Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Aug 2017 20:14:35 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/06/t15020432914up1v9m10e5886m.htm/, Retrieved Sat, 11 May 2024 12:46:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=306982, Retrieved Sat, 11 May 2024 12:46:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-06 18:14:35] [eec775fda337aa2da775a098928b5865] [Current]
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Dataseries X:
3469648
3456726
3443622
3416504
3684772
3670576
3469648
3336060
3348982
3348982
3363360
3389204
3429426
3429426
3403582
3336060
3684772
3737916
3657654
3469648
3550092
3429426
3483844
3509870
3536988
3469648
3483844
3389204
3684772
3778138
3697876
3550092
3710798
3536988
3697876
3684772
3724994
3577210
3737916
3724994
3966144
3911726
3697876
3590132
3737916
3536988
3684772
3710798
3765216
3644732
3710798
3751020
3898804
3778138
3617432
3443622
3604510
3162250
3376282
3496766
3617432
3443622
3443622
3443622
3536988
3403582
3228498
3081988
3188276
2773316
3027570
3175354
3202472
3054688
3067610
3027570
3162250
3067610
2881060
2746198
2974244
2479022
2800616
2947126
2947126
2773316
2612610
2599688
2746198
2612610
2358538
2183454
2371460
1929382
2331238
2545088
2612610
2464826
2278094
2411682
2464826
2424604
2022566
1836016
1969422
1567566
1982526
2130310
2250794
2049866
1861860
1969422
2022566
1916278
1514422
1339338
1500044
1057966
1540266
1836016




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306982&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=306982&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306982&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.379244790290775
beta0.050695464793401
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.379244790290775 \tabularnewline
beta & 0.050695464793401 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306982&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]0.379244790290775[/C][/ROW]
[ROW][C]beta[/C][C]0.050695464793401[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306982&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306982&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
alpha0.379244790290775
beta0.050695464793401
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1334294263429687.03850589-261.038505886216
1434294263422094.755113337331.24488666747
1534035823391281.7045336612300.2954663369
1633360603323329.563515112730.4364849008
1736847723674067.1353098110704.8646901865
1837379163727595.0844883210320.9155116822
1936576543527810.07818111129843.921818894
2034696483451181.4319588418466.5680411607
2135500923483851.9616445566240.0383554483
2234294263524829.48110142-95403.4811014212
2334838443515989.96489445-32145.9648944451
2435098703536223.1501991-26353.1501990966
2535369883564843.25565687-27855.2556568743
2634696483552781.934061-83133.9340609959
2734838443489621.04919109-5777.04919109168
2833892043412663.13048808-23459.1304880837
2936847723753976.09306062-69204.0930606192
3037781383774584.674373313553.32562668901
3136978763641037.5397070856838.4602929181
3235500923463187.0560120786904.9439879251
3337107983548701.17741256162096.822587445
3435369883522492.7101861814495.2898138175
3536978763597321.95828161100554.041718394
3636847723676345.289614868426.71038513631
3737249943723024.349032271969.65096772928
3835772103690122.41984721-112912.41984721
3937379163668573.9758589769342.0241410285
4037249943609198.16249055115795.837509449
4139661444008317.451391-42173.4513909961
4239117264101483.02336381-189757.023363807
4336978763926354.3767128-228478.376712798
4435901323651720.89793915-61588.8979391465
4537379163725347.6568680812568.3431319203
4635369883544595.73427913-7607.73427913105
4736847723658140.8576306926631.1423693141
4837107983644947.3223469965850.6776530123
4937652163703128.6136595162087.3863404859
5036447323615992.6709354728739.3290645294
5137107983760478.08395409-49680.0839540865
5237510203679410.5160534971609.4839465078
