Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Aug 2011 04:11:02 -0400
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/Aug/18/t1313655471anu5tnpx2dgfin0.htm/, Retrieved Wed, 15 May 2024 19:03:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124000, Retrieved Wed, 15 May 2024 19:03:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsYannick De Pelsmaeker
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Tijdreeks A - Sta...] [2011-08-11 09:54:15] [73148e40994d778578e43e2ad3ecd67d]
- R  D    [Exponential Smoothing] [Tijdreeks A stap 32] [2011-08-18 08:11:02] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
567
557
547
527
729
719
567
466
476
476
486
507
446
385
335
335
527
547
395
223
314
314
385
426
416
314
365
345
517
476
314
193
304
335
365
405
324
254
284
294
557
557
405
385
446
416
497
598
618
476
436
395
669
689
638
689
679
598
689
790
831
709
628
689
952
1033
1013
1053
1043
942
1114
1155
1215
1033
962
1043
1236
1408
1367
1367
1387
1317
1499
1499
1468
1296
1327
1347
1479
1651
1529
1590
1539
1509
1742
1691
1620
1519
1620
1671
1732
1813
1732
1782
1721
1711
1964
1985
1904
1762
1883
1934
1995
2086
1995
2066
2035
1924
2157
2157




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124000&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124000&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124000&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.65322086051567
beta0.0529560726860348
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.65322086051567 \tabularnewline
beta & 0.0529560726860348 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124000&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]0.65322086051567[/C][/ROW]
[ROW][C]beta[/C][C]0.0529560726860348[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124000&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124000&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
alpha0.65322086051567
beta0.0529560726860348
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13446538.398504273504-92.3985042735042
14385416.074936045563-31.0749360455633
15335343.317590617708-8.31759061770799
16335331.7630957640743.23690423592586
17527517.3265423430199.67345765698076
18547532.05410424367414.9458957563264
19395385.5760746258629.42392537413832
20223284.608637963609-61.6086379636091
21314249.90174911500964.0982508849907
22314290.35984312955223.6401568704484
23385314.79096006566370.2090399343366
24426382.23718144433943.7628185556611
25416318.63014945208297.369850547918
26314349.674509359831-35.6745093598307
27365289.78683674606575.2131632539346
28345347.67516477416-2.67516477416007
29517542.276210820745-25.2762108207453
30476545.460736238614-69.4607362386139
31314348.47027901271-34.4702790127104
32193199.21788169666-6.2178816966603
33304251.22225523115352.7777447688473
34335276.8002745628358.19972543717
35365347.69576389290717.3042361070932
36405377.32260640245527.6773935975454
37324327.151753003473-3.15175300347261
38254248.2727647455765.72723525442433
39284257.19174553308126.8082544669194
40294258.08514533465835.9148546653424
41557473.02554749252683.9744525074742
42557539.0009354117817.9990645882197
43405421.048737507199-16.0487375071992
44385304.03798790596380.9620120940371
45446446.875237629256-0.875237629256162
46416450.85697321108-34.8569732110801
47497455.13589858808341.8641014119173
48598513.60424262768784.3957573723133
49618500.955395529134117.044604470866
50476518.991349841135-42.9913498411354
51436517.03264500394-81.0326450039399
52395460.545517766787-65.5455177667873
53669632.27165489520336.7283451047972
54689649.26737452188939.7326254781112
55638539.21809492810198.7819050718991
56689540.343814123271148.656185876729
57679710.847930258998-31.8479302589978
