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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 05 Jul 2016 15:27:21 +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/Jul/05/t1467728870x639pxjb60ze53s.htm/, Retrieved Fri, 03 May 2024 14:47:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295799, Retrieved Fri, 03 May 2024 14:47:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-07-05 14:27:21] [fcb50c3fd850be3d4e9c7b78a2663ee0] [Current]
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Dataseries X:
2120
2100
2080
2040
2440
2420
2120
1920
1940
1940
1960
2000
2120
2080
2140
2240
2800
2800
2680
2560
2660
2780
2800
2860
3040
2920
2920
3100
3600
3640
3540
3300
3480
3480
3500
3600
3680
3720
3720
3840
4300
4420
4440
4140
4300
4240
4120
4380
4440
4340
4360
4500
5020
5280
5280
5160
5340
5160
5060
5440
5500
5360
5720
5860
6280
6560
6520
6500
6660
6640
6400
6760
6880
6760
7260
7500
8060
8280
8220
8100
8200
8320
7920
8240
8440
8360
8880
9060
9820
9960
9780
9880
9940
10000
9620
9980
10180
9980
10560
10740
11520
11640
11680
11880
11880
11960
11600
11780
11900
11680
12320
12440
13240
13380
13580
13760
13780
13800
13440
13800




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295799&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295799&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295799&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.214017549706371
beta0.108209004892705
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.214017549706371 \tabularnewline
beta & 0.108209004892705 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295799&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]0.214017549706371[/C][/ROW]
[ROW][C]beta[/C][C]0.108209004892705[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295799&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295799&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
alpha0.214017549706371
beta0.108209004892705
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1321201999.33287401408120.667125985922
1420801982.1882055258297.8117944741759
1521402052.0705842547687.9294157452373
1622402152.8573739787.1426260300004
1728002693.16509977363106.834900226366
1828002696.86556408473103.134435915266
1926802524.31354007775155.686459922252
2025602369.87641072029190.123589279714
2126602491.2910637847168.708936215304
2227802575.51651417901204.483485820986
2328002683.05571679949116.944283200509
2428602792.7658816138267.2341183861799
2530403136.18311689935-96.1831168993549
2629203035.5847102837-115.584710283696
2729203075.0834260504-155.083426050404
2831003156.77280708394-56.7728070839385
2936003893.6301979232-293.630197923197
3036403787.79126722586-147.791267225863
3135403532.596095060737.4039049392677
3233003301.26105392991-1.26105392991303
3334803358.81251722736121.187482772644
3434803454.7438608717225.256139128277
3535003426.1009333661173.8990666338909
3636003470.47967324971129.520326750288
3736803716.12648955903-36.1264895590298
3837203567.87216043112152.127839568878
3937203622.3316437428397.6683562571711
4038403870.46876191952-30.4687619195165
4143004547.70155245847-247.701552458472
4244204571.90405558152-151.904055581517
4344404402.8842920162737.115707983734
4441404103.7759109132736.2240890867342
4543004294.884004381025.11599561898402
4642404278.99188726867-38.9918872686667
4741204264.16663215366-144.166632153656
4843804304.0248226474175.9751773525868
4944404408.2815627030531.7184372969487
5043404407.47219099668-67.4721909966775
5143604348.3758807382211.6241192617781
5245004477.3112778599322.6887221400748
5350205056.0460636413-36.046063641299
5452805208.9103860543471.0896139456627
5552805226.131656065353.8683439346987
5651604863.73551217572296.264487824277
5753405110.51728273495229.482717265051
