Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 Dec 2011 06:55:18 -0500
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/Dec/21/t1324469111pqiqccdn1zq1488.htm/, Retrieved Tue, 07 May 2024 21:45:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158553, Retrieved Tue, 07 May 2024 21:45:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-21 11:55:18] [bd7a66e2f212a6bc9afe853e3942ee45] [Current]
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Dataseries X:
370.47
371.44
372.39
373.32
373.77
373.13
371.51
369.59
368.12
368.38
369.64
371.11
372.38
373.08
373.87
374.93
375.58
375.44
373.91
371.77
370.72
370.5
372.19
373.71
374.92
375.63
376.51
377.75
378.54
378.21
376.65
374.28
373.12
373.1
374.67
375.97
377.03
377.87
378.88
380.42
380.62
379.66
377.48
376.07
374.1
374.47
376.15
377.51
378.43
379.7
380.91
382.2
382.45
382.14
380.6
378.6
376.72
376.98
378.29
380.07
381.36
382.19
382.65
384.65
384.94
384.01
382.15
380.33
378.81
379.06
380.17
381.85
382.88
383.77
384.42
386.36
386.53
386.01
384.45
381.96
380.81
381.09
382.37
383.84
385.42
385.72
385.96
387.18
388.5
387.88
386.38
384.15
383.07
382.98
384.11
385.54
386.92
387.41
388.77
389.46
390.18
389.43
387.74
385.91
384.77
384.38
385.99
387.26




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158553&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158553&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158553&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.56048240064318
beta0
gamma0.162957094258162

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.56048240064318 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.162957094258162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158553&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]0.56048240064318[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.162957094258162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158553&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158553&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
alpha0.56048240064318
beta0
gamma0.162957094258162







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13372.38371.4434962606840.936503739316322
14373.08372.6522115116530.427788488346607
15373.87373.6574674841820.212532515817543
16374.93374.8145762724760.11542372752433
17375.58375.5093406273160.070659372683906
18375.44375.3690153490920.0709846509076328
19373.91373.5663723835880.343627616411823
20371.77371.865707668575-0.0957076685750735
21370.72370.3867199250120.333280074988124
22370.5370.879422261808-0.37942226180752
23372.19371.9589174819320.231082518068149
24373.71373.5614232200180.148576779981624
25374.92374.960177359868-0.0401773598676982
26375.63375.5850445801130.0449554198866053
27376.51376.3603121821550.14968781784512
28377.75377.4752424480160.274757551983953
29378.54378.2561044718020.283895528197775
30378.21378.235317603168-0.0253176031679914
31376.65376.3982262928720.251773707128336
32374.28374.614612782052-0.334612782051806
33373.12373.0324481062860.087551893713794
34373.1373.336378591274-0.236378591273763
35374.67374.5397731564860.13022684351364
36375.97376.079841795857-0.109841795857392
37377.03377.320237826517-0.290237826517341
38377.87377.8110479795520.0589520204476912
39378.88378.6016616271880.278338372812016
40380.42379.7976560733340.622343926666474
41380.62380.773988627633-0.153988627633339
42379.66380.485628775274-0.825628775273913
43377.48378.219823113357-0.739823113356863
44376.07375.8384385634280.231561436571951
45374.1374.603841066976-0.503841066976463
46374.47374.553105490952-0.083105490951823