58598693.569163148907-95.5691631489075
59689693.450394307833-4.45039430783299
60790743.46762959013746.5323704098632
61831723.151191603948107.848808396052
62709685.10865270961423.8913472903863
63628721.3863234061-93.3863234060999
64689669.51191996644319.4880800335571
65952942.5034939404929.49650605950751
661033952.06390066875480.9360993312463
671013900.143229795776112.856770204224
681053938.981764288432114.018235711568
6910431034.289849982138.71015001787441
709421032.83552147526-90.8355214752555
7111141078.9989493701335.0010506298681
7211551185.42315057133-30.423150571326
7312151146.395676123568.6043238764951
7410331062.54023308465-29.5402330846459
759621030.33463322851-68.3346332285096
7610431041.922395333611.07760466638774
7712361306.74152838275-70.741528382754
7814081293.2054779485114.794522051502
7913671280.1854288833986.8145711166062
8013671307.2287466463259.771253353681
8113871333.5197312345553.4802687654458
8213171331.27531110665-14.275311106654
8314991478.2208305426320.7791694573659
8414991559.30915746955-60.3091574695525
8514681540.70826853958-72.7082685395815
8612961331.22980675639-35.2298067563916
8713271282.3775556780444.622444321956
8813471396.25235150608-49.2523515060761
8914791605.97891389829-126.978913898294
9016511620.7914815192530.2085184807461
9115291540.63324661076-11.6332466107579
9215901488.40284917386101.597150826136
9315391535.693153674353.30684632564612
9415091471.3019394779937.6980605220067
9517421660.2753293164981.7246706835106
9616911751.08463349458-60.0846334945834
9716201726.36826670702-106.368266707023
9815191504.7723851085214.2276148914834
9916201514.50192459087105.49807540913
10016711636.2780182664434.7219817335647
10117321877.49914418825-145.499144188252
10218131937.67730929468-124.677309294675
10317321739.43083279098-7.43083279098028
10417821726.9531128578355.0468871421665
10517211705.8821529380215.1178470619782
10617111657.672218837753.3277811623043
10719641869.2033740694494.7966259305624
10819851916.9078246941668.0921753058378
10919041961.83569944436-57.8356994443582
11017621817.40795305344-55.4079530534407
11118831814.5374581320468.4625418679586
11219341887.5330417130646.4669582869412
11319952074.29113257996-79.2911325799605
11420862187.59042649759-101.590426497585
11519952048.53413389148-53.5341338914773
11620662029.462658201136.5373417989033
11720351983.6699488868951.3300511131104
11819241974.83327282126-50.8332728212565
11921572131.569927554325.4300724456957
12021572121.167765918335.8322340816967

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 446 & 538.398504273504 & -92.3985042735042 \tabularnewline
14 & 385 & 416.074936045563 & -31.0749360455633 \tabularnewline
15 & 335 & 343.317590617708 & -8.31759061770799 \tabularnewline
16 & 335 & 331.763095764074 & 3.23690423592586 \tabularnewline
17 & 527 & 517.326542343019 & 9.67345765698076 \tabularnewline
18 & 547 & 532.054104243674 & 14.9458957563264 \tabularnewline
19 & 395 & 385.576074625862 & 9.42392537413832 \tabularnewline
20 & 223 & 284.608637963609 & -61.6086379636091 \tabularnewline
21 & 314 & 249.901749115009 & 64.0982508849907 \tabularnewline
22 & 314 & 290.359843129552 & 23.6401568704484 \tabularnewline
23 & 385 & 314.790960065663 & 70.2090399343366 \tabularnewline
24 & 426 & 382.237181444339 & 43.7628185556611 \tabularnewline
25 & 416 & 318.630149452082 & 97.369850547918 \tabularnewline
26 & 314 & 349.674509359831 & -35.6745093598307 \tabularnewline
27 & 365 & 289.786836746065 & 75.2131632539346 \tabularnewline
28 & 345 & 347.67516477416 & -2.67516477416007 \tabularnewline
29 & 517 & 542.276210820745 & -25.2762108207453 \tabularnewline
30 & 476 & 545.460736238614 & -69.4607362386139 \tabularnewline
