659814836694
56148.798161.941704836096-13.1437048360956
57150.181165.569189583034-15.3881895830336
58152.388159.722069264881-7.33406926488053
59155.694162.357959314036-6.66395931403557
60160.662151.526034917479.13596508252957
61155.52154.5609441714260.959055828573582
62158.262152.4430977410445.81890225895626
63154.338156.230443881107-1.89244388110743
64158.196148.9232546324239.2727453675765
65160.371141.37290545297918.9980945470205
66154.856135.74387555665219.1121244433477
67150.636143.7431543844776.89284561552287
68145.899155.914792482284-10.0157924822835
69141.242160.741487049076-19.4994870490761
70140.834156.626677459881-15.792677459881
71141.119155.151723001848-14.0327230018476
72139.104147.454234569359-8.35023456935872
73134.437137.024722977954-2.58772297795429
74129.425134.920339864681-5.4953398646806
75123.155128.621234219819-5.46623421981917
76119.273123.887511080067-4.6145110800671
77120.472112.3365265919188.13547340808204
78121.52399.9053493451421.6176506548601
79121.983103.02281040379318.9601895962067
80123.658113.7014838022679.95651619773327
81124.794125.052411468092-0.258411468092035
82124.827133.268604243427-8.44160424342707
83120.382136.799624923596-16.4176249235956
84117.395130.438606619547-13.0436066195474
85115.79120.027978352994-4.23797835299443
86114.283115.722650746628-1.43965074662773
87117.271111.7570377096885.51396229031165
88117.448113.7333761905913.71462380940913
89118.764112.881378924385.88262107561951
90120.55105.58789325232714.9621067476732
91123.554104.0849132763619.4690867236396
92125.412111.27651246046814.1354875395316
93124.182120.6968166208733.48518337912689
94119.828127.711090173141-7.88309017314117
95115.361128.380621834522-13.0196218345223
96114.226125.857508714399-11.631508714399
97115.214120.637692373301-5.42369237330057
98115.864117.381886285159-1.51788628515904
99114.276116.934394197803-2.65839419780274
100113.469113.906504100355-0.43750410035463







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
101111.9789217951279.9180345773316144.039809012908
102105.64615524257468.7529674352973142.539343049851
10397.794249798521656.3968842244173139.191615372626
10491.42719645703845.7505652645845137.103827649492
10587.630352119797637.8358139991389137.424890240456
10686.939017718965333.1457422714561140.732293166474
10789.104123634169331.401728142495146.806519125844
10894.046657778878832.5032068585061155.590108699252
10997.869660210802432.5369988634763163.202321558128
11099.283540180687430.2009971882181168.366083173157
11199.114946491498426.311992484433171.917900498564
11298.542722856381422.0409308872353175.044514825528

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
101 & 111.97892179512 & 79.9180345773316 & 144.039809012908 \tabularnewline
102 & 105.646155242574 & 68.7529674352973 & 142.539343049851 \tabularnewline
103 & 97.7942497985216 & 56.3968842244173 & 139.191615372626 \tabularnewline
104 & 91.427196457038 & 45.7505652645845 & 137.103827649492 \tabularnewline
105 & 87.6303521197976 & 37.8358139991389 & 137.424890240456 \tabularnewline
106 & 86.9390177189653 & 33.1457422714561 & 140.732293166474 \tabularnewline
107 & 89.1041236341693 & 31.401728142495 & 146.806519125844 \tabularnewline
108 & 94.0466577788788 & 32.5032068585061 & 155.590108699252 \tabularnewline
109 & 97.8696602108024 & 32.5369988634763 & 163.202321558128 \tabularnewline
110 & 99.2835401806874 & 30.2009971882181 & 168.366083173157 \tabularnewline
111 & 99.1149464914984 & 26.311992484433 & 171.917900498564 \tabularnewline
112 & 98.5427228563814 & 22.0409308872353 & 175.044514825528 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122439&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]111.97892179512[/C][C]79.9180345773316[/C][C]144.039809012908[/C][/ROW]
[ROW][C]102[/C][C]105.646155242574[/C][C]68.7529674352973[/C][C]142.539343049851[/C][/ROW]
[ROW][C]103[/C][C]97.7942497985216[/C][C]56.3968842244173[/C][C]139.191615372626[/C][/ROW]
[ROW][C]104[/C][C]91.427196457038[/C][C]45.7505652645845[/C][C]137.103827649492[/C][/ROW]
[ROW][C]105[/C][C]87.6303521197976[/C][C]37.8358139991389[/C][C]137.424890240456[/C][/ROW]
[ROW][C]106[/C][C]86.9390177189653[/C][C]33.1457422714561[/C][C]140.732293166474[/C][/ROW]
[ROW][C]107[/C][C]89.1041236341693[/C][C]31.401728142495[/C][C]146.806519125844[/C][/ROW]
[ROW][C]108[/C][C]94.0466577788788[/C][C]32.5032068585061[/C][C]155.590108699252[/C][/ROW]
[ROW][C]109[/C][C]97.8696602108024[/C][C]32.5369988634763[/C][C]163.202321558128[/C][/ROW]
[ROW][C]110[/C][C]99.2835401806874[/C][C]30.2009971882181[/C][C]168.366083173157[/C][/ROW]
[ROW][C]111[/C][C]99.1149464914984[/C][C]26.311992484433[/C][C]171.917900498564[/C][/ROW]
[ROW][C]112[/C][C]98.5427228563814[/C][C]22.0409308872353[/C][C]175.044514825528[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122439&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122439&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
101111.9789217951279.9180345773316144.039809012908
102105.64615524257468.7529674352973142.539343049851
10397.794249798521656.3968842244173139.191615372626
10491.42719645703845.7505652645845137.103827649492
10587.630352119797637.8358139991389137.424890240456
10686.939017718965333.1457422714561140.732293166474
10789.104123634169331.401728142495146.806519125844
10894.046657778878832.5032068585061155.590108699252
10997.869660210802432.5369988634763163.202321558128
11099.283540180687430.2009971882181168.366083173157
11199.114946491498426.311992484433171.917900498564
11298.542722856381422.0409308872353175.044514825528



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')