Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 03 Dec 2009 11:00:28 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/03/t1259863290t0mc76zzd2tki4j.htm/, Retrieved Sat, 20 Apr 2024 01:43:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63001, Retrieved Sat, 20 Apr 2024 01:43:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [workshop 9 bereke...] [2009-12-03 18:00:28] [78d370e6d5f4594e9982a5085e7604c6] [Current]
-   PD        [Exponential Smoothing] [review workshop 9] [2009-12-04 10:37:14] [eaf42bcf5162b5692bb3c7f9d4636222]
-    D          [Exponential Smoothing] [review workshop 9] [2009-12-06 10:46:29] [eaf42bcf5162b5692bb3c7f9d4636222]
-   PD        [Exponential Smoothing] [] [2009-12-09 16:18:05] [3425351e86519d261a643e224a0c8ee1]
-   P         [Exponential Smoothing] [] [2009-12-12 17:11:35] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
4716.99
4926.65
4920.10
5170.09
5246.24
5283.61
4979.05
4825.20
4695.12
4711.54
4727.22
4384.96
4378.75
4472.93
4564.07
4310.54
4171.38
4049.38
3591.37
3720.46
4107.23
4101.71
4162.34
4136.22
4125.88
4031.48
3761.36
3408.56
3228.47
3090.45
2741.14
2980.44
3104.33
3181.57
2863.86
2898.01
3112.33
3254.33
3513.47
3587.61
3727.45
3793.34
3817.58
3845.13
3931.86
4197.52
4307.13
4229.43
4362.28
4217.34
4361.28
4327.74
4417.65
4557.68
4650.35
4967.18
5123.42
5290.85
5535.66
5514.06
5493.88
5694.83
5850.41
6116.64
6175.00
6513.58
6383.78
6673.66
6936.61
7300.68
7392.93
7497.31
7584.71
7160.79
7196.19
7245.63
7347.51
7425.75
7778.51
7822.33
8181.22
8371.47
8347.71
8672.11
8802.79
9138.46
9123.29
9023.21
8850.41
8864.58
9163.74
8516.66
8553.44
7555.20
7851.22
7442.00
7992.53
8264.04
7517.39
7200.40
7193.69
6193.58
5104.21
4800.46
4461.61
4398.59
4243.63
4293.82




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63001&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63001&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63001&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.917492764005406
beta0.110092205215912
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.917492764005406 \tabularnewline
beta & 0.110092205215912 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63001&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]0.917492764005406[/C][/ROW]
[ROW][C]beta[/C][C]0.110092205215912[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63001&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63001&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
alpha0.917492764005406
beta0.110092205215912
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134378.754816.92751819308-438.177518193077
144472.934496.21089354897-23.2808935489729
154564.074513.1035845527150.9664154472939
164310.544239.873307264270.666692735802
174171.384106.4558979601564.9241020398476
184049.383977.9488762367471.4311237632651
193591.374149.49506581446-558.125065814463
203720.463399.82009621670320.639903783297
214107.233505.15520732032602.074792679677
224101.714060.6841839455841.0258160544163
234162.344131.5655597404530.7744402595526
244136.223894.08387464931242.136125350693
254125.884154.94897685148-29.068976851484
264031.484325.45935120328-293.979351203282
273761.364154.43857173772-393.078571737716
283408.563533.71369017903-125.15369017903
293228.473243.4310620317-14.9610620316980
303090.453058.5764991859631.8735008140447
312741.143093.76311739398-352.62311739398
322980.442619.18289770903361.257102290968
333104.332805.84420711042298.485792889582
343181.573018.1441663724163.425833627598
352863.863178.15656141591-314.296561415905
362898.012666.39603585652231.613964143483
373112.332845.94875378530266.381246214703