5338988043956708.7654082-57904.765408203
5437781383944168.33424274-166030.334242742
5536174323746437.90147072-129005.901470722
5634436223609272.81207773-165650.812077729
5736045103681924.91268467-77414.9126846706
5831622503451974.47908962-289724.479089617
5933762823459329.98924786-83047.9892478646
6034967663413737.9450834183028.0549165895
6136174323459167.37619213158264.623807865
6234436223384186.4617931359435.5382068711
6334436223474171.09773178-30549.0977317849
6434436223462990.17627502-19368.1762750242
6535369883598222.18525802-61234.1852580179
6634035823507050.33861981-103468.338619809
6732284983351978.03794668-123480.037946682
6830819883190071.30584605-108083.305846047
6931882763310819.36986097-122543.369860973
7027733162946256.12293912-172940.122939117
7130275703092853.95454596-65283.954545965
7231753543137326.7821920338027.2178079691
7332024723192646.914589139825.08541086968
7430546883008466.9693161146221.0306838877
7530676103021706.9205143445903.0794856572
7630275703032529.7020657-4959.70206570113
7731622503119757.7473062442492.2526937597
7830676103040630.9377803426979.0622196635
7928810602926460.48052563-45400.4805256254
8027461982806375.55214558-60177.552145578
8129742442913915.2337692460328.7662307606
8224790222609939.13749066-130917.137490658
8328006162814997.49926681-14381.4992668144
8429471262931510.826007415615.1739926026
8529471262956903.41286019-9777.41286019469
8627733162798130.99766288-24814.9976628846
8726126102780517.85726826-167907.85726826
8825996882674622.28490614-74934.2849061401
8927461982739284.817498436913.18250157358
9026126102640096.59402425-27486.5940242507
9123585382472999.4223937-114461.422393698
9221834542322224.18949024-138770.18949024
9323714602423107.51859104-51647.5185910389
9419293822026715.11000626-97333.1100062639
9523312382234678.2046641496559.7953358614
9625450882369038.54729089176049.452709112
9726126102425957.86835817186652.131641835
9824648262349128.31701236115697.682987643
9922780942301981.49307701-23887.4930770053
10024116822303411.41061985108270.589380146
10124648262475565.52562341-10739.52562341
10224246042361512.7281898263091.2718101786
10320225662194672.23199592-172106.231995918
10418360162018103.83315598-182087.833155975
10519694222133676.78457478-164254.784574778
10615675661713706.77342952-146140.773429524
10719825261966032.9222592916493.0777407144
10821303102086552.9195076943757.0804923067
10922507942087228.12939001163565.870609988
11020498661980612.565803869253.4341962035
11118618601852190.27390279669.72609730042
11219694221920391.2250381849030.7749618213
11320225661973700.1545471948865.8454528141
11419162781930160.78163325-13882.7816332541
11515144221644987.50102241-130565.501022412
11613393381490060.42206892-150722.422068921
11715000441571973.89823792-71929.8982379164
11810579661262087.92827693-204121.92827693
11915402661479248.4852890661017.5147109393
12018360161587240.92633265248775.073667354

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3429426 & 3429687.03850589 & -261.038505886216 \tabularnewline
14 & 3429426 & 3422094.75511333 & 7331.24488666747 \tabularnewline
15 & 3403582 & 3391281.70453366 & 12300.2954663369 \tabularnewline
16 & 3336060 & 3323329.5635151 & 12730.4364849008 \tabularnewline
17 & 3684772 & 3674067.13530981 & 10704.8646901865 \tabularnewline
18 & 3737916 & 3727595.08448832 & 10320.9155116822 \tabularnewline
19 & 3657654 & 3527810.07818111 & 129843.921818894 \tabularnewline
20 & 3469648 & 3451181.43195884 & 18466.5680411607 \tabularnewline
21 & 3550092 & 3483851.96164455 & 66240.0383554483 \tabularnewline
22 & 3429426 & 3524829.48110142 & -95403.4811014212 \tabularnewline
23 & 3483844 & 3515989.96489445 & -32145.9648944451 \tabularnewline
24 & 3509870 & 3536223.1501991 & -26353.1501990966 \tabularnewline
25 & 3536988 & 3564843.25565687 & -27855.2556568743 \tabularnewline
26 & 3469648 & 3552781.934061 & -83133.9340609959 \tabularnewline
27 & 3483844 & 3489621.04919109 & -5777.04919109168 \tabularnewline
