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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 computationTue, 13 Dec 2016 12:14:02 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/13/t14816276962wfee77du19sja0.htm/, Retrieved Sun, 05 May 2024 05:04:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299060, Retrieved Sun, 05 May 2024 05:04:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-13 11:14:02] [94c1b173d9287822f5e2740a4a602bdd] [Current]
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Dataseries X:
13430
13020
11710
9265
7280
5040
3860
6160
13610
15455
14530
13815
12860
11500
10660
9340
8050
6540
5060
6350
14130
16380
16160
15850
15930
15320
13420
12255
8785
6380
4760
5730
10810
12845
12865
13515
13880
12960
12090
9510
8130
6625
4920
4650
10085
13960
14495
14340
13875
13135
13415
9280
7075
5660
4270
5085
11945
14335
14105
13755
12920
11650
10720
8600
7795
6550
4800
5900
14095
15170
14875
15230
13685
12780
11510
9915
8740
7870
6650
5285
13195
13390
13490
13445
13070
12480
11550
10725
9130
7885
6415
5540
9350
12645
11985
10055
10295
10280
9420
9575
8090
5855
4445
3555
12870
14750
13615
13705
13940
11900
9000
7340
6425
5535
4050
3485
8090
11380
11355
10530
9285




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299060&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299060&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299060&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.851943749536549
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.851943749536549 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299060&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]0.851943749536549[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299060&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299060&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
alpha0.851943749536549
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131286012680.546207265179.453792735045
141150011459.91602986440.083970136011
151066010668.8839365591-8.88393655909204
1693409325.5089412174114.4910587825889
1780507985.7981270525364.2018729474748
1865406422.18813029978117.811869700217
1950604301.33416852655758.665831473454
2063507379.16006718509-1029.16006718509
211413014103.858866221926.1411337780773
221638016056.1565939644323.843406035594
231616015416.2465784462743.753421553825
241585015284.7012760165565.298723983504
251593014769.77519843351160.22480156652
261532014364.0721783714955.927821628624
271342014346.0375252388-926.037525238771
281225512224.760076821330.2399231786876
29878510905.8264059937-2120.82640599372
3063807488.63251954299-1108.63251954299
3147604417.79936087463342.200639125374
3257306876.12154297586-1146.12154297586
331081013657.4196827004-2847.41968270036
341284513205.6819161158-360.681916115793
351286512044.7651334209820.234866579127
361351511951.95638663621563.04361336383
371388012375.13535554261504.86464445738
381296012232.798650642727.201349357969
391209011741.2651763456348.734823654437
40951010847.6049160651-1337.60491606514
4181308044.865568912585.1344310875029
4266256656.88786090545-31.8878609054536
4349204718.18550153069201.814498469314
4446506836.55118681494-2186.55118681494
451008512479.5739711501-2394.57397115014
461396012781.81234763161178.18765236842
471449513106.7679861141388.23201388604
481434013607.8383365924732.161663407627
491387513314.5388616388560.461138361219
501313512252.4855810837882.514418916306
511341511837.23577089721577.76422910281
52928011740.9662917147-2460.96629171474
5370758191.83169523288-1116.83169523288
5456605762.52057697941-102.520576979412
5542703798.24421168614471.755788313862
5650855792.97222349653-707.972223496532
571194512664.8620403674-719.862040367445
581433514922.8304683314-587.830468331358
591410513774.3363879126330.66361208743
601375513277.2826326392477.717367360776
611292012741.7895941223178.210405877688
621165011401.7621924406248.237807559446
631072010549.080467763170.919532237009
6486008656.29914497254-56.2991449725359
