Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 12 May 2012 13:34:50 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/12/t1336844126dx38yj74hp4digh.htm/, Retrieved Sun, 05 May 2024 14:23:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166429, Retrieved Sun, 05 May 2024 14:23:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact173
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Additief Triple e...] [2012-05-12 17:34:50] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
62.11
62.15
62.2
62.22
62.02
62.02
62.02
62.07
62.31
62.71
62.77
62.82
62.82
62.82
62.55
62.6
62.47
62.47
62.47
62.72
63.13
64.09
64.31
64.29
64.29
64.29
64.35
64.42
64.24
64.23
64.23
64.2
65.35
65.83
66.15
66.19
66.19
66.56
66.59
66.48
66.4
66.4
66.4
66.49
66.65
67.69
67.91
68.14
68.14
68.16
67.94
68
68.1
68.12
68.12
68.24
68.42
68.97
69.13
69.2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166429&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166429&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166429&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.956068916392835
beta0.0405462289899447
gamma0.293993472656916

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.956068916392835 \tabularnewline
beta & 0.0405462289899447 \tabularnewline
gamma & 0.293993472656916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166429&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]0.956068916392835[/C][/ROW]
[ROW][C]beta[/C][C]0.0405462289899447[/C][/ROW]
[ROW][C]gamma[/C][C]0.293993472656916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166429&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166429&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
alpha0.956068916392835
beta0.0405462289899447
gamma0.293993472656916







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1362.8262.58805555555560.231944444444437
1462.8262.8286502379546-0.00865023795456921
1562.5562.5534678300148-0.00346783001480588
1662.662.57268906415850.02731093584147
1762.4762.41239562775570.057604372244306
1862.4762.40954783713710.0604521628629229
1962.4762.7730161580507-0.303016158050667
2062.7262.53390396381340.186096036186619
2163.1362.97463074595060.155369254049376
2264.0963.56408682757650.525913172423522
2364.3164.18402878350820.125971216491791
2464.2964.4135652731942-0.123565273194188
2564.2964.3527333424018-0.0627333424018275
2664.2964.3331926827601-0.0431926827600506
2764.3564.04841753203010.301582467969894
2864.4264.39487594903670.0251240509632709
2964.2464.2679887321836-0.027988732183573
3064.2364.21513257848340.0148674215165983
3164.2364.5603450585548-0.330345058554812
3264.264.3303829234862-0.130382923486181
3365.3564.48483012233220.865169877667753
3465.8365.80189863570110.0281013642988484
3566.1565.9656434717710.184356528229003
3666.1966.2749514798159-0.0849514798158992
3766.1966.2804935449168-0.0904935449167823
3866.5666.26225934746340.297740652536561
3966.5966.34870391756620.241296082433792
4066.4866.672427838371-0.192427838370961
4166.466.3669006786450.0330993213549675
4266.466.4054111302355-0.00541113023552953
4366.466.7583999538617-0.358399953861706
4466.4966.5347330707572-0.044733070757232
4566.6566.8177807253501-0.16778072535007
4667.6967.13027911757330.559720882426717
4767.9167.81872814183110.0912718581688807
4868.1468.0463753149190.0936246850809539
4968.1468.2403121846026-0.100312184602586
