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 16:50:43 -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/t1313700677j5rw11qdfa0cj1e.htm/, Retrieved Wed, 15 May 2024 15:54:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124159, Retrieved Wed, 15 May 2024 15:54:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmattias debbaut
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks A - Exp...] [2011-08-18 20:50:43] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
21571
21493
21422
21272
22747
22676
21571
20831
20909
20909
20980
21130
21051
21643
21864
21643
22455
21935
20759
20467
20467
20610
20026
20467
20097
20467
21051
21272
21792
21571
20246
19726
19506
19726
19363
19506
19064
19805
20168
20246
21643
21643
19805
19363
19363
19584
18622
18180
17668
17817
18480
17960
19363
19584
18180
17668
17375
17668
16855
16563
15388
15680
15751
15830
17226
17076
15388
14647
14355
14725
13322
12367
10601
10750
10750
10601
11854
11926
10451
10159
9568
10380
8905
8022
6333
6697
6255
6404
7509
7730
6996
6917
6917
7879
6184
5079
3163
4709
4488
4566
6333
6112
5300
5671
5671
6996
5450
4566
3163
5008
4859
4930
6476
6333
5813
5892
6255
7067
5813
4787




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124159&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]1 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=124159&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124159&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.791744303433744
beta0.013084206807497
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.791744303433744 \tabularnewline
beta & 0.013084206807497 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124159&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]0.791744303433744[/C][/ROW]
[ROW][C]beta[/C][C]0.013084206807497[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124159&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124159&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
alpha0.791744303433744
beta0.013084206807497
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132105121137.6057692308-86.6057692307622
142164321681.5136742757-38.5136742757313
152186421876.6825783894-12.6825783894274
162164321647.4633889689-4.46338896892121
172245522479.0387914927-24.0387914926978
182193521978.0331210841-43.0331210840995
192075921255.7930034244-496.79300342438
202046720102.9362997471364.06370025294
212046720413.346115857253.6538841428046
222061020391.3382141599218.661785840053
232002620603.8229051277-577.82290512765
242046720305.0428450636161.957154936445
252009720368.2877254563-271.287725456259
262046720769.0463405358-302.046340535773
272105120751.2703481991299.729651800917
282127220764.6759597868507.324040213225
292179221996.2437424225-204.243742422503
302157121345.6036334265225.396366573546
312024620741.1711892186-495.171189218574
321972619768.6718971987-42.6718971986775
331950619687.9880307106-181.98803071064
341972619506.9162467714219.083753228588
351936319547.0073511862-184.007351186214
361950619711.3163932303-205.316393230263
371906419386.9685748297-322.968574829749
381980519733.287890321271.7121096788178
392016820133.512568754634.4874312454194
402024619974.1554096501271.844590349934
412164320862.6647544093780.335245590661
422164321082.8031645833560.19683541674
431980520598.6218140389-793.621814038881
441936319486.2067697935-123.206769793545
451936319314.057484223548.9425157765254
461958419403.0524041221180.947595877875
471862219332.3116142437-710.311614243652
481818019073.3405664485-893.340566448544
491766818170.4803523421-502.480352342085
501781718445.7356779072-628.735677907232
511848018265.2453146448214.754685355183
521796018281.5249137912-321.524913791171
531936318783.4666955088579.53330449123
541958418774.0293440093809.970655990659
551818018183.505149927-3.50514992701574