31 & 314 & 348.47027901271 & -34.4702790127104 \tabularnewline
32 & 193 & 199.21788169666 & -6.2178816966603 \tabularnewline
33 & 304 & 251.222255231153 & 52.7777447688473 \tabularnewline
34 & 335 & 276.80027456283 & 58.19972543717 \tabularnewline
35 & 365 & 347.695763892907 & 17.3042361070932 \tabularnewline
36 & 405 & 377.322606402455 & 27.6773935975454 \tabularnewline
37 & 324 & 327.151753003473 & -3.15175300347261 \tabularnewline
38 & 254 & 248.272764745576 & 5.72723525442433 \tabularnewline
39 & 284 & 257.191745533081 & 26.8082544669194 \tabularnewline
40 & 294 & 258.085145334658 & 35.9148546653424 \tabularnewline
41 & 557 & 473.025547492526 & 83.9744525074742 \tabularnewline
42 & 557 & 539.00093541178 & 17.9990645882197 \tabularnewline
43 & 405 & 421.048737507199 & -16.0487375071992 \tabularnewline
44 & 385 & 304.037987905963 & 80.9620120940371 \tabularnewline
45 & 446 & 446.875237629256 & -0.875237629256162 \tabularnewline
46 & 416 & 450.85697321108 & -34.8569732110801 \tabularnewline
47 & 497 & 455.135898588083 & 41.8641014119173 \tabularnewline
48 & 598 & 513.604242627687 & 84.3957573723133 \tabularnewline
49 & 618 & 500.955395529134 & 117.044604470866 \tabularnewline
50 & 476 & 518.991349841135 & -42.9913498411354 \tabularnewline
51 & 436 & 517.03264500394 & -81.0326450039399 \tabularnewline
52 & 395 & 460.545517766787 & -65.5455177667873 \tabularnewline
53 & 669 & 632.271654895203 & 36.7283451047972 \tabularnewline
54 & 689 & 649.267374521889 & 39.7326254781112 \tabularnewline
55 & 638 & 539.218094928101 & 98.7819050718991 \tabularnewline
56 & 689 & 540.343814123271 & 148.656185876729 \tabularnewline
57 & 679 & 710.847930258998 & -31.8479302589978 \tabularnewline
58 & 598 & 693.569163148907 & -95.5691631489075 \tabularnewline
59 & 689 & 693.450394307833 & -4.45039430783299 \tabularnewline
60 & 790 & 743.467629590137 & 46.5323704098632 \tabularnewline
61 & 831 & 723.151191603948 & 107.848808396052 \tabularnewline
62 & 709 & 685.108652709614 & 23.8913472903863 \tabularnewline
63 & 628 & 721.3863234061 & -93.3863234060999 \tabularnewline
64 & 689 & 669.511919966443 & 19.4880800335571 \tabularnewline
65 & 952 & 942.503493940492 & 9.49650605950751 \tabularnewline
66 & 1033 & 952.063900668754 & 80.9360993312463 \tabularnewline
67 & 1013 & 900.143229795776 & 112.856770204224 \tabularnewline
68 & 1053 & 938.981764288432 & 114.018235711568 \tabularnewline
69 & 1043 & 1034.28984998213 & 8.71015001787441 \tabularnewline
70 & 942 & 1032.83552147526 & -90.8355214752555 \tabularnewline
71 & 1114 & 1078.99894937013 & 35.0010506298681 \tabularnewline
72 & 1155 & 1185.42315057133 & -30.423150571326 \tabularnewline
73 & 1215 & 1146.3956761235 & 68.6043238764951 \tabularnewline
74 & 1033 & 1062.54023308465 & -29.5402330846459 \tabularnewline
75 & 962 & 1030.33463322851 & -68.3346332285096 \tabularnewline
76 & 1043 & 1041.92239533361 & 1.07760466638774 \tabularnewline
77 & 1236 & 1306.74152838275 & -70.741528382754 \tabularnewline
78 & 1408 & 1293.2054779485 & 114.794522051502 \tabularnewline
79 & 1367 & 1280.18542888339 & 86.8145711166062 \tabularnewline
80 & 1367 & 1307.22874664632 & 59.771253353681 \tabularnewline
81 & 1387 & 1333.51973123455 & 53.4802687654458 \tabularnewline
82 & 1317 & 1331.27531110665 & -14.275311106654 \tabularnewline
83 & 1499 & 1478.22083054263 & 20.7791694573659 \tabularnewline
84 & 1499 & 1559.30915746955 & -60.3091574695525 \tabularnewline
85 & 1468 & 1540.70826853958 & -72.7082685395815 \tabularnewline
86 & 1296 & 1331.22980675639 & -35.2298067563916 \tabularnewline
87 & 1327 & 1282.37755567804 & 44.622444321956 \tabularnewline
88 & 1347 & 1396.25235150608 & -49.2523515060761 \tabularnewline
89 & 1479 & 1605.97891389829 & -126.978913898294 \tabularnewline