6577957354.81322234689440.186777653111
6665506402.16936095358147.830639046419
6748004736.2033547174963.7966452825112
6859006208.70701856069-308.707018560688
691409513418.9879694795676.012030520482
701517016885.710686775-1715.710686775
711487514912.3148936469-37.3148936469115
721523014123.53637807171106.46362192826
731368514079.3559034732-394.355903473224
741278012261.9022078674518.097792132554
751151011627.6785563604-117.678556360434
7699159455.38675047828459.613249521717
7787408666.9370117622973.0629882377107
7878707358.23917898828511.760821011721
7966505989.87945851707660.120541482929
8052857915.26604267498-2630.26604267498
811319513293.5031039864-98.5031039863607
821339015746.2729958463-2356.27299584625
831349013475.651135240414.348864759615
841344512900.2307940939544.769205906072
851307012155.3125610624914.687438937553
861248011588.1846317889891.815368211128
871155011178.2166710227371.783328977266
88107259508.39051919261216.6094808074
8991309307.62780584179-177.627805841792
9078857850.3074741923634.6925258076444
9164156097.47798545275317.522014547249
9255407243.82759576171-1703.82759576171
93935013786.1814290158-4436.18142901577
941264512209.2164397686435.783560231361
951198512668.2550944136-683.255094413631
961005511577.0474674773-1522.04746747727
97102959126.086394679631168.91360532037
98102808772.158505792451507.84149420755
9994208810.01615877035609.98384122965
10095757468.205236823472106.79476317653
10180907819.40476579886270.595234201142
10258556775.38060371344-920.38060371344
10344454250.75720555132194.242794448681
10435554992.80641067146-1437.80641067146
1051287011357.25326631641512.74673368357
1061475015569.7653104201-819.765310420087
1071361514793.4662851455-1178.4662851455
1081370513156.1781258914548.821874108575
1091394012867.89485134621072.10514865376
1101190012481.6719953058-581.671995305789
111900010606.4482537707-1606.44825377067
11273407597.97407497226-257.974074972264
11364255662.66275582513762.337244174871
11455354861.24370856717673.756291432832
11540503859.76223514123190.237764858774
11634854356.7642944536-871.764294453596
117809011640.2950283312-3550.29502833117
1181138011194.037302233185.962697766976
1191135511221.4540459118133.545954088177
1201053010957.6623215174-427.662321517404
12192859914.94479954684-629.944799546838

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 12860 & 12680.546207265 & 179.453792735045 \tabularnewline
14 & 11500 & 11459.916029864 & 40.083970136011 \tabularnewline
15 & 10660 & 10668.8839365591 & -8.88393655909204 \tabularnewline
16 & 9340 & 9325.50894121741 & 14.4910587825889 \tabularnewline
17 & 8050 & 7985.79812705253 & 64.2018729474748 \tabularnewline
18 & 6540 & 6422.18813029978 & 117.811869700217 \tabularnewline
19 & 5060 & 4301.33416852655 & 758.665831473454 \tabularnewline
20 & 6350 & 7379.16006718509 & -1029.16006718509 \tabularnewline
21 & 14130 & 14103.8588662219 & 26.1411337780773 \tabularnewline
22 & 16380 & 16056.1565939644 & 323.843406035594 \tabularnewline
23 & 16160 & 15416.2465784462 & 743.753421553825 \tabularnewline
24 & 15850 & 15284.7012760165 & 565.298723983504 \tabularnewline
25 & 15930 & 14769.7751984335 & 1160.22480156652 \tabularnewline
26 & 15320 & 14364.0721783714 & 955.927821628624 \tabularnewline
27 & 13420 & 14346.0375252388 & -926.037525238771 \tabularnewline
28 & 12255 & 12224.7600768213 & 30.2399231786876 \tabularnewline
29 & 8785 & 10905.8264059937 & -2120.82640599372 \tabularnewline
30 & 6380 & 7488.63251954299 & -1108.63251954299 \tabularnewline
31 & 4760 & 4417.79936087463 & 342.200639125374 \tabularnewline
32 & 5730 & 6876.12154297586 & -1146.12154297586 \tabularnewline
33 & 10810 & 13657.4196827004 & -2847.41968270036 \tabularnewline
34 & 12845 & 13205.6819161158 & -360.681916115793 \tabularnewline
35 & 12865 & 12044.7651334209 & 820.234866579127 \tabularnewline
36 & 13515 & 11951.9563866362 & 1563.04361336383 \tabularnewline
37 & 13880 & 12375.1353555426 & 1504.86464445738 \tabularnewline
38 & 12960 & 12232.798650642 & 727.201349357969 \tabularnewline