5851605096.413418731263.5865812688007
5950605002.6107488871257.3892511128761
6054405317.14449791575122.855502084253
6155005414.6469871380185.3530128619877
6253605334.9637151834825.0362848165223
6357205370.81187117363349.18812882637
6458605630.23016546345229.769834536545
6562806367.21857894633-87.218578946331
6665606679.35900282317-119.359002823167
6765206655.79568500932-135.795685009316
6865006404.4510980398595.5489019601491
6966606591.3713157731468.628684226861
7066406367.3419709066272.6580290934
7164006290.37097628155109.629023718453
7267606760.20112662436-0.20112662435622
7368806814.1270173310665.8729826689387
7467606649.20206391913110.797936080868
7572607026.51058067622233.489419323781
7675007185.60077961551314.399220384493
7780607794.64810480806265.35189519194
7882808239.62640418140.3735958189955
7982208244.01137364094-24.0113736409421
8081008200.00716681117-100.007166811167
8182008369.27479250209-169.27479250209
8283208235.245690879784.7543091202951
8379207922.96923848368-2.96923848368351
8482408362.51044204811-122.510442048111
8584408458.90019569948-18.9001956994834
8683608268.4756688836491.5243311163576
8788808827.5530690314352.4469309685719
8890609030.8658043627929.1341956372053
8998209618.17600504559201.823994954409
9099609888.9222469125471.0777530874584
9197809814.17793271452-34.1779327145196
9298809665.62642183583214.373578164168
9399409857.7118805327282.2881194672827
94100009987.2803234171212.7196765828758
9596209499.05984419403120.940155805965
9699809931.9486477701848.0513522298243
971018010183.3787213353-3.37872133529163
98998010057.8370711601-77.8370711601256
991056010643.619931636-83.6199316359871
1001074010822.1463992081-82.1463992081481
1011152011643.9891632464-123.989163246368
1021164011743.2416177613-103.241617761258
1031168011493.4733617487186.526638251313
1041188011576.9251386867303.074861313298
1051188011673.6214947913206.378505208682
1061196011769.9025397031190.097460296925
1071160011319.8777523506280.122247649428
1081178011785.156260196-5.15626019595584
1091190012011.5443560805-111.544356080465
1101168011760.4566331091-80.4566331090646
1111232012435.3082198746-115.308219874587
1121244012631.1098796896-191.109879689562
1131324013521.2022572628-281.20225726283
1141338013610.0159605913-230.015960591343
1151358013541.586135747338.4138642527141
1161376013682.844873699977.1551263001056
1171378013620.4889433835159.511056616495
1181380013670.9404720588129.059527941188
1191344013187.8556591222252.14434087783
1201380013418.9625855632381.037414436807

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2120 & 1999.33287401408 & 120.667125985922 \tabularnewline
14 & 2080 & 1982.18820552582 & 97.8117944741759 \tabularnewline
15 & 2140 & 2052.07058425476 & 87.9294157452373 \tabularnewline
16 & 2240 & 2152.85737397 & 87.1426260300004 \tabularnewline
17 & 2800 & 2693.16509977363 & 106.834900226366 \tabularnewline
18 & 2800 & 2696.86556408473 & 103.134435915266 \tabularnewline
19 & 2680 & 2524.31354007775 & 155.686459922252 \tabularnewline
20 & 2560 & 2369.87641072029 & 190.123589279714 \tabularnewline
21 & 2660 & 2491.2910637847 & 168.708936215304 \tabularnewline
22 & 2780 & 2575.51651417901 & 204.483485820986 \tabularnewline
23 & 2800 & 2683.05571679949 & 116.944283200509 \tabularnewline
24 & 2860 & 2792.76588161382 & 67.2341183861799 \tabularnewline
25 & 3040 & 3136.18311689935 & -96.1831168993549 \tabularnewline
26 & 2920 & 3035.5847102837 & -115.584710283696 \tabularnewline
27 & 2920 & 3075.0834260504 & -155.083426050404 \tabularnewline
28 & 3100 & 3156.77280708394 & -56.7728070839385 \tabularnewline
29 & 3600 & 3893.6301979232 & -293.630197923197 \tabularnewline
30 & 3640 & 3787.79126722586 & -147.791267225863 \tabularnewline
31 & 3540 & 3532.59609506073 & 7.4039049392677 \tabularnewline