561766817822.3039203764-154.303920376373
571737517647.0882610185-272.088261018478
581766817491.7775817697176.222418230274
591685517214.0147817301-359.014781730137
601656317181.0323134164-618.032313416381
611538816566.3648554491-1178.36485544909
621568016262.0175125311-582.017512531093
631575116276.4800607712-525.480060771175
641583015569.6337840368260.366215963242
651722616700.5971205608525.4028794392
661707616676.3935094317399.606490568338
671538815567.4050548783-179.405054878329
681464715009.5593670505-362.559367050542
691435514616.799986377-261.799986377035
701472514534.9754247044190.024575295563
711332214128.7943712655-806.794371265465
721236713654.8245467426-1287.82454674259
731060112353.7033095586-1752.70330955861
741075011673.4125776197-923.412577619707
751075011380.4082235504-630.408223550396
761060110704.1120975528-103.112097552794
771185411548.6930093407305.306990659345
781192611267.955932405658.044067594998
791045110189.6027638055261.397236194467
80101599893.78453282241265.21546717759
8195689976.71703565003-408.717035650026
82103809828.8158310325551.1841689675
8389059460.87803679064-555.878036790637
8480229047.88227798398-1025.88227798398
8563337822.54200151744-1489.54200151744
8666977491.2417464063-794.241746406297
8762557330.79510459987-1075.79510459987
8864046376.332574453927.6674255461039
8975097375.5215204543133.478479545702
9077306996.42816339105733.571836608951
9169965860.280590854761135.71940914524
9269176231.56541146783685.434588532172
9369176485.27520581041431.724794189593
9478797189.82183302208689.178166977925
9561846689.14542409408-505.145424094084
9650796207.51885273163-1128.51885273163
9731634792.37661736163-1629.37661736163
9847094481.73448865805227.265511341953
9944885068.57860366674-580.578603666743
10045664738.28668943866-172.286689438656
10163335601.41087929202731.589120707985
10261125827.24913105784284.750868942156
10353004421.25820094845878.741799051553
10456714494.404527657721176.59547234228
10556715088.33619348546582.663806514543
10669965971.752234444691024.24776555531
10754505496.85986112432-46.8598611243242
10845665262.22402585912-696.224025859115
10931634103.4873860616-940.487386061598
11050084750.5072354138257.492764586197
11148595218.94015536988-359.940155369884
11249305176.54695104212-246.546951042122
11364766196.52435883459279.475641165408
11463335994.07519781828338.924802181717
11558134777.966842704831035.03315729517
11658925061.79343952919830.206560470805
11762555279.1033955146975.896604485397
11870676591.21466455058475.785335449418
11958135478.72733483856334.27266516144
12047875434.27681663482-647.276816634815

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 21051 & 21137.6057692308 & -86.6057692307622 \tabularnewline
14 & 21643 & 21681.5136742757 & -38.5136742757313 \tabularnewline
15 & 21864 & 21876.6825783894 & -12.6825783894274 \tabularnewline
16 & 21643 & 21647.4633889689 & -4.46338896892121 \tabularnewline
17 & 22455 & 22479.0387914927 & -24.0387914926978 \tabularnewline
18 & 21935 & 21978.0331210841 & -43.0331210840995 \tabularnewline
19 & 20759 & 21255.7930034244 & -496.79300342438 \tabularnewline
20 & 20467 & 20102.9362997471 & 364.06370025294 \tabularnewline
21 & 20467 & 20413.3461158572 & 53.6538841428046 \tabularnewline
22 & 20610 & 20391.3382141599 & 218.661785840053 \tabularnewline
23 & 20026 & 20603.8229051277 & -577.82290512765 \tabularnewline
24 & 20467 & 20305.0428450636 & 161.957154936445 \tabularnewline
25 & 20097 & 20368.2877254563 & -271.287725456259 \tabularnewline
26 & 20467 & 20769.0463405358 & -302.046340535773 \tabularnewline
27 & 21051 & 20751.2703481991 & 299.729651800917 \tabularnewline
28 & 21272 & 20764.6759597868 & 507.324040213225 \tabularnewline
29 & 21792 & 21996.2437424225 & -204.243742422503 \tabularnewline