383254.333205.7240063557648.6059936442371
393513.473336.80918577878176.660814221217
403587.613351.7434447048235.866555295201
413727.453514.10829742696213.341702573044
423793.343668.52619479052124.813805209481
433817.583918.55387384301-100.97387384301
443845.133923.99556679087-78.865566790866
453931.863813.57699870634118.283001293661
464197.523958.53144217852238.988557821479
474307.134271.7702522396135.3597477603889
484229.434224.393986436045.03601356396393
494362.284336.9391548960925.3408451039068
504217.344616.91599552967-399.575995529669
514361.284449.25934087327-87.9793408732712
524327.744228.6982951567299.0417048432819
534417.654269.9900805267147.659919473294
544557.684355.87501902967201.804980970327
554650.354693.94957717584-43.5995771758407
564967.184796.15524089788171.024759102120
575123.424969.59510852716153.824891472836
585290.855214.3227324512776.527267548734
595535.665405.21553752457130.444462475433
605514.065448.853270534865.2067294652006
615493.885685.92969523329-192.049695233293
625694.835801.12967084213-106.299670842128
635850.416061.60435771929-211.194357719291
646116.645743.8688776575372.771122342502
6561756085.8350064765789.1649935234327
666513.586155.59766721843357.982332781573
676383.786731.26288163338-347.482881633385
686673.666665.485760034588.17423996541947
696936.616705.65235616964230.957643830358
707300.687063.28912002935237.390879970652
717392.937478.45176447565-85.5217644756458
727497.317294.2860237131203.023976286897
737584.717704.13622379215-119.426223792146
747160.798031.94951232763-871.15951232763
757196.197636.49312696004-440.303126960045
767245.637084.15881646387161.471183536134
777347.517129.29084442936218.219155570639
787425.757276.55492610909149.195073890907
797778.517542.82985474693235.68014525307
807822.338071.68707261266-249.35707261266
818181.227850.98990210087330.230097899135
828371.478279.8257099748291.6442900251823
838347.718500.08610434749-152.376104347488
848672.118206.79113280938465.318867190617
858802.798819.95727301461-17.1672730146129
869138.469200.11413671316-61.6541367131595
879123.299759.3846864971-636.094686497105
889023.219098.31483897915-75.104838979154
898850.418927.78492225431-77.3749222543138
908864.588775.4210599146689.1589400853445
919163.749000.88602495431162.853975045686
928516.669441.0806518963-924.420651896304
938553.448567.95779799683-14.5177979968266
947555.28549.0755763182-993.8755763182
957851.227534.92877157304316.291228426959
9674427566.61549329302-124.615493293017
977992.537373.89045050445618.639549495546
988264.048144.3513033938119.688696606198
997517.398625.34025516097-1107.95025516096
1007200.47399.17629217925-198.776292179252
1017193.696945.38035085194248.309649148064
1026193.586961.52078944754-767.940789447538
1035104.216128.92308453093-1024.71308453093
1044800.464961.83056552194-161.370565521944
1054461.614540.5469052901-78.9369052900956
1064398.594113.92388901846284.666110981540
1074243.634156.7289643610186.9010356389854
1084293.823851.46523822392442.35476177608

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4378.75 & 4816.92751819308 & -438.177518193077 \tabularnewline
14 & 4472.93 & 4496.21089354897 & -23.2808935489729 \tabularnewline
15 & 4564.07 & 4513.10358455271 & 50.9664154472939 \tabularnewline
16 & 4310.54 & 4239.8733072642 & 70.666692735802 \tabularnewline
17 & 4171.38 & 4106.45589796015 & 64.9241020398476 \tabularnewline
18 & 4049.38 & 3977.94887623674 & 71.4311237632651 \tabularnewline
19 & 3591.37 & 4149.49506581446 & -558.125065814463 \tabularnewline
20 & 3720.46 & 3399.82009621670 & 320.639903783297 \tabularnewline
21 & 4107.23 & 3505.15520732032 & 602.074792679677 \tabularnewline