39 & 12090 & 11741.2651763456 & 348.734823654437 \tabularnewline
40 & 9510 & 10847.6049160651 & -1337.60491606514 \tabularnewline
41 & 8130 & 8044.8655689125 & 85.1344310875029 \tabularnewline
42 & 6625 & 6656.88786090545 & -31.8878609054536 \tabularnewline
43 & 4920 & 4718.18550153069 & 201.814498469314 \tabularnewline
44 & 4650 & 6836.55118681494 & -2186.55118681494 \tabularnewline
45 & 10085 & 12479.5739711501 & -2394.57397115014 \tabularnewline
46 & 13960 & 12781.8123476316 & 1178.18765236842 \tabularnewline
47 & 14495 & 13106.767986114 & 1388.23201388604 \tabularnewline
48 & 14340 & 13607.8383365924 & 732.161663407627 \tabularnewline
49 & 13875 & 13314.5388616388 & 560.461138361219 \tabularnewline
50 & 13135 & 12252.4855810837 & 882.514418916306 \tabularnewline
51 & 13415 & 11837.2357708972 & 1577.76422910281 \tabularnewline
52 & 9280 & 11740.9662917147 & -2460.96629171474 \tabularnewline
53 & 7075 & 8191.83169523288 & -1116.83169523288 \tabularnewline
54 & 5660 & 5762.52057697941 & -102.520576979412 \tabularnewline
55 & 4270 & 3798.24421168614 & 471.755788313862 \tabularnewline
56 & 5085 & 5792.97222349653 & -707.972223496532 \tabularnewline
57 & 11945 & 12664.8620403674 & -719.862040367445 \tabularnewline
58 & 14335 & 14922.8304683314 & -587.830468331358 \tabularnewline
59 & 14105 & 13774.3363879126 & 330.66361208743 \tabularnewline
60 & 13755 & 13277.2826326392 & 477.717367360776 \tabularnewline
61 & 12920 & 12741.7895941223 & 178.210405877688 \tabularnewline
62 & 11650 & 11401.7621924406 & 248.237807559446 \tabularnewline
63 & 10720 & 10549.080467763 & 170.919532237009 \tabularnewline
64 & 8600 & 8656.29914497254 & -56.2991449725359 \tabularnewline
65 & 7795 & 7354.81322234689 & 440.186777653111 \tabularnewline
66 & 6550 & 6402.16936095358 & 147.830639046419 \tabularnewline
67 & 4800 & 4736.20335471749 & 63.7966452825112 \tabularnewline
68 & 5900 & 6208.70701856069 & -308.707018560688 \tabularnewline
69 & 14095 & 13418.9879694795 & 676.012030520482 \tabularnewline
70 & 15170 & 16885.710686775 & -1715.710686775 \tabularnewline
71 & 14875 & 14912.3148936469 & -37.3148936469115 \tabularnewline
72 & 15230 & 14123.5363780717 & 1106.46362192826 \tabularnewline
73 & 13685 & 14079.3559034732 & -394.355903473224 \tabularnewline
74 & 12780 & 12261.9022078674 & 518.097792132554 \tabularnewline
75 & 11510 & 11627.6785563604 & -117.678556360434 \tabularnewline
76 & 9915 & 9455.38675047828 & 459.613249521717 \tabularnewline
77 & 8740 & 8666.93701176229 & 73.0629882377107 \tabularnewline
78 & 7870 & 7358.23917898828 & 511.760821011721 \tabularnewline
79 & 6650 & 5989.87945851707 & 660.120541482929 \tabularnewline
80 & 5285 & 7915.26604267498 & -2630.26604267498 \tabularnewline
81 & 13195 & 13293.5031039864 & -98.5031039863607 \tabularnewline
82 & 13390 & 15746.2729958463 & -2356.27299584625 \tabularnewline
83 & 13490 & 13475.6511352404 & 14.348864759615 \tabularnewline
84 & 13445 & 12900.2307940939 & 544.769205906072 \tabularnewline
85 & 13070 & 12155.3125610624 & 914.687438937553 \tabularnewline
86 & 12480 & 11588.1846317889 & 891.815368211128 \tabularnewline
87 & 11550 & 11178.2166710227 & 371.783328977266 \tabularnewline
88 & 10725 & 9508.3905191926 & 1216.6094808074 \tabularnewline
89 & 9130 & 9307.62780584179 & -177.627805841792 \tabularnewline
90 & 7885 & 7850.30747419236 & 34.6925258076444 \tabularnewline
91 & 6415 & 6097.47798545275 & 317.522014547249 \tabularnewline
92 & 5540 & 7243.82759576171 & -1703.82759576171 \tabularnewline
93 & 9350 & 13786.1814290158 & -4436.18142901577 \tabularnewline
94 & 12645 & 12209.2164397686 & 435.783560231361 \tabularnewline
95 & 11985 & 12668.2550944136 & -683.255094413631 \tabularnewline
96 & 10055 & 11577.0474674773 & -1522.04746747727 \tabularnewline
97 & 10295 & 9126.08639467963 & 1168.91360532037 \tabularnewline
98 & 10280 & 8772.15850579245 & 1507.84149420755 \tabularnewline
99 & 9420 & 8810.01615877035 & 609.98384122965 \tabularnewline