47376.15375.8686641331240.281335866876248
48377.51377.4762324019360.0337675980641734
49378.43378.78419855379-0.354198553789558
50379.7379.2641696984650.435830301535134
51380.91380.2817299912410.628270008759159
52382.2381.6984935022820.501506497717855
53382.45382.551495917511-0.101495917510874
54382.14382.244452751564-0.104452751564395
55380.6380.3889991756550.211000824344637
56378.6378.610107709401-0.010107709401268
57376.72377.187387536052-0.467387536051547
58376.98377.187217660917-0.207217660917422
59378.29378.459315821229-0.169315821229191
60380.07379.7965702890150.273429710985113
61381.36381.2110757273350.148924272665226
62382.19382.0296222118750.160377788124777
63382.65382.906579233694-0.256579233693628
64384.65383.8183211961710.831678803829391
65384.94384.8131908311170.12680916888263
66384.01384.633896872193-0.623896872192631
67382.15382.509897585722-0.359897585722365
68380.33380.39519125971-0.0651912597097066
69378.81378.908846196494-0.0988461964938665
70379.06379.1338712758-0.0738712758002293
71380.17380.483422363084-0.313422363084442
72381.85381.7716181970350.0783818029652252
73382.88383.067885323518-0.187885323518287
74383.77383.6984762865660.0715237134344306
75384.42384.495768654468-0.0757686544684475
76386.36385.5867955375690.77320446243067
77386.53386.4984068001850.031593199815461
78386.01386.211978514753-0.201978514752966
79384.45384.34336533390.106634666100149
80381.96382.511249731403-0.551249731403402
81380.81380.7500669980440.0599330019558124
82381.09381.0658737901990.024126209801409
83382.37382.453193493118-0.0831934931177329
84383.84383.898490554945-0.0584905549448536
85385.42385.0989724135250.321027586474827
86385.72386.033379632652-0.313379632651731
87385.96386.604390999904-0.64439099990409
88387.18387.437520652066-0.257520652066262
89388.5387.718312567390.781687432610397
90387.88387.8355699055990.0444300944012639
91386.38386.1271680644430.252831935557253
92384.15384.32987412609-0.179874126089999
93383.07382.8206153254990.249384674501414
94382.98383.240041873527-0.26004187352703
95384.11384.460403860328-0.35040386032756
96385.54385.757703500522-0.21770350052185
97386.92386.896131347360.023868652640374
98387.41387.618548375932-0.208548375932423
99388.77388.2246079523650.545392047634721
100389.46389.752298688949-0.292298688948563
101390.18390.0880288190080.0919711809922319
102389.43389.76590811503-0.335908115030065
103387.74387.859259664328-0.119259664328467
104385.91385.822423438210.0875765617897741
105384.77384.4938106343250.276189365674725
106384.38384.891774331539-0.511774331539129
107385.99385.9645727535720.0254272464283076
108387.26387.482023447679-0.222023447679135

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 372.38 & 371.443496260684 & 0.936503739316322 \tabularnewline
14 & 373.08 & 372.652211511653 & 0.427788488346607 \tabularnewline
15 & 373.87 & 373.657467484182 & 0.212532515817543 \tabularnewline
16 & 374.93 & 374.814576272476 & 0.11542372752433 \tabularnewline
17 & 375.58 & 375.509340627316 & 0.070659372683906 \tabularnewline
18 & 375.44 & 375.369015349092 & 0.0709846509076328 \tabularnewline
19 & 373.91 & 373.566372383588 & 0.343627616411823 \tabularnewline
20 & 371.77 & 371.865707668575 & -0.0957076685750735 \tabularnewline
21 & 370.72 & 370.386719925012 & 0.333280074988124 \tabularnewline
22 & 370.5 & 370.879422261808 & -0.37942226180752 \tabularnewline
23 & 372.19 & 371.958917481932 & 0.231082518068149 \tabularnewline
24 & 373.71 & 373.561423220018 & 0.148576779981624 \tabularnewline
25 & 374.92 & 374.960177359868 & -0.0401773598676982 \tabularnewline
