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 computationFri, 21 Dec 2012 15:03:17 -0500
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/Dec/21/t1356120207cwznap46hu72zce.htm/, Retrieved Fri, 29 Mar 2024 07:15:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204187, Retrieved Fri, 29 Mar 2024 07:15:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Decomposition by Loess] [] [2012-11-11 14:33:50] [d67971843857ce8a39847b8686da437b]
- RMP     [Exponential Smoothing] [] [2012-12-21 20:03:17] [13972f3e090f04e91ee8432db4988af4] [Current]
Feedback Forum

Post a new message
Dataseries X:
9700
9081
9084
9743
8587
9731
9563
9998
9437
10038
9918
9252
9737
9035
9133
9487
8700
9627
8947
9283
8829
9947
9628
9318
9605
8640
9214
9567
8547
9185
9470
9123
9278
10170
9434
9655
9429
8739
9552
9687
9019
9672
9206
9069
9788
10312
10105
9863
9656
9295
9946
9701
9049
10190
9706
9765
9893
9994
10433
10073
10112
9266
9820
10097
9115
10411
9678
10408
10153
10368
10581
10597
10680
9738
9556




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204187&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204187&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204187&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 time4 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.536600454093893
beta0.263284283989902
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.536600454093893 \tabularnewline
beta & 0.263284283989902 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204187&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]0.536600454093893[/C][/ROW]
[ROW][C]beta[/C][C]0.263284283989902[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204187&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204187&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
alpha0.536600454093893
beta0.263284283989902
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
390848462622
497438264.640688512851478.35931148715
585878735.66450867064-148.664508670643
697318312.62351432531418.3764856747
795638930.84348372501632.156516274987
899989216.48756363634781.512436363664
994379692.68697652768-255.686976527675
10100389576.20164956744461.798350432558
1199189909.961437569438.03856243056907
12925210001.3691930518-749.369193051811
1397379580.48187268773156.518127312265
1490359667.80674077075-632.806740770753
1591339242.1775603841-109.177560384098
1694879082.10359767941404.896402320592
1787009255.08509954827-555.085099548267
1896278834.51852003755792.481479962451
1989479249.01734710976-302.017347109762
2092839033.53905896061249.46094103939
2188299149.22772981818-320.227729818183
2299478913.979918651661033.02008134834
2396289550.8289902548977.171009745105
2493189685.67161789368-367.671617893677
2596059529.8674072466575.1325927533508
2686409622.2867545842-982.286754584204
2792149008.51843377432205.481566225675
2895679061.13725380785505.86274619215
2985479346.40826437562-799.408264375625
3091858818.33108438282366.668915617183
3194708967.77387073737502.22612926263
3291239260.91045679027-137.910456790267
3392789191.0656822568386.9343177431711
34101709254.15466292216915.845337077842
3594349891.42689759726-457.426897597265
3696559727.17605699379-72.1760569937887
3794299759.4540697593-330.454069759297
3887399606.45393941938-867.453939419383
3995529042.74687298561509.253127014388
4096879289.72794432034397.272055679659
4190199532.74590867499-513.74590867499
4296729214.32998560074457.67001439926
4392069481.83520568848-275.835205688483
4490699316.77161677334-247.771616773343
4597889131.76216839207656.237831607932
46103129524.55687492434787.443125075661
471010510099.00515855535.9948414446626
48986310254.9748803443-391.974880344331
49965610142.016258765-486.016258765008