90 & 1651 & 1620.79148151925 & 30.2085184807461 \tabularnewline
91 & 1529 & 1540.63324661076 & -11.6332466107579 \tabularnewline
92 & 1590 & 1488.40284917386 & 101.597150826136 \tabularnewline
93 & 1539 & 1535.69315367435 & 3.30684632564612 \tabularnewline
94 & 1509 & 1471.30193947799 & 37.6980605220067 \tabularnewline
95 & 1742 & 1660.27532931649 & 81.7246706835106 \tabularnewline
96 & 1691 & 1751.08463349458 & -60.0846334945834 \tabularnewline
97 & 1620 & 1726.36826670702 & -106.368266707023 \tabularnewline
98 & 1519 & 1504.77238510852 & 14.2276148914834 \tabularnewline
99 & 1620 & 1514.50192459087 & 105.49807540913 \tabularnewline
100 & 1671 & 1636.27801826644 & 34.7219817335647 \tabularnewline
101 & 1732 & 1877.49914418825 & -145.499144188252 \tabularnewline
102 & 1813 & 1937.67730929468 & -124.677309294675 \tabularnewline
103 & 1732 & 1739.43083279098 & -7.43083279098028 \tabularnewline
104 & 1782 & 1726.95311285783 & 55.0468871421665 \tabularnewline
105 & 1721 & 1705.88215293802 & 15.1178470619782 \tabularnewline
106 & 1711 & 1657.6722188377 & 53.3277811623043 \tabularnewline
107 & 1964 & 1869.20337406944 & 94.7966259305624 \tabularnewline
108 & 1985 & 1916.90782469416 & 68.0921753058378 \tabularnewline
109 & 1904 & 1961.83569944436 & -57.8356994443582 \tabularnewline
110 & 1762 & 1817.40795305344 & -55.4079530534407 \tabularnewline
111 & 1883 & 1814.53745813204 & 68.4625418679586 \tabularnewline
112 & 1934 & 1887.53304171306 & 46.4669582869412 \tabularnewline
113 & 1995 & 2074.29113257996 & -79.2911325799605 \tabularnewline
114 & 2086 & 2187.59042649759 & -101.590426497585 \tabularnewline
115 & 1995 & 2048.53413389148 & -53.5341338914773 \tabularnewline
116 & 2066 & 2029.4626582011 & 36.5373417989033 \tabularnewline
117 & 2035 & 1983.66994888689 & 51.3300511131104 \tabularnewline
118 & 1924 & 1974.83327282126 & -50.8332728212565 \tabularnewline
119 & 2157 & 2131.5699275543 & 25.4300724456957 \tabularnewline
120 & 2157 & 2121.1677659183 & 35.8322340816967 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124000&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]446[/C][C]538.398504273504[/C][C]-92.3985042735042[/C][/ROW]
[ROW][C]14[/C][C]385[/C][C]416.074936045563[/C][C]-31.0749360455633[/C][/ROW]
[ROW][C]15[/C][C]335[/C][C]343.317590617708[/C][C]-8.31759061770799[/C][/ROW]
[ROW][C]16[/C][C]335[/C][C]331.763095764074[/C][C]3.23690423592586[/C][/ROW]
[ROW][C]17[/C][C]527[/C][C]517.326542343019[/C][C]9.67345765698076[/C][/ROW]
[ROW][C]18[/C][C]547[/C][C]532.054104243674[/C][C]14.9458957563264[/C][/ROW]
[ROW][C]19[/C][C]395[/C][C]385.576074625862[/C][C]9.42392537413832[/C][/ROW]
[ROW][C]20[/C][C]223[/C][C]284.608637963609[/C][C]-61.6086379636091[/C][/ROW]
[ROW][C]21[/C][C]314[/C][C]249.901749115009[/C][C]64.0982508849907[/C][/ROW]
[ROW][C]22[/C][C]314[/C][C]290.359843129552[/C][C]23.6401568704484[/C][/ROW]
[ROW][C]23[/C][C]385[/C][C]314.790960065663[/C][C]70.2090399343366[/C][/ROW]
[ROW][C]24[/C][C]426[/C][C]382.237181444339[/C][C]43.7628185556611[/C][/ROW]
[ROW][C]25[/C][C]416[/C][C]318.630149452082[/C][C]97.369850547918[/C][/ROW]
[ROW][C]26[/C][C]314[/C][C]349.674509359831[/C][C]-35.6745093598307[/C][/ROW]
[ROW][C]27[/C][C]365[/C][C]289.786836746065[/C][C]75.2131632539346[/C][/ROW]
[ROW][C]28[/C][C]345[/C][C]347.67516477416[/C][C]-2.67516477416007[/C][/ROW]
[ROW][C]29[/C][C]517[/C][C]542.276210820745[/C][C]-25.2762108207453[/C][/ROW]
[ROW][C]30[/C][C]476[/C][C]545.460736238614[/C][C]-69.4607362386139[/C][/ROW]
[ROW][C]31[/C][C]314[/C][C]348.47027901271[/C][C]-34.4702790127104[/C][/ROW]
[ROW][C]32[/C][C]193[/C][C]199.21788169666[/C][C]-6.2178816966603[/C][/ROW]
[ROW][C]33[/C][C]304[/C][C]251.222255231153[/C][C]52.7777447688473[/C][/ROW]
