Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 26 Nov 2016 19:17:10 +0000
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/Nov/26/t1480187872x1qkt1orl5bi055.htm/, Retrieved Sat, 04 May 2024 00:17:45 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 00:17:45 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
97,78
97,73
97,61
97,69
97,68
97,67
97,67
97,96
98,27
99,52
99,59
99,75
99,75
99,8
99,99
100,25
100,08
100,08
100,08
100,06
101
101,81
101,82
101,96
101,96
101,93
102,03
102,11
102,07
102,34
102,34
102,33
102,77
103,08
103,38
103,44
99,1
99,15
99,21
99,01
99,08
99,11
100,11
100,31
100,55
101,38
101,49
101,5
100,69
100,8
100,58
100,34
100,38
100,33
101,06
101,15
101,36
101,98
102,24
102,34
101,91
101,8
101,8
101,73
101,8
101,81
102,28
101,7
101,7
102,37
102,43
102,41




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999944876394625
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999944876394625 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.999944876394625[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.999944876394625
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
297.7397.78-0.0499999999999972
397.6197.7300027561803-0.12000275618027
497.6997.61000661498460.0799933850154133
597.6897.6899955904762-0.00999559047620835
697.6797.680000550993-0.0100005509929986
797.6797.6700005512664-5.51266424508867e-07
897.9697.67000000003040.289999999969609
998.2797.95998401415440.310015985845553
1099.5298.26998291080111.25001708919886
1199.5999.51993109455130.0700689054487356
1299.7599.58999613754930.160003862450679
1399.7599.74999118001028.81998977320109e-06
1499.899.74999999951380.0500000004861931
1599.9999.79999724381970.190002756180291
16100.2599.9899895263630.260010473636953
17100.08100.249985667285-0.16998566728526
18100.08100.080009370223-9.37022284119848e-06
19100.08100.080000000517-5.16521936333447e-10
20100.06100.08-0.0200000000000244
21101100.0600011024720.939998897527886
22101.81100.9999481838720.810051816128279
23101.82101.8099553470230.0100446529766316
24101.96101.8199994463030.14000055369749
25101.96101.9599922826657.71733527926699e-06
26101.93101.959999999575-0.029999999574585
27102.03101.9300016537080.0999983462918692
28102.11102.0299944877310.0800055122693806
29102.07102.109995589808-0.0399955898077167
30102.34102.0700022047010.269997795298892
31102.34102.3399851167481.48832519215603e-05
32102.33102.33999999918-0.00999999917958405
33102.77102.3300005512360.439999448763984
34103.08102.7699757456440.31002425435598
35103.38103.0799829103450.300017089654645
36103.44103.3799834619760.0600165380236461
3799.1103.439996691672-4.33999669167204
3899.1599.1002392362650.0497607637350512
3999.2199.14999725700730.0600027429926939
4099.0199.2099966924325-0.199996692432464
4199.0899.01001102453880.0699889754612428
4299.1199.07999614195530.0300038580446653
43100.1199.10999834607921.00000165392083
44100.31100.1099448763030.200055123696544
45100.55100.309988972240.240011027759678
46101.38100.5499867697270.830013230273181