22 & 4101.71 & 4060.68418394558 & 41.0258160544163 \tabularnewline
23 & 4162.34 & 4131.56555974045 & 30.7744402595526 \tabularnewline
24 & 4136.22 & 3894.08387464931 & 242.136125350693 \tabularnewline
25 & 4125.88 & 4154.94897685148 & -29.068976851484 \tabularnewline
26 & 4031.48 & 4325.45935120328 & -293.979351203282 \tabularnewline
27 & 3761.36 & 4154.43857173772 & -393.078571737716 \tabularnewline
28 & 3408.56 & 3533.71369017903 & -125.15369017903 \tabularnewline
29 & 3228.47 & 3243.4310620317 & -14.9610620316980 \tabularnewline
30 & 3090.45 & 3058.57649918596 & 31.8735008140447 \tabularnewline
31 & 2741.14 & 3093.76311739398 & -352.62311739398 \tabularnewline
32 & 2980.44 & 2619.18289770903 & 361.257102290968 \tabularnewline
33 & 3104.33 & 2805.84420711042 & 298.485792889582 \tabularnewline
34 & 3181.57 & 3018.1441663724 & 163.425833627598 \tabularnewline
35 & 2863.86 & 3178.15656141591 & -314.296561415905 \tabularnewline
36 & 2898.01 & 2666.39603585652 & 231.613964143483 \tabularnewline
37 & 3112.33 & 2845.94875378530 & 266.381246214703 \tabularnewline
38 & 3254.33 & 3205.72400635576 & 48.6059936442371 \tabularnewline
39 & 3513.47 & 3336.80918577878 & 176.660814221217 \tabularnewline
40 & 3587.61 & 3351.7434447048 & 235.866555295201 \tabularnewline
41 & 3727.45 & 3514.10829742696 & 213.341702573044 \tabularnewline
42 & 3793.34 & 3668.52619479052 & 124.813805209481 \tabularnewline
43 & 3817.58 & 3918.55387384301 & -100.97387384301 \tabularnewline
44 & 3845.13 & 3923.99556679087 & -78.865566790866 \tabularnewline
45 & 3931.86 & 3813.57699870634 & 118.283001293661 \tabularnewline
46 & 4197.52 & 3958.53144217852 & 238.988557821479 \tabularnewline
47 & 4307.13 & 4271.77025223961 & 35.3597477603889 \tabularnewline
48 & 4229.43 & 4224.39398643604 & 5.03601356396393 \tabularnewline
49 & 4362.28 & 4336.93915489609 & 25.3408451039068 \tabularnewline
50 & 4217.34 & 4616.91599552967 & -399.575995529669 \tabularnewline
51 & 4361.28 & 4449.25934087327 & -87.9793408732712 \tabularnewline
52 & 4327.74 & 4228.69829515672 & 99.0417048432819 \tabularnewline
53 & 4417.65 & 4269.9900805267 & 147.659919473294 \tabularnewline
54 & 4557.68 & 4355.87501902967 & 201.804980970327 \tabularnewline
55 & 4650.35 & 4693.94957717584 & -43.5995771758407 \tabularnewline
56 & 4967.18 & 4796.15524089788 & 171.024759102120 \tabularnewline
57 & 5123.42 & 4969.59510852716 & 153.824891472836 \tabularnewline
58 & 5290.85 & 5214.32273245127 & 76.527267548734 \tabularnewline
59 & 5535.66 & 5405.21553752457 & 130.444462475433 \tabularnewline
60 & 5514.06 & 5448.8532705348 & 65.2067294652006 \tabularnewline
61 & 5493.88 & 5685.92969523329 & -192.049695233293 \tabularnewline
62 & 5694.83 & 5801.12967084213 & -106.299670842128 \tabularnewline
63 & 5850.41 & 6061.60435771929 & -211.194357719291 \tabularnewline
64 & 6116.64 & 5743.8688776575 & 372.771122342502 \tabularnewline
65 & 6175 & 6085.83500647657 & 89.1649935234327 \tabularnewline
66 & 6513.58 & 6155.59766721843 & 357.982332781573 \tabularnewline
67 & 6383.78 & 6731.26288163338 & -347.482881633385 \tabularnewline
68 & 6673.66 & 6665.48576003458 & 8.17423996541947 \tabularnewline
69 & 6936.61 & 6705.65235616964 & 230.957643830358 \tabularnewline
70 & 7300.68 & 7063.28912002935 & 237.390879970652 \tabularnewline
71 & 7392.93 & 7478.45176447565 & -85.5217644756458 \tabularnewline
72 & 7497.31 & 7294.2860237131 & 203.023976286897 \tabularnewline
73 & 7584.71 & 7704.13622379215 & -119.426223792146 \tabularnewline
74 & 7160.79 & 8031.94951232763 & -871.15951232763 \tabularnewline
75 & 7196.19 & 7636.49312696004 & -440.303126960045 \tabularnewline