26 & 375.63 & 375.585044580113 & 0.0449554198866053 \tabularnewline
27 & 376.51 & 376.360312182155 & 0.14968781784512 \tabularnewline
28 & 377.75 & 377.475242448016 & 0.274757551983953 \tabularnewline
29 & 378.54 & 378.256104471802 & 0.283895528197775 \tabularnewline
30 & 378.21 & 378.235317603168 & -0.0253176031679914 \tabularnewline
31 & 376.65 & 376.398226292872 & 0.251773707128336 \tabularnewline
32 & 374.28 & 374.614612782052 & -0.334612782051806 \tabularnewline
33 & 373.12 & 373.032448106286 & 0.087551893713794 \tabularnewline
34 & 373.1 & 373.336378591274 & -0.236378591273763 \tabularnewline
35 & 374.67 & 374.539773156486 & 0.13022684351364 \tabularnewline
36 & 375.97 & 376.079841795857 & -0.109841795857392 \tabularnewline
37 & 377.03 & 377.320237826517 & -0.290237826517341 \tabularnewline
38 & 377.87 & 377.811047979552 & 0.0589520204476912 \tabularnewline
39 & 378.88 & 378.601661627188 & 0.278338372812016 \tabularnewline
40 & 380.42 & 379.797656073334 & 0.622343926666474 \tabularnewline
41 & 380.62 & 380.773988627633 & -0.153988627633339 \tabularnewline
42 & 379.66 & 380.485628775274 & -0.825628775273913 \tabularnewline
43 & 377.48 & 378.219823113357 & -0.739823113356863 \tabularnewline
44 & 376.07 & 375.838438563428 & 0.231561436571951 \tabularnewline
45 & 374.1 & 374.603841066976 & -0.503841066976463 \tabularnewline
46 & 374.47 & 374.553105490952 & -0.083105490951823 \tabularnewline
47 & 376.15 & 375.868664133124 & 0.281335866876248 \tabularnewline
48 & 377.51 & 377.476232401936 & 0.0337675980641734 \tabularnewline
49 & 378.43 & 378.78419855379 & -0.354198553789558 \tabularnewline
50 & 379.7 & 379.264169698465 & 0.435830301535134 \tabularnewline
51 & 380.91 & 380.281729991241 & 0.628270008759159 \tabularnewline
52 & 382.2 & 381.698493502282 & 0.501506497717855 \tabularnewline
53 & 382.45 & 382.551495917511 & -0.101495917510874 \tabularnewline
54 & 382.14 & 382.244452751564 & -0.104452751564395 \tabularnewline
55 & 380.6 & 380.388999175655 & 0.211000824344637 \tabularnewline
56 & 378.6 & 378.610107709401 & -0.010107709401268 \tabularnewline
57 & 376.72 & 377.187387536052 & -0.467387536051547 \tabularnewline
58 & 376.98 & 377.187217660917 & -0.207217660917422 \tabularnewline
59 & 378.29 & 378.459315821229 & -0.169315821229191 \tabularnewline
60 & 380.07 & 379.796570289015 & 0.273429710985113 \tabularnewline
61 & 381.36 & 381.211075727335 & 0.148924272665226 \tabularnewline
62 & 382.19 & 382.029622211875 & 0.160377788124777 \tabularnewline
63 & 382.65 & 382.906579233694 & -0.256579233693628 \tabularnewline
64 & 384.65 & 383.818321196171 & 0.831678803829391 \tabularnewline
65 & 384.94 & 384.813190831117 & 0.12680916888263 \tabularnewline
66 & 384.01 & 384.633896872193 & -0.623896872192631 \tabularnewline
67 & 382.15 & 382.509897585722 & -0.359897585722365 \tabularnewline
68 & 380.33 & 380.39519125971 & -0.0651912597097066 \tabularnewline
69 & 378.81 & 378.908846196494 & -0.0988461964938665 \tabularnewline
70 & 379.06 & 379.1338712758 & -0.0738712758002293 \tabularnewline
71 & 380.17 & 380.483422363084 & -0.313422363084442 \tabularnewline
72 & 381.85 & 381.771618197035 & 0.0783818029652252 \tabularnewline
73 & 382.88 & 383.067885323518 & -0.187885323518287 \tabularnewline
74 & 383.77 & 383.698476286566 & 0.0715237134344306 \tabularnewline
75 & 384.42 & 384.495768654468 & -0.0757686544684475 \tabularnewline
76 & 386.36 & 385.586795537569 & 0.77320446243067 \tabularnewline
77 & 386.53 & 386.498406800185 & 0.031593199815461 \tabularnewline
78 & 386.01 & 386.211978514753 & -0.201978514752966 \tabularnewline