30 & 21571 & 21345.6036334265 & 225.396366573546 \tabularnewline
31 & 20246 & 20741.1711892186 & -495.171189218574 \tabularnewline
32 & 19726 & 19768.6718971987 & -42.6718971986775 \tabularnewline
33 & 19506 & 19687.9880307106 & -181.98803071064 \tabularnewline
34 & 19726 & 19506.9162467714 & 219.083753228588 \tabularnewline
35 & 19363 & 19547.0073511862 & -184.007351186214 \tabularnewline
36 & 19506 & 19711.3163932303 & -205.316393230263 \tabularnewline
37 & 19064 & 19386.9685748297 & -322.968574829749 \tabularnewline
38 & 19805 & 19733.2878903212 & 71.7121096788178 \tabularnewline
39 & 20168 & 20133.5125687546 & 34.4874312454194 \tabularnewline
40 & 20246 & 19974.1554096501 & 271.844590349934 \tabularnewline
41 & 21643 & 20862.6647544093 & 780.335245590661 \tabularnewline
42 & 21643 & 21082.8031645833 & 560.19683541674 \tabularnewline
43 & 19805 & 20598.6218140389 & -793.621814038881 \tabularnewline
44 & 19363 & 19486.2067697935 & -123.206769793545 \tabularnewline
45 & 19363 & 19314.0574842235 & 48.9425157765254 \tabularnewline
46 & 19584 & 19403.0524041221 & 180.947595877875 \tabularnewline
47 & 18622 & 19332.3116142437 & -710.311614243652 \tabularnewline
48 & 18180 & 19073.3405664485 & -893.340566448544 \tabularnewline
49 & 17668 & 18170.4803523421 & -502.480352342085 \tabularnewline
50 & 17817 & 18445.7356779072 & -628.735677907232 \tabularnewline
51 & 18480 & 18265.2453146448 & 214.754685355183 \tabularnewline
52 & 17960 & 18281.5249137912 & -321.524913791171 \tabularnewline
53 & 19363 & 18783.4666955088 & 579.53330449123 \tabularnewline
54 & 19584 & 18774.0293440093 & 809.970655990659 \tabularnewline
55 & 18180 & 18183.505149927 & -3.50514992701574 \tabularnewline
56 & 17668 & 17822.3039203764 & -154.303920376373 \tabularnewline
57 & 17375 & 17647.0882610185 & -272.088261018478 \tabularnewline
58 & 17668 & 17491.7775817697 & 176.222418230274 \tabularnewline
59 & 16855 & 17214.0147817301 & -359.014781730137 \tabularnewline
60 & 16563 & 17181.0323134164 & -618.032313416381 \tabularnewline
61 & 15388 & 16566.3648554491 & -1178.36485544909 \tabularnewline
62 & 15680 & 16262.0175125311 & -582.017512531093 \tabularnewline
63 & 15751 & 16276.4800607712 & -525.480060771175 \tabularnewline
64 & 15830 & 15569.6337840368 & 260.366215963242 \tabularnewline
65 & 17226 & 16700.5971205608 & 525.4028794392 \tabularnewline
66 & 17076 & 16676.3935094317 & 399.606490568338 \tabularnewline
67 & 15388 & 15567.4050548783 & -179.405054878329 \tabularnewline
68 & 14647 & 15009.5593670505 & -362.559367050542 \tabularnewline
69 & 14355 & 14616.799986377 & -261.799986377035 \tabularnewline
70 & 14725 & 14534.9754247044 & 190.024575295563 \tabularnewline
71 & 13322 & 14128.7943712655 & -806.794371265465 \tabularnewline
72 & 12367 & 13654.8245467426 & -1287.82454674259 \tabularnewline
73 & 10601 & 12353.7033095586 & -1752.70330955861 \tabularnewline
74 & 10750 & 11673.4125776197 & -923.412577619707 \tabularnewline
75 & 10750 & 11380.4082235504 & -630.408223550396 \tabularnewline
76 & 10601 & 10704.1120975528 & -103.112097552794 \tabularnewline
77 & 11854 & 11548.6930093407 & 305.306990659345 \tabularnewline
78 & 11926 & 11267.955932405 & 658.044067594998 \tabularnewline
79 & 10451 & 10189.6027638055 & 261.397236194467 \tabularnewline
80 & 10159 & 9893.78453282241 & 265.21546717759 \tabularnewline
81 & 9568 & 9976.71703565003 & -408.717035650026 \tabularnewline
82 & 10380 & 9828.8158310325 & 551.1841689675 \tabularnewline
83 & 8905 & 9460.87803679064 & -555.878036790637 \tabularnewline
84 & 8022 & 9047.88227798398 & -1025.88227798398 \tabularnewline
85 & 6333 & 7822.54200151744 & -1489.54200151744 \tabularnewline
86 & 6697 & 7491.2417464063 & -794.241746406297 \tabularnewline
87 & 6255 & 7330.79510459987 & -1075.79510459987 \tabularnewline