76 & 7245.63 & 7084.15881646387 & 161.471183536134 \tabularnewline
77 & 7347.51 & 7129.29084442936 & 218.219155570639 \tabularnewline
78 & 7425.75 & 7276.55492610909 & 149.195073890907 \tabularnewline
79 & 7778.51 & 7542.82985474693 & 235.68014525307 \tabularnewline
80 & 7822.33 & 8071.68707261266 & -249.35707261266 \tabularnewline
81 & 8181.22 & 7850.98990210087 & 330.230097899135 \tabularnewline
82 & 8371.47 & 8279.82570997482 & 91.6442900251823 \tabularnewline
83 & 8347.71 & 8500.08610434749 & -152.376104347488 \tabularnewline
84 & 8672.11 & 8206.79113280938 & 465.318867190617 \tabularnewline
85 & 8802.79 & 8819.95727301461 & -17.1672730146129 \tabularnewline
86 & 9138.46 & 9200.11413671316 & -61.6541367131595 \tabularnewline
87 & 9123.29 & 9759.3846864971 & -636.094686497105 \tabularnewline
88 & 9023.21 & 9098.31483897915 & -75.104838979154 \tabularnewline
89 & 8850.41 & 8927.78492225431 & -77.3749222543138 \tabularnewline
90 & 8864.58 & 8775.42105991466 & 89.1589400853445 \tabularnewline
91 & 9163.74 & 9000.88602495431 & 162.853975045686 \tabularnewline
92 & 8516.66 & 9441.0806518963 & -924.420651896304 \tabularnewline
93 & 8553.44 & 8567.95779799683 & -14.5177979968266 \tabularnewline
94 & 7555.2 & 8549.0755763182 & -993.8755763182 \tabularnewline
95 & 7851.22 & 7534.92877157304 & 316.291228426959 \tabularnewline
96 & 7442 & 7566.61549329302 & -124.615493293017 \tabularnewline
97 & 7992.53 & 7373.89045050445 & 618.639549495546 \tabularnewline
98 & 8264.04 & 8144.3513033938 & 119.688696606198 \tabularnewline
99 & 7517.39 & 8625.34025516097 & -1107.95025516096 \tabularnewline
100 & 7200.4 & 7399.17629217925 & -198.776292179252 \tabularnewline
101 & 7193.69 & 6945.38035085194 & 248.309649148064 \tabularnewline
102 & 6193.58 & 6961.52078944754 & -767.940789447538 \tabularnewline
103 & 5104.21 & 6128.92308453093 & -1024.71308453093 \tabularnewline
104 & 4800.46 & 4961.83056552194 & -161.370565521944 \tabularnewline
105 & 4461.61 & 4540.5469052901 & -78.9369052900956 \tabularnewline
106 & 4398.59 & 4113.92388901846 & 284.666110981540 \tabularnewline
107 & 4243.63 & 4156.72896436101 & 86.9010356389854 \tabularnewline
108 & 4293.82 & 3851.46523822392 & 442.35476177608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63001&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]4378.75[/C][C]4816.92751819308[/C][C]-438.177518193077[/C][/ROW]
[ROW][C]14[/C][C]4472.93[/C][C]4496.21089354897[/C][C]-23.2808935489729[/C][/ROW]
[ROW][C]15[/C][C]4564.07[/C][C]4513.10358455271[/C][C]50.9664154472939[/C][/ROW]
[ROW][C]16[/C][C]4310.54[/C][C]4239.8733072642[/C][C]70.666692735802[/C][/ROW]
[ROW][C]17[/C][C]4171.38[/C][C]4106.45589796015[/C][C]64.9241020398476[/C][/ROW]
[ROW][C]18[/C][C]4049.38[/C][C]3977.94887623674[/C][C]71.4311237632651[/C][/ROW]
[ROW][C]19[/C][C]3591.37[/C][C]4149.49506581446[/C][C]-558.125065814463[/C][/ROW]
[ROW][C]20[/C][C]3720.46[/C][C]3399.82009621670[/C][C]320.639903783297[/C][/ROW]
[ROW][C]21[/C][C]4107.23[/C][C]3505.15520732032[/C][C]602.074792679677[/C][/ROW]
[ROW][C]22[/C][C]4101.71[/C][C]4060.68418394558[/C][C]41.0258160544163[/C][/ROW]
[ROW][C]23[/C][C]4162.34[/C][C]4131.56555974045[/C][C]30.7744402595526[/C][/ROW]
[ROW][C]24[/C][C]4136.22[/C][C]3894.08387464931[/C][C]242.136125350693[/C][/ROW]
[ROW][C]25[/C][C]4125.88[/C][C]4154.94897685148[/C][C]-29.068976851484[/C][/ROW]
[ROW][C]26[/C][C]4031.48[/C][C]4325.45935120328[/C][C]-293.979351203282[/C][/ROW]
[ROW][C]27[/C][C]3761.36[/C][C]4154.43857173772[/C][C]-393.078571737716[/C][/ROW]
[ROW][C]28[/C][C]3408.56[/C][C]3533.71369017903[/C][C]-125.15369017903[/C][/ROW]