5092959909.93135916459-614.931359164593
5199469521.79399882012424.206001179877
5297019751.18939116337-50.1893911633651
5390499718.93332034484-669.933320344835
54101909259.47522365402930.524776345979
5597069790.28678170371-84.2867817037095
5697659764.642089631970.357910368031298
5798939784.46834279045108.531657209553
5899949877.67386370554116.326136294456
59104339991.49628376852441.50371623148
601007310342.1841088016-269.184108801554
611011210273.486606147-161.486606146995
62926610239.76505227-973.765052269981
6398209632.60248218786187.397517812142
64100979674.99550840195422.004491598051
6591159902.89889064673-787.898890646728
66104119370.254421663911040.74557833609
6796789965.89634427598-287.896344275976
68104089807.91485390065600.085146099349
691015310211.2037436049-58.2037436048886
701036810253.0315805368114.968419463155
711058110404.0262407874176.973759212629
721059710613.2955757885-16.2955757885393
731068010716.55428391-36.5542839100453
74973810803.7778268851-1065.77782688506
75955610188.148092489-632.148092488971

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 9084 & 8462 & 622 \tabularnewline
4 & 9743 & 8264.64068851285 & 1478.35931148715 \tabularnewline
5 & 8587 & 8735.66450867064 & -148.664508670643 \tabularnewline
6 & 9731 & 8312.6235143253 & 1418.3764856747 \tabularnewline
7 & 9563 & 8930.84348372501 & 632.156516274987 \tabularnewline
8 & 9998 & 9216.48756363634 & 781.512436363664 \tabularnewline
9 & 9437 & 9692.68697652768 & -255.686976527675 \tabularnewline
10 & 10038 & 9576.20164956744 & 461.798350432558 \tabularnewline
11 & 9918 & 9909.96143756943 & 8.03856243056907 \tabularnewline
12 & 9252 & 10001.3691930518 & -749.369193051811 \tabularnewline
13 & 9737 & 9580.48187268773 & 156.518127312265 \tabularnewline
14 & 9035 & 9667.80674077075 & -632.806740770753 \tabularnewline
15 & 9133 & 9242.1775603841 & -109.177560384098 \tabularnewline
16 & 9487 & 9082.10359767941 & 404.896402320592 \tabularnewline
17 & 8700 & 9255.08509954827 & -555.085099548267 \tabularnewline
18 & 9627 & 8834.51852003755 & 792.481479962451 \tabularnewline
19 & 8947 & 9249.01734710976 & -302.017347109762 \tabularnewline
20 & 9283 & 9033.53905896061 & 249.46094103939 \tabularnewline
21 & 8829 & 9149.22772981818 & -320.227729818183 \tabularnewline
22 & 9947 & 8913.97991865166 & 1033.02008134834 \tabularnewline
23 & 9628 & 9550.82899025489 & 77.171009745105 \tabularnewline
24 & 9318 & 9685.67161789368 & -367.671617893677 \tabularnewline
25 & 9605 & 9529.86740724665 & 75.1325927533508 \tabularnewline
26 & 8640 & 9622.2867545842 & -982.286754584204 \tabularnewline
27 & 9214 & 9008.51843377432 & 205.481566225675 \tabularnewline
28 & 9567 & 9061.13725380785 & 505.86274619215 \tabularnewline
29 & 8547 & 9346.40826437562 & -799.408264375625 \tabularnewline
30 & 9185 & 8818.33108438282 & 366.668915617183 \tabularnewline
31 & 9470 & 8967.77387073737 & 502.22612926263 \tabularnewline
32 & 9123 & 9260.91045679027 & -137.910456790267 \tabularnewline
33 & 9278 & 9191.06568225683 & 86.9343177431711 \tabularnewline
34 & 10170 & 9254.15466292216 & 915.845337077842 \tabularnewline
35 & 9434 & 9891.42689759726 & -457.426897597265 \tabularnewline
36 & 9655 & 9727.17605699379 & -72.1760569937887 \tabularnewline
37 & 9429 & 9759.4540697593 & -330.454069759297 \tabularnewline
38 & 8739 & 9606.45393941938 & -867.453939419383 \tabularnewline
39 & 9552 & 9042.74687298561 & 509.253127014388 \tabularnewline
40 & 9687 & 9289.72794432034 & 397.272055679659 \tabularnewline
41 & 9019 & 9532.74590867499 & -513.74590867499 \tabularnewline
42 & 9672 & 9214.32998560074 & 457.67001439926 \tabularnewline
43 & 9206 & 9481.83520568848 & -275.835205688483 \tabularnewline