88 & 6404 & 6376.3325744539 & 27.6674255461039 \tabularnewline
89 & 7509 & 7375.5215204543 & 133.478479545702 \tabularnewline
90 & 7730 & 6996.42816339105 & 733.571836608951 \tabularnewline
91 & 6996 & 5860.28059085476 & 1135.71940914524 \tabularnewline
92 & 6917 & 6231.56541146783 & 685.434588532172 \tabularnewline
93 & 6917 & 6485.27520581041 & 431.724794189593 \tabularnewline
94 & 7879 & 7189.82183302208 & 689.178166977925 \tabularnewline
95 & 6184 & 6689.14542409408 & -505.145424094084 \tabularnewline
96 & 5079 & 6207.51885273163 & -1128.51885273163 \tabularnewline
97 & 3163 & 4792.37661736163 & -1629.37661736163 \tabularnewline
98 & 4709 & 4481.73448865805 & 227.265511341953 \tabularnewline
99 & 4488 & 5068.57860366674 & -580.578603666743 \tabularnewline
100 & 4566 & 4738.28668943866 & -172.286689438656 \tabularnewline
101 & 6333 & 5601.41087929202 & 731.589120707985 \tabularnewline
102 & 6112 & 5827.24913105784 & 284.750868942156 \tabularnewline
103 & 5300 & 4421.25820094845 & 878.741799051553 \tabularnewline
104 & 5671 & 4494.40452765772 & 1176.59547234228 \tabularnewline
105 & 5671 & 5088.33619348546 & 582.663806514543 \tabularnewline
106 & 6996 & 5971.75223444469 & 1024.24776555531 \tabularnewline
107 & 5450 & 5496.85986112432 & -46.8598611243242 \tabularnewline
108 & 4566 & 5262.22402585912 & -696.224025859115 \tabularnewline
109 & 3163 & 4103.4873860616 & -940.487386061598 \tabularnewline
110 & 5008 & 4750.5072354138 & 257.492764586197 \tabularnewline
111 & 4859 & 5218.94015536988 & -359.940155369884 \tabularnewline
112 & 4930 & 5176.54695104212 & -246.546951042122 \tabularnewline
113 & 6476 & 6196.52435883459 & 279.475641165408 \tabularnewline
114 & 6333 & 5994.07519781828 & 338.924802181717 \tabularnewline
115 & 5813 & 4777.96684270483 & 1035.03315729517 \tabularnewline
116 & 5892 & 5061.79343952919 & 830.206560470805 \tabularnewline
117 & 6255 & 5279.1033955146 & 975.896604485397 \tabularnewline
118 & 7067 & 6591.21466455058 & 475.785335449418 \tabularnewline
119 & 5813 & 5478.72733483856 & 334.27266516144 \tabularnewline
120 & 4787 & 5434.27681663482 & -647.276816634815 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124159&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]21051[/C][C]21137.6057692308[/C][C]-86.6057692307622[/C][/ROW]
[ROW][C]14[/C][C]21643[/C][C]21681.5136742757[/C][C]-38.5136742757313[/C][/ROW]
[ROW][C]15[/C][C]21864[/C][C]21876.6825783894[/C][C]-12.6825783894274[/C][/ROW]
[ROW][C]16[/C][C]21643[/C][C]21647.4633889689[/C][C]-4.46338896892121[/C][/ROW]
[ROW][C]17[/C][C]22455[/C][C]22479.0387914927[/C][C]-24.0387914926978[/C][/ROW]
[ROW][C]18[/C][C]21935[/C][C]21978.0331210841[/C][C]-43.0331210840995[/C][/ROW]
[ROW][C]19[/C][C]20759[/C][C]21255.7930034244[/C][C]-496.79300342438[/C][/ROW]
[ROW][C]20[/C][C]20467[/C][C]20102.9362997471[/C][C]364.06370025294[/C][/ROW]
[ROW][C]21[/C][C]20467[/C][C]20413.3461158572[/C][C]53.6538841428046[/C][/ROW]
[ROW][C]22[/C][C]20610[/C][C]20391.3382141599[/C][C]218.661785840053[/C][/ROW]
[ROW][C]23[/C][C]20026[/C][C]20603.8229051277[/C][C]-577.82290512765[/C][/ROW]
[ROW][C]24[/C][C]20467[/C][C]20305.0428450636[/C][C]161.957154936445[/C][/ROW]
[ROW][C]25[/C][C]20097[/C][C]20368.2877254563[/C][C]-271.287725456259[/C][/ROW]
[ROW][C]26[/C][C]20467[/C][C]20769.0463405358[/C][C]-302.046340535773[/C][/ROW]
[ROW][C]27[/C][C]21051[/C][C]20751.2703481991[/C][C]299.729651800917[/C][/ROW]
[ROW][C]28[/C][C]21272[/C][C]20764.6759597868[/C][C]507.324040213225[/C][/ROW]
[ROW][C]29[/C][C]21792[/C][C]21996.2437424225[/C][C]-204.243742422503[/C][/ROW]
[ROW][C]30[/C][C]21571[/C][C]21345.6036334265[/C][C]225.396366573546[/C][/ROW]
[ROW][C]31[/C][C]20246[/C][C]20741.1711892186[/C][C]-495.171189218574[/C][/ROW]
[ROW][C]32[/C][C]19726[/C][C]19768.6718971987[/C][C]-42.6718971986775[/C][/ROW]