79 & 384.45 & 384.3433653339 & 0.106634666100149 \tabularnewline
80 & 381.96 & 382.511249731403 & -0.551249731403402 \tabularnewline
81 & 380.81 & 380.750066998044 & 0.0599330019558124 \tabularnewline
82 & 381.09 & 381.065873790199 & 0.024126209801409 \tabularnewline
83 & 382.37 & 382.453193493118 & -0.0831934931177329 \tabularnewline
84 & 383.84 & 383.898490554945 & -0.0584905549448536 \tabularnewline
85 & 385.42 & 385.098972413525 & 0.321027586474827 \tabularnewline
86 & 385.72 & 386.033379632652 & -0.313379632651731 \tabularnewline
87 & 385.96 & 386.604390999904 & -0.64439099990409 \tabularnewline
88 & 387.18 & 387.437520652066 & -0.257520652066262 \tabularnewline
89 & 388.5 & 387.71831256739 & 0.781687432610397 \tabularnewline
90 & 387.88 & 387.835569905599 & 0.0444300944012639 \tabularnewline
91 & 386.38 & 386.127168064443 & 0.252831935557253 \tabularnewline
92 & 384.15 & 384.32987412609 & -0.179874126089999 \tabularnewline
93 & 383.07 & 382.820615325499 & 0.249384674501414 \tabularnewline
94 & 382.98 & 383.240041873527 & -0.26004187352703 \tabularnewline
95 & 384.11 & 384.460403860328 & -0.35040386032756 \tabularnewline
96 & 385.54 & 385.757703500522 & -0.21770350052185 \tabularnewline
97 & 386.92 & 386.89613134736 & 0.023868652640374 \tabularnewline
98 & 387.41 & 387.618548375932 & -0.208548375932423 \tabularnewline
99 & 388.77 & 388.224607952365 & 0.545392047634721 \tabularnewline
100 & 389.46 & 389.752298688949 & -0.292298688948563 \tabularnewline
101 & 390.18 & 390.088028819008 & 0.0919711809922319 \tabularnewline
102 & 389.43 & 389.76590811503 & -0.335908115030065 \tabularnewline
103 & 387.74 & 387.859259664328 & -0.119259664328467 \tabularnewline
104 & 385.91 & 385.82242343821 & 0.0875765617897741 \tabularnewline
105 & 384.77 & 384.493810634325 & 0.276189365674725 \tabularnewline
106 & 384.38 & 384.891774331539 & -0.511774331539129 \tabularnewline
107 & 385.99 & 385.964572753572 & 0.0254272464283076 \tabularnewline
108 & 387.26 & 387.482023447679 & -0.222023447679135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158553&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]372.38[/C][C]371.443496260684[/C][C]0.936503739316322[/C][/ROW]
[ROW][C]14[/C][C]373.08[/C][C]372.652211511653[/C][C]0.427788488346607[/C][/ROW]
[ROW][C]15[/C][C]373.87[/C][C]373.657467484182[/C][C]0.212532515817543[/C][/ROW]
[ROW][C]16[/C][C]374.93[/C][C]374.814576272476[/C][C]0.11542372752433[/C][/ROW]
[ROW][C]17[/C][C]375.58[/C][C]375.509340627316[/C][C]0.070659372683906[/C][/ROW]
[ROW][C]18[/C][C]375.44[/C][C]375.369015349092[/C][C]0.0709846509076328[/C][/ROW]
[ROW][C]19[/C][C]373.91[/C][C]373.566372383588[/C][C]0.343627616411823[/C][/ROW]
[ROW][C]20[/C][C]371.77[/C][C]371.865707668575[/C][C]-0.0957076685750735[/C][/ROW]
[ROW][C]21[/C][C]370.72[/C][C]370.386719925012[/C][C]0.333280074988124[/C][/ROW]
[ROW][C]22[/C][C]370.5[/C][C]370.879422261808[/C][C]-0.37942226180752[/C][/ROW]
[ROW][C]23[/C][C]372.19[/C][C]371.958917481932[/C][C]0.231082518068149[/C][/ROW]
[ROW][C]24[/C][C]373.71[/C][C]373.561423220018[/C][C]0.148576779981624[/C][/ROW]
[ROW][C]25[/C][C]374.92[/C][C]374.960177359868[/C][C]-0.0401773598676982[/C][/ROW]
[ROW][C]26[/C][C]375.63[/C][C]375.585044580113[/C][C]0.0449554198866053[/C][/ROW]
[ROW][C]27[/C][C]376.51[/C][C]376.360312182155[/C][C]0.14968781784512[/C][/ROW]
[ROW][C]28[/C][C]377.75[/C][C]377.475242448016[/C][C]0.274757551983953[/C][/ROW]
[ROW][C]29[/C][C]378.54[/C][C]378.256104471802[/C][C]0.283895528197775[/C][/ROW]
[ROW][C]30[/C][C]378.21[/C][C]378.235317603168[/C][C]-0.0253176031679914[/C][/ROW]