[ROW][C]29[/C][C]3228.47[/C][C]3243.4310620317[/C][C]-14.9610620316980[/C][/ROW]
[ROW][C]30[/C][C]3090.45[/C][C]3058.57649918596[/C][C]31.8735008140447[/C][/ROW]
[ROW][C]31[/C][C]2741.14[/C][C]3093.76311739398[/C][C]-352.62311739398[/C][/ROW]
[ROW][C]32[/C][C]2980.44[/C][C]2619.18289770903[/C][C]361.257102290968[/C][/ROW]
[ROW][C]33[/C][C]3104.33[/C][C]2805.84420711042[/C][C]298.485792889582[/C][/ROW]
[ROW][C]34[/C][C]3181.57[/C][C]3018.1441663724[/C][C]163.425833627598[/C][/ROW]
[ROW][C]35[/C][C]2863.86[/C][C]3178.15656141591[/C][C]-314.296561415905[/C][/ROW]
[ROW][C]36[/C][C]2898.01[/C][C]2666.39603585652[/C][C]231.613964143483[/C][/ROW]
[ROW][C]37[/C][C]3112.33[/C][C]2845.94875378530[/C][C]266.381246214703[/C][/ROW]
[ROW][C]38[/C][C]3254.33[/C][C]3205.72400635576[/C][C]48.6059936442371[/C][/ROW]
[ROW][C]39[/C][C]3513.47[/C][C]3336.80918577878[/C][C]176.660814221217[/C][/ROW]
[ROW][C]40[/C][C]3587.61[/C][C]3351.7434447048[/C][C]235.866555295201[/C][/ROW]
[ROW][C]41[/C][C]3727.45[/C][C]3514.10829742696[/C][C]213.341702573044[/C][/ROW]
[ROW][C]42[/C][C]3793.34[/C][C]3668.52619479052[/C][C]124.813805209481[/C][/ROW]
[ROW][C]43[/C][C]3817.58[/C][C]3918.55387384301[/C][C]-100.97387384301[/C][/ROW]
[ROW][C]44[/C][C]3845.13[/C][C]3923.99556679087[/C][C]-78.865566790866[/C][/ROW]
[ROW][C]45[/C][C]3931.86[/C][C]3813.57699870634[/C][C]118.283001293661[/C][/ROW]
[ROW][C]46[/C][C]4197.52[/C][C]3958.53144217852[/C][C]238.988557821479[/C][/ROW]
[ROW][C]47[/C][C]4307.13[/C][C]4271.77025223961[/C][C]35.3597477603889[/C][/ROW]
[ROW][C]48[/C][C]4229.43[/C][C]4224.39398643604[/C][C]5.03601356396393[/C][/ROW]
[ROW][C]49[/C][C]4362.28[/C][C]4336.93915489609[/C][C]25.3408451039068[/C][/ROW]
[ROW][C]50[/C][C]4217.34[/C][C]4616.91599552967[/C][C]-399.575995529669[/C][/ROW]
[ROW][C]51[/C][C]4361.28[/C][C]4449.25934087327[/C][C]-87.9793408732712[/C][/ROW]
[ROW][C]52[/C][C]4327.74[/C][C]4228.69829515672[/C][C]99.0417048432819[/C][/ROW]
[ROW][C]53[/C][C]4417.65[/C][C]4269.9900805267[/C][C]147.659919473294[/C][/ROW]
[ROW][C]54[/C][C]4557.68[/C][C]4355.87501902967[/C][C]201.804980970327[/C][/ROW]
[ROW][C]55[/C][C]4650.35[/C][C]4693.94957717584[/C][C]-43.5995771758407[/C][/ROW]
[ROW][C]56[/C][C]4967.18[/C][C]4796.15524089788[/C][C]171.024759102120[/C][/ROW]
[ROW][C]57[/C][C]5123.42[/C][C]4969.59510852716[/C][C]153.824891472836[/C][/ROW]
[ROW][C]58[/C][C]5290.85[/C][C]5214.32273245127[/C][C]76.527267548734[/C][/ROW]
[ROW][C]59[/C][C]5535.66[/C][C]5405.21553752457[/C][C]130.444462475433[/C][/ROW]
[ROW][C]60[/C][C]5514.06[/C][C]5448.8532705348[/C][C]65.2067294652006[/C][/ROW]
[ROW][C]61[/C][C]5493.88[/C][C]5685.92969523329[/C][C]-192.049695233293[/C][/ROW]
[ROW][C]62[/C][C]5694.83[/C][C]5801.12967084213[/C][C]-106.299670842128[/C][/ROW]
[ROW][C]63[/C][C]5850.41[/C][C]6061.60435771929[/C][C]-211.194357719291[/C][/ROW]
[ROW][C]64[/C][C]6116.64[/C][C]5743.8688776575[/C][C]372.771122342502[/C][/ROW]
[ROW][C]65[/C][C]6175[/C][C]6085.83500647657[/C][C]89.1649935234327[/C][/ROW]
[ROW][C]66[/C][C]6513.58[/C][C]6155.59766721843[/C][C]357.982332781573[/C][/ROW]
[ROW][C]67[/C][C]6383.78[/C][C]6731.26288163338[/C][C]-347.482881633385[/C][/ROW]
[ROW][C]68[/C][C]6673.66[/C][C]6665.48576003458[/C][C]8.17423996541947[/C][/ROW]
[ROW][C]69[/C][C]6936.61[/C][C]6705.65235616964[/C][C]230.957643830358[/C][/ROW]
[ROW][C]70[/C][C]7300.68[/C][C]7063.28912002935[/C][C]237.390879970652[/C][/ROW]
[ROW][C]71[/C][C]7392.93[/C][C]7478.45176447565[/C][C]-85.5217644756458[/C][/ROW]
[ROW][C]72[/C][C]7497.31[/C][C]7294.2860237131[/C][C]203.023976286897[/C][/ROW]
[ROW][C]73[/C][C]7584.71[/C][C]7704.13622379215[/C][C]-119.426223792146[/C][/ROW]