[ROW][C]33[/C][C]19506[/C][C]19687.9880307106[/C][C]-181.98803071064[/C][/ROW]
[ROW][C]34[/C][C]19726[/C][C]19506.9162467714[/C][C]219.083753228588[/C][/ROW]
[ROW][C]35[/C][C]19363[/C][C]19547.0073511862[/C][C]-184.007351186214[/C][/ROW]
[ROW][C]36[/C][C]19506[/C][C]19711.3163932303[/C][C]-205.316393230263[/C][/ROW]
[ROW][C]37[/C][C]19064[/C][C]19386.9685748297[/C][C]-322.968574829749[/C][/ROW]
[ROW][C]38[/C][C]19805[/C][C]19733.2878903212[/C][C]71.7121096788178[/C][/ROW]
[ROW][C]39[/C][C]20168[/C][C]20133.5125687546[/C][C]34.4874312454194[/C][/ROW]
[ROW][C]40[/C][C]20246[/C][C]19974.1554096501[/C][C]271.844590349934[/C][/ROW]
[ROW][C]41[/C][C]21643[/C][C]20862.6647544093[/C][C]780.335245590661[/C][/ROW]
[ROW][C]42[/C][C]21643[/C][C]21082.8031645833[/C][C]560.19683541674[/C][/ROW]
[ROW][C]43[/C][C]19805[/C][C]20598.6218140389[/C][C]-793.621814038881[/C][/ROW]
[ROW][C]44[/C][C]19363[/C][C]19486.2067697935[/C][C]-123.206769793545[/C][/ROW]
[ROW][C]45[/C][C]19363[/C][C]19314.0574842235[/C][C]48.9425157765254[/C][/ROW]
[ROW][C]46[/C][C]19584[/C][C]19403.0524041221[/C][C]180.947595877875[/C][/ROW]
[ROW][C]47[/C][C]18622[/C][C]19332.3116142437[/C][C]-710.311614243652[/C][/ROW]
[ROW][C]48[/C][C]18180[/C][C]19073.3405664485[/C][C]-893.340566448544[/C][/ROW]
[ROW][C]49[/C][C]17668[/C][C]18170.4803523421[/C][C]-502.480352342085[/C][/ROW]
[ROW][C]50[/C][C]17817[/C][C]18445.7356779072[/C][C]-628.735677907232[/C][/ROW]
[ROW][C]51[/C][C]18480[/C][C]18265.2453146448[/C][C]214.754685355183[/C][/ROW]
[ROW][C]52[/C][C]17960[/C][C]18281.5249137912[/C][C]-321.524913791171[/C][/ROW]
[ROW][C]53[/C][C]19363[/C][C]18783.4666955088[/C][C]579.53330449123[/C][/ROW]
[ROW][C]54[/C][C]19584[/C][C]18774.0293440093[/C][C]809.970655990659[/C][/ROW]
[ROW][C]55[/C][C]18180[/C][C]18183.505149927[/C][C]-3.50514992701574[/C][/ROW]
[ROW][C]56[/C][C]17668[/C][C]17822.3039203764[/C][C]-154.303920376373[/C][/ROW]
[ROW][C]57[/C][C]17375[/C][C]17647.0882610185[/C][C]-272.088261018478[/C][/ROW]
[ROW][C]58[/C][C]17668[/C][C]17491.7775817697[/C][C]176.222418230274[/C][/ROW]
[ROW][C]59[/C][C]16855[/C][C]17214.0147817301[/C][C]-359.014781730137[/C][/ROW]
[ROW][C]60[/C][C]16563[/C][C]17181.0323134164[/C][C]-618.032313416381[/C][/ROW]
[ROW][C]61[/C][C]15388[/C][C]16566.3648554491[/C][C]-1178.36485544909[/C][/ROW]
[ROW][C]62[/C][C]15680[/C][C]16262.0175125311[/C][C]-582.017512531093[/C][/ROW]
[ROW][C]63[/C][C]15751[/C][C]16276.4800607712[/C][C]-525.480060771175[/C][/ROW]
[ROW][C]64[/C][C]15830[/C][C]15569.6337840368[/C][C]260.366215963242[/C][/ROW]
[ROW][C]65[/C][C]17226[/C][C]16700.5971205608[/C][C]525.4028794392[/C][/ROW]
[ROW][C]66[/C][C]17076[/C][C]16676.3935094317[/C][C]399.606490568338[/C][/ROW]
[ROW][C]67[/C][C]15388[/C][C]15567.4050548783[/C][C]-179.405054878329[/C][/ROW]
[ROW][C]68[/C][C]14647[/C][C]15009.5593670505[/C][C]-362.559367050542[/C][/ROW]
[ROW][C]69[/C][C]14355[/C][C]14616.799986377[/C][C]-261.799986377035[/C][/ROW]
[ROW][C]70[/C][C]14725[/C][C]14534.9754247044[/C][C]190.024575295563[/C][/ROW]
[ROW][C]71[/C][C]13322[/C][C]14128.7943712655[/C][C]-806.794371265465[/C][/ROW]
[ROW][C]72[/C][C]12367[/C][C]13654.8245467426[/C][C]-1287.82454674259[/C][/ROW]
[ROW][C]73[/C][C]10601[/C][C]12353.7033095586[/C][C]-1752.70330955861[/C][/ROW]
[ROW][C]74[/C][C]10750[/C][C]11673.4125776197[/C][C]-923.412577619707[/C][/ROW]
[ROW][C]75[/C][C]10750[/C][C]11380.4082235504[/C][C]-630.408223550396[/C][/ROW]
[ROW][C]76[/C][C]10601[/C][C]10704.1120975528[/C][C]-103.112097552794[/C][/ROW]
[ROW][C]77[/C][C]11854[/C][C]11548.6930093407[/C][C]305.306990659345[/C][/ROW]
[ROW][C]78[/C][C]11926[/C][C]11267.955932405[/C][C]658.044067594998[/C][/ROW]
[ROW][C]79[/C][C]10451[/C][C]10189.6027638055[/C][C]261.397236194467[/C][/ROW]
