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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 14 Dec 2016 12:47:36 +0100
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/Dec/14/t1481716076v20ox8xp1acal33.htm/, Retrieved Fri, 03 May 2024 16:48:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299323, Retrieved Fri, 03 May 2024 16:48:53 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-14 11:47:36] [349958aef20b862f8399a5ba04d6f6e3] [Current]
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Dataseries X:
6830
6827
6841
6754
6869
6809
6836
6766
6759
6719
6702
6627
6630
6606
6512
6550
6578
6499
6371
6332
6291
6307
6252
6250
6164
6213
6174
6154
6091
6096
6046
6001
5979
5921
5863
5818
5758
5786
5734
5678
5610
5578
5589
5553
5533
5521
5464
5419
5346
5296
5255
5235
5164
5164
5172
5093
5070
5108
5051
5021
5001
4918
4886




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299323&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299323&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299323&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999943724901011
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999943724901011 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299323&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]0.999943724901011[/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=299323&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299323&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
alpha0.999943724901011
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
268276830-3
368416827.000168825313.9998311747031
467546840.99921215811-86.9992121581145
568696754.00489588928114.995104110724
668096868.99352863913-59.9935286391337
768366809.0033761417626.9966238582374
867666835.99848076232-69.9984807623196
967596766.00393917143-7.00393917143447
1067196759.00039414737-40.0003941473706
1167026719.00225102614-17.0022510261397
1266276702.00095680336-75.0009568033593
1366306627.004220686272.99577931373187
1466066629.99983141222-23.9998314122222
1565126606.00135059289-94.0013505928891
1665506512.0052899353137.9947100646905
1765786549.9978618439328.00213815607
1864996577.9984241769-78.9984241769034
1963716499.00444564414-128.004445644141
2063326371.00720346285-39.0072034628492
2162916332.00219513424-41.0021951342369
2263076291.0023074025915.9976925974097
2362526306.99909972827-54.9990997282657
2462506252.00309507978-2.00309507978182
2561646250.00011272437-86.000112724374
2662136164.0048396648648.9951603351428
2761746212.9972427925-38.9972427925022
2861546174.0021945737-20.002194573698
2960916154.00112562548-63.0011256254802
3060966091.003545394584.99645460541979
3160466095.99971882402-49.9997188240222
3260016046.00281373913-45.0028137391264
3359796001.0025325378-22.0025325377983
3459215979.0012381947-58.0012381946963
3558635921.00326402542-58.0032640254203
3658185863.00326413942-45.0032641394246
3757585818.00253256314-60.002532563145
3857865758.0033766484627.9966233515406
3957345785.99842448725-51.9984244872494
4056785734.00292621649-56.0029262164853
4156105678.00315157022-68.0031515702167
4255785610.00382688409-32.0038268840863
4355895578.0018010185310.9981989814742
4455535588.99938107526-35.999381075263
4555335553.00202586873-20.0020258687337
4655215533.00112561599-12.001125615986