[ROW][C]74[/C][C]7160.79[/C][C]8031.94951232763[/C][C]-871.15951232763[/C][/ROW]
[ROW][C]75[/C][C]7196.19[/C][C]7636.49312696004[/C][C]-440.303126960045[/C][/ROW]
[ROW][C]76[/C][C]7245.63[/C][C]7084.15881646387[/C][C]161.471183536134[/C][/ROW]
[ROW][C]77[/C][C]7347.51[/C][C]7129.29084442936[/C][C]218.219155570639[/C][/ROW]
[ROW][C]78[/C][C]7425.75[/C][C]7276.55492610909[/C][C]149.195073890907[/C][/ROW]
[ROW][C]79[/C][C]7778.51[/C][C]7542.82985474693[/C][C]235.68014525307[/C][/ROW]
[ROW][C]80[/C][C]7822.33[/C][C]8071.68707261266[/C][C]-249.35707261266[/C][/ROW]
[ROW][C]81[/C][C]8181.22[/C][C]7850.98990210087[/C][C]330.230097899135[/C][/ROW]
[ROW][C]82[/C][C]8371.47[/C][C]8279.82570997482[/C][C]91.6442900251823[/C][/ROW]
[ROW][C]83[/C][C]8347.71[/C][C]8500.08610434749[/C][C]-152.376104347488[/C][/ROW]
[ROW][C]84[/C][C]8672.11[/C][C]8206.79113280938[/C][C]465.318867190617[/C][/ROW]
[ROW][C]85[/C][C]8802.79[/C][C]8819.95727301461[/C][C]-17.1672730146129[/C][/ROW]
[ROW][C]86[/C][C]9138.46[/C][C]9200.11413671316[/C][C]-61.6541367131595[/C][/ROW]
[ROW][C]87[/C][C]9123.29[/C][C]9759.3846864971[/C][C]-636.094686497105[/C][/ROW]
[ROW][C]88[/C][C]9023.21[/C][C]9098.31483897915[/C][C]-75.104838979154[/C][/ROW]
[ROW][C]89[/C][C]8850.41[/C][C]8927.78492225431[/C][C]-77.3749222543138[/C][/ROW]
[ROW][C]90[/C][C]8864.58[/C][C]8775.42105991466[/C][C]89.1589400853445[/C][/ROW]
[ROW][C]91[/C][C]9163.74[/C][C]9000.88602495431[/C][C]162.853975045686[/C][/ROW]
[ROW][C]92[/C][C]8516.66[/C][C]9441.0806518963[/C][C]-924.420651896304[/C][/ROW]
[ROW][C]93[/C][C]8553.44[/C][C]8567.95779799683[/C][C]-14.5177979968266[/C][/ROW]
[ROW][C]94[/C][C]7555.2[/C][C]8549.0755763182[/C][C]-993.8755763182[/C][/ROW]
[ROW][C]95[/C][C]7851.22[/C][C]7534.92877157304[/C][C]316.291228426959[/C][/ROW]
[ROW][C]96[/C][C]7442[/C][C]7566.61549329302[/C][C]-124.615493293017[/C][/ROW]
[ROW][C]97[/C][C]7992.53[/C][C]7373.89045050445[/C][C]618.639549495546[/C][/ROW]
[ROW][C]98[/C][C]8264.04[/C][C]8144.3513033938[/C][C]119.688696606198[/C][/ROW]
[ROW][C]99[/C][C]7517.39[/C][C]8625.34025516097[/C][C]-1107.95025516096[/C][/ROW]
[ROW][C]100[/C][C]7200.4[/C][C]7399.17629217925[/C][C]-198.776292179252[/C][/ROW]
[ROW][C]101[/C][C]7193.69[/C][C]6945.38035085194[/C][C]248.309649148064[/C][/ROW]
[ROW][C]102[/C][C]6193.58[/C][C]6961.52078944754[/C][C]-767.940789447538[/C][/ROW]
[ROW][C]103[/C][C]5104.21[/C][C]6128.92308453093[/C][C]-1024.71308453093[/C][/ROW]
[ROW][C]104[/C][C]4800.46[/C][C]4961.83056552194[/C][C]-161.370565521944[/C][/ROW]
[ROW][C]105[/C][C]4461.61[/C][C]4540.5469052901[/C][C]-78.9369052900956[/C][/ROW]
[ROW][C]106[/C][C]4398.59[/C][C]4113.92388901846[/C][C]284.666110981540[/C][/ROW]
[ROW][C]107[/C][C]4243.63[/C][C]4156.72896436101[/C][C]86.9010356389854[/C][/ROW]
[ROW][C]108[/C][C]4293.82[/C][C]3851.46523822392[/C][C]442.35476177608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63001&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63001&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
134378.754816.92751819308-438.177518193077
144472.934496.21089354897-23.2808935489729
154564.074513.1035845527150.9664154472939
164310.544239.873307264270.666692735802
174171.384106.4558979601564.9241020398476
184049.383977.9488762367471.4311237632651
193591.374149.49506581446-558.125065814463
203720.463399.82009621670320.639903783297
214107.233505.15520732032602.074792679677
224101.714060.6841839455841.0258160544163
234162.344131.5655597404530.7744402595526
244136.223894.08387464931242.136125350693
254125.884154.94897685148-29.068976851484
264031.484325.45935120328-293.979351203282