[ROW][C]31[/C][C]376.65[/C][C]376.398226292872[/C][C]0.251773707128336[/C][/ROW]
[ROW][C]32[/C][C]374.28[/C][C]374.614612782052[/C][C]-0.334612782051806[/C][/ROW]
[ROW][C]33[/C][C]373.12[/C][C]373.032448106286[/C][C]0.087551893713794[/C][/ROW]
[ROW][C]34[/C][C]373.1[/C][C]373.336378591274[/C][C]-0.236378591273763[/C][/ROW]
[ROW][C]35[/C][C]374.67[/C][C]374.539773156486[/C][C]0.13022684351364[/C][/ROW]
[ROW][C]36[/C][C]375.97[/C][C]376.079841795857[/C][C]-0.109841795857392[/C][/ROW]
[ROW][C]37[/C][C]377.03[/C][C]377.320237826517[/C][C]-0.290237826517341[/C][/ROW]
[ROW][C]38[/C][C]377.87[/C][C]377.811047979552[/C][C]0.0589520204476912[/C][/ROW]
[ROW][C]39[/C][C]378.88[/C][C]378.601661627188[/C][C]0.278338372812016[/C][/ROW]
[ROW][C]40[/C][C]380.42[/C][C]379.797656073334[/C][C]0.622343926666474[/C][/ROW]
[ROW][C]41[/C][C]380.62[/C][C]380.773988627633[/C][C]-0.153988627633339[/C][/ROW]
[ROW][C]42[/C][C]379.66[/C][C]380.485628775274[/C][C]-0.825628775273913[/C][/ROW]
[ROW][C]43[/C][C]377.48[/C][C]378.219823113357[/C][C]-0.739823113356863[/C][/ROW]
[ROW][C]44[/C][C]376.07[/C][C]375.838438563428[/C][C]0.231561436571951[/C][/ROW]
[ROW][C]45[/C][C]374.1[/C][C]374.603841066976[/C][C]-0.503841066976463[/C][/ROW]
[ROW][C]46[/C][C]374.47[/C][C]374.553105490952[/C][C]-0.083105490951823[/C][/ROW]
[ROW][C]47[/C][C]376.15[/C][C]375.868664133124[/C][C]0.281335866876248[/C][/ROW]
[ROW][C]48[/C][C]377.51[/C][C]377.476232401936[/C][C]0.0337675980641734[/C][/ROW]
[ROW][C]49[/C][C]378.43[/C][C]378.78419855379[/C][C]-0.354198553789558[/C][/ROW]
[ROW][C]50[/C][C]379.7[/C][C]379.264169698465[/C][C]0.435830301535134[/C][/ROW]
[ROW][C]51[/C][C]380.91[/C][C]380.281729991241[/C][C]0.628270008759159[/C][/ROW]
[ROW][C]52[/C][C]382.2[/C][C]381.698493502282[/C][C]0.501506497717855[/C][/ROW]
[ROW][C]53[/C][C]382.45[/C][C]382.551495917511[/C][C]-0.101495917510874[/C][/ROW]
[ROW][C]54[/C][C]382.14[/C][C]382.244452751564[/C][C]-0.104452751564395[/C][/ROW]
[ROW][C]55[/C][C]380.6[/C][C]380.388999175655[/C][C]0.211000824344637[/C][/ROW]
[ROW][C]56[/C][C]378.6[/C][C]378.610107709401[/C][C]-0.010107709401268[/C][/ROW]
[ROW][C]57[/C][C]376.72[/C][C]377.187387536052[/C][C]-0.467387536051547[/C][/ROW]
[ROW][C]58[/C][C]376.98[/C][C]377.187217660917[/C][C]-0.207217660917422[/C][/ROW]
[ROW][C]59[/C][C]378.29[/C][C]378.459315821229[/C][C]-0.169315821229191[/C][/ROW]
[ROW][C]60[/C][C]380.07[/C][C]379.796570289015[/C][C]0.273429710985113[/C][/ROW]
[ROW][C]61[/C][C]381.36[/C][C]381.211075727335[/C][C]0.148924272665226[/C][/ROW]
[ROW][C]62[/C][C]382.19[/C][C]382.029622211875[/C][C]0.160377788124777[/C][/ROW]
[ROW][C]63[/C][C]382.65[/C][C]382.906579233694[/C][C]-0.256579233693628[/C][/ROW]
[ROW][C]64[/C][C]384.65[/C][C]383.818321196171[/C][C]0.831678803829391[/C][/ROW]
[ROW][C]65[/C][C]384.94[/C][C]384.813190831117[/C][C]0.12680916888263[/C][/ROW]
[ROW][C]66[/C][C]384.01[/C][C]384.633896872193[/C][C]-0.623896872192631[/C][/ROW]
[ROW][C]67[/C][C]382.15[/C][C]382.509897585722[/C][C]-0.359897585722365[/C][/ROW]
[ROW][C]68[/C][C]380.33[/C][C]380.39519125971[/C][C]-0.0651912597097066[/C][/ROW]
[ROW][C]69[/C][C]378.81[/C][C]378.908846196494[/C][C]-0.0988461964938665[/C][/ROW]
[ROW][C]70[/C][C]379.06[/C][C]379.1338712758[/C][C]-0.0738712758002293[/C][/ROW]
[ROW][C]71[/C][C]380.17[/C][C]380.483422363084[/C][C]-0.313422363084442[/C][/ROW]
[ROW][C]72[/C][C]381.85[/C][C]381.771618197035[/C][C]0.0783818029652252[/C][/ROW]
[ROW][C]73[/C][C]382.88[/C][C]383.067885323518[/C][C]-0.187885323518287[/C][/ROW]
[ROW][C]74[/C][C]383.77[/C][C]383.698476286566[/C][C]0.0715237134344306[/C][/ROW]