[ROW][C]80[/C][C]10159[/C][C]9893.78453282241[/C][C]265.21546717759[/C][/ROW]
[ROW][C]81[/C][C]9568[/C][C]9976.71703565003[/C][C]-408.717035650026[/C][/ROW]
[ROW][C]82[/C][C]10380[/C][C]9828.8158310325[/C][C]551.1841689675[/C][/ROW]
[ROW][C]83[/C][C]8905[/C][C]9460.87803679064[/C][C]-555.878036790637[/C][/ROW]
[ROW][C]84[/C][C]8022[/C][C]9047.88227798398[/C][C]-1025.88227798398[/C][/ROW]
[ROW][C]85[/C][C]6333[/C][C]7822.54200151744[/C][C]-1489.54200151744[/C][/ROW]
[ROW][C]86[/C][C]6697[/C][C]7491.2417464063[/C][C]-794.241746406297[/C][/ROW]
[ROW][C]87[/C][C]6255[/C][C]7330.79510459987[/C][C]-1075.79510459987[/C][/ROW]
[ROW][C]88[/C][C]6404[/C][C]6376.3325744539[/C][C]27.6674255461039[/C][/ROW]
[ROW][C]89[/C][C]7509[/C][C]7375.5215204543[/C][C]133.478479545702[/C][/ROW]
[ROW][C]90[/C][C]7730[/C][C]6996.42816339105[/C][C]733.571836608951[/C][/ROW]
[ROW][C]91[/C][C]6996[/C][C]5860.28059085476[/C][C]1135.71940914524[/C][/ROW]
[ROW][C]92[/C][C]6917[/C][C]6231.56541146783[/C][C]685.434588532172[/C][/ROW]
[ROW][C]93[/C][C]6917[/C][C]6485.27520581041[/C][C]431.724794189593[/C][/ROW]
[ROW][C]94[/C][C]7879[/C][C]7189.82183302208[/C][C]689.178166977925[/C][/ROW]
[ROW][C]95[/C][C]6184[/C][C]6689.14542409408[/C][C]-505.145424094084[/C][/ROW]
[ROW][C]96[/C][C]5079[/C][C]6207.51885273163[/C][C]-1128.51885273163[/C][/ROW]
[ROW][C]97[/C][C]3163[/C][C]4792.37661736163[/C][C]-1629.37661736163[/C][/ROW]
[ROW][C]98[/C][C]4709[/C][C]4481.73448865805[/C][C]227.265511341953[/C][/ROW]
[ROW][C]99[/C][C]4488[/C][C]5068.57860366674[/C][C]-580.578603666743[/C][/ROW]
[ROW][C]100[/C][C]4566[/C][C]4738.28668943866[/C][C]-172.286689438656[/C][/ROW]
[ROW][C]101[/C][C]6333[/C][C]5601.41087929202[/C][C]731.589120707985[/C][/ROW]
[ROW][C]102[/C][C]6112[/C][C]5827.24913105784[/C][C]284.750868942156[/C][/ROW]
[ROW][C]103[/C][C]5300[/C][C]4421.25820094845[/C][C]878.741799051553[/C][/ROW]
[ROW][C]104[/C][C]5671[/C][C]4494.40452765772[/C][C]1176.59547234228[/C][/ROW]
[ROW][C]105[/C][C]5671[/C][C]5088.33619348546[/C][C]582.663806514543[/C][/ROW]
[ROW][C]106[/C][C]6996[/C][C]5971.75223444469[/C][C]1024.24776555531[/C][/ROW]
[ROW][C]107[/C][C]5450[/C][C]5496.85986112432[/C][C]-46.8598611243242[/C][/ROW]
[ROW][C]108[/C][C]4566[/C][C]5262.22402585912[/C][C]-696.224025859115[/C][/ROW]
[ROW][C]109[/C][C]3163[/C][C]4103.4873860616[/C][C]-940.487386061598[/C][/ROW]
[ROW][C]110[/C][C]5008[/C][C]4750.5072354138[/C][C]257.492764586197[/C][/ROW]
[ROW][C]111[/C][C]4859[/C][C]5218.94015536988[/C][C]-359.940155369884[/C][/ROW]
[ROW][C]112[/C][C]4930[/C][C]5176.54695104212[/C][C]-246.546951042122[/C][/ROW]
[ROW][C]113[/C][C]6476[/C][C]6196.52435883459[/C][C]279.475641165408[/C][/ROW]
[ROW][C]114[/C][C]6333[/C][C]5994.07519781828[/C][C]338.924802181717[/C][/ROW]
[ROW][C]115[/C][C]5813[/C][C]4777.96684270483[/C][C]1035.03315729517[/C][/ROW]
[ROW][C]116[/C][C]5892[/C][C]5061.79343952919[/C][C]830.206560470805[/C][/ROW]
[ROW][C]117[/C][C]6255[/C][C]5279.1033955146[/C][C]975.896604485397[/C][/ROW]
[ROW][C]118[/C][C]7067[/C][C]6591.21466455058[/C][C]475.785335449418[/C][/ROW]
[ROW][C]119[/C][C]5813[/C][C]5478.72733483856[/C][C]334.27266516144[/C][/ROW]
[ROW][C]120[/C][C]4787[/C][C]5434.27681663482[/C][C]-647.276816634815[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124159&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124159&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
132105121137.6057692308-86.6057692307622
142164321681.5136742757-38.5136742757313
152186421876.6825783894-12.6825783894274
162164321647.4633889689-4.46338896892121
172245522479.0387914927-24.0387914926978
182193521978.0331210841-43.0331210840995
192075921255.7930034244-496.79300342438
202046720102.9362997471364.06370025294
212046720413.346115857253.6538841428046
222061020391.3382141599218.661785840053