273761.364154.43857173772-393.078571737716
283408.563533.71369017903-125.15369017903
293228.473243.4310620317-14.9610620316980
303090.453058.5764991859631.8735008140447
312741.143093.76311739398-352.62311739398
322980.442619.18289770903361.257102290968
333104.332805.84420711042298.485792889582
343181.573018.1441663724163.425833627598
352863.863178.15656141591-314.296561415905
362898.012666.39603585652231.613964143483
373112.332845.94875378530266.381246214703
383254.333205.7240063557648.6059936442371
393513.473336.80918577878176.660814221217
403587.613351.7434447048235.866555295201
413727.453514.10829742696213.341702573044
423793.343668.52619479052124.813805209481
433817.583918.55387384301-100.97387384301
443845.133923.99556679087-78.865566790866
453931.863813.57699870634118.283001293661
464197.523958.53144217852238.988557821479
474307.134271.7702522396135.3597477603889
484229.434224.393986436045.03601356396393
494362.284336.9391548960925.3408451039068
504217.344616.91599552967-399.575995529669
514361.284449.25934087327-87.9793408732712
524327.744228.6982951567299.0417048432819
534417.654269.9900805267147.659919473294
544557.684355.87501902967201.804980970327
554650.354693.94957717584-43.5995771758407
564967.184796.15524089788171.024759102120
575123.424969.59510852716153.824891472836
585290.855214.3227324512776.527267548734
595535.665405.21553752457130.444462475433
605514.065448.853270534865.2067294652006
615493.885685.92969523329-192.049695233293
625694.835801.12967084213-106.299670842128
635850.416061.60435771929-211.194357719291
646116.645743.8688776575372.771122342502
6561756085.8350064765789.1649935234327
666513.586155.59766721843357.982332781573
676383.786731.26288163338-347.482881633385
686673.666665.485760034588.17423996541947
696936.616705.65235616964230.957643830358
707300.687063.28912002935237.390879970652
717392.937478.45176447565-85.5217644756458
727497.317294.2860237131203.023976286897
737584.717704.13622379215-119.426223792146
747160.798031.94951232763-871.15951232763
757196.197636.49312696004-440.303126960045
767245.637084.15881646387161.471183536134
777347.517129.29084442936218.219155570639
787425.757276.55492610909149.195073890907
797778.517542.82985474693235.68014525307
807822.338071.68707261266-249.35707261266
818181.227850.98990210087330.230097899135
828371.478279.8257099748291.6442900251823
838347.718500.08610434749-152.376104347488
848672.118206.79113280938465.318867190617
858802.798819.95727301461-17.1672730146129
869138.469200.11413671316-61.6541367131595
879123.299759.3846864971-636.094686497105
889023.219098.31483897915-75.104838979154
898850.418927.78492225431-77.3749222543138
908864.588775.4210599146689.1589400853445
919163.749000.88602495431162.853975045686
928516.669441.0806518963-924.420651896304
938553.448567.95779799683-14.5177979968266
947555.28549.0755763182-993.8755763182
957851.227534.92877157304316.291228426959
9674427566.61549329302-124.615493293017
977992.537373.89045050445618.639549495546
988264.048144.3513033938119.688696606198
997517.398625.34025516097-1107.95025516096
1007200.47399.17629217925-198.776292179252
1017193.696945.38035085194248.309649148064
1026193.586961.52078944754-767.940789447538
1035104.216128.92308453093-1024.71308453093
1044800.464961.83056552194-161.370565521944
1054461.614540.5469052901-78.9369052900956
1064398.594113.92388901846284.666110981540
1074243.634156.7289643610186.9010356389854
1084293.823851.46523822392442.35476177608







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1094072.206884610993414.036534622144730.37723459984
1103940.977504400112991.76610783094890.18890096933