28 & 3389204 & 3412663.13048808 & -23459.1304880837 \tabularnewline
29 & 3684772 & 3753976.09306062 & -69204.0930606192 \tabularnewline
30 & 3778138 & 3774584.67437331 & 3553.32562668901 \tabularnewline
31 & 3697876 & 3641037.53970708 & 56838.4602929181 \tabularnewline
32 & 3550092 & 3463187.05601207 & 86904.9439879251 \tabularnewline
33 & 3710798 & 3548701.17741256 & 162096.822587445 \tabularnewline
34 & 3536988 & 3522492.71018618 & 14495.2898138175 \tabularnewline
35 & 3697876 & 3597321.95828161 & 100554.041718394 \tabularnewline
36 & 3684772 & 3676345.28961486 & 8426.71038513631 \tabularnewline
37 & 3724994 & 3723024.34903227 & 1969.65096772928 \tabularnewline
38 & 3577210 & 3690122.41984721 & -112912.41984721 \tabularnewline
39 & 3737916 & 3668573.97585897 & 69342.0241410285 \tabularnewline
40 & 3724994 & 3609198.16249055 & 115795.837509449 \tabularnewline
41 & 3966144 & 4008317.451391 & -42173.4513909961 \tabularnewline
42 & 3911726 & 4101483.02336381 & -189757.023363807 \tabularnewline
43 & 3697876 & 3926354.3767128 & -228478.376712798 \tabularnewline
44 & 3590132 & 3651720.89793915 & -61588.8979391465 \tabularnewline
45 & 3737916 & 3725347.65686808 & 12568.3431319203 \tabularnewline
46 & 3536988 & 3544595.73427913 & -7607.73427913105 \tabularnewline
47 & 3684772 & 3658140.85763069 & 26631.1423693141 \tabularnewline
48 & 3710798 & 3644947.32234699 & 65850.6776530123 \tabularnewline
49 & 3765216 & 3703128.61365951 & 62087.3863404859 \tabularnewline
50 & 3644732 & 3615992.67093547 & 28739.3290645294 \tabularnewline
51 & 3710798 & 3760478.08395409 & -49680.0839540865 \tabularnewline
52 & 3751020 & 3679410.51605349 & 71609.4839465078 \tabularnewline
53 & 3898804 & 3956708.7654082 & -57904.765408203 \tabularnewline
54 & 3778138 & 3944168.33424274 & -166030.334242742 \tabularnewline
55 & 3617432 & 3746437.90147072 & -129005.901470722 \tabularnewline
56 & 3443622 & 3609272.81207773 & -165650.812077729 \tabularnewline
57 & 3604510 & 3681924.91268467 & -77414.9126846706 \tabularnewline
58 & 3162250 & 3451974.47908962 & -289724.479089617 \tabularnewline
59 & 3376282 & 3459329.98924786 & -83047.9892478646 \tabularnewline
60 & 3496766 & 3413737.94508341 & 83028.0549165895 \tabularnewline
61 & 3617432 & 3459167.37619213 & 158264.623807865 \tabularnewline
62 & 3443622 & 3384186.46179313 & 59435.5382068711 \tabularnewline
63 & 3443622 & 3474171.09773178 & -30549.0977317849 \tabularnewline
64 & 3443622 & 3462990.17627502 & -19368.1762750242 \tabularnewline
65 & 3536988 & 3598222.18525802 & -61234.1852580179 \tabularnewline
66 & 3403582 & 3507050.33861981 & -103468.338619809 \tabularnewline
67 & 3228498 & 3351978.03794668 & -123480.037946682 \tabularnewline
68 & 3081988 & 3190071.30584605 & -108083.305846047 \tabularnewline
69 & 3188276 & 3310819.36986097 & -122543.369860973 \tabularnewline
70 & 2773316 & 2946256.12293912 & -172940.122939117 \tabularnewline
71 & 3027570 & 3092853.95454596 & -65283.954545965 \tabularnewline
72 & 3175354 & 3137326.78219203 & 38027.2178079691 \tabularnewline
73 & 3202472 & 3192646.91458913 & 9825.08541086968 \tabularnewline
74 & 3054688 & 3008466.96931611 & 46221.0306838877 \tabularnewline
75 & 3067610 & 3021706.92051434 & 45903.0794856572 \tabularnewline
76 & 3027570 & 3032529.7020657 & -4959.70206570113 \tabularnewline
77 & 3162250 & 3119757.74730624 & 42492.2526937597 \tabularnewline
78 & 3067610 & 3040630.93778034 & 26979.0622196635 \tabularnewline
79 & 2881060 & 2926460.48052563 & -45400.4805256254 \tabularnewline
80 & 2746198 & 2806375.55214558 & -60177.552145578 \tabularnewline
81 & 2974244 & 2913915.23376924 & 60328.7662307606 \tabularnewline
82 & 2479022 & 2609939.13749066 & -130917.137490658 \tabularnewline
83 & 2800616 & 2814997.49926681 & -14381.4992668144 \tabularnewline
84 & 2947126 & 2931510.8260074 & 15615.1739926026 \tabularnewline
85 & 2947126 & 2956903.41286019 & -9777.41286019469 \tabularnewline
86 & 2773316 & 2798130.99766288 & -24814.9976628846 \tabularnewline