47101.49101.3799542466780.110045753321756
48101.5101.4899939338810.0100060661186774
49100.69101.49999944843-0.809999448429565
50100.8100.690044650090.109955349910038
51100.58100.799993938865-0.219993938864675
52100.34100.580012126859-0.240012126859071
53100.38100.3400132303340.0399867696662284
54100.33100.379997795785-0.0499977957850888
55101.06100.3300027560590.729997243941241
56101.15101.059959759920.0900402400800004
57101.36101.1499950366570.210004963342655
58101.98101.3599884237690.620011576230723
59102.24101.9799658227270.260034177273454
60102.34102.2399856659790.100014334021381
61101.91102.339994486849-0.429994486849324
62101.8101.910023702846-0.110023702846405
63101.8101.800006064903-6.06490317522912e-06
64101.73101.800000000334-0.0700000003343035
65101.8101.7300038586520.0699961413476018
66101.81101.799996141560.0100038584396884
67102.28101.8099994485510.470000551448734
68101.7102.279974091875-0.579974091875073
69101.7101.700031970263-3.19702629667518e-05
70102.37101.7000000017620.669999998237685
71102.43102.3699630671850.0600369328155068
72102.41102.429996690548-0.0199966905478135

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 97.73 & 97.78 & -0.0499999999999972 \tabularnewline
3 & 97.61 & 97.7300027561803 & -0.12000275618027 \tabularnewline
4 & 97.69 & 97.6100066149846 & 0.0799933850154133 \tabularnewline
5 & 97.68 & 97.6899955904762 & -0.00999559047620835 \tabularnewline
6 & 97.67 & 97.680000550993 & -0.0100005509929986 \tabularnewline
7 & 97.67 & 97.6700005512664 & -5.51266424508867e-07 \tabularnewline
8 & 97.96 & 97.6700000000304 & 0.289999999969609 \tabularnewline
9 & 98.27 & 97.9599840141544 & 0.310015985845553 \tabularnewline
10 & 99.52 & 98.2699829108011 & 1.25001708919886 \tabularnewline
11 & 99.59 & 99.5199310945513 & 0.0700689054487356 \tabularnewline
12 & 99.75 & 99.5899961375493 & 0.160003862450679 \tabularnewline
13 & 99.75 & 99.7499911800102 & 8.81998977320109e-06 \tabularnewline
14 & 99.8 & 99.7499999995138 & 0.0500000004861931 \tabularnewline
15 & 99.99 & 99.7999972438197 & 0.190002756180291 \tabularnewline
16 & 100.25 & 99.989989526363 & 0.260010473636953 \tabularnewline
17 & 100.08 & 100.249985667285 & -0.16998566728526 \tabularnewline
18 & 100.08 & 100.080009370223 & -9.37022284119848e-06 \tabularnewline
19 & 100.08 & 100.080000000517 & -5.16521936333447e-10 \tabularnewline
20 & 100.06 & 100.08 & -0.0200000000000244 \tabularnewline
21 & 101 & 100.060001102472 & 0.939998897527886 \tabularnewline
22 & 101.81 & 100.999948183872 & 0.810051816128279 \tabularnewline
23 & 101.82 & 101.809955347023 & 0.0100446529766316 \tabularnewline
24 & 101.96 & 101.819999446303 & 0.14000055369749 \tabularnewline
25 & 101.96 & 101.959992282665 & 7.71733527926699e-06 \tabularnewline
26 & 101.93 & 101.959999999575 & -0.029999999574585 \tabularnewline
27 & 102.03 & 101.930001653708 & 0.0999983462918692 \tabularnewline
28 & 102.11 & 102.029994487731 & 0.0800055122693806 \tabularnewline
29 & 102.07 & 102.109995589808 & -0.0399955898077167 \tabularnewline