[ROW][C]75[/C][C]384.42[/C][C]384.495768654468[/C][C]-0.0757686544684475[/C][/ROW]
[ROW][C]76[/C][C]386.36[/C][C]385.586795537569[/C][C]0.77320446243067[/C][/ROW]
[ROW][C]77[/C][C]386.53[/C][C]386.498406800185[/C][C]0.031593199815461[/C][/ROW]
[ROW][C]78[/C][C]386.01[/C][C]386.211978514753[/C][C]-0.201978514752966[/C][/ROW]
[ROW][C]79[/C][C]384.45[/C][C]384.3433653339[/C][C]0.106634666100149[/C][/ROW]
[ROW][C]80[/C][C]381.96[/C][C]382.511249731403[/C][C]-0.551249731403402[/C][/ROW]
[ROW][C]81[/C][C]380.81[/C][C]380.750066998044[/C][C]0.0599330019558124[/C][/ROW]
[ROW][C]82[/C][C]381.09[/C][C]381.065873790199[/C][C]0.024126209801409[/C][/ROW]
[ROW][C]83[/C][C]382.37[/C][C]382.453193493118[/C][C]-0.0831934931177329[/C][/ROW]
[ROW][C]84[/C][C]383.84[/C][C]383.898490554945[/C][C]-0.0584905549448536[/C][/ROW]
[ROW][C]85[/C][C]385.42[/C][C]385.098972413525[/C][C]0.321027586474827[/C][/ROW]
[ROW][C]86[/C][C]385.72[/C][C]386.033379632652[/C][C]-0.313379632651731[/C][/ROW]
[ROW][C]87[/C][C]385.96[/C][C]386.604390999904[/C][C]-0.64439099990409[/C][/ROW]
[ROW][C]88[/C][C]387.18[/C][C]387.437520652066[/C][C]-0.257520652066262[/C][/ROW]
[ROW][C]89[/C][C]388.5[/C][C]387.71831256739[/C][C]0.781687432610397[/C][/ROW]
[ROW][C]90[/C][C]387.88[/C][C]387.835569905599[/C][C]0.0444300944012639[/C][/ROW]
[ROW][C]91[/C][C]386.38[/C][C]386.127168064443[/C][C]0.252831935557253[/C][/ROW]
[ROW][C]92[/C][C]384.15[/C][C]384.32987412609[/C][C]-0.179874126089999[/C][/ROW]
[ROW][C]93[/C][C]383.07[/C][C]382.820615325499[/C][C]0.249384674501414[/C][/ROW]
[ROW][C]94[/C][C]382.98[/C][C]383.240041873527[/C][C]-0.26004187352703[/C][/ROW]
[ROW][C]95[/C][C]384.11[/C][C]384.460403860328[/C][C]-0.35040386032756[/C][/ROW]
[ROW][C]96[/C][C]385.54[/C][C]385.757703500522[/C][C]-0.21770350052185[/C][/ROW]
[ROW][C]97[/C][C]386.92[/C][C]386.89613134736[/C][C]0.023868652640374[/C][/ROW]
[ROW][C]98[/C][C]387.41[/C][C]387.618548375932[/C][C]-0.208548375932423[/C][/ROW]
[ROW][C]99[/C][C]388.77[/C][C]388.224607952365[/C][C]0.545392047634721[/C][/ROW]
[ROW][C]100[/C][C]389.46[/C][C]389.752298688949[/C][C]-0.292298688948563[/C][/ROW]
[ROW][C]101[/C][C]390.18[/C][C]390.088028819008[/C][C]0.0919711809922319[/C][/ROW]
[ROW][C]102[/C][C]389.43[/C][C]389.76590811503[/C][C]-0.335908115030065[/C][/ROW]
[ROW][C]103[/C][C]387.74[/C][C]387.859259664328[/C][C]-0.119259664328467[/C][/ROW]
[ROW][C]104[/C][C]385.91[/C][C]385.82242343821[/C][C]0.0875765617897741[/C][/ROW]
[ROW][C]105[/C][C]384.77[/C][C]384.493810634325[/C][C]0.276189365674725[/C][/ROW]
[ROW][C]106[/C][C]384.38[/C][C]384.891774331539[/C][C]-0.511774331539129[/C][/ROW]
[ROW][C]107[/C][C]385.99[/C][C]385.964572753572[/C][C]0.0254272464283076[/C][/ROW]
[ROW][C]108[/C][C]387.26[/C][C]387.482023447679[/C][C]-0.222023447679135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158553&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158553&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
13372.38371.4434962606840.936503739316322
14373.08372.6522115116530.427788488346607
15373.87373.6574674841820.212532515817543
16374.93374.8145762724760.11542372752433
17375.58375.5093406273160.070659372683906
18375.44375.3690153490920.0709846509076328
19373.91373.5663723835880.343627616411823
20371.77371.865707668575-0.0957076685750735
21370.72370.3867199250120.333280074988124
22370.5370.879422261808-0.37942226180752
23372.19371.9589174819320.231082518068149
24373.71373.5614232200180.148576779981624
25374.92374.960177359868-0.0401773598676982
26375.63375.5850445801130.0449554198866053