100 & 9575 & 7468.20523682347 & 2106.79476317653 \tabularnewline
101 & 8090 & 7819.40476579886 & 270.595234201142 \tabularnewline
102 & 5855 & 6775.38060371344 & -920.38060371344 \tabularnewline
103 & 4445 & 4250.75720555132 & 194.242794448681 \tabularnewline
104 & 3555 & 4992.80641067146 & -1437.80641067146 \tabularnewline
105 & 12870 & 11357.2532663164 & 1512.74673368357 \tabularnewline
106 & 14750 & 15569.7653104201 & -819.765310420087 \tabularnewline
107 & 13615 & 14793.4662851455 & -1178.4662851455 \tabularnewline
108 & 13705 & 13156.1781258914 & 548.821874108575 \tabularnewline
109 & 13940 & 12867.8948513462 & 1072.10514865376 \tabularnewline
110 & 11900 & 12481.6719953058 & -581.671995305789 \tabularnewline
111 & 9000 & 10606.4482537707 & -1606.44825377067 \tabularnewline
112 & 7340 & 7597.97407497226 & -257.974074972264 \tabularnewline
113 & 6425 & 5662.66275582513 & 762.337244174871 \tabularnewline
114 & 5535 & 4861.24370856717 & 673.756291432832 \tabularnewline
115 & 4050 & 3859.76223514123 & 190.237764858774 \tabularnewline
116 & 3485 & 4356.7642944536 & -871.764294453596 \tabularnewline
117 & 8090 & 11640.2950283312 & -3550.29502833117 \tabularnewline
118 & 11380 & 11194.037302233 & 185.962697766976 \tabularnewline
119 & 11355 & 11221.4540459118 & 133.545954088177 \tabularnewline
120 & 10530 & 10957.6623215174 & -427.662321517404 \tabularnewline
121 & 9285 & 9914.94479954684 & -629.944799546838 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299060&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]12860[/C][C]12680.546207265[/C][C]179.453792735045[/C][/ROW]
[ROW][C]14[/C][C]11500[/C][C]11459.916029864[/C][C]40.083970136011[/C][/ROW]
[ROW][C]15[/C][C]10660[/C][C]10668.8839365591[/C][C]-8.88393655909204[/C][/ROW]
[ROW][C]16[/C][C]9340[/C][C]9325.50894121741[/C][C]14.4910587825889[/C][/ROW]
[ROW][C]17[/C][C]8050[/C][C]7985.79812705253[/C][C]64.2018729474748[/C][/ROW]
[ROW][C]18[/C][C]6540[/C][C]6422.18813029978[/C][C]117.811869700217[/C][/ROW]
[ROW][C]19[/C][C]5060[/C][C]4301.33416852655[/C][C]758.665831473454[/C][/ROW]
[ROW][C]20[/C][C]6350[/C][C]7379.16006718509[/C][C]-1029.16006718509[/C][/ROW]
[ROW][C]21[/C][C]14130[/C][C]14103.8588662219[/C][C]26.1411337780773[/C][/ROW]
[ROW][C]22[/C][C]16380[/C][C]16056.1565939644[/C][C]323.843406035594[/C][/ROW]
[ROW][C]23[/C][C]16160[/C][C]15416.2465784462[/C][C]743.753421553825[/C][/ROW]
[ROW][C]24[/C][C]15850[/C][C]15284.7012760165[/C][C]565.298723983504[/C][/ROW]
[ROW][C]25[/C][C]15930[/C][C]14769.7751984335[/C][C]1160.22480156652[/C][/ROW]
[ROW][C]26[/C][C]15320[/C][C]14364.0721783714[/C][C]955.927821628624[/C][/ROW]
[ROW][C]27[/C][C]13420[/C][C]14346.0375252388[/C][C]-926.037525238771[/C][/ROW]
[ROW][C]28[/C][C]12255[/C][C]12224.7600768213[/C][C]30.2399231786876[/C][/ROW]
[ROW][C]29[/C][C]8785[/C][C]10905.8264059937[/C][C]-2120.82640599372[/C][/ROW]
[ROW][C]30[/C][C]6380[/C][C]7488.63251954299[/C][C]-1108.63251954299[/C][/ROW]
[ROW][C]31[/C][C]4760[/C][C]4417.79936087463[/C][C]342.200639125374[/C][/ROW]
[ROW][C]32[/C][C]5730[/C][C]6876.12154297586[/C][C]-1146.12154297586[/C][/ROW]
[ROW][C]33[/C][C]10810[/C][C]13657.4196827004[/C][C]-2847.41968270036[/C][/ROW]
[ROW][C]34[/C][C]12845[/C][C]13205.6819161158[/C][C]-360.681916115793[/C][/ROW]
[ROW][C]35[/C][C]12865[/C][C]12044.7651334209[/C][C]820.234866579127[/C][/ROW]
[ROW][C]36[/C][C]13515[/C][C]11951.9563866362[/C][C]1563.04361336383[/C][/ROW]
[ROW][C]37[/C][C]13880[/C][C]12375.1353555426[/C][C]1504.86464445738[/C][/ROW]
[ROW][C]38[/C][C]12960[/C][C]12232.798650642[/C][C]727.201349357969[/C][/ROW]
[ROW][C]39[/C][C]12090[/C][C]11741.2651763456[/C][C]348.734823654437[/C][/ROW]
[ROW][C]40[/C][C]9510[/C][C]10847.6049160651[/C][C]-1337.60491606514[/C][/ROW]
[ROW][C]41[/C][C]8130[/C][C]8044.8655689125[/C][C]85.1344310875029[/C][/ROW]
[ROW][C]42[/C][C]6625[/C][C]6656.88786090545[/C][C]-31.8878609054536[/C][/ROW]
[ROW][C]43[/C][C]4920[/C][C]4718.18550153069[/C][C]201.814498469314[/C][/ROW]
[ROW][C]44[/C][C]4650[/C][C]6836.55118681494[/C][C]-2186.55118681494[/C][/ROW]