87 & 2612610 & 2780517.85726826 & -167907.85726826 \tabularnewline
88 & 2599688 & 2674622.28490614 & -74934.2849061401 \tabularnewline
89 & 2746198 & 2739284.81749843 & 6913.18250157358 \tabularnewline
90 & 2612610 & 2640096.59402425 & -27486.5940242507 \tabularnewline
91 & 2358538 & 2472999.4223937 & -114461.422393698 \tabularnewline
92 & 2183454 & 2322224.18949024 & -138770.18949024 \tabularnewline
93 & 2371460 & 2423107.51859104 & -51647.5185910389 \tabularnewline
94 & 1929382 & 2026715.11000626 & -97333.1100062639 \tabularnewline
95 & 2331238 & 2234678.20466414 & 96559.7953358614 \tabularnewline
96 & 2545088 & 2369038.54729089 & 176049.452709112 \tabularnewline
97 & 2612610 & 2425957.86835817 & 186652.131641835 \tabularnewline
98 & 2464826 & 2349128.31701236 & 115697.682987643 \tabularnewline
99 & 2278094 & 2301981.49307701 & -23887.4930770053 \tabularnewline
100 & 2411682 & 2303411.41061985 & 108270.589380146 \tabularnewline
101 & 2464826 & 2475565.52562341 & -10739.52562341 \tabularnewline
102 & 2424604 & 2361512.72818982 & 63091.2718101786 \tabularnewline
103 & 2022566 & 2194672.23199592 & -172106.231995918 \tabularnewline
104 & 1836016 & 2018103.83315598 & -182087.833155975 \tabularnewline
105 & 1969422 & 2133676.78457478 & -164254.784574778 \tabularnewline
106 & 1567566 & 1713706.77342952 & -146140.773429524 \tabularnewline
107 & 1982526 & 1966032.92225929 & 16493.0777407144 \tabularnewline
108 & 2130310 & 2086552.91950769 & 43757.0804923067 \tabularnewline
109 & 2250794 & 2087228.12939001 & 163565.870609988 \tabularnewline
110 & 2049866 & 1980612.5658038 & 69253.4341962035 \tabularnewline
111 & 1861860 & 1852190.2739027 & 9669.72609730042 \tabularnewline
112 & 1969422 & 1920391.22503818 & 49030.7749618213 \tabularnewline
113 & 2022566 & 1973700.15454719 & 48865.8454528141 \tabularnewline
114 & 1916278 & 1930160.78163325 & -13882.7816332541 \tabularnewline
115 & 1514422 & 1644987.50102241 & -130565.501022412 \tabularnewline
116 & 1339338 & 1490060.42206892 & -150722.422068921 \tabularnewline
117 & 1500044 & 1571973.89823792 & -71929.8982379164 \tabularnewline
118 & 1057966 & 1262087.92827693 & -204121.92827693 \tabularnewline
119 & 1540266 & 1479248.48528906 & 61017.5147109393 \tabularnewline
120 & 1836016 & 1587240.92633265 & 248775.073667354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306982&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]3429426[/C][C]3429687.03850589[/C][C]-261.038505886216[/C][/ROW]
[ROW][C]14[/C][C]3429426[/C][C]3422094.75511333[/C][C]7331.24488666747[/C][/ROW]
[ROW][C]15[/C][C]3403582[/C][C]3391281.70453366[/C][C]12300.2954663369[/C][/ROW]
[ROW][C]16[/C][C]3336060[/C][C]3323329.5635151[/C][C]12730.4364849008[/C][/ROW]
[ROW][C]17[/C][C]3684772[/C][C]3674067.13530981[/C][C]10704.8646901865[/C][/ROW]
[ROW][C]18[/C][C]3737916[/C][C]3727595.08448832[/C][C]10320.9155116822[/C][/ROW]
[ROW][C]19[/C][C]3657654[/C][C]3527810.07818111[/C][C]129843.921818894[/C][/ROW]
[ROW][C]20[/C][C]3469648[/C][C]3451181.43195884[/C][C]18466.5680411607[/C][/ROW]
[ROW][C]21[/C][C]3550092[/C][C]3483851.96164455[/C][C]66240.0383554483[/C][/ROW]
[ROW][C]22[/C][C]3429426[/C][C]3524829.48110142[/C][C]-95403.4811014212[/C][/ROW]
[ROW][C]23[/C][C]3483844[/C][C]3515989.96489445[/C][C]-32145.9648944451[/C][/ROW]
[ROW][C]24[/C][C]3509870[/C][C]3536223.1501991[/C][C]-26353.1501990966[/C][/ROW]
[ROW][C]25[/C][C]3536988[/C][C]3564843.25565687[/C][C]-27855.2556568743[/C][/ROW]
[ROW][C]26[/C][C]3469648[/C][C]3552781.934061[/C][C]-83133.9340609959[/C][/ROW]
[ROW][C]27[/C][C]3483844[/C][C]3489621.04919109[/C][C]-5777.04919109168[/C][/ROW]
[ROW][C]28[/C][C]3389204[/C][C]3412663.13048808[/C][C]-23459.1304880837[/C][/ROW]
[ROW][C]29[/C][C]3684772[/C][C]3753976.09306062[/C][C]-69204.0930606192[/C][/ROW]
[ROW][C]30[/C][C]3778138[/C][C]3774584.67437331[/C][C]3553.32562668901[/C][/ROW]
[ROW][C]31[/C][C]3697876[/C][C]3641037.53970708[/C][C]56838.4602929181[/C][/ROW]
[ROW][C]32[/C][C]3550092[/C][C]3463187.05601207[/C][C]86904.9439879251[/C][/ROW]