30 & 102.34 & 102.070002204701 & 0.269997795298892 \tabularnewline
31 & 102.34 & 102.339985116748 & 1.48832519215603e-05 \tabularnewline
32 & 102.33 & 102.33999999918 & -0.00999999917958405 \tabularnewline
33 & 102.77 & 102.330000551236 & 0.439999448763984 \tabularnewline
34 & 103.08 & 102.769975745644 & 0.31002425435598 \tabularnewline
35 & 103.38 & 103.079982910345 & 0.300017089654645 \tabularnewline
36 & 103.44 & 103.379983461976 & 0.0600165380236461 \tabularnewline
37 & 99.1 & 103.439996691672 & -4.33999669167204 \tabularnewline
38 & 99.15 & 99.100239236265 & 0.0497607637350512 \tabularnewline
39 & 99.21 & 99.1499972570073 & 0.0600027429926939 \tabularnewline
40 & 99.01 & 99.2099966924325 & -0.199996692432464 \tabularnewline
41 & 99.08 & 99.0100110245388 & 0.0699889754612428 \tabularnewline
42 & 99.11 & 99.0799961419553 & 0.0300038580446653 \tabularnewline
43 & 100.11 & 99.1099983460792 & 1.00000165392083 \tabularnewline
44 & 100.31 & 100.109944876303 & 0.200055123696544 \tabularnewline
45 & 100.55 & 100.30998897224 & 0.240011027759678 \tabularnewline
46 & 101.38 & 100.549986769727 & 0.830013230273181 \tabularnewline
47 & 101.49 & 101.379954246678 & 0.110045753321756 \tabularnewline
48 & 101.5 & 101.489993933881 & 0.0100060661186774 \tabularnewline
49 & 100.69 & 101.49999944843 & -0.809999448429565 \tabularnewline
50 & 100.8 & 100.69004465009 & 0.109955349910038 \tabularnewline
51 & 100.58 & 100.799993938865 & -0.219993938864675 \tabularnewline
52 & 100.34 & 100.580012126859 & -0.240012126859071 \tabularnewline
53 & 100.38 & 100.340013230334 & 0.0399867696662284 \tabularnewline
54 & 100.33 & 100.379997795785 & -0.0499977957850888 \tabularnewline
55 & 101.06 & 100.330002756059 & 0.729997243941241 \tabularnewline
56 & 101.15 & 101.05995975992 & 0.0900402400800004 \tabularnewline
57 & 101.36 & 101.149995036657 & 0.210004963342655 \tabularnewline
58 & 101.98 & 101.359988423769 & 0.620011576230723 \tabularnewline
59 & 102.24 & 101.979965822727 & 0.260034177273454 \tabularnewline
60 & 102.34 & 102.239985665979 & 0.100014334021381 \tabularnewline
61 & 101.91 & 102.339994486849 & -0.429994486849324 \tabularnewline
62 & 101.8 & 101.910023702846 & -0.110023702846405 \tabularnewline
63 & 101.8 & 101.800006064903 & -6.06490317522912e-06 \tabularnewline
64 & 101.73 & 101.800000000334 & -0.0700000003343035 \tabularnewline
65 & 101.8 & 101.730003858652 & 0.0699961413476018 \tabularnewline
66 & 101.81 & 101.79999614156 & 0.0100038584396884 \tabularnewline
67 & 102.28 & 101.809999448551 & 0.470000551448734 \tabularnewline
68 & 101.7 & 102.279974091875 & -0.579974091875073 \tabularnewline
69 & 101.7 & 101.700031970263 & -3.19702629667518e-05 \tabularnewline
70 & 102.37 & 101.700000001762 & 0.669999998237685 \tabularnewline
71 & 102.43 & 102.369963067185 & 0.0600369328155068 \tabularnewline
72 & 102.41 & 102.429996690548 & -0.0199966905478135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]2[/C][C]97.73[/C][C]97.78[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]3[/C][C]97.61[/C][C]97.7300027561803[/C][C]-0.12000275618027[/C][/ROW]