27376.51376.3603121821550.14968781784512
28377.75377.4752424480160.274757551983953
29378.54378.2561044718020.283895528197775
30378.21378.235317603168-0.0253176031679914
31376.65376.3982262928720.251773707128336
32374.28374.614612782052-0.334612782051806
33373.12373.0324481062860.087551893713794
34373.1373.336378591274-0.236378591273763
35374.67374.5397731564860.13022684351364
36375.97376.079841795857-0.109841795857392
37377.03377.320237826517-0.290237826517341
38377.87377.8110479795520.0589520204476912
39378.88378.6016616271880.278338372812016
40380.42379.7976560733340.622343926666474
41380.62380.773988627633-0.153988627633339
42379.66380.485628775274-0.825628775273913
43377.48378.219823113357-0.739823113356863
44376.07375.8384385634280.231561436571951
45374.1374.603841066976-0.503841066976463
46374.47374.553105490952-0.083105490951823
47376.15375.8686641331240.281335866876248
48377.51377.4762324019360.0337675980641734
49378.43378.78419855379-0.354198553789558
50379.7379.2641696984650.435830301535134
51380.91380.2817299912410.628270008759159
52382.2381.6984935022820.501506497717855
53382.45382.551495917511-0.101495917510874
54382.14382.244452751564-0.104452751564395
55380.6380.3889991756550.211000824344637
56378.6378.610107709401-0.010107709401268
57376.72377.187387536052-0.467387536051547
58376.98377.187217660917-0.207217660917422
59378.29378.459315821229-0.169315821229191
60380.07379.7965702890150.273429710985113
61381.36381.2110757273350.148924272665226
62382.19382.0296222118750.160377788124777
63382.65382.906579233694-0.256579233693628
64384.65383.8183211961710.831678803829391
65384.94384.8131908311170.12680916888263
66384.01384.633896872193-0.623896872192631
67382.15382.509897585722-0.359897585722365
68380.33380.39519125971-0.0651912597097066
69378.81378.908846196494-0.0988461964938665
70379.06379.1338712758-0.0738712758002293
71380.17380.483422363084-0.313422363084442
72381.85381.7716181970350.0783818029652252
73382.88383.067885323518-0.187885323518287
74383.77383.6984762865660.0715237134344306
75384.42384.495768654468-0.0757686544684475
76386.36385.5867955375690.77320446243067
77386.53386.4984068001850.031593199815461
78386.01386.211978514753-0.201978514752966
79384.45384.34336533390.106634666100149
80381.96382.511249731403-0.551249731403402
81380.81380.7500669980440.0599330019558124
82381.09381.0658737901990.024126209801409
83382.37382.453193493118-0.0831934931177329
84383.84383.898490554945-0.0584905549448536
85385.42385.0989724135250.321027586474827
86385.72386.033379632652-0.313379632651731
87385.96386.604390999904-0.64439099990409
88387.18387.437520652066-0.257520652066262
89388.5387.718312567390.781687432610397
90387.88387.8355699055990.0444300944012639
91386.38386.1271680644430.252831935557253
92384.15384.32987412609-0.179874126089999
93383.07382.8206153254990.249384674501414
94382.98383.240041873527-0.26004187352703
95384.11384.460403860328-0.35040386032756
96385.54385.757703500522-0.21770350052185
97386.92386.896131347360.023868652640374
98387.41387.618548375932-0.208548375932423
99388.77388.2246079523650.545392047634721
100389.46389.752298688949-0.292298688948563
101390.18390.0880288190080.0919711809922319
102389.43389.76590811503-0.335908115030065
103387.74387.859259664328-0.119259664328467
104385.91385.822423438210.0875765617897741
105384.77384.4938106343250.276189365674725
106384.38384.891774331539-0.511774331539129
107385.99385.9645727535720.0254272464283076
108387.26387.482023447679-0.222023447679135







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109388.635332044328387.975887762532389.294776326125