4754645521.00067536453-57.0006753645321
4854195464.00320771865-45.0032077186488
4953465419.00253255997-73.002532559969
5052965346.00410822475-50.0041082247462
5152555296.00281398614-41.0028139861397
5252355255.00230743742-20.0023074374167
5351645235.00112563183-71.0011256318303
5451645164.00399559537-0.0039955953734534
5551725164.000000224857.99999977514744
5650935171.99954979922-78.9995497992204
5750705093.00444570749-23.0044457074855
5851085070.0012945774637.9987054225403
5950515107.99786161909-56.9978616190901
6050215051.0032075603-30.0032075603049
6150015021.00168843348-20.0016884334755
6249185001.001125597-83.0011255969966
6348864918.00467089656-32.0046708965592

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6827 & 6830 & -3 \tabularnewline
3 & 6841 & 6827.0001688253 & 13.9998311747031 \tabularnewline
4 & 6754 & 6840.99921215811 & -86.9992121581145 \tabularnewline
5 & 6869 & 6754.00489588928 & 114.995104110724 \tabularnewline
6 & 6809 & 6868.99352863913 & -59.9935286391337 \tabularnewline
7 & 6836 & 6809.00337614176 & 26.9966238582374 \tabularnewline
8 & 6766 & 6835.99848076232 & -69.9984807623196 \tabularnewline
9 & 6759 & 6766.00393917143 & -7.00393917143447 \tabularnewline
10 & 6719 & 6759.00039414737 & -40.0003941473706 \tabularnewline
11 & 6702 & 6719.00225102614 & -17.0022510261397 \tabularnewline
12 & 6627 & 6702.00095680336 & -75.0009568033593 \tabularnewline
13 & 6630 & 6627.00422068627 & 2.99577931373187 \tabularnewline
14 & 6606 & 6629.99983141222 & -23.9998314122222 \tabularnewline
15 & 6512 & 6606.00135059289 & -94.0013505928891 \tabularnewline
16 & 6550 & 6512.00528993531 & 37.9947100646905 \tabularnewline
17 & 6578 & 6549.99786184393 & 28.00213815607 \tabularnewline
18 & 6499 & 6577.9984241769 & -78.9984241769034 \tabularnewline
19 & 6371 & 6499.00444564414 & -128.004445644141 \tabularnewline
20 & 6332 & 6371.00720346285 & -39.0072034628492 \tabularnewline
21 & 6291 & 6332.00219513424 & -41.0021951342369 \tabularnewline
22 & 6307 & 6291.00230740259 & 15.9976925974097 \tabularnewline
23 & 6252 & 6306.99909972827 & -54.9990997282657 \tabularnewline
24 & 6250 & 6252.00309507978 & -2.00309507978182 \tabularnewline
25 & 6164 & 6250.00011272437 & -86.000112724374 \tabularnewline
26 & 6213 & 6164.00483966486 & 48.9951603351428 \tabularnewline
27 & 6174 & 6212.9972427925 & -38.9972427925022 \tabularnewline
28 & 6154 & 6174.0021945737 & -20.002194573698 \tabularnewline
29 & 6091 & 6154.00112562548 & -63.0011256254802 \tabularnewline
30 & 6096 & 6091.00354539458 & 4.99645460541979 \tabularnewline
31 & 6046 & 6095.99971882402 & -49.9997188240222 \tabularnewline
32 & 6001 & 6046.00281373913 & -45.0028137391264 \tabularnewline
33 & 5979 & 6001.0025325378 & -22.0025325377983 \tabularnewline
34 & 5921 & 5979.0012381947 & -58.0012381946963 \tabularnewline
35 & 5863 & 5921.00326402542 & -58.0032640254203 \tabularnewline
36 & 5818 & 5863.00326413942 & -45.0032641394246 \tabularnewline
37 & 5758 & 5818.00253256314 & -60.002532563145 \tabularnewline
38 & 5786 & 5758.00337664846 & 27.9966233515406 \tabularnewline
39 & 5734 & 5785.99842448725 & -51.9984244872494 \tabularnewline
40 & 5678 & 5734.00292621649 & -56.0029262164853 \tabularnewline
41 & 5610 & 5678.00315157022 & -68.0031515702167 \tabularnewline
42 & 5578 & 5610.00382688409 & -32.0038268840863 \tabularnewline