5068.1668.2350595539487-0.0750595539487335
5167.9467.967255474426-0.0272554744259992
526868.0211165076036-0.0211165076035655
5368.167.88142110204770.218578897952256
5468.1268.10308907598280.0169109240171963
5568.1268.4800492702919-0.360049270291853
5668.2468.265981699409-0.0259816994090443
5768.4268.5732196608156-0.153219660815608
5868.9768.91745182529230.0525481747077237
5969.1369.10371439219940.0262856078006308
6069.269.2554972623938-0.0554972623938284

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 62.82 & 62.5880555555556 & 0.231944444444437 \tabularnewline
14 & 62.82 & 62.8286502379546 & -0.00865023795456921 \tabularnewline
15 & 62.55 & 62.5534678300148 & -0.00346783001480588 \tabularnewline
16 & 62.6 & 62.5726890641585 & 0.02731093584147 \tabularnewline
17 & 62.47 & 62.4123956277557 & 0.057604372244306 \tabularnewline
18 & 62.47 & 62.4095478371371 & 0.0604521628629229 \tabularnewline
19 & 62.47 & 62.7730161580507 & -0.303016158050667 \tabularnewline
20 & 62.72 & 62.5339039638134 & 0.186096036186619 \tabularnewline
21 & 63.13 & 62.9746307459506 & 0.155369254049376 \tabularnewline
22 & 64.09 & 63.5640868275765 & 0.525913172423522 \tabularnewline
23 & 64.31 & 64.1840287835082 & 0.125971216491791 \tabularnewline
24 & 64.29 & 64.4135652731942 & -0.123565273194188 \tabularnewline
25 & 64.29 & 64.3527333424018 & -0.0627333424018275 \tabularnewline
26 & 64.29 & 64.3331926827601 & -0.0431926827600506 \tabularnewline
27 & 64.35 & 64.0484175320301 & 0.301582467969894 \tabularnewline
28 & 64.42 & 64.3948759490367 & 0.0251240509632709 \tabularnewline
29 & 64.24 & 64.2679887321836 & -0.027988732183573 \tabularnewline
30 & 64.23 & 64.2151325784834 & 0.0148674215165983 \tabularnewline
31 & 64.23 & 64.5603450585548 & -0.330345058554812 \tabularnewline
32 & 64.2 & 64.3303829234862 & -0.130382923486181 \tabularnewline
33 & 65.35 & 64.4848301223322 & 0.865169877667753 \tabularnewline
34 & 65.83 & 65.8018986357011 & 0.0281013642988484 \tabularnewline
35 & 66.15 & 65.965643471771 & 0.184356528229003 \tabularnewline
36 & 66.19 & 66.2749514798159 & -0.0849514798158992 \tabularnewline
37 & 66.19 & 66.2804935449168 & -0.0904935449167823 \tabularnewline
38 & 66.56 & 66.2622593474634 & 0.297740652536561 \tabularnewline
39 & 66.59 & 66.3487039175662 & 0.241296082433792 \tabularnewline
40 & 66.48 & 66.672427838371 & -0.192427838370961 \tabularnewline
41 & 66.4 & 66.366900678645 & 0.0330993213549675 \tabularnewline
42 & 66.4 & 66.4054111302355 & -0.00541113023552953 \tabularnewline
43 & 66.4 & 66.7583999538617 & -0.358399953861706 \tabularnewline
44 & 66.49 & 66.5347330707572 & -0.044733070757232 \tabularnewline
45 & 66.65 & 66.8177807253501 & -0.16778072535007 \tabularnewline
46 & 67.69 & 67.1302791175733 & 0.559720882426717 \tabularnewline
47 & 67.91 & 67.8187281418311 & 0.0912718581688807 \tabularnewline
48 & 68.14 & 68.046375314919 & 0.0936246850809539 \tabularnewline
49 & 68.14 & 68.2403121846026 & -0.100312184602586 \tabularnewline
50 & 68.16 & 68.2350595539487 & -0.0750595539487335 \tabularnewline
51 & 67.94 & 67.967255474426 & -0.0272554744259992 \tabularnewline
52 & 68 & 68.0211165076036 & -0.0211165076035655 \tabularnewline
53 & 68.1 & 67.8814211020477 & 0.218578897952256 \tabularnewline
54 & 68.12 & 68.1030890759828 & 0.0169109240171963 \tabularnewline
55 & 68.12 & 68.4800492702919 & -0.360049270291853 \tabularnewline