[ROW][C]45[/C][C]10085[/C][C]12479.5739711501[/C][C]-2394.57397115014[/C][/ROW]
[ROW][C]46[/C][C]13960[/C][C]12781.8123476316[/C][C]1178.18765236842[/C][/ROW]
[ROW][C]47[/C][C]14495[/C][C]13106.767986114[/C][C]1388.23201388604[/C][/ROW]
[ROW][C]48[/C][C]14340[/C][C]13607.8383365924[/C][C]732.161663407627[/C][/ROW]
[ROW][C]49[/C][C]13875[/C][C]13314.5388616388[/C][C]560.461138361219[/C][/ROW]
[ROW][C]50[/C][C]13135[/C][C]12252.4855810837[/C][C]882.514418916306[/C][/ROW]
[ROW][C]51[/C][C]13415[/C][C]11837.2357708972[/C][C]1577.76422910281[/C][/ROW]
[ROW][C]52[/C][C]9280[/C][C]11740.9662917147[/C][C]-2460.96629171474[/C][/ROW]
[ROW][C]53[/C][C]7075[/C][C]8191.83169523288[/C][C]-1116.83169523288[/C][/ROW]
[ROW][C]54[/C][C]5660[/C][C]5762.52057697941[/C][C]-102.520576979412[/C][/ROW]
[ROW][C]55[/C][C]4270[/C][C]3798.24421168614[/C][C]471.755788313862[/C][/ROW]
[ROW][C]56[/C][C]5085[/C][C]5792.97222349653[/C][C]-707.972223496532[/C][/ROW]
[ROW][C]57[/C][C]11945[/C][C]12664.8620403674[/C][C]-719.862040367445[/C][/ROW]
[ROW][C]58[/C][C]14335[/C][C]14922.8304683314[/C][C]-587.830468331358[/C][/ROW]
[ROW][C]59[/C][C]14105[/C][C]13774.3363879126[/C][C]330.66361208743[/C][/ROW]
[ROW][C]60[/C][C]13755[/C][C]13277.2826326392[/C][C]477.717367360776[/C][/ROW]
[ROW][C]61[/C][C]12920[/C][C]12741.7895941223[/C][C]178.210405877688[/C][/ROW]
[ROW][C]62[/C][C]11650[/C][C]11401.7621924406[/C][C]248.237807559446[/C][/ROW]
[ROW][C]63[/C][C]10720[/C][C]10549.080467763[/C][C]170.919532237009[/C][/ROW]
[ROW][C]64[/C][C]8600[/C][C]8656.29914497254[/C][C]-56.2991449725359[/C][/ROW]
[ROW][C]65[/C][C]7795[/C][C]7354.81322234689[/C][C]440.186777653111[/C][/ROW]
[ROW][C]66[/C][C]6550[/C][C]6402.16936095358[/C][C]147.830639046419[/C][/ROW]
[ROW][C]67[/C][C]4800[/C][C]4736.20335471749[/C][C]63.7966452825112[/C][/ROW]
[ROW][C]68[/C][C]5900[/C][C]6208.70701856069[/C][C]-308.707018560688[/C][/ROW]
[ROW][C]69[/C][C]14095[/C][C]13418.9879694795[/C][C]676.012030520482[/C][/ROW]
[ROW][C]70[/C][C]15170[/C][C]16885.710686775[/C][C]-1715.710686775[/C][/ROW]
[ROW][C]71[/C][C]14875[/C][C]14912.3148936469[/C][C]-37.3148936469115[/C][/ROW]
[ROW][C]72[/C][C]15230[/C][C]14123.5363780717[/C][C]1106.46362192826[/C][/ROW]
[ROW][C]73[/C][C]13685[/C][C]14079.3559034732[/C][C]-394.355903473224[/C][/ROW]
[ROW][C]74[/C][C]12780[/C][C]12261.9022078674[/C][C]518.097792132554[/C][/ROW]
[ROW][C]75[/C][C]11510[/C][C]11627.6785563604[/C][C]-117.678556360434[/C][/ROW]
[ROW][C]76[/C][C]9915[/C][C]9455.38675047828[/C][C]459.613249521717[/C][/ROW]
[ROW][C]77[/C][C]8740[/C][C]8666.93701176229[/C][C]73.0629882377107[/C][/ROW]
[ROW][C]78[/C][C]7870[/C][C]7358.23917898828[/C][C]511.760821011721[/C][/ROW]
[ROW][C]79[/C][C]6650[/C][C]5989.87945851707[/C][C]660.120541482929[/C][/ROW]
[ROW][C]80[/C][C]5285[/C][C]7915.26604267498[/C][C]-2630.26604267498[/C][/ROW]
[ROW][C]81[/C][C]13195[/C][C]13293.5031039864[/C][C]-98.5031039863607[/C][/ROW]
[ROW][C]82[/C][C]13390[/C][C]15746.2729958463[/C][C]-2356.27299584625[/C][/ROW]
[ROW][C]83[/C][C]13490[/C][C]13475.6511352404[/C][C]14.348864759615[/C][/ROW]
[ROW][C]84[/C][C]13445[/C][C]12900.2307940939[/C][C]544.769205906072[/C][/ROW]
[ROW][C]85[/C][C]13070[/C][C]12155.3125610624[/C][C]914.687438937553[/C][/ROW]
[ROW][C]86[/C][C]12480[/C][C]11588.1846317889[/C][C]891.815368211128[/C][/ROW]
[ROW][C]87[/C][C]11550[/C][C]11178.2166710227[/C][C]371.783328977266[/C][/ROW]
[ROW][C]88[/C][C]10725[/C][C]9508.3905191926[/C][C]1216.6094808074[/C][/ROW]
[ROW][C]89[/C][C]9130[/C][C]9307.62780584179[/C][C]-177.627805841792[/C][/ROW]
[ROW][C]90[/C][C]7885[/C][C]7850.30747419236[/C][C]34.6925258076444[/C][/ROW]
[ROW][C]91[/C][C]6415[/C][C]6097.47798545275[/C][C]317.522014547249[/C][/ROW]
[ROW][C]92[/C][C]5540[/C][C]7243.82759576171[/C][C]-1703.82759576171[/C][/ROW]
[ROW][C]93[/C][C]9350[/C][C]13786.1814290158[/C][C]-4436.18142901577[/C][/ROW]
[ROW][C]94[/C][C]12645[/C][C]12209.2164397686[/C][C]435.783560231361[/C][/ROW]