44 & 9069 & 9316.77161677334 & -247.771616773343 \tabularnewline
45 & 9788 & 9131.76216839207 & 656.237831607932 \tabularnewline
46 & 10312 & 9524.55687492434 & 787.443125075661 \tabularnewline
47 & 10105 & 10099.0051585553 & 5.9948414446626 \tabularnewline
48 & 9863 & 10254.9748803443 & -391.974880344331 \tabularnewline
49 & 9656 & 10142.016258765 & -486.016258765008 \tabularnewline
50 & 9295 & 9909.93135916459 & -614.931359164593 \tabularnewline
51 & 9946 & 9521.79399882012 & 424.206001179877 \tabularnewline
52 & 9701 & 9751.18939116337 & -50.1893911633651 \tabularnewline
53 & 9049 & 9718.93332034484 & -669.933320344835 \tabularnewline
54 & 10190 & 9259.47522365402 & 930.524776345979 \tabularnewline
55 & 9706 & 9790.28678170371 & -84.2867817037095 \tabularnewline
56 & 9765 & 9764.64208963197 & 0.357910368031298 \tabularnewline
57 & 9893 & 9784.46834279045 & 108.531657209553 \tabularnewline
58 & 9994 & 9877.67386370554 & 116.326136294456 \tabularnewline
59 & 10433 & 9991.49628376852 & 441.50371623148 \tabularnewline
60 & 10073 & 10342.1841088016 & -269.184108801554 \tabularnewline
61 & 10112 & 10273.486606147 & -161.486606146995 \tabularnewline
62 & 9266 & 10239.76505227 & -973.765052269981 \tabularnewline
63 & 9820 & 9632.60248218786 & 187.397517812142 \tabularnewline
64 & 10097 & 9674.99550840195 & 422.004491598051 \tabularnewline
65 & 9115 & 9902.89889064673 & -787.898890646728 \tabularnewline
66 & 10411 & 9370.25442166391 & 1040.74557833609 \tabularnewline
67 & 9678 & 9965.89634427598 & -287.896344275976 \tabularnewline
68 & 10408 & 9807.91485390065 & 600.085146099349 \tabularnewline
69 & 10153 & 10211.2037436049 & -58.2037436048886 \tabularnewline
70 & 10368 & 10253.0315805368 & 114.968419463155 \tabularnewline
71 & 10581 & 10404.0262407874 & 176.973759212629 \tabularnewline
72 & 10597 & 10613.2955757885 & -16.2955757885393 \tabularnewline
73 & 10680 & 10716.55428391 & -36.5542839100453 \tabularnewline
74 & 9738 & 10803.7778268851 & -1065.77782688506 \tabularnewline
75 & 9556 & 10188.148092489 & -632.148092488971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204187&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]3[/C][C]9084[/C][C]8462[/C][C]622[/C][/ROW]
[ROW][C]4[/C][C]9743[/C][C]8264.64068851285[/C][C]1478.35931148715[/C][/ROW]
[ROW][C]5[/C][C]8587[/C][C]8735.66450867064[/C][C]-148.664508670643[/C][/ROW]
[ROW][C]6[/C][C]9731[/C][C]8312.6235143253[/C][C]1418.3764856747[/C][/ROW]
[ROW][C]7[/C][C]9563[/C][C]8930.84348372501[/C][C]632.156516274987[/C][/ROW]
[ROW][C]8[/C][C]9998[/C][C]9216.48756363634[/C][C]781.512436363664[/C][/ROW]
[ROW][C]9[/C][C]9437[/C][C]9692.68697652768[/C][C]-255.686976527675[/C][/ROW]
[ROW][C]10[/C][C]10038[/C][C]9576.20164956744[/C][C]461.798350432558[/C][/ROW]
[ROW][C]11[/C][C]9918[/C][C]9909.96143756943[/C][C]8.03856243056907[/C][/ROW]
[ROW][C]12[/C][C]9252[/C][C]10001.3691930518[/C][C]-749.369193051811[/C][/ROW]
[ROW][C]13[/C][C]9737[/C][C]9580.48187268773[/C][C]156.518127312265[/C][/ROW]
[ROW][C]14[/C][C]9035[/C][C]9667.80674077075[/C][C]-632.806740770753[/C][/ROW]
[ROW][C]15[/C][C]9133[/C][C]9242.1775603841[/C][C]-109.177560384098[/C][/ROW]
[ROW][C]16[/C][C]9487[/C][C]9082.10359767941[/C][C]404.896402320592[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]9255.08509954827[/C][C]-555.085099548267[/C][/ROW]
[ROW][C]18[/C][C]9627[/C][C]8834.51852003755[/C][C]792.481479962451[/C][/ROW]
[ROW][C]19[/C][C]8947[/C][C]9249.01734710976[/C][C]-302.017347109762[/C][/ROW]
[ROW][C]20[/C][C]9283[/C][C]9033.53905896061[/C][C]249.46094103939[/C][/ROW]
[ROW][C]21[/C][C]8829[/C][C]9149.22772981818[/C][C]-320.227729818183[/C][/ROW]
[ROW][C]22[/C][C]9947[/C][C]8913.97991865166[/C][C]1033.02008134834[/C][/ROW]