[ROW][C]34[/C][C]335[/C][C]276.80027456283[/C][C]58.19972543717[/C][/ROW]
[ROW][C]35[/C][C]365[/C][C]347.695763892907[/C][C]17.3042361070932[/C][/ROW]
[ROW][C]36[/C][C]405[/C][C]377.322606402455[/C][C]27.6773935975454[/C][/ROW]
[ROW][C]37[/C][C]324[/C][C]327.151753003473[/C][C]-3.15175300347261[/C][/ROW]
[ROW][C]38[/C][C]254[/C][C]248.272764745576[/C][C]5.72723525442433[/C][/ROW]
[ROW][C]39[/C][C]284[/C][C]257.191745533081[/C][C]26.8082544669194[/C][/ROW]
[ROW][C]40[/C][C]294[/C][C]258.085145334658[/C][C]35.9148546653424[/C][/ROW]
[ROW][C]41[/C][C]557[/C][C]473.025547492526[/C][C]83.9744525074742[/C][/ROW]
[ROW][C]42[/C][C]557[/C][C]539.00093541178[/C][C]17.9990645882197[/C][/ROW]
[ROW][C]43[/C][C]405[/C][C]421.048737507199[/C][C]-16.0487375071992[/C][/ROW]
[ROW][C]44[/C][C]385[/C][C]304.037987905963[/C][C]80.9620120940371[/C][/ROW]
[ROW][C]45[/C][C]446[/C][C]446.875237629256[/C][C]-0.875237629256162[/C][/ROW]
[ROW][C]46[/C][C]416[/C][C]450.85697321108[/C][C]-34.8569732110801[/C][/ROW]
[ROW][C]47[/C][C]497[/C][C]455.135898588083[/C][C]41.8641014119173[/C][/ROW]
[ROW][C]48[/C][C]598[/C][C]513.604242627687[/C][C]84.3957573723133[/C][/ROW]
[ROW][C]49[/C][C]618[/C][C]500.955395529134[/C][C]117.044604470866[/C][/ROW]
[ROW][C]50[/C][C]476[/C][C]518.991349841135[/C][C]-42.9913498411354[/C][/ROW]
[ROW][C]51[/C][C]436[/C][C]517.03264500394[/C][C]-81.0326450039399[/C][/ROW]
[ROW][C]52[/C][C]395[/C][C]460.545517766787[/C][C]-65.5455177667873[/C][/ROW]
[ROW][C]53[/C][C]669[/C][C]632.271654895203[/C][C]36.7283451047972[/C][/ROW]
[ROW][C]54[/C][C]689[/C][C]649.267374521889[/C][C]39.7326254781112[/C][/ROW]
[ROW][C]55[/C][C]638[/C][C]539.218094928101[/C][C]98.7819050718991[/C][/ROW]
[ROW][C]56[/C][C]689[/C][C]540.343814123271[/C][C]148.656185876729[/C][/ROW]
[ROW][C]57[/C][C]679[/C][C]710.847930258998[/C][C]-31.8479302589978[/C][/ROW]
[ROW][C]58[/C][C]598[/C][C]693.569163148907[/C][C]-95.5691631489075[/C][/ROW]
[ROW][C]59[/C][C]689[/C][C]693.450394307833[/C][C]-4.45039430783299[/C][/ROW]
[ROW][C]60[/C][C]790[/C][C]743.467629590137[/C][C]46.5323704098632[/C][/ROW]
[ROW][C]61[/C][C]831[/C][C]723.151191603948[/C][C]107.848808396052[/C][/ROW]
[ROW][C]62[/C][C]709[/C][C]685.108652709614[/C][C]23.8913472903863[/C][/ROW]
[ROW][C]63[/C][C]628[/C][C]721.3863234061[/C][C]-93.3863234060999[/C][/ROW]
[ROW][C]64[/C][C]689[/C][C]669.511919966443[/C][C]19.4880800335571[/C][/ROW]
[ROW][C]65[/C][C]952[/C][C]942.503493940492[/C][C]9.49650605950751[/C][/ROW]
[ROW][C]66[/C][C]1033[/C][C]952.063900668754[/C][C]80.9360993312463[/C][/ROW]
[ROW][C]67[/C][C]1013[/C][C]900.143229795776[/C][C]112.856770204224[/C][/ROW]
[ROW][C]68[/C][C]1053[/C][C]938.981764288432[/C][C]114.018235711568[/C][/ROW]
[ROW][C]69[/C][C]1043[/C][C]1034.28984998213[/C][C]8.71015001787441[/C][/ROW]
[ROW][C]70[/C][C]942[/C][C]1032.83552147526[/C][C]-90.8355214752555[/C][/ROW]
[ROW][C]71[/C][C]1114[/C][C]1078.99894937013[/C][C]35.0010506298681[/C][/ROW]
[ROW][C]72[/C][C]1155[/C][C]1185.42315057133[/C][C]-30.423150571326[/C][/ROW]
[ROW][C]73[/C][C]1215[/C][C]1146.3956761235[/C][C]68.6043238764951[/C][/ROW]
[ROW][C]74[/C][C]1033[/C][C]1062.54023308465[/C][C]-29.5402330846459[/C][/ROW]
[ROW][C]75[/C][C]962[/C][C]1030.33463322851[/C][C]-68.3346332285096[/C][/ROW]
[ROW][C]76[/C][C]1043[/C][C]1041.92239533361[/C][C]1.07760466638774[/C][/ROW]
[ROW][C]77[/C][C]1236[/C][C]1306.74152838275[/C][C]-70.741528382754[/C][/ROW]
[ROW][C]78[/C][C]1408[/C][C]1293.2054779485[/C][C]114.794522051502[/C][/ROW]
[ROW][C]79[/C][C]1367[/C][C]1280.18542888339[/C][C]86.8145711166062[/C][/ROW]
[ROW][C]80[/C][C]1367[/C][C]1307.22874664632[/C][C]59.771253353681[/C][/ROW]
[ROW][C]81[/C][C]1387[/C][C]1333.51973123455[/C][C]53.4802687654458[/C][/ROW]