[ROW][C]95[/C][C]11985[/C][C]12668.2550944136[/C][C]-683.255094413631[/C][/ROW]
[ROW][C]96[/C][C]10055[/C][C]11577.0474674773[/C][C]-1522.04746747727[/C][/ROW]
[ROW][C]97[/C][C]10295[/C][C]9126.08639467963[/C][C]1168.91360532037[/C][/ROW]
[ROW][C]98[/C][C]10280[/C][C]8772.15850579245[/C][C]1507.84149420755[/C][/ROW]
[ROW][C]99[/C][C]9420[/C][C]8810.01615877035[/C][C]609.98384122965[/C][/ROW]
[ROW][C]100[/C][C]9575[/C][C]7468.20523682347[/C][C]2106.79476317653[/C][/ROW]
[ROW][C]101[/C][C]8090[/C][C]7819.40476579886[/C][C]270.595234201142[/C][/ROW]
[ROW][C]102[/C][C]5855[/C][C]6775.38060371344[/C][C]-920.38060371344[/C][/ROW]
[ROW][C]103[/C][C]4445[/C][C]4250.75720555132[/C][C]194.242794448681[/C][/ROW]
[ROW][C]104[/C][C]3555[/C][C]4992.80641067146[/C][C]-1437.80641067146[/C][/ROW]
[ROW][C]105[/C][C]12870[/C][C]11357.2532663164[/C][C]1512.74673368357[/C][/ROW]
[ROW][C]106[/C][C]14750[/C][C]15569.7653104201[/C][C]-819.765310420087[/C][/ROW]
[ROW][C]107[/C][C]13615[/C][C]14793.4662851455[/C][C]-1178.4662851455[/C][/ROW]
[ROW][C]108[/C][C]13705[/C][C]13156.1781258914[/C][C]548.821874108575[/C][/ROW]
[ROW][C]109[/C][C]13940[/C][C]12867.8948513462[/C][C]1072.10514865376[/C][/ROW]
[ROW][C]110[/C][C]11900[/C][C]12481.6719953058[/C][C]-581.671995305789[/C][/ROW]
[ROW][C]111[/C][C]9000[/C][C]10606.4482537707[/C][C]-1606.44825377067[/C][/ROW]
[ROW][C]112[/C][C]7340[/C][C]7597.97407497226[/C][C]-257.974074972264[/C][/ROW]
[ROW][C]113[/C][C]6425[/C][C]5662.66275582513[/C][C]762.337244174871[/C][/ROW]
[ROW][C]114[/C][C]5535[/C][C]4861.24370856717[/C][C]673.756291432832[/C][/ROW]
[ROW][C]115[/C][C]4050[/C][C]3859.76223514123[/C][C]190.237764858774[/C][/ROW]
[ROW][C]116[/C][C]3485[/C][C]4356.7642944536[/C][C]-871.764294453596[/C][/ROW]
[ROW][C]117[/C][C]8090[/C][C]11640.2950283312[/C][C]-3550.29502833117[/C][/ROW]
[ROW][C]118[/C][C]11380[/C][C]11194.037302233[/C][C]185.962697766976[/C][/ROW]
[ROW][C]119[/C][C]11355[/C][C]11221.4540459118[/C][C]133.545954088177[/C][/ROW]
[ROW][C]120[/C][C]10530[/C][C]10957.6623215174[/C][C]-427.662321517404[/C][/ROW]
[ROW][C]121[/C][C]9285[/C][C]9914.94479954684[/C][C]-629.944799546838[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299060&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299060&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
131286012680.546207265179.453792735045
141150011459.91602986440.083970136011
151066010668.8839365591-8.88393655909204
1693409325.5089412174114.4910587825889
1780507985.7981270525364.2018729474748
1865406422.18813029978117.811869700217
1950604301.33416852655758.665831473454
2063507379.16006718509-1029.16006718509
211413014103.858866221926.1411337780773
221638016056.1565939644323.843406035594
231616015416.2465784462743.753421553825
241585015284.7012760165565.298723983504
251593014769.77519843351160.22480156652
261532014364.0721783714955.927821628624
271342014346.0375252388-926.037525238771
281225512224.760076821330.2399231786876
29878510905.8264059937-2120.82640599372
3063807488.63251954299-1108.63251954299
3147604417.79936087463342.200639125374
3257306876.12154297586-1146.12154297586
331081013657.4196827004-2847.41968270036
341284513205.6819161158-360.681916115793
351286512044.7651334209820.234866579127
361351511951.95638663621563.04361336383
371388012375.13535554261504.86464445738
381296012232.798650642727.201349357969
391209011741.2651763456348.734823654437
40951010847.6049160651-1337.60491606514
4181308044.865568912585.1344310875029
4266256656.88786090545-31.8878609054536
4349204718.18550153069201.814498469314
4446506836.55118681494-2186.55118681494
451008512479.5739711501-2394.57397115014
461396012781.81234763161178.18765236842
471449513106.7679861141388.23201388604
481434013607.8383365924732.161663407627
491387513314.5388616388560.461138361219
501313512252.4855810837882.514418916306
511341511837.23577089721577.76422910281
52928011740.9662917147-2460.96629171474
5370758191.83169523288-1116.83169523288
5456605762.52057697941-102.520576979412
5542703798.24421168614471.755788313862