[ROW][C]23[/C][C]9628[/C][C]9550.82899025489[/C][C]77.171009745105[/C][/ROW]
[ROW][C]24[/C][C]9318[/C][C]9685.67161789368[/C][C]-367.671617893677[/C][/ROW]
[ROW][C]25[/C][C]9605[/C][C]9529.86740724665[/C][C]75.1325927533508[/C][/ROW]
[ROW][C]26[/C][C]8640[/C][C]9622.2867545842[/C][C]-982.286754584204[/C][/ROW]
[ROW][C]27[/C][C]9214[/C][C]9008.51843377432[/C][C]205.481566225675[/C][/ROW]
[ROW][C]28[/C][C]9567[/C][C]9061.13725380785[/C][C]505.86274619215[/C][/ROW]
[ROW][C]29[/C][C]8547[/C][C]9346.40826437562[/C][C]-799.408264375625[/C][/ROW]
[ROW][C]30[/C][C]9185[/C][C]8818.33108438282[/C][C]366.668915617183[/C][/ROW]
[ROW][C]31[/C][C]9470[/C][C]8967.77387073737[/C][C]502.22612926263[/C][/ROW]
[ROW][C]32[/C][C]9123[/C][C]9260.91045679027[/C][C]-137.910456790267[/C][/ROW]
[ROW][C]33[/C][C]9278[/C][C]9191.06568225683[/C][C]86.9343177431711[/C][/ROW]
[ROW][C]34[/C][C]10170[/C][C]9254.15466292216[/C][C]915.845337077842[/C][/ROW]
[ROW][C]35[/C][C]9434[/C][C]9891.42689759726[/C][C]-457.426897597265[/C][/ROW]
[ROW][C]36[/C][C]9655[/C][C]9727.17605699379[/C][C]-72.1760569937887[/C][/ROW]
[ROW][C]37[/C][C]9429[/C][C]9759.4540697593[/C][C]-330.454069759297[/C][/ROW]
[ROW][C]38[/C][C]8739[/C][C]9606.45393941938[/C][C]-867.453939419383[/C][/ROW]
[ROW][C]39[/C][C]9552[/C][C]9042.74687298561[/C][C]509.253127014388[/C][/ROW]
[ROW][C]40[/C][C]9687[/C][C]9289.72794432034[/C][C]397.272055679659[/C][/ROW]
[ROW][C]41[/C][C]9019[/C][C]9532.74590867499[/C][C]-513.74590867499[/C][/ROW]
[ROW][C]42[/C][C]9672[/C][C]9214.32998560074[/C][C]457.67001439926[/C][/ROW]
[ROW][C]43[/C][C]9206[/C][C]9481.83520568848[/C][C]-275.835205688483[/C][/ROW]
[ROW][C]44[/C][C]9069[/C][C]9316.77161677334[/C][C]-247.771616773343[/C][/ROW]
[ROW][C]45[/C][C]9788[/C][C]9131.76216839207[/C][C]656.237831607932[/C][/ROW]
[ROW][C]46[/C][C]10312[/C][C]9524.55687492434[/C][C]787.443125075661[/C][/ROW]
[ROW][C]47[/C][C]10105[/C][C]10099.0051585553[/C][C]5.9948414446626[/C][/ROW]
[ROW][C]48[/C][C]9863[/C][C]10254.9748803443[/C][C]-391.974880344331[/C][/ROW]
[ROW][C]49[/C][C]9656[/C][C]10142.016258765[/C][C]-486.016258765008[/C][/ROW]
[ROW][C]50[/C][C]9295[/C][C]9909.93135916459[/C][C]-614.931359164593[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]9521.79399882012[/C][C]424.206001179877[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]9751.18939116337[/C][C]-50.1893911633651[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]9718.93332034484[/C][C]-669.933320344835[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]9259.47522365402[/C][C]930.524776345979[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]9790.28678170371[/C][C]-84.2867817037095[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]9764.64208963197[/C][C]0.357910368031298[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]9784.46834279045[/C][C]108.531657209553[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]9877.67386370554[/C][C]116.326136294456[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]9991.49628376852[/C][C]441.50371623148[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]10342.1841088016[/C][C]-269.184108801554[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]10273.486606147[/C][C]-161.486606146995[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]10239.76505227[/C][C]-973.765052269981[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]9632.60248218786[/C][C]187.397517812142[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9674.99550840195[/C][C]422.004491598051[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9902.89889064673[/C][C]-787.898890646728[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]9370.25442166391[/C][C]1040.74557833609[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