[ROW][C]4[/C][C]97.69[/C][C]97.6100066149846[/C][C]0.0799933850154133[/C][/ROW]
[ROW][C]5[/C][C]97.68[/C][C]97.6899955904762[/C][C]-0.00999559047620835[/C][/ROW]
[ROW][C]6[/C][C]97.67[/C][C]97.680000550993[/C][C]-0.0100005509929986[/C][/ROW]
[ROW][C]7[/C][C]97.67[/C][C]97.6700005512664[/C][C]-5.51266424508867e-07[/C][/ROW]
[ROW][C]8[/C][C]97.96[/C][C]97.6700000000304[/C][C]0.289999999969609[/C][/ROW]
[ROW][C]9[/C][C]98.27[/C][C]97.9599840141544[/C][C]0.310015985845553[/C][/ROW]
[ROW][C]10[/C][C]99.52[/C][C]98.2699829108011[/C][C]1.25001708919886[/C][/ROW]
[ROW][C]11[/C][C]99.59[/C][C]99.5199310945513[/C][C]0.0700689054487356[/C][/ROW]
[ROW][C]12[/C][C]99.75[/C][C]99.5899961375493[/C][C]0.160003862450679[/C][/ROW]
[ROW][C]13[/C][C]99.75[/C][C]99.7499911800102[/C][C]8.81998977320109e-06[/C][/ROW]
[ROW][C]14[/C][C]99.8[/C][C]99.7499999995138[/C][C]0.0500000004861931[/C][/ROW]
[ROW][C]15[/C][C]99.99[/C][C]99.7999972438197[/C][C]0.190002756180291[/C][/ROW]
[ROW][C]16[/C][C]100.25[/C][C]99.989989526363[/C][C]0.260010473636953[/C][/ROW]
[ROW][C]17[/C][C]100.08[/C][C]100.249985667285[/C][C]-0.16998566728526[/C][/ROW]
[ROW][C]18[/C][C]100.08[/C][C]100.080009370223[/C][C]-9.37022284119848e-06[/C][/ROW]
[ROW][C]19[/C][C]100.08[/C][C]100.080000000517[/C][C]-5.16521936333447e-10[/C][/ROW]
[ROW][C]20[/C][C]100.06[/C][C]100.08[/C][C]-0.0200000000000244[/C][/ROW]
[ROW][C]21[/C][C]101[/C][C]100.060001102472[/C][C]0.939998897527886[/C][/ROW]
[ROW][C]22[/C][C]101.81[/C][C]100.999948183872[/C][C]0.810051816128279[/C][/ROW]
[ROW][C]23[/C][C]101.82[/C][C]101.809955347023[/C][C]0.0100446529766316[/C][/ROW]
[ROW][C]24[/C][C]101.96[/C][C]101.819999446303[/C][C]0.14000055369749[/C][/ROW]
[ROW][C]25[/C][C]101.96[/C][C]101.959992282665[/C][C]7.71733527926699e-06[/C][/ROW]
[ROW][C]26[/C][C]101.93[/C][C]101.959999999575[/C][C]-0.029999999574585[/C][/ROW]
[ROW][C]27[/C][C]102.03[/C][C]101.930001653708[/C][C]0.0999983462918692[/C][/ROW]
[ROW][C]28[/C][C]102.11[/C][C]102.029994487731[/C][C]0.0800055122693806[/C][/ROW]
[ROW][C]29[/C][C]102.07[/C][C]102.109995589808[/C][C]-0.0399955898077167[/C][/ROW]
[ROW][C]30[/C][C]102.34[/C][C]102.070002204701[/C][C]0.269997795298892[/C][/ROW]
[ROW][C]31[/C][C]102.34[/C][C]102.339985116748[/C][C]1.48832519215603e-05[/C][/ROW]
[ROW][C]32[/C][C]102.33[/C][C]102.33999999918[/C][C]-0.00999999917958405[/C][/ROW]
[ROW][C]33[/C][C]102.77[/C][C]102.330000551236[/C][C]0.439999448763984[/C][/ROW]
[ROW][C]34[/C][C]103.08[/C][C]102.769975745644[/C][C]0.31002425435598[/C][/ROW]
[ROW][C]35[/C][C]103.38[/C][C]103.079982910345[/C][C]0.300017089654645[/C][/ROW]
[ROW][C]36[/C][C]103.44[/C][C]103.379983461976[/C][C]0.0600165380236461[/C][/ROW]
[ROW][C]37[/C][C]99.1[/C][C]103.439996691672[/C][C]-4.33999669167204[/C][/ROW]
[ROW][C]38[/C][C]99.15[/C][C]99.100239236265[/C][C]0.0497607637350512[/C][/ROW]
[ROW][C]39[/C][C]99.21[/C][C]99.1499972570073[/C][C]0.0600027429926939[/C][/ROW]