5650855792.97222349653-707.972223496532
571194512664.8620403674-719.862040367445
581433514922.8304683314-587.830468331358
591410513774.3363879126330.66361208743
601375513277.2826326392477.717367360776
611292012741.7895941223178.210405877688
621165011401.7621924406248.237807559446
631072010549.080467763170.919532237009
6486008656.29914497254-56.2991449725359
6577957354.81322234689440.186777653111
6665506402.16936095358147.830639046419
6748004736.2033547174963.7966452825112
6859006208.70701856069-308.707018560688
691409513418.9879694795676.012030520482
701517016885.710686775-1715.710686775
711487514912.3148936469-37.3148936469115
721523014123.53637807171106.46362192826
731368514079.3559034732-394.355903473224
741278012261.9022078674518.097792132554
751151011627.6785563604-117.678556360434
7699159455.38675047828459.613249521717
7787408666.9370117622973.0629882377107
7878707358.23917898828511.760821011721
7966505989.87945851707660.120541482929
8052857915.26604267498-2630.26604267498
811319513293.5031039864-98.5031039863607
821339015746.2729958463-2356.27299584625
831349013475.651135240414.348864759615
841344512900.2307940939544.769205906072
851307012155.3125610624914.687438937553
861248011588.1846317889891.815368211128
871155011178.2166710227371.783328977266
88107259508.39051919261216.6094808074
8991309307.62780584179-177.627805841792
9078857850.3074741923634.6925258076444
9164156097.47798545275317.522014547249
9255407243.82759576171-1703.82759576171
93935013786.1814290158-4436.18142901577
941264512209.2164397686435.783560231361
951198512668.2550944136-683.255094413631
961005511577.0474674773-1522.04746747727
97102959126.086394679631168.91360532037
98102808772.158505792451507.84149420755
9994208810.01615877035609.98384122965
10095757468.205236823472106.79476317653
10180907819.40476579886270.595234201142
10258556775.38060371344-920.38060371344
10344454250.75720555132194.242794448681
10435554992.80641067146-1437.80641067146
1051287011357.25326631641512.74673368357
1061475015569.7653104201-819.765310420087
1071361514793.4662851455-1178.4662851455
1081370513156.1781258914548.821874108575
1091394012867.89485134621072.10514865376
1101190012481.6719953058-581.671995305789
111900010606.4482537707-1606.44825377067
11273407597.97407497226-257.974074972264
11364255662.66275582513762.337244174871
11455354861.24370856717673.756291432832
11540503859.76223514123190.237764858774
11634854356.7642944536-871.764294453596
117809011640.2950283312-3550.29502833117
1181138011194.037302233185.962697766976
1191135511221.4540459118133.545954088177
1201053010957.6623215174-427.662321517404
12192859914.94479954684-629.944799546838







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1227833.819085701075612.9326941850210054.7054772171
1236302.422634454913384.843791084879220.00147782494
1244862.202035171384.818500018948339.58557032106
1253297.7335849563-661.0700466727017256.5372165853
1261833.73112375917-2553.985382244636221.44762976298
127186.659249061939-4591.623505267014964.94200339089
128364.35339079082-4774.899086328475503.60586791011
1297994.005049188242517.5238827058813470.4862156706
13011125.57529117875331.4596632251916919.6909191322
13110986.80165031744891.5817319424617082.0215686923
13210526.14589204644144.0117821570416908.2800019358
1339817.823426573423161.1301228472416474.5167302996
1348366.64251227451349.2425590229915384.042465526
1356835.24606102833-432.75449257329514103.24661463
1365395.02546174342-2115.2183419165312905.2692654034
1373830.55701152972-3914.3569281904611575.4709512499
1382366.5545503326-5606.1251671106710339.2342677759
139719.482675635362-7474.634227374418913.59957864514

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
122 & 7833.81908570107 & 5612.93269418502 & 10054.7054772171 \tabularnewline
123 & 6302.42263445491 & 3384.84379108487 & 9220.00147782494 \tabularnewline
124 & 4862.20203517 & 1384.81850001894 & 8339.58557032106 \tabularnewline
125 & 3297.7335849563 & -661.070046672701 & 7256.5372165853 \tabularnewline