32 & 3300 & 3301.26105392991 & -1.26105392991303 \tabularnewline
33 & 3480 & 3358.81251722736 & 121.187482772644 \tabularnewline
34 & 3480 & 3454.74386087172 & 25.256139128277 \tabularnewline
35 & 3500 & 3426.10093336611 & 73.8990666338909 \tabularnewline
36 & 3600 & 3470.47967324971 & 129.520326750288 \tabularnewline
37 & 3680 & 3716.12648955903 & -36.1264895590298 \tabularnewline
38 & 3720 & 3567.87216043112 & 152.127839568878 \tabularnewline
39 & 3720 & 3622.33164374283 & 97.6683562571711 \tabularnewline
40 & 3840 & 3870.46876191952 & -30.4687619195165 \tabularnewline
41 & 4300 & 4547.70155245847 & -247.701552458472 \tabularnewline
42 & 4420 & 4571.90405558152 & -151.904055581517 \tabularnewline
43 & 4440 & 4402.88429201627 & 37.115707983734 \tabularnewline
44 & 4140 & 4103.77591091327 & 36.2240890867342 \tabularnewline
45 & 4300 & 4294.88400438102 & 5.11599561898402 \tabularnewline
46 & 4240 & 4278.99188726867 & -38.9918872686667 \tabularnewline
47 & 4120 & 4264.16663215366 & -144.166632153656 \tabularnewline
48 & 4380 & 4304.02482264741 & 75.9751773525868 \tabularnewline
49 & 4440 & 4408.28156270305 & 31.7184372969487 \tabularnewline
50 & 4340 & 4407.47219099668 & -67.4721909966775 \tabularnewline
51 & 4360 & 4348.37588073822 & 11.6241192617781 \tabularnewline
52 & 4500 & 4477.31127785993 & 22.6887221400748 \tabularnewline
53 & 5020 & 5056.0460636413 & -36.046063641299 \tabularnewline
54 & 5280 & 5208.91038605434 & 71.0896139456627 \tabularnewline
55 & 5280 & 5226.1316560653 & 53.8683439346987 \tabularnewline
56 & 5160 & 4863.73551217572 & 296.264487824277 \tabularnewline
57 & 5340 & 5110.51728273495 & 229.482717265051 \tabularnewline
58 & 5160 & 5096.4134187312 & 63.5865812688007 \tabularnewline
59 & 5060 & 5002.61074888712 & 57.3892511128761 \tabularnewline
60 & 5440 & 5317.14449791575 & 122.855502084253 \tabularnewline
61 & 5500 & 5414.64698713801 & 85.3530128619877 \tabularnewline
62 & 5360 & 5334.96371518348 & 25.0362848165223 \tabularnewline
63 & 5720 & 5370.81187117363 & 349.18812882637 \tabularnewline
64 & 5860 & 5630.23016546345 & 229.769834536545 \tabularnewline
65 & 6280 & 6367.21857894633 & -87.218578946331 \tabularnewline
66 & 6560 & 6679.35900282317 & -119.359002823167 \tabularnewline
67 & 6520 & 6655.79568500932 & -135.795685009316 \tabularnewline
68 & 6500 & 6404.45109803985 & 95.5489019601491 \tabularnewline
69 & 6660 & 6591.37131577314 & 68.628684226861 \tabularnewline
70 & 6640 & 6367.3419709066 & 272.6580290934 \tabularnewline
71 & 6400 & 6290.37097628155 & 109.629023718453 \tabularnewline
72 & 6760 & 6760.20112662436 & -0.20112662435622 \tabularnewline
73 & 6880 & 6814.12701733106 & 65.8729826689387 \tabularnewline
74 & 6760 & 6649.20206391913 & 110.797936080868 \tabularnewline
75 & 7260 & 7026.51058067622 & 233.489419323781 \tabularnewline
76 & 7500 & 7185.60077961551 & 314.399220384493 \tabularnewline
77 & 8060 & 7794.64810480806 & 265.35189519194 \tabularnewline
78 & 8280 & 8239.626404181 & 40.3735958189955 \tabularnewline
79 & 8220 & 8244.01137364094 & -24.0113736409421 \tabularnewline
80 & 8100 & 8200.00716681117 & -100.007166811167 \tabularnewline
81 & 8200 & 8369.27479250209 & -169.27479250209 \tabularnewline
82 & 8320 & 8235.2456908797 & 84.7543091202951 \tabularnewline
83 & 7920 & 7922.96923848368 & -2.96923848368351 \tabularnewline
84 & 8240 & 8362.51044204811 & -122.510442048111 \tabularnewline
85 & 8440 & 8458.90019569948 & -18.9001956994834 \tabularnewline
86 & 8360 & 8268.47566888364 & 91.5243311163576 \tabularnewline
87 & 8880 & 8827.55306903143 & 52.4469309685719 \tabularnewline
88 & 9060 & 9030.86580436279 & 29.1341956372053 \tabularnewline
89 & 9820 & 9618.17600504559 & 201.823994954409 \tabularnewline