56 & 68.24 & 68.265981699409 & -0.0259816994090443 \tabularnewline
57 & 68.42 & 68.5732196608156 & -0.153219660815608 \tabularnewline
58 & 68.97 & 68.9174518252923 & 0.0525481747077237 \tabularnewline
59 & 69.13 & 69.1037143921994 & 0.0262856078006308 \tabularnewline
60 & 69.2 & 69.2554972623938 & -0.0554972623938284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166429&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]62.82[/C][C]62.5880555555556[/C][C]0.231944444444437[/C][/ROW]
[ROW][C]14[/C][C]62.82[/C][C]62.8286502379546[/C][C]-0.00865023795456921[/C][/ROW]
[ROW][C]15[/C][C]62.55[/C][C]62.5534678300148[/C][C]-0.00346783001480588[/C][/ROW]
[ROW][C]16[/C][C]62.6[/C][C]62.5726890641585[/C][C]0.02731093584147[/C][/ROW]
[ROW][C]17[/C][C]62.47[/C][C]62.4123956277557[/C][C]0.057604372244306[/C][/ROW]
[ROW][C]18[/C][C]62.47[/C][C]62.4095478371371[/C][C]0.0604521628629229[/C][/ROW]
[ROW][C]19[/C][C]62.47[/C][C]62.7730161580507[/C][C]-0.303016158050667[/C][/ROW]
[ROW][C]20[/C][C]62.72[/C][C]62.5339039638134[/C][C]0.186096036186619[/C][/ROW]
[ROW][C]21[/C][C]63.13[/C][C]62.9746307459506[/C][C]0.155369254049376[/C][/ROW]
[ROW][C]22[/C][C]64.09[/C][C]63.5640868275765[/C][C]0.525913172423522[/C][/ROW]
[ROW][C]23[/C][C]64.31[/C][C]64.1840287835082[/C][C]0.125971216491791[/C][/ROW]
[ROW][C]24[/C][C]64.29[/C][C]64.4135652731942[/C][C]-0.123565273194188[/C][/ROW]
[ROW][C]25[/C][C]64.29[/C][C]64.3527333424018[/C][C]-0.0627333424018275[/C][/ROW]
[ROW][C]26[/C][C]64.29[/C][C]64.3331926827601[/C][C]-0.0431926827600506[/C][/ROW]
[ROW][C]27[/C][C]64.35[/C][C]64.0484175320301[/C][C]0.301582467969894[/C][/ROW]
[ROW][C]28[/C][C]64.42[/C][C]64.3948759490367[/C][C]0.0251240509632709[/C][/ROW]
[ROW][C]29[/C][C]64.24[/C][C]64.2679887321836[/C][C]-0.027988732183573[/C][/ROW]
[ROW][C]30[/C][C]64.23[/C][C]64.2151325784834[/C][C]0.0148674215165983[/C][/ROW]
[ROW][C]31[/C][C]64.23[/C][C]64.5603450585548[/C][C]-0.330345058554812[/C][/ROW]
[ROW][C]32[/C][C]64.2[/C][C]64.3303829234862[/C][C]-0.130382923486181[/C][/ROW]
[ROW][C]33[/C][C]65.35[/C][C]64.4848301223322[/C][C]0.865169877667753[/C][/ROW]
[ROW][C]34[/C][C]65.83[/C][C]65.8018986357011[/C][C]0.0281013642988484[/C][/ROW]
[ROW][C]35[/C][C]66.15[/C][C]65.965643471771[/C][C]0.184356528229003[/C][/ROW]
[ROW][C]36[/C][C]66.19[/C][C]66.2749514798159[/C][C]-0.0849514798158992[/C][/ROW]
[ROW][C]37[/C][C]66.19[/C][C]66.2804935449168[/C][C]-0.0904935449167823[/C][/ROW]
[ROW][C]38[/C][C]66.56[/C][C]66.2622593474634[/C][C]0.297740652536561[/C][/ROW]
[ROW][C]39[/C][C]66.59[/C][C]66.3487039175662[/C][C]0.241296082433792[/C][/ROW]
[ROW][C]40[/C][C]66.48[/C][C]66.672427838371[/C][C]-0.192427838370961[/C][/ROW]
[ROW][C]41[/C][C]66.4[/C][C]66.366900678645[/C][C]0.0330993213549675[/C][/ROW]
[ROW][C]42[/C][C]66.4[/C][C]66.4054111302355[/C][C]-0.00541113023552953[/C][/ROW]
[ROW][C]43[/C][C]66.4[/C][C]66.7583999538617[/C][C]-0.358399953861706[/C][/ROW]
[ROW][C]44[/C][C]66.49[/C][C]66.5347330707572[/C][C]-0.044733070757232[/C][/ROW]
[ROW][C]45[/C][C]66.65[/C][C]66.8177807253501[/C][C]-0.16778072535007[/C][/ROW]
[ROW][C]46[/C][C]67.69[/C][C]67.1302791175733[/C][C]0.559720882426717[/C][/ROW]
[ROW][C]47[/C][C]67.91[/C][C]67.8187281418311[/C][C]0.0912718581688807[/C][/ROW]
[ROW][C]48[/C][C]68.14[/C][C]68.046375314919[/C][C]0.0936246850809539[/C][/ROW]