[ROW][C]40[/C][C]99.01[/C][C]99.2099966924325[/C][C]-0.199996692432464[/C][/ROW]
[ROW][C]41[/C][C]99.08[/C][C]99.0100110245388[/C][C]0.0699889754612428[/C][/ROW]
[ROW][C]42[/C][C]99.11[/C][C]99.0799961419553[/C][C]0.0300038580446653[/C][/ROW]
[ROW][C]43[/C][C]100.11[/C][C]99.1099983460792[/C][C]1.00000165392083[/C][/ROW]
[ROW][C]44[/C][C]100.31[/C][C]100.109944876303[/C][C]0.200055123696544[/C][/ROW]
[ROW][C]45[/C][C]100.55[/C][C]100.30998897224[/C][C]0.240011027759678[/C][/ROW]
[ROW][C]46[/C][C]101.38[/C][C]100.549986769727[/C][C]0.830013230273181[/C][/ROW]
[ROW][C]47[/C][C]101.49[/C][C]101.379954246678[/C][C]0.110045753321756[/C][/ROW]
[ROW][C]48[/C][C]101.5[/C][C]101.489993933881[/C][C]0.0100060661186774[/C][/ROW]
[ROW][C]49[/C][C]100.69[/C][C]101.49999944843[/C][C]-0.809999448429565[/C][/ROW]
[ROW][C]50[/C][C]100.8[/C][C]100.69004465009[/C][C]0.109955349910038[/C][/ROW]
[ROW][C]51[/C][C]100.58[/C][C]100.799993938865[/C][C]-0.219993938864675[/C][/ROW]
[ROW][C]52[/C][C]100.34[/C][C]100.580012126859[/C][C]-0.240012126859071[/C][/ROW]
[ROW][C]53[/C][C]100.38[/C][C]100.340013230334[/C][C]0.0399867696662284[/C][/ROW]
[ROW][C]54[/C][C]100.33[/C][C]100.379997795785[/C][C]-0.0499977957850888[/C][/ROW]
[ROW][C]55[/C][C]101.06[/C][C]100.330002756059[/C][C]0.729997243941241[/C][/ROW]
[ROW][C]56[/C][C]101.15[/C][C]101.05995975992[/C][C]0.0900402400800004[/C][/ROW]
[ROW][C]57[/C][C]101.36[/C][C]101.149995036657[/C][C]0.210004963342655[/C][/ROW]
[ROW][C]58[/C][C]101.98[/C][C]101.359988423769[/C][C]0.620011576230723[/C][/ROW]
[ROW][C]59[/C][C]102.24[/C][C]101.979965822727[/C][C]0.260034177273454[/C][/ROW]
[ROW][C]60[/C][C]102.34[/C][C]102.239985665979[/C][C]0.100014334021381[/C][/ROW]
[ROW][C]61[/C][C]101.91[/C][C]102.339994486849[/C][C]-0.429994486849324[/C][/ROW]
[ROW][C]62[/C][C]101.8[/C][C]101.910023702846[/C][C]-0.110023702846405[/C][/ROW]
[ROW][C]63[/C][C]101.8[/C][C]101.800006064903[/C][C]-6.06490317522912e-06[/C][/ROW]
[ROW][C]64[/C][C]101.73[/C][C]101.800000000334[/C][C]-0.0700000003343035[/C][/ROW]
[ROW][C]65[/C][C]101.8[/C][C]101.730003858652[/C][C]0.0699961413476018[/C][/ROW]
[ROW][C]66[/C][C]101.81[/C][C]101.79999614156[/C][C]0.0100038584396884[/C][/ROW]
[ROW][C]67[/C][C]102.28[/C][C]101.809999448551[/C][C]0.470000551448734[/C][/ROW]
[ROW][C]68[/C][C]101.7[/C][C]102.279974091875[/C][C]-0.579974091875073[/C][/ROW]
[ROW][C]69[/C][C]101.7[/C][C]101.700031970263[/C][C]-3.19702629667518e-05[/C][/ROW]
[ROW][C]70[/C][C]102.37[/C][C]101.700000001762[/C][C]0.669999998237685[/C][/ROW]
[ROW][C]71[/C][C]102.43[/C][C]102.369963067185[/C][C]0.0600369328155068[/C][/ROW]
[ROW][C]72[/C][C]102.41[/C][C]102.429996690548[/C][C]-0.0199966905478135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
297.7397.78-0.0499999999999972
397.6197.7300027561803-0.12000275618027
497.6997.61000661498460.0799933850154133
597.6897.6899955904762-0.00999559047620835
697.6797.680000550993-0.0100005509929986
797.6797.6700005512664-5.51266424508867e-07
897.9697.67000000003040.289999999969609
998.2797.95998401415440.310015985845553