90 & 9960 & 9888.92224691254 & 71.0777530874584 \tabularnewline
91 & 9780 & 9814.17793271452 & -34.1779327145196 \tabularnewline
92 & 9880 & 9665.62642183583 & 214.373578164168 \tabularnewline
93 & 9940 & 9857.71188053272 & 82.2881194672827 \tabularnewline
94 & 10000 & 9987.28032341712 & 12.7196765828758 \tabularnewline
95 & 9620 & 9499.05984419403 & 120.940155805965 \tabularnewline
96 & 9980 & 9931.94864777018 & 48.0513522298243 \tabularnewline
97 & 10180 & 10183.3787213353 & -3.37872133529163 \tabularnewline
98 & 9980 & 10057.8370711601 & -77.8370711601256 \tabularnewline
99 & 10560 & 10643.619931636 & -83.6199316359871 \tabularnewline
100 & 10740 & 10822.1463992081 & -82.1463992081481 \tabularnewline
101 & 11520 & 11643.9891632464 & -123.989163246368 \tabularnewline
102 & 11640 & 11743.2416177613 & -103.241617761258 \tabularnewline
103 & 11680 & 11493.4733617487 & 186.526638251313 \tabularnewline
104 & 11880 & 11576.9251386867 & 303.074861313298 \tabularnewline
105 & 11880 & 11673.6214947913 & 206.378505208682 \tabularnewline
106 & 11960 & 11769.9025397031 & 190.097460296925 \tabularnewline
107 & 11600 & 11319.8777523506 & 280.122247649428 \tabularnewline
108 & 11780 & 11785.156260196 & -5.15626019595584 \tabularnewline
109 & 11900 & 12011.5443560805 & -111.544356080465 \tabularnewline
110 & 11680 & 11760.4566331091 & -80.4566331090646 \tabularnewline
111 & 12320 & 12435.3082198746 & -115.308219874587 \tabularnewline
112 & 12440 & 12631.1098796896 & -191.109879689562 \tabularnewline
113 & 13240 & 13521.2022572628 & -281.20225726283 \tabularnewline
114 & 13380 & 13610.0159605913 & -230.015960591343 \tabularnewline
115 & 13580 & 13541.5861357473 & 38.4138642527141 \tabularnewline
116 & 13760 & 13682.8448736999 & 77.1551263001056 \tabularnewline
117 & 13780 & 13620.4889433835 & 159.511056616495 \tabularnewline
118 & 13800 & 13670.9404720588 & 129.059527941188 \tabularnewline
119 & 13440 & 13187.8556591222 & 252.14434087783 \tabularnewline
120 & 13800 & 13418.9625855632 & 381.037414436807 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295799&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]2120[/C][C]1999.33287401408[/C][C]120.667125985922[/C][/ROW]
[ROW][C]14[/C][C]2080[/C][C]1982.18820552582[/C][C]97.8117944741759[/C][/ROW]
[ROW][C]15[/C][C]2140[/C][C]2052.07058425476[/C][C]87.9294157452373[/C][/ROW]
[ROW][C]16[/C][C]2240[/C][C]2152.85737397[/C][C]87.1426260300004[/C][/ROW]
[ROW][C]17[/C][C]2800[/C][C]2693.16509977363[/C][C]106.834900226366[/C][/ROW]
[ROW][C]18[/C][C]2800[/C][C]2696.86556408473[/C][C]103.134435915266[/C][/ROW]
[ROW][C]19[/C][C]2680[/C][C]2524.31354007775[/C][C]155.686459922252[/C][/ROW]
[ROW][C]20[/C][C]2560[/C][C]2369.87641072029[/C][C]190.123589279714[/C][/ROW]
[ROW][C]21[/C][C]2660[/C][C]2491.2910637847[/C][C]168.708936215304[/C][/ROW]
[ROW][C]22[/C][C]2780[/C][C]2575.51651417901[/C][C]204.483485820986[/C][/ROW]
[ROW][C]23[/C][C]2800[/C][C]2683.05571679949[/C][C]116.944283200509[/C][/ROW]
[ROW][C]24[/C][C]2860[/C][C]2792.76588161382[/C][C]67.2341183861799[/C][/ROW]
[ROW][C]25[/C][C]3040[/C][C]3136.18311689935[/C][C]-96.1831168993549[/C][/ROW]
[ROW][C]26[/C][C]2920[/C][C]3035.5847102837[/C][C]-115.584710283696[/C][/ROW]
[ROW][C]27[/C][C]2920[/C][C]3075.0834260504[/C][C]-155.083426050404[/C][/ROW]
[ROW][C]28[/C][C]3100[/C][C]3156.77280708394[/C][C]-56.7728070839385[/C][/ROW]
[ROW][C]29[/C][C]3600[/C][C]3893.6301979232[/C][C]-293.630197923197[/C][/ROW]
[ROW][C]30[/C][C]3640[/C][C]3787.79126722586[/C][C]-147.791267225863[/C][/ROW]
[ROW][C]31[/C][C]3540[/C][C]3532.59609506073[/C][C]7.4039049392677[/C][/ROW]
[ROW][C]32[/C][C]3300[/C][C]3301.26105392991[/C][C]-1.26105392991303[/C][/ROW]
[ROW][C]33[/C][C]3480[/C][C]3358.81251722736[/C][C]121.187482772644[/C][/ROW]