[ROW][C]33[/C][C]3710798[/C][C]3548701.17741256[/C][C]162096.822587445[/C][/ROW]
[ROW][C]34[/C][C]3536988[/C][C]3522492.71018618[/C][C]14495.2898138175[/C][/ROW]
[ROW][C]35[/C][C]3697876[/C][C]3597321.95828161[/C][C]100554.041718394[/C][/ROW]
[ROW][C]36[/C][C]3684772[/C][C]3676345.28961486[/C][C]8426.71038513631[/C][/ROW]
[ROW][C]37[/C][C]3724994[/C][C]3723024.34903227[/C][C]1969.65096772928[/C][/ROW]
[ROW][C]38[/C][C]3577210[/C][C]3690122.41984721[/C][C]-112912.41984721[/C][/ROW]
[ROW][C]39[/C][C]3737916[/C][C]3668573.97585897[/C][C]69342.0241410285[/C][/ROW]
[ROW][C]40[/C][C]3724994[/C][C]3609198.16249055[/C][C]115795.837509449[/C][/ROW]
[ROW][C]41[/C][C]3966144[/C][C]4008317.451391[/C][C]-42173.4513909961[/C][/ROW]
[ROW][C]42[/C][C]3911726[/C][C]4101483.02336381[/C][C]-189757.023363807[/C][/ROW]
[ROW][C]43[/C][C]3697876[/C][C]3926354.3767128[/C][C]-228478.376712798[/C][/ROW]
[ROW][C]44[/C][C]3590132[/C][C]3651720.89793915[/C][C]-61588.8979391465[/C][/ROW]
[ROW][C]45[/C][C]3737916[/C][C]3725347.65686808[/C][C]12568.3431319203[/C][/ROW]
[ROW][C]46[/C][C]3536988[/C][C]3544595.73427913[/C][C]-7607.73427913105[/C][/ROW]
[ROW][C]47[/C][C]3684772[/C][C]3658140.85763069[/C][C]26631.1423693141[/C][/ROW]
[ROW][C]48[/C][C]3710798[/C][C]3644947.32234699[/C][C]65850.6776530123[/C][/ROW]
[ROW][C]49[/C][C]3765216[/C][C]3703128.61365951[/C][C]62087.3863404859[/C][/ROW]
[ROW][C]50[/C][C]3644732[/C][C]3615992.67093547[/C][C]28739.3290645294[/C][/ROW]
[ROW][C]51[/C][C]3710798[/C][C]3760478.08395409[/C][C]-49680.0839540865[/C][/ROW]
[ROW][C]52[/C][C]3751020[/C][C]3679410.51605349[/C][C]71609.4839465078[/C][/ROW]
[ROW][C]53[/C][C]3898804[/C][C]3956708.7654082[/C][C]-57904.765408203[/C][/ROW]
[ROW][C]54[/C][C]3778138[/C][C]3944168.33424274[/C][C]-166030.334242742[/C][/ROW]
[ROW][C]55[/C][C]3617432[/C][C]3746437.90147072[/C][C]-129005.901470722[/C][/ROW]
[ROW][C]56[/C][C]3443622[/C][C]3609272.81207773[/C][C]-165650.812077729[/C][/ROW]
[ROW][C]57[/C][C]3604510[/C][C]3681924.91268467[/C][C]-77414.9126846706[/C][/ROW]
[ROW][C]58[/C][C]3162250[/C][C]3451974.47908962[/C][C]-289724.479089617[/C][/ROW]
[ROW][C]59[/C][C]3376282[/C][C]3459329.98924786[/C][C]-83047.9892478646[/C][/ROW]
[ROW][C]60[/C][C]3496766[/C][C]3413737.94508341[/C][C]83028.0549165895[/C][/ROW]
[ROW][C]61[/C][C]3617432[/C][C]3459167.37619213[/C][C]158264.623807865[/C][/ROW]
[ROW][C]62[/C][C]3443622[/C][C]3384186.46179313[/C][C]59435.5382068711[/C][/ROW]
[ROW][C]63[/C][C]3443622[/C][C]3474171.09773178[/C][C]-30549.0977317849[/C][/ROW]
[ROW][C]64[/C][C]3443622[/C][C]3462990.17627502[/C][C]-19368.1762750242[/C][/ROW]
[ROW][C]65[/C][C]3536988[/C][C]3598222.18525802[/C][C]-61234.1852580179[/C][/ROW]
[ROW][C]66[/C][C]3403582[/C][C]3507050.33861981[/C][C]-103468.338619809[/C][/ROW]
[ROW][C]67[/C][C]3228498[/C][C]3351978.03794668[/C][C]-123480.037946682[/C][/ROW]
[ROW][C]68[/C][C]3081988[/C][C]3190071.30584605[/C][C]-108083.305846047[/C][/ROW]
[ROW][C]69[/C][C]3188276[/C][C]3310819.36986097[/C][C]-122543.369860973[/C][/ROW]
[ROW][C]70[/C][C]2773316[/C][C]2946256.12293912[/C][C]-172940.122939117[/C][/ROW]
[ROW][C]71[/C][C]3027570[/C][C]3092853.95454596[/C][C]-65283.954545965[/C][/ROW]
[ROW][C]72[/C][C]3175354[/C][C]3137326.78219203[/C][C]38027.2178079691[/C][/ROW]
[ROW][C]73[/C][C]3202472[/C][C]3192646.91458913[/C][C]9825.08541086968[/C][/ROW]
[ROW][C]74[/C][C]3054688[/C][C]3008466.96931611[/C][C]46221.0306838877[/C][/ROW]
[ROW][C]75[/C][C]3067610[/C][C]3021706.92051434[/C][C]45903.0794856572[/C][/ROW]
[ROW][C]76[/C][C]3027570[/C][C]3032529.7020657[/C][C]-4959.70206570113[/C][/ROW]
[ROW][C]77[/C][C]3162250[/C][C]3119757.74730624[/C][C]42492.2526937597[/C][/ROW]
[ROW][C]78[/C][C]3067610[/C][C]3040630.93778034[/C][C]26979.0622196635[/C][/ROW]
[ROW][C]79[/C][C]2881060[/C][C]2926460.48052563[/C][C]-45400.4805256254[/C][/ROW]
[ROW][C]80[/C][C]2746198[/C][C]2806375.55214558[/C][C]-60177.552145578[/C][/ROW]
[ROW][C]81[/C][C]2974244[/C][C]2913915.23376924[/C][C]60328.7662307606[/C][/ROW]