110389.327724822015388.571764484575390.083685159455
111390.10467119902389.263193152502390.946149245538
112391.26668177757390.347609107015392.185754448124
113391.793762551451390.803154735639392.784370367264
114391.389447829632390.332133725055392.446761934209
115389.686586871652388.566532236054390.806641507251
116387.73140771835386.551945273965388.910870162735
117386.367218715469385.13120054056387.603236890377
118386.553947195511385.263850222531387.844044168491
119387.952061849328386.610063536854389.294060161801
120389.437537979288388.045572196062390.829503762513

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 388.635332044328 & 387.975887762532 & 389.294776326125 \tabularnewline
110 & 389.327724822015 & 388.571764484575 & 390.083685159455 \tabularnewline
111 & 390.10467119902 & 389.263193152502 & 390.946149245538 \tabularnewline
112 & 391.26668177757 & 390.347609107015 & 392.185754448124 \tabularnewline
113 & 391.793762551451 & 390.803154735639 & 392.784370367264 \tabularnewline
114 & 391.389447829632 & 390.332133725055 & 392.446761934209 \tabularnewline
115 & 389.686586871652 & 388.566532236054 & 390.806641507251 \tabularnewline
116 & 387.73140771835 & 386.551945273965 & 388.910870162735 \tabularnewline
117 & 386.367218715469 & 385.13120054056 & 387.603236890377 \tabularnewline
118 & 386.553947195511 & 385.263850222531 & 387.844044168491 \tabularnewline
119 & 387.952061849328 & 386.610063536854 & 389.294060161801 \tabularnewline
120 & 389.437537979288 & 388.045572196062 & 390.829503762513 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158553&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]109[/C][C]388.635332044328[/C][C]387.975887762532[/C][C]389.294776326125[/C][/ROW]
[ROW][C]110[/C][C]389.327724822015[/C][C]388.571764484575[/C][C]390.083685159455[/C][/ROW]
[ROW][C]111[/C][C]390.10467119902[/C][C]389.263193152502[/C][C]390.946149245538[/C][/ROW]
[ROW][C]112[/C][C]391.26668177757[/C][C]390.347609107015[/C][C]392.185754448124[/C][/ROW]
[ROW][C]113[/C][C]391.793762551451[/C][C]390.803154735639[/C][C]392.784370367264[/C][/ROW]
[ROW][C]114[/C][C]391.389447829632[/C][C]390.332133725055[/C][C]392.446761934209[/C][/ROW]
[ROW][C]115[/C][C]389.686586871652[/C][C]388.566532236054[/C][C]390.806641507251[/C][/ROW]
[ROW][C]116[/C][C]387.73140771835[/C][C]386.551945273965[/C][C]388.910870162735[/C][/ROW]
[ROW][C]117[/C][C]386.367218715469[/C][C]385.13120054056[/C][C]387.603236890377[/C][/ROW]
[ROW][C]118[/C][C]386.553947195511[/C][C]385.263850222531[/C][C]387.844044168491[/C][/ROW]
[ROW][C]119[/C][C]387.952061849328[/C][C]386.610063536854[/C][C]389.294060161801[/C][/ROW]
[ROW][C]120[/C][C]389.437537979288[/C][C]388.045572196062[/C][C]390.829503762513[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158553&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158553&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
109388.635332044328387.975887762532389.294776326125
110389.327724822015388.571764484575390.083685159455
111390.10467119902389.263193152502390.946149245538
112391.26668177757390.347609107015392.185754448124
113391.793762551451390.803154735639392.784370367264
114391.389447829632390.332133725055392.446761934209
115389.686586871652388.566532236054390.806641507251
116387.73140771835386.551945273965388.910870162735
117386.367218715469385.13120054056387.603236890377
118386.553947195511385.263850222531387.844044168491
119387.952061849328386.610063536854389.294060161801
120389.437537979288388.045572196062390.829503762513



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')