[ROW][C]34[/C][C]3480[/C][C]3454.74386087172[/C][C]25.256139128277[/C][/ROW]
[ROW][C]35[/C][C]3500[/C][C]3426.10093336611[/C][C]73.8990666338909[/C][/ROW]
[ROW][C]36[/C][C]3600[/C][C]3470.47967324971[/C][C]129.520326750288[/C][/ROW]
[ROW][C]37[/C][C]3680[/C][C]3716.12648955903[/C][C]-36.1264895590298[/C][/ROW]
[ROW][C]38[/C][C]3720[/C][C]3567.87216043112[/C][C]152.127839568878[/C][/ROW]
[ROW][C]39[/C][C]3720[/C][C]3622.33164374283[/C][C]97.6683562571711[/C][/ROW]
[ROW][C]40[/C][C]3840[/C][C]3870.46876191952[/C][C]-30.4687619195165[/C][/ROW]
[ROW][C]41[/C][C]4300[/C][C]4547.70155245847[/C][C]-247.701552458472[/C][/ROW]
[ROW][C]42[/C][C]4420[/C][C]4571.90405558152[/C][C]-151.904055581517[/C][/ROW]
[ROW][C]43[/C][C]4440[/C][C]4402.88429201627[/C][C]37.115707983734[/C][/ROW]
[ROW][C]44[/C][C]4140[/C][C]4103.77591091327[/C][C]36.2240890867342[/C][/ROW]
[ROW][C]45[/C][C]4300[/C][C]4294.88400438102[/C][C]5.11599561898402[/C][/ROW]
[ROW][C]46[/C][C]4240[/C][C]4278.99188726867[/C][C]-38.9918872686667[/C][/ROW]
[ROW][C]47[/C][C]4120[/C][C]4264.16663215366[/C][C]-144.166632153656[/C][/ROW]
[ROW][C]48[/C][C]4380[/C][C]4304.02482264741[/C][C]75.9751773525868[/C][/ROW]
[ROW][C]49[/C][C]4440[/C][C]4408.28156270305[/C][C]31.7184372969487[/C][/ROW]
[ROW][C]50[/C][C]4340[/C][C]4407.47219099668[/C][C]-67.4721909966775[/C][/ROW]
[ROW][C]51[/C][C]4360[/C][C]4348.37588073822[/C][C]11.6241192617781[/C][/ROW]
[ROW][C]52[/C][C]4500[/C][C]4477.31127785993[/C][C]22.6887221400748[/C][/ROW]
[ROW][C]53[/C][C]5020[/C][C]5056.0460636413[/C][C]-36.046063641299[/C][/ROW]
[ROW][C]54[/C][C]5280[/C][C]5208.91038605434[/C][C]71.0896139456627[/C][/ROW]
[ROW][C]55[/C][C]5280[/C][C]5226.1316560653[/C][C]53.8683439346987[/C][/ROW]
[ROW][C]56[/C][C]5160[/C][C]4863.73551217572[/C][C]296.264487824277[/C][/ROW]
[ROW][C]57[/C][C]5340[/C][C]5110.51728273495[/C][C]229.482717265051[/C][/ROW]
[ROW][C]58[/C][C]5160[/C][C]5096.4134187312[/C][C]63.5865812688007[/C][/ROW]
[ROW][C]59[/C][C]5060[/C][C]5002.61074888712[/C][C]57.3892511128761[/C][/ROW]
[ROW][C]60[/C][C]5440[/C][C]5317.14449791575[/C][C]122.855502084253[/C][/ROW]
[ROW][C]61[/C][C]5500[/C][C]5414.64698713801[/C][C]85.3530128619877[/C][/ROW]
[ROW][C]62[/C][C]5360[/C][C]5334.96371518348[/C][C]25.0362848165223[/C][/ROW]
[ROW][C]63[/C][C]5720[/C][C]5370.81187117363[/C][C]349.18812882637[/C][/ROW]
[ROW][C]64[/C][C]5860[/C][C]5630.23016546345[/C][C]229.769834536545[/C][/ROW]
[ROW][C]65[/C][C]6280[/C][C]6367.21857894633[/C][C]-87.218578946331[/C][/ROW]
[ROW][C]66[/C][C]6560[/C][C]6679.35900282317[/C][C]-119.359002823167[/C][/ROW]
[ROW][C]67[/C][C]6520[/C][C]6655.79568500932[/C][C]-135.795685009316[/C][/ROW]
[ROW][C]68[/C][C]6500[/C][C]6404.45109803985[/C][C]95.5489019601491[/C][/ROW]
[ROW][C]69[/C][C]6660[/C][C]6591.37131577314[/C][C]68.628684226861[/C][/ROW]
[ROW][C]70[/C][C]6640[/C][C]6367.3419709066[/C][C]272.6580290934[/C][/ROW]
[ROW][C]71[/C][C]6400[/C][C]6290.37097628155[/C][C]109.629023718453[/C][/ROW]
[ROW][C]72[/C][C]6760[/C][C]6760.20112662436[/C][C]-0.20112662435622[/C][/ROW]
[ROW][C]73[/C][C]6880[/C][C]6814.12701733106[/C][C]65.8729826689387[/C][/ROW]
[ROW][C]74[/C][C]6760[/C][C]6649.20206391913[/C][C]110.797936080868[/C][/ROW]
[ROW][C]75[/C][C]7260[/C][C]7026.51058067622[/C][C]233.489419323781[/C][/ROW]
[ROW][C]76[/C][C]7500[/C][C]7185.60077961551[/C][C]314.399220384493[/C][/ROW]
[ROW][C]77[/C][C]8060[/C][C]7794.64810480806[/C][C]265.35189519194[/C][/ROW]
[ROW][C]78[/C][C]8280[/C][C]8239.626404181[/C][C]40.3735958189955[/C][/ROW]
[ROW][C]79[/C][C]8220[/C][C]8244.01137364094[/C][C]-24.0113736409421[/C][/ROW]
[ROW][C]80[/C][C]8100[/C][C]8200.00716681117[/C][C]-100.007166811167[/C][/ROW]
[ROW][C]81[/C][C]8200[/C][C]8369.27479250209[/C][C]-169.27479250209[/C][/ROW]