[ROW][C]82[/C][C]2479022[/C][C]2609939.13749066[/C][C]-130917.137490658[/C][/ROW]
[ROW][C]83[/C][C]2800616[/C][C]2814997.49926681[/C][C]-14381.4992668144[/C][/ROW]
[ROW][C]84[/C][C]2947126[/C][C]2931510.8260074[/C][C]15615.1739926026[/C][/ROW]
[ROW][C]85[/C][C]2947126[/C][C]2956903.41286019[/C][C]-9777.41286019469[/C][/ROW]
[ROW][C]86[/C][C]2773316[/C][C]2798130.99766288[/C][C]-24814.9976628846[/C][/ROW]
[ROW][C]87[/C][C]2612610[/C][C]2780517.85726826[/C][C]-167907.85726826[/C][/ROW]
[ROW][C]88[/C][C]2599688[/C][C]2674622.28490614[/C][C]-74934.2849061401[/C][/ROW]
[ROW][C]89[/C][C]2746198[/C][C]2739284.81749843[/C][C]6913.18250157358[/C][/ROW]
[ROW][C]90[/C][C]2612610[/C][C]2640096.59402425[/C][C]-27486.5940242507[/C][/ROW]
[ROW][C]91[/C][C]2358538[/C][C]2472999.4223937[/C][C]-114461.422393698[/C][/ROW]
[ROW][C]92[/C][C]2183454[/C][C]2322224.18949024[/C][C]-138770.18949024[/C][/ROW]
[ROW][C]93[/C][C]2371460[/C][C]2423107.51859104[/C][C]-51647.5185910389[/C][/ROW]
[ROW][C]94[/C][C]1929382[/C][C]2026715.11000626[/C][C]-97333.1100062639[/C][/ROW]
[ROW][C]95[/C][C]2331238[/C][C]2234678.20466414[/C][C]96559.7953358614[/C][/ROW]
[ROW][C]96[/C][C]2545088[/C][C]2369038.54729089[/C][C]176049.452709112[/C][/ROW]
[ROW][C]97[/C][C]2612610[/C][C]2425957.86835817[/C][C]186652.131641835[/C][/ROW]
[ROW][C]98[/C][C]2464826[/C][C]2349128.31701236[/C][C]115697.682987643[/C][/ROW]
[ROW][C]99[/C][C]2278094[/C][C]2301981.49307701[/C][C]-23887.4930770053[/C][/ROW]
[ROW][C]100[/C][C]2411682[/C][C]2303411.41061985[/C][C]108270.589380146[/C][/ROW]
[ROW][C]101[/C][C]2464826[/C][C]2475565.52562341[/C][C]-10739.52562341[/C][/ROW]
[ROW][C]102[/C][C]2424604[/C][C]2361512.72818982[/C][C]63091.2718101786[/C][/ROW]
[ROW][C]103[/C][C]2022566[/C][C]2194672.23199592[/C][C]-172106.231995918[/C][/ROW]
[ROW][C]104[/C][C]1836016[/C][C]2018103.83315598[/C][C]-182087.833155975[/C][/ROW]
[ROW][C]105[/C][C]1969422[/C][C]2133676.78457478[/C][C]-164254.784574778[/C][/ROW]
[ROW][C]106[/C][C]1567566[/C][C]1713706.77342952[/C][C]-146140.773429524[/C][/ROW]
[ROW][C]107[/C][C]1982526[/C][C]1966032.92225929[/C][C]16493.0777407144[/C][/ROW]
[ROW][C]108[/C][C]2130310[/C][C]2086552.91950769[/C][C]43757.0804923067[/C][/ROW]
[ROW][C]109[/C][C]2250794[/C][C]2087228.12939001[/C][C]163565.870609988[/C][/ROW]
[ROW][C]110[/C][C]2049866[/C][C]1980612.5658038[/C][C]69253.4341962035[/C][/ROW]
[ROW][C]111[/C][C]1861860[/C][C]1852190.2739027[/C][C]9669.72609730042[/C][/ROW]
[ROW][C]112[/C][C]1969422[/C][C]1920391.22503818[/C][C]49030.7749618213[/C][/ROW]
[ROW][C]113[/C][C]2022566[/C][C]1973700.15454719[/C][C]48865.8454528141[/C][/ROW]
[ROW][C]114[/C][C]1916278[/C][C]1930160.78163325[/C][C]-13882.7816332541[/C][/ROW]
[ROW][C]115[/C][C]1514422[/C][C]1644987.50102241[/C][C]-130565.501022412[/C][/ROW]
[ROW][C]116[/C][C]1339338[/C][C]1490060.42206892[/C][C]-150722.422068921[/C][/ROW]
[ROW][C]117[/C][C]1500044[/C][C]1571973.89823792[/C][C]-71929.8982379164[/C][/ROW]
[ROW][C]118[/C][C]1057966[/C][C]1262087.92827693[/C][C]-204121.92827693[/C][/ROW]
[ROW][C]119[/C][C]1540266[/C][C]1479248.48528906[/C][C]61017.5147109393[/C][/ROW]
[ROW][C]120[/C][C]1836016[/C][C]1587240.92633265[/C][C]248775.073667354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306982&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306982&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
1334294263429687.03850589-261.038505886216
1434294263422094.755113337331.24488666747
1534035823391281.7045336612300.2954663369
1633360603323329.563515112730.4364849008
1736847723674067.1353098110704.8646901865
1837379163727595.0844883210320.9155116822
1936576543527810.07818111129843.921818894
2034696483451181.4319588418466.5680411607
2135500923483851.9616445566240.0383554483
2234294263524829.48110142-95403.4811014212
2334838443515989.96489445-32145.9648944451
2435098703536223.1501991-26353.1501990966
2535369883564843.25565687-27855.2556568743
2634696483552781.934061-83133.9340609959