[ROW][C]82[/C][C]1317[/C][C]1331.27531110665[/C][C]-14.275311106654[/C][/ROW]
[ROW][C]83[/C][C]1499[/C][C]1478.22083054263[/C][C]20.7791694573659[/C][/ROW]
[ROW][C]84[/C][C]1499[/C][C]1559.30915746955[/C][C]-60.3091574695525[/C][/ROW]
[ROW][C]85[/C][C]1468[/C][C]1540.70826853958[/C][C]-72.7082685395815[/C][/ROW]
[ROW][C]86[/C][C]1296[/C][C]1331.22980675639[/C][C]-35.2298067563916[/C][/ROW]
[ROW][C]87[/C][C]1327[/C][C]1282.37755567804[/C][C]44.622444321956[/C][/ROW]
[ROW][C]88[/C][C]1347[/C][C]1396.25235150608[/C][C]-49.2523515060761[/C][/ROW]
[ROW][C]89[/C][C]1479[/C][C]1605.97891389829[/C][C]-126.978913898294[/C][/ROW]
[ROW][C]90[/C][C]1651[/C][C]1620.79148151925[/C][C]30.2085184807461[/C][/ROW]
[ROW][C]91[/C][C]1529[/C][C]1540.63324661076[/C][C]-11.6332466107579[/C][/ROW]
[ROW][C]92[/C][C]1590[/C][C]1488.40284917386[/C][C]101.597150826136[/C][/ROW]
[ROW][C]93[/C][C]1539[/C][C]1535.69315367435[/C][C]3.30684632564612[/C][/ROW]
[ROW][C]94[/C][C]1509[/C][C]1471.30193947799[/C][C]37.6980605220067[/C][/ROW]
[ROW][C]95[/C][C]1742[/C][C]1660.27532931649[/C][C]81.7246706835106[/C][/ROW]
[ROW][C]96[/C][C]1691[/C][C]1751.08463349458[/C][C]-60.0846334945834[/C][/ROW]
[ROW][C]97[/C][C]1620[/C][C]1726.36826670702[/C][C]-106.368266707023[/C][/ROW]
[ROW][C]98[/C][C]1519[/C][C]1504.77238510852[/C][C]14.2276148914834[/C][/ROW]
[ROW][C]99[/C][C]1620[/C][C]1514.50192459087[/C][C]105.49807540913[/C][/ROW]
[ROW][C]100[/C][C]1671[/C][C]1636.27801826644[/C][C]34.7219817335647[/C][/ROW]
[ROW][C]101[/C][C]1732[/C][C]1877.49914418825[/C][C]-145.499144188252[/C][/ROW]
[ROW][C]102[/C][C]1813[/C][C]1937.67730929468[/C][C]-124.677309294675[/C][/ROW]
[ROW][C]103[/C][C]1732[/C][C]1739.43083279098[/C][C]-7.43083279098028[/C][/ROW]
[ROW][C]104[/C][C]1782[/C][C]1726.95311285783[/C][C]55.0468871421665[/C][/ROW]
[ROW][C]105[/C][C]1721[/C][C]1705.88215293802[/C][C]15.1178470619782[/C][/ROW]
[ROW][C]106[/C][C]1711[/C][C]1657.6722188377[/C][C]53.3277811623043[/C][/ROW]
[ROW][C]107[/C][C]1964[/C][C]1869.20337406944[/C][C]94.7966259305624[/C][/ROW]
[ROW][C]108[/C][C]1985[/C][C]1916.90782469416[/C][C]68.0921753058378[/C][/ROW]
[ROW][C]109[/C][C]1904[/C][C]1961.83569944436[/C][C]-57.8356994443582[/C][/ROW]
[ROW][C]110[/C][C]1762[/C][C]1817.40795305344[/C][C]-55.4079530534407[/C][/ROW]
[ROW][C]111[/C][C]1883[/C][C]1814.53745813204[/C][C]68.4625418679586[/C][/ROW]
[ROW][C]112[/C][C]1934[/C][C]1887.53304171306[/C][C]46.4669582869412[/C][/ROW]
[ROW][C]113[/C][C]1995[/C][C]2074.29113257996[/C][C]-79.2911325799605[/C][/ROW]
[ROW][C]114[/C][C]2086[/C][C]2187.59042649759[/C][C]-101.590426497585[/C][/ROW]
[ROW][C]115[/C][C]1995[/C][C]2048.53413389148[/C][C]-53.5341338914773[/C][/ROW]
[ROW][C]116[/C][C]2066[/C][C]2029.4626582011[/C][C]36.5373417989033[/C][/ROW]
[ROW][C]117[/C][C]2035[/C][C]1983.66994888689[/C][C]51.3300511131104[/C][/ROW]
[ROW][C]118[/C][C]1924[/C][C]1974.83327282126[/C][C]-50.8332728212565[/C][/ROW]
[ROW][C]119[/C][C]2157[/C][C]2131.5699275543[/C][C]25.4300724456957[/C][/ROW]
[ROW][C]120[/C][C]2157[/C][C]2121.1677659183[/C][C]35.8322340816967[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124000&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124000&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
13446538.398504273504-92.3985042735042
14385416.074936045563-31.0749360455633
15335343.317590617708-8.31759061770799
16335331.7630957640743.23690423592586
17527517.3265423430199.67345765698076
18547532.05410424367414.9458957563264
19395385.5760746258629.42392537413832
20223284.608637963609-61.6086379636091
21314249.90174911500964.0982508849907
22314290.35984312955223.6401568704484
23385314.79096006566370.2090399343366
24426382.23718144433943.7628185556611