232002620603.8229051277-577.82290512765
242046720305.0428450636161.957154936445
252009720368.2877254563-271.287725456259
262046720769.0463405358-302.046340535773
272105120751.2703481991299.729651800917
282127220764.6759597868507.324040213225
292179221996.2437424225-204.243742422503
302157121345.6036334265225.396366573546
312024620741.1711892186-495.171189218574
321972619768.6718971987-42.6718971986775
331950619687.9880307106-181.98803071064
341972619506.9162467714219.083753228588
351936319547.0073511862-184.007351186214
361950619711.3163932303-205.316393230263
371906419386.9685748297-322.968574829749
381980519733.287890321271.7121096788178
392016820133.512568754634.4874312454194
402024619974.1554096501271.844590349934
412164320862.6647544093780.335245590661
422164321082.8031645833560.19683541674
431980520598.6218140389-793.621814038881
441936319486.2067697935-123.206769793545
451936319314.057484223548.9425157765254
461958419403.0524041221180.947595877875
471862219332.3116142437-710.311614243652
481818019073.3405664485-893.340566448544
491766818170.4803523421-502.480352342085
501781718445.7356779072-628.735677907232
511848018265.2453146448214.754685355183
521796018281.5249137912-321.524913791171
531936318783.4666955088579.53330449123
541958418774.0293440093809.970655990659
551818018183.505149927-3.50514992701574
561766817822.3039203764-154.303920376373
571737517647.0882610185-272.088261018478
581766817491.7775817697176.222418230274
591685517214.0147817301-359.014781730137
601656317181.0323134164-618.032313416381
611538816566.3648554491-1178.36485544909
621568016262.0175125311-582.017512531093
631575116276.4800607712-525.480060771175
641583015569.6337840368260.366215963242
651722616700.5971205608525.4028794392
661707616676.3935094317399.606490568338
671538815567.4050548783-179.405054878329
681464715009.5593670505-362.559367050542
691435514616.799986377-261.799986377035
701472514534.9754247044190.024575295563
711332214128.7943712655-806.794371265465
721236713654.8245467426-1287.82454674259
731060112353.7033095586-1752.70330955861
741075011673.4125776197-923.412577619707
751075011380.4082235504-630.408223550396
761060110704.1120975528-103.112097552794
771185411548.6930093407305.306990659345
781192611267.955932405658.044067594998
791045110189.6027638055261.397236194467
80101599893.78453282241265.21546717759
8195689976.71703565003-408.717035650026
82103809828.8158310325551.1841689675
8389059460.87803679064-555.878036790637
8480229047.88227798398-1025.88227798398
8563337822.54200151744-1489.54200151744
8666977491.2417464063-794.241746406297
8762557330.79510459987-1075.79510459987
8864046376.332574453927.6674255461039
8975097375.5215204543133.478479545702
9077306996.42816339105733.571836608951
9169965860.280590854761135.71940914524
9269176231.56541146783685.434588532172
9369176485.27520581041431.724794189593
9478797189.82183302208689.178166977925
9561846689.14542409408-505.145424094084
9650796207.51885273163-1128.51885273163
9731634792.37661736163-1629.37661736163
9847094481.73448865805227.265511341953
9944885068.57860366674-580.578603666743
10045664738.28668943866-172.286689438656
10163335601.41087929202731.589120707985
10261125827.24913105784284.750868942156
10353004421.25820094845878.741799051553
10456714494.404527657721176.59547234228
10556715088.33619348546582.663806514543
10669965971.752234444691024.24776555531
10754505496.85986112432-46.8598611243242
10845665262.22402585912-696.224025859115
10931634103.4873860616-940.487386061598
11050084750.5072354138257.492764586197
11148595218.94015536988-359.940155369884
11249305176.54695104212-246.546951042122
11364766196.52435883459279.475641165408
11463335994.07519781828338.924802181717
11558134777.966842704831035.03315729517
11658925061.79343952919830.206560470805
11762555279.1033955146975.896604485397