[ROW][C]82[/C][C]8320[/C][C]8235.2456908797[/C][C]84.7543091202951[/C][/ROW]
[ROW][C]83[/C][C]7920[/C][C]7922.96923848368[/C][C]-2.96923848368351[/C][/ROW]
[ROW][C]84[/C][C]8240[/C][C]8362.51044204811[/C][C]-122.510442048111[/C][/ROW]
[ROW][C]85[/C][C]8440[/C][C]8458.90019569948[/C][C]-18.9001956994834[/C][/ROW]
[ROW][C]86[/C][C]8360[/C][C]8268.47566888364[/C][C]91.5243311163576[/C][/ROW]
[ROW][C]87[/C][C]8880[/C][C]8827.55306903143[/C][C]52.4469309685719[/C][/ROW]
[ROW][C]88[/C][C]9060[/C][C]9030.86580436279[/C][C]29.1341956372053[/C][/ROW]
[ROW][C]89[/C][C]9820[/C][C]9618.17600504559[/C][C]201.823994954409[/C][/ROW]
[ROW][C]90[/C][C]9960[/C][C]9888.92224691254[/C][C]71.0777530874584[/C][/ROW]
[ROW][C]91[/C][C]9780[/C][C]9814.17793271452[/C][C]-34.1779327145196[/C][/ROW]
[ROW][C]92[/C][C]9880[/C][C]9665.62642183583[/C][C]214.373578164168[/C][/ROW]
[ROW][C]93[/C][C]9940[/C][C]9857.71188053272[/C][C]82.2881194672827[/C][/ROW]
[ROW][C]94[/C][C]10000[/C][C]9987.28032341712[/C][C]12.7196765828758[/C][/ROW]
[ROW][C]95[/C][C]9620[/C][C]9499.05984419403[/C][C]120.940155805965[/C][/ROW]
[ROW][C]96[/C][C]9980[/C][C]9931.94864777018[/C][C]48.0513522298243[/C][/ROW]
[ROW][C]97[/C][C]10180[/C][C]10183.3787213353[/C][C]-3.37872133529163[/C][/ROW]
[ROW][C]98[/C][C]9980[/C][C]10057.8370711601[/C][C]-77.8370711601256[/C][/ROW]
[ROW][C]99[/C][C]10560[/C][C]10643.619931636[/C][C]-83.6199316359871[/C][/ROW]
[ROW][C]100[/C][C]10740[/C][C]10822.1463992081[/C][C]-82.1463992081481[/C][/ROW]
[ROW][C]101[/C][C]11520[/C][C]11643.9891632464[/C][C]-123.989163246368[/C][/ROW]
[ROW][C]102[/C][C]11640[/C][C]11743.2416177613[/C][C]-103.241617761258[/C][/ROW]
[ROW][C]103[/C][C]11680[/C][C]11493.4733617487[/C][C]186.526638251313[/C][/ROW]
[ROW][C]104[/C][C]11880[/C][C]11576.9251386867[/C][C]303.074861313298[/C][/ROW]
[ROW][C]105[/C][C]11880[/C][C]11673.6214947913[/C][C]206.378505208682[/C][/ROW]
[ROW][C]106[/C][C]11960[/C][C]11769.9025397031[/C][C]190.097460296925[/C][/ROW]
[ROW][C]107[/C][C]11600[/C][C]11319.8777523506[/C][C]280.122247649428[/C][/ROW]
[ROW][C]108[/C][C]11780[/C][C]11785.156260196[/C][C]-5.15626019595584[/C][/ROW]
[ROW][C]109[/C][C]11900[/C][C]12011.5443560805[/C][C]-111.544356080465[/C][/ROW]
[ROW][C]110[/C][C]11680[/C][C]11760.4566331091[/C][C]-80.4566331090646[/C][/ROW]
[ROW][C]111[/C][C]12320[/C][C]12435.3082198746[/C][C]-115.308219874587[/C][/ROW]
[ROW][C]112[/C][C]12440[/C][C]12631.1098796896[/C][C]-191.109879689562[/C][/ROW]
[ROW][C]113[/C][C]13240[/C][C]13521.2022572628[/C][C]-281.20225726283[/C][/ROW]
[ROW][C]114[/C][C]13380[/C][C]13610.0159605913[/C][C]-230.015960591343[/C][/ROW]
[ROW][C]115[/C][C]13580[/C][C]13541.5861357473[/C][C]38.4138642527141[/C][/ROW]
[ROW][C]116[/C][C]13760[/C][C]13682.8448736999[/C][C]77.1551263001056[/C][/ROW]
[ROW][C]117[/C][C]13780[/C][C]13620.4889433835[/C][C]159.511056616495[/C][/ROW]
[ROW][C]118[/C][C]13800[/C][C]13670.9404720588[/C][C]129.059527941188[/C][/ROW]
[ROW][C]119[/C][C]13440[/C][C]13187.8556591222[/C][C]252.14434087783[/C][/ROW]
[ROW][C]120[/C][C]13800[/C][C]13418.9625855632[/C][C]381.037414436807[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295799&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295799&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
1321201999.33287401408120.667125985922
1420801982.1882055258297.8117944741759
1521402052.0705842547687.9294157452373
1622402152.8573739787.1426260300004
1728002693.16509977363106.834900226366
1828002696.86556408473103.134435915266
1926802524.31354007775155.686459922252
2025602369.87641072029190.123589279714
2126602491.2910637847168.708936215304
2227802575.51651417901204.483485820986
2328002683.05571679949116.944283200509
2428602792.7658816138267.2341183861799
2530403136.18311689935-96.1831168993549