1113837.979003586322609.532292775385066.42571439726
1123600.047352844542132.450319641655067.64438604742
1133325.078457965781638.791221024135011.36569490742
1143016.927759479441138.422700394484895.43281856441
1152808.12376982676685.8072964254954930.44024322802
1162658.59980265358238.9447570629955078.25484824416
1172457.07454951061-228.9774958211415143.12659484237
1182227.64673066096-699.3719999815625154.66546130347
1192030.17168991497-1184.402375927375244.74575575732
1201770.22206128955-1566.957279545015107.40140212411

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 4072.20688461099 & 3414.03653462214 & 4730.37723459984 \tabularnewline
110 & 3940.97750440011 & 2991.7661078309 & 4890.18890096933 \tabularnewline
111 & 3837.97900358632 & 2609.53229277538 & 5066.42571439726 \tabularnewline
112 & 3600.04735284454 & 2132.45031964165 & 5067.64438604742 \tabularnewline
113 & 3325.07845796578 & 1638.79122102413 & 5011.36569490742 \tabularnewline
114 & 3016.92775947944 & 1138.42270039448 & 4895.43281856441 \tabularnewline
115 & 2808.12376982676 & 685.807296425495 & 4930.44024322802 \tabularnewline
116 & 2658.59980265358 & 238.944757062995 & 5078.25484824416 \tabularnewline
117 & 2457.07454951061 & -228.977495821141 & 5143.12659484237 \tabularnewline
118 & 2227.64673066096 & -699.371999981562 & 5154.66546130347 \tabularnewline
119 & 2030.17168991497 & -1184.40237592737 & 5244.74575575732 \tabularnewline
120 & 1770.22206128955 & -1566.95727954501 & 5107.40140212411 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63001&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]4072.20688461099[/C][C]3414.03653462214[/C][C]4730.37723459984[/C][/ROW]
[ROW][C]110[/C][C]3940.97750440011[/C][C]2991.7661078309[/C][C]4890.18890096933[/C][/ROW]
[ROW][C]111[/C][C]3837.97900358632[/C][C]2609.53229277538[/C][C]5066.42571439726[/C][/ROW]
[ROW][C]112[/C][C]3600.04735284454[/C][C]2132.45031964165[/C][C]5067.64438604742[/C][/ROW]
[ROW][C]113[/C][C]3325.07845796578[/C][C]1638.79122102413[/C][C]5011.36569490742[/C][/ROW]
[ROW][C]114[/C][C]3016.92775947944[/C][C]1138.42270039448[/C][C]4895.43281856441[/C][/ROW]
[ROW][C]115[/C][C]2808.12376982676[/C][C]685.807296425495[/C][C]4930.44024322802[/C][/ROW]
[ROW][C]116[/C][C]2658.59980265358[/C][C]238.944757062995[/C][C]5078.25484824416[/C][/ROW]
[ROW][C]117[/C][C]2457.07454951061[/C][C]-228.977495821141[/C][C]5143.12659484237[/C][/ROW]
[ROW][C]118[/C][C]2227.64673066096[/C][C]-699.371999981562[/C][C]5154.66546130347[/C][/ROW]
[ROW][C]119[/C][C]2030.17168991497[/C][C]-1184.40237592737[/C][C]5244.74575575732[/C][/ROW]
[ROW][C]120[/C][C]1770.22206128955[/C][C]-1566.95727954501[/C][C]5107.40140212411[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63001&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63001&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
1094072.206884610993414.036534622144730.37723459984
1103940.977504400112991.76610783094890.18890096933
1113837.979003586322609.532292775385066.42571439726
1123600.047352844542132.450319641655067.64438604742
1133325.078457965781638.791221024135011.36569490742
1143016.927759479441138.422700394484895.43281856441
1152808.12376982676685.8072964254954930.44024322802
1162658.59980265358238.9447570629955078.25484824416
1172457.07454951061-228.9774958211415143.12659484237
1182227.64673066096-699.3719999815625154.66546130347
1192030.17168991497-1184.402375927375244.74575575732
1201770.22206128955-1566.957279545015107.40140212411



Parameters (Session):
par1 = FALSE ; par2 = 0.2 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 0 ; par8 = 0 ; par9 = 0 ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')