1099.5298.26998291080111.25001708919886
1199.5999.51993109455130.0700689054487356
1299.7599.58999613754930.160003862450679
1399.7599.74999118001028.81998977320109e-06
1499.899.74999999951380.0500000004861931
1599.9999.79999724381970.190002756180291
16100.2599.9899895263630.260010473636953
17100.08100.249985667285-0.16998566728526
18100.08100.080009370223-9.37022284119848e-06
19100.08100.080000000517-5.16521936333447e-10
20100.06100.08-0.0200000000000244
21101100.0600011024720.939998897527886
22101.81100.9999481838720.810051816128279
23101.82101.8099553470230.0100446529766316
24101.96101.8199994463030.14000055369749
25101.96101.9599922826657.71733527926699e-06
26101.93101.959999999575-0.029999999574585
27102.03101.9300016537080.0999983462918692
28102.11102.0299944877310.0800055122693806
29102.07102.109995589808-0.0399955898077167
30102.34102.0700022047010.269997795298892
31102.34102.3399851167481.48832519215603e-05
32102.33102.33999999918-0.00999999917958405
33102.77102.3300005512360.439999448763984
34103.08102.7699757456440.31002425435598
35103.38103.0799829103450.300017089654645
36103.44103.3799834619760.0600165380236461
3799.1103.439996691672-4.33999669167204
3899.1599.1002392362650.0497607637350512
3999.2199.14999725700730.0600027429926939
4099.0199.2099966924325-0.199996692432464
4199.0899.01001102453880.0699889754612428
4299.1199.07999614195530.0300038580446653
43100.1199.10999834607921.00000165392083
44100.31100.1099448763030.200055123696544
45100.55100.309988972240.240011027759678
46101.38100.5499867697270.830013230273181
47101.49101.3799542466780.110045753321756
48101.5101.4899939338810.0100060661186774
49100.69101.49999944843-0.809999448429565
50100.8100.690044650090.109955349910038
51100.58100.799993938865-0.219993938864675
52100.34100.580012126859-0.240012126859071
53100.38100.3400132303340.0399867696662284
54100.33100.379997795785-0.0499977957850888
55101.06100.3300027560590.729997243941241
56101.15101.059959759920.0900402400800004
57101.36101.1499950366570.210004963342655
58101.98101.3599884237690.620011576230723
59102.24101.9799658227270.260034177273454
60102.34102.2399856659790.100014334021381
61101.91102.339994486849-0.429994486849324
62101.8101.910023702846-0.110023702846405
63101.8101.800006064903-6.06490317522912e-06
64101.73101.800000000334-0.0700000003343035
65101.8101.7300038586520.0699961413476018
66101.81101.799996141560.0100038584396884
67102.28101.8099994485510.470000551448734
68101.7102.279974091875-0.579974091875073
69101.7101.700031970263-3.19702629667518e-05
70102.37101.7000000017620.669999998237685
71102.43102.3699630671850.0600369328155068
72102.41102.429996690548-0.0199966905478135







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.41000110229101.183904682399103.63609752218
74102.41000110229100.676086706968104.143915497611
75102.41000110229100.286417849922104.533584354658
76102.4100011022999.9579096420923104.862092562487
77102.4100011022999.6684870628203105.151515141759
78102.4100011022999.4068284585607105.413173746019