126 & 1833.73112375917 & -2553.98538224463 & 6221.44762976298 \tabularnewline
127 & 186.659249061939 & -4591.62350526701 & 4964.94200339089 \tabularnewline
128 & 364.35339079082 & -4774.89908632847 & 5503.60586791011 \tabularnewline
129 & 7994.00504918824 & 2517.52388270588 & 13470.4862156706 \tabularnewline
130 & 11125.5752911787 & 5331.45966322519 & 16919.6909191322 \tabularnewline
131 & 10986.8016503174 & 4891.58173194246 & 17082.0215686923 \tabularnewline
132 & 10526.1458920464 & 4144.01178215704 & 16908.2800019358 \tabularnewline
133 & 9817.82342657342 & 3161.13012284724 & 16474.5167302996 \tabularnewline
134 & 8366.6425122745 & 1349.24255902299 & 15384.042465526 \tabularnewline
135 & 6835.24606102833 & -432.754492573295 & 14103.24661463 \tabularnewline
136 & 5395.02546174342 & -2115.21834191653 & 12905.2692654034 \tabularnewline
137 & 3830.55701152972 & -3914.35692819046 & 11575.4709512499 \tabularnewline
138 & 2366.5545503326 & -5606.12516711067 & 10339.2342677759 \tabularnewline
139 & 719.482675635362 & -7474.63422737441 & 8913.59957864514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299060&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]122[/C][C]7833.81908570107[/C][C]5612.93269418502[/C][C]10054.7054772171[/C][/ROW]
[ROW][C]123[/C][C]6302.42263445491[/C][C]3384.84379108487[/C][C]9220.00147782494[/C][/ROW]
[ROW][C]124[/C][C]4862.20203517[/C][C]1384.81850001894[/C][C]8339.58557032106[/C][/ROW]
[ROW][C]125[/C][C]3297.7335849563[/C][C]-661.070046672701[/C][C]7256.5372165853[/C][/ROW]
[ROW][C]126[/C][C]1833.73112375917[/C][C]-2553.98538224463[/C][C]6221.44762976298[/C][/ROW]
[ROW][C]127[/C][C]186.659249061939[/C][C]-4591.62350526701[/C][C]4964.94200339089[/C][/ROW]
[ROW][C]128[/C][C]364.35339079082[/C][C]-4774.89908632847[/C][C]5503.60586791011[/C][/ROW]
[ROW][C]129[/C][C]7994.00504918824[/C][C]2517.52388270588[/C][C]13470.4862156706[/C][/ROW]
[ROW][C]130[/C][C]11125.5752911787[/C][C]5331.45966322519[/C][C]16919.6909191322[/C][/ROW]
[ROW][C]131[/C][C]10986.8016503174[/C][C]4891.58173194246[/C][C]17082.0215686923[/C][/ROW]
[ROW][C]132[/C][C]10526.1458920464[/C][C]4144.01178215704[/C][C]16908.2800019358[/C][/ROW]
[ROW][C]133[/C][C]9817.82342657342[/C][C]3161.13012284724[/C][C]16474.5167302996[/C][/ROW]
[ROW][C]134[/C][C]8366.6425122745[/C][C]1349.24255902299[/C][C]15384.042465526[/C][/ROW]
[ROW][C]135[/C][C]6835.24606102833[/C][C]-432.754492573295[/C][C]14103.24661463[/C][/ROW]
[ROW][C]136[/C][C]5395.02546174342[/C][C]-2115.21834191653[/C][C]12905.2692654034[/C][/ROW]
[ROW][C]137[/C][C]3830.55701152972[/C][C]-3914.35692819046[/C][C]11575.4709512499[/C][/ROW]
[ROW][C]138[/C][C]2366.5545503326[/C][C]-5606.12516711067[/C][C]10339.2342677759[/C][/ROW]
[ROW][C]139[/C][C]719.482675635362[/C][C]-7474.63422737441[/C][C]8913.59957864514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299060&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299060&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
1227833.819085701075612.9326941850210054.7054772171
1236302.422634454913384.843791084879220.00147782494
1244862.202035171384.818500018948339.58557032106
1253297.7335849563-661.0700466727017256.5372165853
1261833.73112375917-2553.985382244636221.44762976298
127186.659249061939-4591.623505267014964.94200339089
128364.35339079082-4774.899086328475503.60586791011
1297994.005049188242517.5238827058813470.4862156706
13011125.57529117875331.4596632251916919.6909191322
13110986.80165031744891.5817319424617082.0215686923
13210526.14589204644144.0117821570416908.2800019358
1339817.823426573423161.1301228472416474.5167302996
1348366.64251227451349.2425590229915384.042465526
1356835.24606102833-432.75449257329514103.24661463
1365395.02546174342-2115.2183419165312905.2692654034
1373830.55701152972-3914.3569281904611575.4709512499
1382366.5545503326-5606.1251671106710339.2342677759
139719.482675635362-7474.634227374418913.59957864514



Parameters (Session):
par1 = 8 ; par2 = 0 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')