[ROW][C]49[/C][C]68.14[/C][C]68.2403121846026[/C][C]-0.100312184602586[/C][/ROW]
[ROW][C]50[/C][C]68.16[/C][C]68.2350595539487[/C][C]-0.0750595539487335[/C][/ROW]
[ROW][C]51[/C][C]67.94[/C][C]67.967255474426[/C][C]-0.0272554744259992[/C][/ROW]
[ROW][C]52[/C][C]68[/C][C]68.0211165076036[/C][C]-0.0211165076035655[/C][/ROW]
[ROW][C]53[/C][C]68.1[/C][C]67.8814211020477[/C][C]0.218578897952256[/C][/ROW]
[ROW][C]54[/C][C]68.12[/C][C]68.1030890759828[/C][C]0.0169109240171963[/C][/ROW]
[ROW][C]55[/C][C]68.12[/C][C]68.4800492702919[/C][C]-0.360049270291853[/C][/ROW]
[ROW][C]56[/C][C]68.24[/C][C]68.265981699409[/C][C]-0.0259816994090443[/C][/ROW]
[ROW][C]57[/C][C]68.42[/C][C]68.5732196608156[/C][C]-0.153219660815608[/C][/ROW]
[ROW][C]58[/C][C]68.97[/C][C]68.9174518252923[/C][C]0.0525481747077237[/C][/ROW]
[ROW][C]59[/C][C]69.13[/C][C]69.1037143921994[/C][C]0.0262856078006308[/C][/ROW]
[ROW][C]60[/C][C]69.2[/C][C]69.2554972623938[/C][C]-0.0554972623938284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166429&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166429&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
1362.8262.58805555555560.231944444444437
1462.8262.8286502379546-0.00865023795456921
1562.5562.5534678300148-0.00346783001480588
1662.662.57268906415850.02731093584147
1762.4762.41239562775570.057604372244306
1862.4762.40954783713710.0604521628629229
1962.4762.7730161580507-0.303016158050667
2062.7262.53390396381340.186096036186619
2163.1362.97463074595060.155369254049376
2264.0963.56408682757650.525913172423522
2364.3164.18402878350820.125971216491791
2464.2964.4135652731942-0.123565273194188
2564.2964.3527333424018-0.0627333424018275
2664.2964.3331926827601-0.0431926827600506
2764.3564.04841753203010.301582467969894
2864.4264.39487594903670.0251240509632709
2964.2464.2679887321836-0.027988732183573
3064.2364.21513257848340.0148674215165983
3164.2364.5603450585548-0.330345058554812
3264.264.3303829234862-0.130382923486181
3365.3564.48483012233220.865169877667753
3465.8365.80189863570110.0281013642988484
3566.1565.9656434717710.184356528229003
3666.1966.2749514798159-0.0849514798158992
3766.1966.2804935449168-0.0904935449167823
3866.5666.26225934746340.297740652536561
3966.5966.34870391756620.241296082433792
4066.4866.672427838371-0.192427838370961
4166.466.3669006786450.0330993213549675
4266.466.4054111302355-0.00541113023552953
4366.466.7583999538617-0.358399953861706
4466.4966.5347330707572-0.044733070757232
4566.6566.8177807253501-0.16778072535007
4667.6967.13027911757330.559720882426717
4767.9167.81872814183110.0912718581688807
4868.1468.0463753149190.0936246850809539
4968.1468.2403121846026-0.100312184602586
5068.1668.2350595539487-0.0750595539487335
5167.9467.967255474426-0.0272554744259992
526868.0211165076036-0.0211165076035655
5368.167.88142110204770.218578897952256
5468.1268.10308907598280.0169109240171963
5568.1268.4800492702919-0.360049270291853
5668.2468.265981699409-0.0259816994090443
5768.4268.5732196608156-0.153219660815608
5868.9768.91745182529230.0525481747077237
5969.1369.10371439219940.0262856078006308
6069.269.2554972623938-0.0554972623938284







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6169.284814423615368.843078934199669.7265499130309
6269.360137837052768.737041078552469.9832345955531
6369.151967491346868.379495864809169.9244391178844
6469.220276698248868.314128130620770.126425265877