25416318.63014945208297.369850547918
26314349.674509359831-35.6745093598307
27365289.78683674606575.2131632539346
28345347.67516477416-2.67516477416007
29517542.276210820745-25.2762108207453
30476545.460736238614-69.4607362386139
31314348.47027901271-34.4702790127104
32193199.21788169666-6.2178816966603
33304251.22225523115352.7777447688473
34335276.8002745628358.19972543717
35365347.69576389290717.3042361070932
36405377.32260640245527.6773935975454
37324327.151753003473-3.15175300347261
38254248.2727647455765.72723525442433
39284257.19174553308126.8082544669194
40294258.08514533465835.9148546653424
41557473.02554749252683.9744525074742
42557539.0009354117817.9990645882197
43405421.048737507199-16.0487375071992
44385304.03798790596380.9620120940371
45446446.875237629256-0.875237629256162
46416450.85697321108-34.8569732110801
47497455.13589858808341.8641014119173
48598513.60424262768784.3957573723133
49618500.955395529134117.044604470866
50476518.991349841135-42.9913498411354
51436517.03264500394-81.0326450039399
52395460.545517766787-65.5455177667873
53669632.27165489520336.7283451047972
54689649.26737452188939.7326254781112
55638539.21809492810198.7819050718991
56689540.343814123271148.656185876729
57679710.847930258998-31.8479302589978
58598693.569163148907-95.5691631489075
59689693.450394307833-4.45039430783299
60790743.46762959013746.5323704098632
61831723.151191603948107.848808396052
62709685.10865270961423.8913472903863
63628721.3863234061-93.3863234060999
64689669.51191996644319.4880800335571
65952942.5034939404929.49650605950751
661033952.06390066875480.9360993312463
671013900.143229795776112.856770204224
681053938.981764288432114.018235711568
6910431034.289849982138.71015001787441
709421032.83552147526-90.8355214752555
7111141078.9989493701335.0010506298681
7211551185.42315057133-30.423150571326
7312151146.395676123568.6043238764951
7410331062.54023308465-29.5402330846459
759621030.33463322851-68.3346332285096
7610431041.922395333611.07760466638774
7712361306.74152838275-70.741528382754
7814081293.2054779485114.794522051502
7913671280.1854288833986.8145711166062
8013671307.2287466463259.771253353681
8113871333.5197312345553.4802687654458
8213171331.27531110665-14.275311106654
8314991478.2208305426320.7791694573659
8414991559.30915746955-60.3091574695525
8514681540.70826853958-72.7082685395815
8612961331.22980675639-35.2298067563916
8713271282.3775556780444.622444321956
8813471396.25235150608-49.2523515060761
8914791605.97891389829-126.978913898294
9016511620.7914815192530.2085184807461
9115291540.63324661076-11.6332466107579
9215901488.40284917386101.597150826136
9315391535.693153674353.30684632564612
9415091471.3019394779937.6980605220067
9517421660.2753293164981.7246706835106
9616911751.08463349458-60.0846334945834
9716201726.36826670702-106.368266707023
9815191504.7723851085214.2276148914834
9916201514.50192459087105.49807540913
10016711636.2780182664434.7219817335647
10117321877.49914418825-145.499144188252
10218131937.67730929468-124.677309294675
10317321739.43083279098-7.43083279098028
10417821726.9531128578355.0468871421665
10517211705.8821529380215.1178470619782
10617111657.672218837753.3277811623043
10719641869.2033740694494.7966259305624
10819851916.9078246941668.0921753058378
10919041961.83569944436-57.8356994443582
11017621817.40795305344-55.4079530534407
11118831814.5374581320468.4625418679586
11219341887.5330417130646.4669582869412
11319952074.29113257996-79.2911325799605
11420862187.59042649759-101.590426497585
11519952048.53413389148-53.5341338914773
11620662029.462658201136.5373417989033
11720351983.6699488868951.3300511131104
11819241974.83327282126-50.8332728212565
11921572131.569927554325.4300724456957