9965.89634427598[/C][C]-287.896344275976[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]9807.91485390065[/C][C]600.085146099349[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]10211.2037436049[/C][C]-58.2037436048886[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10253.0315805368[/C][C]114.968419463155[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10404.0262407874[/C][C]176.973759212629[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10613.2955757885[/C][C]-16.2955757885393[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10716.55428391[/C][C]-36.5542839100453[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]10803.7778268851[/C][C]-1065.77782688506[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]10188.148092489[/C][C]-632.148092488971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204187&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204187&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
390848462622
497438264.640688512851478.35931148715
585878735.66450867064-148.664508670643
697318312.62351432531418.3764856747
795638930.84348372501632.156516274987
899989216.48756363634781.512436363664
994379692.68697652768-255.686976527675
10100389576.20164956744461.798350432558
1199189909.961437569438.03856243056907
12925210001.3691930518-749.369193051811
1397379580.48187268773156.518127312265
1490359667.80674077075-632.806740770753
1591339242.1775603841-109.177560384098
1694879082.10359767941404.896402320592
1787009255.08509954827-555.085099548267
1896278834.51852003755792.481479962451
1989479249.01734710976-302.017347109762
2092839033.53905896061249.46094103939
2188299149.22772981818-320.227729818183
2299478913.979918651661033.02008134834
2396289550.8289902548977.171009745105
2493189685.67161789368-367.671617893677
2596059529.8674072466575.1325927533508
2686409622.2867545842-982.286754584204
2792149008.51843377432205.481566225675
2895679061.13725380785505.86274619215
2985479346.40826437562-799.408264375625
3091858818.33108438282366.668915617183
3194708967.77387073737502.22612926263
3291239260.91045679027-137.910456790267
3392789191.0656822568386.9343177431711
34101709254.15466292216915.845337077842
3594349891.42689759726-457.426897597265
3696559727.17605699379-72.1760569937887
3794299759.4540697593-330.454069759297
3887399606.45393941938-867.453939419383
3995529042.74687298561509.253127014388
4096879289.72794432034397.272055679659
4190199532.74590867499-513.74590867499
4296729214.32998560074457.67001439926
4392069481.83520568848-275.835205688483
4490699316.77161677334-247.771616773343
4597889131.76216839207656.237831607932
46103129524.55687492434787.443125075661
471010510099.00515855535.9948414446626
48986310254.9748803443-391.974880344331
49965610142.016258765-486.016258765008
5092959909.93135916459-614.931359164593
5199469521.79399882012424.206001179877
5297019751.18939116337-50.1893911633651
5390499718.93332034484-669.933320344835
54101909259.47522365402930.524776345979
5597069790.28678170371-84.2867817037095
5697659764.642089631970.357910368031298
5798939784.46834279045108.531657209553
5899949877.67386370554116.326136294456
59104339991.49628376852441.50371623148
601007310342.1841088016-269.184108801554
611011210273.486606147-161.486606146995
62926610239.76505227-973.765052269981
6398209632.60248218786187.397517812142
64100979674.99550840195422.004491598051
6591159902.89889064673-787.898890646728
66104119370.254421663911040.74557833609
6796789965.89634427598-287.896344275976
68104089807.91485390065600.085146099349
691015310211.2037436049-58.2037436048886
701036810253.0315805368114.968419463155
711058110404.0262407874176.973759212629
721059710613.2955757885-16.2955757885393