2629203035.5847102837-115.584710283696
2729203075.0834260504-155.083426050404
2831003156.77280708394-56.7728070839385
2936003893.6301979232-293.630197923197
3036403787.79126722586-147.791267225863
3135403532.596095060737.4039049392677
3233003301.26105392991-1.26105392991303
3334803358.81251722736121.187482772644
3434803454.7438608717225.256139128277
3535003426.1009333661173.8990666338909
3636003470.47967324971129.520326750288
3736803716.12648955903-36.1264895590298
3837203567.87216043112152.127839568878
3937203622.3316437428397.6683562571711
4038403870.46876191952-30.4687619195165
4143004547.70155245847-247.701552458472
4244204571.90405558152-151.904055581517
4344404402.8842920162737.115707983734
4441404103.7759109132736.2240890867342
4543004294.884004381025.11599561898402
4642404278.99188726867-38.9918872686667
4741204264.16663215366-144.166632153656
4843804304.0248226474175.9751773525868
4944404408.2815627030531.7184372969487
5043404407.47219099668-67.4721909966775
5143604348.3758807382211.6241192617781
5245004477.3112778599322.6887221400748
5350205056.0460636413-36.046063641299
5452805208.9103860543471.0896139456627
5552805226.131656065353.8683439346987
5651604863.73551217572296.264487824277
5753405110.51728273495229.482717265051
5851605096.413418731263.5865812688007
5950605002.6107488871257.3892511128761
6054405317.14449791575122.855502084253
6155005414.6469871380185.3530128619877
6253605334.9637151834825.0362848165223
6357205370.81187117363349.18812882637
6458605630.23016546345229.769834536545
6562806367.21857894633-87.218578946331
6665606679.35900282317-119.359002823167
6765206655.79568500932-135.795685009316
6865006404.4510980398595.5489019601491
6966606591.3713157731468.628684226861
7066406367.3419709066272.6580290934
7164006290.37097628155109.629023718453
7267606760.20112662436-0.20112662435622
7368806814.1270173310665.8729826689387
7467606649.20206391913110.797936080868
7572607026.51058067622233.489419323781
7675007185.60077961551314.399220384493
7780607794.64810480806265.35189519194
7882808239.62640418140.3735958189955
7982208244.01137364094-24.0113736409421
8081008200.00716681117-100.007166811167
8182008369.27479250209-169.27479250209
8283208235.245690879784.7543091202951
8379207922.96923848368-2.96923848368351
8482408362.51044204811-122.510442048111
8584408458.90019569948-18.9001956994834
8683608268.4756688836491.5243311163576
8788808827.5530690314352.4469309685719
8890609030.8658043627929.1341956372053
8998209618.17600504559201.823994954409
9099609888.9222469125471.0777530874584
9197809814.17793271452-34.1779327145196
9298809665.62642183583214.373578164168
9399409857.7118805327282.2881194672827
94100009987.2803234171212.7196765828758
9596209499.05984419403120.940155805965
9699809931.9486477701848.0513522298243
971018010183.3787213353-3.37872133529163
98998010057.8370711601-77.8370711601256
991056010643.619931636-83.6199316359871
1001074010822.1463992081-82.1463992081481
1011152011643.9891632464-123.989163246368
1021164011743.2416177613-103.241617761258
1031168011493.4733617487186.526638251313
1041188011576.9251386867303.074861313298
1051188011673.6214947913206.378505208682
1061196011769.9025397031190.097460296925
1071160011319.8777523506280.122247649428
1081178011785.156260196-5.15626019595584
1091190012011.5443560805-111.544356080465
1101168011760.4566331091-80.4566331090646
1111232012435.3082198746-115.308219874587
1121244012631.1098796896-191.109879689562
1131324013521.2022572628-281.20225726283
1141338013610.0159605913-230.015960591343
1151358013541.586135747338.4138642527141
1161376013682.844873699977.1551263001056
1171378013620.4889433835159.511056616495
1181380013670.9404720588129.059527941188
1191344013187.8556591222252.14434087783