12021572121.167765918335.8322340816967







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1212096.703291711021972.667788638042220.73879478401
1221988.247253308851837.704399689322138.79010692838
1232063.79309616361888.601768554892238.98442377231
1242081.338656026011882.572017367482280.10529468454
1252189.424638671941967.730037836212411.11923950766
1262344.819825039332100.586783461272589.0528666174
1272290.337855785812023.787966532852556.88774503877
1282340.871173042132052.110874927132629.63147115713
1292278.477683847951967.531391605332589.42397609057
1302201.043799315611867.875788730042534.21180990119
1312419.551531913582064.080986350822775.02207747634
1322397.384678181282019.49637159362775.27298476896

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 2096.70329171102 & 1972.66778863804 & 2220.73879478401 \tabularnewline
122 & 1988.24725330885 & 1837.70439968932 & 2138.79010692838 \tabularnewline
123 & 2063.7930961636 & 1888.60176855489 & 2238.98442377231 \tabularnewline
124 & 2081.33865602601 & 1882.57201736748 & 2280.10529468454 \tabularnewline
125 & 2189.42463867194 & 1967.73003783621 & 2411.11923950766 \tabularnewline
126 & 2344.81982503933 & 2100.58678346127 & 2589.0528666174 \tabularnewline
127 & 2290.33785578581 & 2023.78796653285 & 2556.88774503877 \tabularnewline
128 & 2340.87117304213 & 2052.11087492713 & 2629.63147115713 \tabularnewline
129 & 2278.47768384795 & 1967.53139160533 & 2589.42397609057 \tabularnewline
130 & 2201.04379931561 & 1867.87578873004 & 2534.21180990119 \tabularnewline
131 & 2419.55153191358 & 2064.08098635082 & 2775.02207747634 \tabularnewline
132 & 2397.38467818128 & 2019.4963715936 & 2775.27298476896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124000&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]2096.70329171102[/C][C]1972.66778863804[/C][C]2220.73879478401[/C][/ROW]
[ROW][C]122[/C][C]1988.24725330885[/C][C]1837.70439968932[/C][C]2138.79010692838[/C][/ROW]
[ROW][C]123[/C][C]2063.7930961636[/C][C]1888.60176855489[/C][C]2238.98442377231[/C][/ROW]
[ROW][C]124[/C][C]2081.33865602601[/C][C]1882.57201736748[/C][C]2280.10529468454[/C][/ROW]
[ROW][C]125[/C][C]2189.42463867194[/C][C]1967.73003783621[/C][C]2411.11923950766[/C][/ROW]
[ROW][C]126[/C][C]2344.81982503933[/C][C]2100.58678346127[/C][C]2589.0528666174[/C][/ROW]
[ROW][C]127[/C][C]2290.33785578581[/C][C]2023.78796653285[/C][C]2556.88774503877[/C][/ROW]
[ROW][C]128[/C][C]2340.87117304213[/C][C]2052.11087492713[/C][C]2629.63147115713[/C][/ROW]
[ROW][C]129[/C][C]2278.47768384795[/C][C]1967.53139160533[/C][C]2589.42397609057[/C][/ROW]
[ROW][C]130[/C][C]2201.04379931561[/C][C]1867.87578873004[/C][C]2534.21180990119[/C][/ROW]
[ROW][C]131[/C][C]2419.55153191358[/C][C]2064.08098635082[/C][C]2775.02207747634[/C][/ROW]
[ROW][C]132[/C][C]2397.38467818128[/C][C]2019.4963715936[/C][C]2775.27298476896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124000&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124000&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
1212096.703291711021972.667788638042220.73879478401
1221988.247253308851837.704399689322138.79010692838
1232063.79309616361888.601768554892238.98442377231
1242081.338656026011882.572017367482280.10529468454
1252189.424638671941967.730037836212411.11923950766
1262344.819825039332100.586783461272589.0528666174
1272290.337855785812023.787966532852556.88774503877
1282340.871173042132052.110874927132629.63147115713
1292278.477683847951967.531391605332589.42397609057
1302201.043799315611867.875788730042534.21180990119
1312419.551531913582064.080986350822775.02207747634
1322397.384678181282019.49637159362775.27298476896



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')