2734838443489621.04919109-5777.04919109168
2833892043412663.13048808-23459.1304880837
2936847723753976.09306062-69204.0930606192
3037781383774584.674373313553.32562668901
3136978763641037.5397070856838.4602929181
3235500923463187.0560120786904.9439879251
3337107983548701.17741256162096.822587445
3435369883522492.7101861814495.2898138175
3536978763597321.95828161100554.041718394
3636847723676345.289614868426.71038513631
3737249943723024.349032271969.65096772928
3835772103690122.41984721-112912.41984721
3937379163668573.9758589769342.0241410285
4037249943609198.16249055115795.837509449
4139661444008317.451391-42173.4513909961
4239117264101483.02336381-189757.023363807
4336978763926354.3767128-228478.376712798
4435901323651720.89793915-61588.8979391465
4537379163725347.6568680812568.3431319203
4635369883544595.73427913-7607.73427913105
4736847723658140.8576306926631.1423693141
4837107983644947.3223469965850.6776530123
4937652163703128.6136595162087.3863404859
5036447323615992.6709354728739.3290645294
5137107983760478.08395409-49680.0839540865
5237510203679410.5160534971609.4839465078
5338988043956708.7654082-57904.765408203
5437781383944168.33424274-166030.334242742
5536174323746437.90147072-129005.901470722
5634436223609272.81207773-165650.812077729
5736045103681924.91268467-77414.9126846706
5831622503451974.47908962-289724.479089617
5933762823459329.98924786-83047.9892478646
6034967663413737.9450834183028.0549165895
6136174323459167.37619213158264.623807865
6234436223384186.4617931359435.5382068711
6334436223474171.09773178-30549.0977317849
6434436223462990.17627502-19368.1762750242
6535369883598222.18525802-61234.1852580179
6634035823507050.33861981-103468.338619809
6732284983351978.03794668-123480.037946682
6830819883190071.30584605-108083.305846047
6931882763310819.36986097-122543.369860973
7027733162946256.12293912-172940.122939117
7130275703092853.95454596-65283.954545965
7231753543137326.7821920338027.2178079691
7332024723192646.914589139825.08541086968
7430546883008466.9693161146221.0306838877
7530676103021706.9205143445903.0794856572
7630275703032529.7020657-4959.70206570113
7731622503119757.7473062442492.2526937597
7830676103040630.9377803426979.0622196635
7928810602926460.48052563-45400.4805256254
8027461982806375.55214558-60177.552145578
8129742442913915.2337692460328.7662307606
8224790222609939.13749066-130917.137490658
8328006162814997.49926681-14381.4992668144
8429471262931510.826007415615.1739926026
8529471262956903.41286019-9777.41286019469
8627733162798130.99766288-24814.9976628846
8726126102780517.85726826-167907.85726826
8825996882674622.28490614-74934.2849061401
8927461982739284.817498436913.18250157358
9026126102640096.59402425-27486.5940242507
9123585382472999.4223937-114461.422393698
9221834542322224.18949024-138770.18949024
9323714602423107.51859104-51647.5185910389
9419293822026715.11000626-97333.1100062639
9523312382234678.2046641496559.7953358614
9625450882369038.54729089176049.452709112
9726126102425957.86835817186652.131641835
9824648262349128.31701236115697.682987643
9922780942301981.49307701-23887.4930770053
10024116822303411.41061985108270.589380146
10124648262475565.52562341-10739.52562341
10224246042361512.7281898263091.2718101786
10320225662194672.23199592-172106.231995918
10418360162018103.83315598-182087.833155975
10519694222133676.78457478-164254.784574778
10615675661713706.77342952-146140.773429524
10719825261966032.9222592916493.0777407144
10821303102086552.9195076943757.0804923067
10922507942087228.12939001163565.870609988
11020498661980612.565803869253.4341962035
11118618601852190.27390279669.72609730042
11219694221920391.2250381849030.7749618213
11320225661973700.1545471948865.8454528141
11419162781930160.78163325-13882.7816332541
11515144221644987.50102241-130565.501022412
11613393381490060.42206892-150722.422068921
11715000441571973.89823792-71929.8982379164
11810579661262087.92827693-204121.92827693
11915402661479248.4852890661017.5147109393