6569.092995259182768.062454399813670.1235361185518
6669.083738256865767.934814161723370.2326623520082
6769.419662426218868.156441138687470.6828837137503
6869.54809930580568.173433800527670.9227648110825
6969.873499308102168.389402033416571.3575965827877
7070.367782252182768.775666401118471.9598981032469
7170.502333560245668.80317017999372.2014969404982
7270.625777964374968.820202958061872.431352970688

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 69.2848144236153 & 68.8430789341996 & 69.7265499130309 \tabularnewline
62 & 69.3601378370527 & 68.7370410785524 & 69.9832345955531 \tabularnewline
63 & 69.1519674913468 & 68.3794958648091 & 69.9244391178844 \tabularnewline
64 & 69.2202766982488 & 68.3141281306207 & 70.126425265877 \tabularnewline
65 & 69.0929952591827 & 68.0624543998136 & 70.1235361185518 \tabularnewline
66 & 69.0837382568657 & 67.9348141617233 & 70.2326623520082 \tabularnewline
67 & 69.4196624262188 & 68.1564411386874 & 70.6828837137503 \tabularnewline
68 & 69.548099305805 & 68.1734338005276 & 70.9227648110825 \tabularnewline
69 & 69.8734993081021 & 68.3894020334165 & 71.3575965827877 \tabularnewline
70 & 70.3677822521827 & 68.7756664011184 & 71.9598981032469 \tabularnewline
71 & 70.5023335602456 & 68.803170179993 & 72.2014969404982 \tabularnewline
72 & 70.6257779643749 & 68.8202029580618 & 72.431352970688 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166429&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]61[/C][C]69.2848144236153[/C][C]68.8430789341996[/C][C]69.7265499130309[/C][/ROW]
[ROW][C]62[/C][C]69.3601378370527[/C][C]68.7370410785524[/C][C]69.9832345955531[/C][/ROW]
[ROW][C]63[/C][C]69.1519674913468[/C][C]68.3794958648091[/C][C]69.9244391178844[/C][/ROW]
[ROW][C]64[/C][C]69.2202766982488[/C][C]68.3141281306207[/C][C]70.126425265877[/C][/ROW]
[ROW][C]65[/C][C]69.0929952591827[/C][C]68.0624543998136[/C][C]70.1235361185518[/C][/ROW]
[ROW][C]66[/C][C]69.0837382568657[/C][C]67.9348141617233[/C][C]70.2326623520082[/C][/ROW]
[ROW][C]67[/C][C]69.4196624262188[/C][C]68.1564411386874[/C][C]70.6828837137503[/C][/ROW]
[ROW][C]68[/C][C]69.548099305805[/C][C]68.1734338005276[/C][C]70.9227648110825[/C][/ROW]
[ROW][C]69[/C][C]69.8734993081021[/C][C]68.3894020334165[/C][C]71.3575965827877[/C][/ROW]
[ROW][C]70[/C][C]70.3677822521827[/C][C]68.7756664011184[/C][C]71.9598981032469[/C][/ROW]
[ROW][C]71[/C][C]70.5023335602456[/C][C]68.803170179993[/C][C]72.2014969404982[/C][/ROW]
[ROW][C]72[/C][C]70.6257779643749[/C][C]68.8202029580618[/C][C]72.431352970688[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166429&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166429&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
6169.284814423615368.843078934199669.7265499130309
6269.360137837052768.737041078552469.9832345955531
6369.151967491346868.379495864809169.9244391178844
6469.220276698248868.314128130620770.126425265877
6569.092995259182768.062454399813670.1235361185518
6669.083738256865767.934814161723370.2326623520082
6769.419662426218868.156441138687470.6828837137503
6869.54809930580568.173433800527670.9227648110825
6969.873499308102168.389402033416571.3575965827877
7070.367782252182768.775666401118471.9598981032469
7170.502333560245668.80317017999372.2014969404982
7270.625777964374968.820202958061872.431352970688



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')