731068010716.55428391-36.5542839100453
74973810803.7778268851-1065.77782688506
75955610188.148092489-632.148092488971







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
769715.895357468838605.8465242501510825.9441906875
779582.853575932858241.7970472392210923.9101046265
789449.811794396887829.5440223360811070.0795664577
799316.77001286097377.207608938611256.3324167832
809183.728231324936890.7987958125111476.6576668373
819050.686449788956374.6211157083911726.7517838695
828917.644668252985831.7911504573412003.4981860486
838784.6028867175264.6294541739812304.57631926
848651.561105181034674.9196131281712628.2025972339
858518.519323645064064.0749709437912972.9636763463
868385.477542109083433.2464734599513337.7086107582
878252.435760573112783.3937475000313721.4777736462

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 9715.89535746883 & 8605.84652425015 & 10825.9441906875 \tabularnewline
77 & 9582.85357593285 & 8241.79704723922 & 10923.9101046265 \tabularnewline
78 & 9449.81179439688 & 7829.54402233608 & 11070.0795664577 \tabularnewline
79 & 9316.7700128609 & 7377.2076089386 & 11256.3324167832 \tabularnewline
80 & 9183.72823132493 & 6890.79879581251 & 11476.6576668373 \tabularnewline
81 & 9050.68644978895 & 6374.62111570839 & 11726.7517838695 \tabularnewline
82 & 8917.64466825298 & 5831.79115045734 & 12003.4981860486 \tabularnewline
83 & 8784.602886717 & 5264.62945417398 & 12304.57631926 \tabularnewline
84 & 8651.56110518103 & 4674.91961312817 & 12628.2025972339 \tabularnewline
85 & 8518.51932364506 & 4064.07497094379 & 12972.9636763463 \tabularnewline
86 & 8385.47754210908 & 3433.24647345995 & 13337.7086107582 \tabularnewline
87 & 8252.43576057311 & 2783.39374750003 & 13721.4777736462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204187&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]76[/C][C]9715.89535746883[/C][C]8605.84652425015[/C][C]10825.9441906875[/C][/ROW]
[ROW][C]77[/C][C]9582.85357593285[/C][C]8241.79704723922[/C][C]10923.9101046265[/C][/ROW]
[ROW][C]78[/C][C]9449.81179439688[/C][C]7829.54402233608[/C][C]11070.0795664577[/C][/ROW]
[ROW][C]79[/C][C]9316.7700128609[/C][C]7377.2076089386[/C][C]11256.3324167832[/C][/ROW]
[ROW][C]80[/C][C]9183.72823132493[/C][C]6890.79879581251[/C][C]11476.6576668373[/C][/ROW]
[ROW][C]81[/C][C]9050.68644978895[/C][C]6374.62111570839[/C][C]11726.7517838695[/C][/ROW]
[ROW][C]82[/C][C]8917.64466825298[/C][C]5831.79115045734[/C][C]12003.4981860486[/C][/ROW]
[ROW][C]83[/C][C]8784.602886717[/C][C]5264.62945417398[/C][C]12304.57631926[/C][/ROW]
[ROW][C]84[/C][C]8651.56110518103[/C][C]4674.91961312817[/C][C]12628.2025972339[/C][/ROW]
[ROW][C]85[/C][C]8518.51932364506[/C][C]4064.07497094379[/C][C]12972.9636763463[/C][/ROW]
[ROW][C]86[/C][C]8385.47754210908[/C][C]3433.24647345995[/C][C]13337.7086107582[/C][/ROW]
[ROW][C]87[/C][C]8252.43576057311[/C][C]2783.39374750003[/C][C]13721.4777736462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204187&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204187&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
769715.895357468838605.8465242501510825.9441906875
779582.853575932858241.7970472392210923.9101046265
789449.811794396887829.5440223360811070.0795664577
799316.77001286097377.207608938611256.3324167832
809183.728231324936890.7987958125111476.6576668373
819050.686449788956374.6211157083911726.7517838695
828917.644668252985831.7911504573412003.4981860486
838784.6028867175264.6294541739812304.57631926
848651.561105181034674.9196131281712628.2025972339
858518.519323645064064.0749709437912972.9636763463
868385.477542109083433.2464734599513337.7086107582
878252.435760573112783.3937475000313721.4777736462



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