79102.4100011022999.1662081638491105.65379404073
80102.4100011022998.9422439990727105.877758205507
81102.4100011022998.7318920736791106.0881101309
82102.4100011022998.5329361394884106.287066065091
83102.4100011022998.343703102239106.47629910234
84102.4100011022998.1628931304281106.657109074151

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.41000110229 & 101.183904682399 & 103.63609752218 \tabularnewline
74 & 102.41000110229 & 100.676086706968 & 104.143915497611 \tabularnewline
75 & 102.41000110229 & 100.286417849922 & 104.533584354658 \tabularnewline
76 & 102.41000110229 & 99.9579096420923 & 104.862092562487 \tabularnewline
77 & 102.41000110229 & 99.6684870628203 & 105.151515141759 \tabularnewline
78 & 102.41000110229 & 99.4068284585607 & 105.413173746019 \tabularnewline
79 & 102.41000110229 & 99.1662081638491 & 105.65379404073 \tabularnewline
80 & 102.41000110229 & 98.9422439990727 & 105.877758205507 \tabularnewline
81 & 102.41000110229 & 98.7318920736791 & 106.0881101309 \tabularnewline
82 & 102.41000110229 & 98.5329361394884 & 106.287066065091 \tabularnewline
83 & 102.41000110229 & 98.343703102239 & 106.47629910234 \tabularnewline
84 & 102.41000110229 & 98.1628931304281 & 106.657109074151 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]73[/C][C]102.41000110229[/C][C]101.183904682399[/C][C]103.63609752218[/C][/ROW]
[ROW][C]74[/C][C]102.41000110229[/C][C]100.676086706968[/C][C]104.143915497611[/C][/ROW]
[ROW][C]75[/C][C]102.41000110229[/C][C]100.286417849922[/C][C]104.533584354658[/C][/ROW]
[ROW][C]76[/C][C]102.41000110229[/C][C]99.9579096420923[/C][C]104.862092562487[/C][/ROW]
[ROW][C]77[/C][C]102.41000110229[/C][C]99.6684870628203[/C][C]105.151515141759[/C][/ROW]
[ROW][C]78[/C][C]102.41000110229[/C][C]99.4068284585607[/C][C]105.413173746019[/C][/ROW]
[ROW][C]79[/C][C]102.41000110229[/C][C]99.1662081638491[/C][C]105.65379404073[/C][/ROW]
[ROW][C]80[/C][C]102.41000110229[/C][C]98.9422439990727[/C][C]105.877758205507[/C][/ROW]
[ROW][C]81[/C][C]102.41000110229[/C][C]98.7318920736791[/C][C]106.0881101309[/C][/ROW]
[ROW][C]82[/C][C]102.41000110229[/C][C]98.5329361394884[/C][C]106.287066065091[/C][/ROW]
[ROW][C]83[/C][C]102.41000110229[/C][C]98.343703102239[/C][C]106.47629910234[/C][/ROW]
[ROW][C]84[/C][C]102.41000110229[/C][C]98.1628931304281[/C][C]106.657109074151[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
73102.41000110229101.183904682399103.63609752218
74102.41000110229100.676086706968104.143915497611
75102.41000110229100.286417849922104.533584354658
76102.4100011022999.9579096420923104.862092562487
77102.4100011022999.6684870628203105.151515141759
78102.4100011022999.4068284585607105.413173746019
79102.4100011022999.1662081638491105.65379404073
80102.4100011022998.9422439990727105.877758205507
81102.4100011022998.7318920736791106.0881101309
82102.4100011022998.5329361394884106.287066065091
83102.4100011022998.343703102239106.47629910234
84102.4100011022998.1628931304281106.657109074151



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')