12018360161587240.92633265248775.073667354







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1211715906.775547471524063.363057171907750.18803777
1221530357.111229921326211.464391081734502.75806875
1231374883.045490771159741.115897161590024.97508437
1241426818.873353781191916.971496021661720.77521154
1251436556.858301621182631.573227971690482.14337527
1261349140.250944081083982.47318871614298.02869946
1271086380.10771699829922.357718641342837.85771534
128988904.620510051725289.6499134051252519.5911067
1291118164.54832419813641.2368218621422687.85982652
130834221.417421322558466.067462431109976.76738021
1311192710.37169937816299.6997487431569121.04364999
1321336611.60036299937414.0958584561735809.10486752

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 1715906.77554747 & 1524063.36305717 & 1907750.18803777 \tabularnewline
122 & 1530357.11122992 & 1326211.46439108 & 1734502.75806875 \tabularnewline
123 & 1374883.04549077 & 1159741.11589716 & 1590024.97508437 \tabularnewline
124 & 1426818.87335378 & 1191916.97149602 & 1661720.77521154 \tabularnewline
125 & 1436556.85830162 & 1182631.57322797 & 1690482.14337527 \tabularnewline
126 & 1349140.25094408 & 1083982.4731887 & 1614298.02869946 \tabularnewline
127 & 1086380.10771699 & 829922.35771864 & 1342837.85771534 \tabularnewline
128 & 988904.620510051 & 725289.649913405 & 1252519.5911067 \tabularnewline
129 & 1118164.54832419 & 813641.236821862 & 1422687.85982652 \tabularnewline
130 & 834221.417421322 & 558466.06746243 & 1109976.76738021 \tabularnewline
131 & 1192710.37169937 & 816299.699748743 & 1569121.04364999 \tabularnewline
132 & 1336611.60036299 & 937414.095858456 & 1735809.10486752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306982&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]1715906.77554747[/C][C]1524063.36305717[/C][C]1907750.18803777[/C][/ROW]
[ROW][C]122[/C][C]1530357.11122992[/C][C]1326211.46439108[/C][C]1734502.75806875[/C][/ROW]
[ROW][C]123[/C][C]1374883.04549077[/C][C]1159741.11589716[/C][C]1590024.97508437[/C][/ROW]
[ROW][C]124[/C][C]1426818.87335378[/C][C]1191916.97149602[/C][C]1661720.77521154[/C][/ROW]
[ROW][C]125[/C][C]1436556.85830162[/C][C]1182631.57322797[/C][C]1690482.14337527[/C][/ROW]
[ROW][C]126[/C][C]1349140.25094408[/C][C]1083982.4731887[/C][C]1614298.02869946[/C][/ROW]
[ROW][C]127[/C][C]1086380.10771699[/C][C]829922.35771864[/C][C]1342837.85771534[/C][/ROW]
[ROW][C]128[/C][C]988904.620510051[/C][C]725289.649913405[/C][C]1252519.5911067[/C][/ROW]
[ROW][C]129[/C][C]1118164.54832419[/C][C]813641.236821862[/C][C]1422687.85982652[/C][/ROW]
[ROW][C]130[/C][C]834221.417421322[/C][C]558466.06746243[/C][C]1109976.76738021[/C][/ROW]
[ROW][C]131[/C][C]1192710.37169937[/C][C]816299.699748743[/C][C]1569121.04364999[/C][/ROW]
[ROW][C]132[/C][C]1336611.60036299[/C][C]937414.095858456[/C][C]1735809.10486752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306982&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306982&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
1211715906.775547471524063.363057171907750.18803777
1221530357.111229921326211.464391081734502.75806875
1231374883.045490771159741.115897161590024.97508437
1241426818.873353781191916.971496021661720.77521154
1251436556.858301621182631.573227971690482.14337527
1261349140.250944081083982.47318871614298.02869946
1271086380.10771699829922.357718641342837.85771534
128988904.620510051725289.6499134051252519.5911067
1291118164.54832419813641.2368218621422687.85982652
130834221.417421322558466.067462431109976.76738021
1311192710.37169937816299.6997487431569121.04364999
1321336611.60036299937414.0958584561735809.10486752



Parameters (Session):
par1 = 121260additive12grey0.10.0112481212additive12 ; par2 = 112Tripleno0.990.99112Triple ; par3 = 0multiplicative0.10.010multiplicative ; par4 = 012012 ; par5 = 1212 ; par6 = White NoiseWhite Noise ; par7 = 0.950.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
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')