11870676591.21466455058475.785335449418
11958135478.72733483856334.27266516144
12047875434.27681663482-647.276816634815







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1214287.591272744553092.400794273935482.78175121517
1225962.632335700994430.469806571537494.79486483045
1236129.854939091544315.893444095537943.81643408756
1246431.027863589974367.635087955798494.42063922415
1257793.279462452215502.1598808862710084.3990440182
1267416.567341813244913.433211458259919.70147216824
1276108.204357077373405.011623148811.39709101475
1285550.289396759062656.460275757048444.11851776108
1295152.424776843792075.579778062788229.26977562479
1305589.410754484832335.837019430118842.98448953955
1314067.50975768099642.4762851386877492.5432302233
1323547.28212536249-44.7393751367297139.3036258617

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 4287.59127274455 & 3092.40079427393 & 5482.78175121517 \tabularnewline
122 & 5962.63233570099 & 4430.46980657153 & 7494.79486483045 \tabularnewline
123 & 6129.85493909154 & 4315.89344409553 & 7943.81643408756 \tabularnewline
124 & 6431.02786358997 & 4367.63508795579 & 8494.42063922415 \tabularnewline
125 & 7793.27946245221 & 5502.15988088627 & 10084.3990440182 \tabularnewline
126 & 7416.56734181324 & 4913.43321145825 & 9919.70147216824 \tabularnewline
127 & 6108.20435707737 & 3405.01162314 & 8811.39709101475 \tabularnewline
128 & 5550.28939675906 & 2656.46027575704 & 8444.11851776108 \tabularnewline
129 & 5152.42477684379 & 2075.57977806278 & 8229.26977562479 \tabularnewline
130 & 5589.41075448483 & 2335.83701943011 & 8842.98448953955 \tabularnewline
131 & 4067.50975768099 & 642.476285138687 & 7492.5432302233 \tabularnewline
132 & 3547.28212536249 & -44.739375136729 & 7139.3036258617 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124159&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]4287.59127274455[/C][C]3092.40079427393[/C][C]5482.78175121517[/C][/ROW]
[ROW][C]122[/C][C]5962.63233570099[/C][C]4430.46980657153[/C][C]7494.79486483045[/C][/ROW]
[ROW][C]123[/C][C]6129.85493909154[/C][C]4315.89344409553[/C][C]7943.81643408756[/C][/ROW]
[ROW][C]124[/C][C]6431.02786358997[/C][C]4367.63508795579[/C][C]8494.42063922415[/C][/ROW]
[ROW][C]125[/C][C]7793.27946245221[/C][C]5502.15988088627[/C][C]10084.3990440182[/C][/ROW]
[ROW][C]126[/C][C]7416.56734181324[/C][C]4913.43321145825[/C][C]9919.70147216824[/C][/ROW]
[ROW][C]127[/C][C]6108.20435707737[/C][C]3405.01162314[/C][C]8811.39709101475[/C][/ROW]
[ROW][C]128[/C][C]5550.28939675906[/C][C]2656.46027575704[/C][C]8444.11851776108[/C][/ROW]
[ROW][C]129[/C][C]5152.42477684379[/C][C]2075.57977806278[/C][C]8229.26977562479[/C][/ROW]
[ROW][C]130[/C][C]5589.41075448483[/C][C]2335.83701943011[/C][C]8842.98448953955[/C][/ROW]
[ROW][C]131[/C][C]4067.50975768099[/C][C]642.476285138687[/C][C]7492.5432302233[/C][/ROW]
[ROW][C]132[/C][C]3547.28212536249[/C][C]-44.739375136729[/C][C]7139.3036258617[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124159&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124159&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
1214287.591272744553092.400794273935482.78175121517
1225962.632335700994430.469806571537494.79486483045
1236129.854939091544315.893444095537943.81643408756
1246431.027863589974367.635087955798494.42063922415
1257793.279462452215502.1598808862710084.3990440182
1267416.567341813244913.433211458259919.70147216824
1276108.204357077373405.011623148811.39709101475
1285550.289396759062656.460275757048444.11851776108
1295152.424776843792075.579778062788229.26977562479
1305589.410754484832335.837019430118842.98448953955
1314067.50975768099642.4762851386877492.5432302233
1323547.28212536249-44.7393751367297139.3036258617



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')