1201380013418.9625855632381.037414436807







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12113643.88669214313371.48630341713916.2870808689
12213393.379932454913113.855313323513672.9045515863
12314138.861838614713849.184493250814428.5391839786
12414309.350970928214009.340086256914609.3618555994
12515288.177133266514972.308033467115604.046233066
12615503.150833384315173.523101913415832.7785648553
12715728.084770903615383.257279524716072.9122622825
12815919.134114997315558.094563932916280.1736660617
12915902.307615627415526.185010548816278.430220706
13015889.328629852815497.409718652216281.2475410533
13115405.011086530315003.359232061715806.6629409989
13215709.177877690115385.322360706816033.0333946735

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 13643.886692143 & 13371.486303417 & 13916.2870808689 \tabularnewline
122 & 13393.3799324549 & 13113.8553133235 & 13672.9045515863 \tabularnewline
123 & 14138.8618386147 & 13849.1844932508 & 14428.5391839786 \tabularnewline
124 & 14309.3509709282 & 14009.3400862569 & 14609.3618555994 \tabularnewline
125 & 15288.1771332665 & 14972.3080334671 & 15604.046233066 \tabularnewline
126 & 15503.1508333843 & 15173.5231019134 & 15832.7785648553 \tabularnewline
127 & 15728.0847709036 & 15383.2572795247 & 16072.9122622825 \tabularnewline
128 & 15919.1341149973 & 15558.0945639329 & 16280.1736660617 \tabularnewline
129 & 15902.3076156274 & 15526.1850105488 & 16278.430220706 \tabularnewline
130 & 15889.3286298528 & 15497.4097186522 & 16281.2475410533 \tabularnewline
131 & 15405.0110865303 & 15003.3592320617 & 15806.6629409989 \tabularnewline
132 & 15709.1778776901 & 15385.3223607068 & 16033.0333946735 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295799&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]13643.886692143[/C][C]13371.486303417[/C][C]13916.2870808689[/C][/ROW]
[ROW][C]122[/C][C]13393.3799324549[/C][C]13113.8553133235[/C][C]13672.9045515863[/C][/ROW]
[ROW][C]123[/C][C]14138.8618386147[/C][C]13849.1844932508[/C][C]14428.5391839786[/C][/ROW]
[ROW][C]124[/C][C]14309.3509709282[/C][C]14009.3400862569[/C][C]14609.3618555994[/C][/ROW]
[ROW][C]125[/C][C]15288.1771332665[/C][C]14972.3080334671[/C][C]15604.046233066[/C][/ROW]
[ROW][C]126[/C][C]15503.1508333843[/C][C]15173.5231019134[/C][C]15832.7785648553[/C][/ROW]
[ROW][C]127[/C][C]15728.0847709036[/C][C]15383.2572795247[/C][C]16072.9122622825[/C][/ROW]
[ROW][C]128[/C][C]15919.1341149973[/C][C]15558.0945639329[/C][C]16280.1736660617[/C][/ROW]
[ROW][C]129[/C][C]15902.3076156274[/C][C]15526.1850105488[/C][C]16278.430220706[/C][/ROW]
[ROW][C]130[/C][C]15889.3286298528[/C][C]15497.4097186522[/C][C]16281.2475410533[/C][/ROW]
[ROW][C]131[/C][C]15405.0110865303[/C][C]15003.3592320617[/C][C]15806.6629409989[/C][/ROW]
[ROW][C]132[/C][C]15709.1778776901[/C][C]15385.3223607068[/C][C]16033.0333946735[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295799&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295799&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
12113643.88669214313371.48630341713916.2870808689
12213393.379932454913113.855313323513672.9045515863
12314138.861838614713849.184493250814428.5391839786
12414309.350970928214009.340086256914609.3618555994
12515288.177133266514972.308033467115604.046233066
12615503.150833384315173.523101913415832.7785648553
12715728.084770903615383.257279524716072.9122622825
12815919.134114997315558.094563932916280.1736660617
12915902.307615627415526.185010548816278.430220706
13015889.328629852815497.409718652216281.2475410533
13115405.011086530315003.359232061715806.6629409989
13215709.177877690115385.322360706816033.0333946735



Parameters (Session):
par1 = 0 ; par2 = no ; par3 = 512 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')