43 & 5589 & 5578.00180101853 & 10.9981989814742 \tabularnewline
44 & 5553 & 5588.99938107526 & -35.999381075263 \tabularnewline
45 & 5533 & 5553.00202586873 & -20.0020258687337 \tabularnewline
46 & 5521 & 5533.00112561599 & -12.001125615986 \tabularnewline
47 & 5464 & 5521.00067536453 & -57.0006753645321 \tabularnewline
48 & 5419 & 5464.00320771865 & -45.0032077186488 \tabularnewline
49 & 5346 & 5419.00253255997 & -73.002532559969 \tabularnewline
50 & 5296 & 5346.00410822475 & -50.0041082247462 \tabularnewline
51 & 5255 & 5296.00281398614 & -41.0028139861397 \tabularnewline
52 & 5235 & 5255.00230743742 & -20.0023074374167 \tabularnewline
53 & 5164 & 5235.00112563183 & -71.0011256318303 \tabularnewline
54 & 5164 & 5164.00399559537 & -0.0039955953734534 \tabularnewline
55 & 5172 & 5164.00000022485 & 7.99999977514744 \tabularnewline
56 & 5093 & 5171.99954979922 & -78.9995497992204 \tabularnewline
57 & 5070 & 5093.00444570749 & -23.0044457074855 \tabularnewline
58 & 5108 & 5070.00129457746 & 37.9987054225403 \tabularnewline
59 & 5051 & 5107.99786161909 & -56.9978616190901 \tabularnewline
60 & 5021 & 5051.0032075603 & -30.0032075603049 \tabularnewline
61 & 5001 & 5021.00168843348 & -20.0016884334755 \tabularnewline
62 & 4918 & 5001.001125597 & -83.0011255969966 \tabularnewline
63 & 4886 & 4918.00467089656 & -32.0046708965592 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299323&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]6827[/C][C]6830[/C][C]-3[/C][/ROW]
[ROW][C]3[/C][C]6841[/C][C]6827.0001688253[/C][C]13.9998311747031[/C][/ROW]
[ROW][C]4[/C][C]6754[/C][C]6840.99921215811[/C][C]-86.9992121581145[/C][/ROW]
[ROW][C]5[/C][C]6869[/C][C]6754.00489588928[/C][C]114.995104110724[/C][/ROW]
[ROW][C]6[/C][C]6809[/C][C]6868.99352863913[/C][C]-59.9935286391337[/C][/ROW]
[ROW][C]7[/C][C]6836[/C][C]6809.00337614176[/C][C]26.9966238582374[/C][/ROW]
[ROW][C]8[/C][C]6766[/C][C]6835.99848076232[/C][C]-69.9984807623196[/C][/ROW]
[ROW][C]9[/C][C]6759[/C][C]6766.00393917143[/C][C]-7.00393917143447[/C][/ROW]
[ROW][C]10[/C][C]6719[/C][C]6759.00039414737[/C][C]-40.0003941473706[/C][/ROW]
[ROW][C]11[/C][C]6702[/C][C]6719.00225102614[/C][C]-17.0022510261397[/C][/ROW]
[ROW][C]12[/C][C]6627[/C][C]6702.00095680336[/C][C]-75.0009568033593[/C][/ROW]
[ROW][C]13[/C][C]6630[/C][C]6627.00422068627[/C][C]2.99577931373187[/C][/ROW]
[ROW][C]14[/C][C]6606[/C][C]6629.99983141222[/C][C]-23.9998314122222[/C][/ROW]
[ROW][C]15[/C][C]6512[/C][C]6606.00135059289[/C][C]-94.0013505928891[/C][/ROW]
[ROW][C]16[/C][C]6550[/C][C]6512.00528993531[/C][C]37.9947100646905[/C][/ROW]
[ROW][C]17[/C][C]6578[/C][C]6549.99786184393[/C][C]28.00213815607[/C][/ROW]
[ROW][C]18[/C][C]6499[/C][C]6577.9984241769[/C][C]-78.9984241769034[/C][/ROW]
[ROW][C]19[/C][C]6371[/C][C]6499.00444564414[/C][C]-128.004445644141[/C][/ROW]
[ROW][C]20[/C][C]6332[/C][C]6371.00720346285[/C][C]-39.0072034628492[/C][/ROW]
[ROW][C]21[/C][C]6291[/C][C]6332.00219513424[/C][C]-41.0021951342369[/C][/ROW]
[ROW][C]22[/C][C]6307[/C][C]6291.00230740259[/C][C]15.9976925974097[/C][/ROW]
[ROW][C]23[/C][C]6252[/C][C]6306.99909972827[/C][C]-54.9990997282657[/C][/ROW]
[ROW][C]24[/C][C]6250[/C][C]6252.00309507978[/C][C]-2.00309507978182[/C][/ROW]
[ROW][C]25[/C][C]6164[/C][C]6250.00011272437[/C][C]-86.000112724374[/C][/ROW]
[ROW][C]26[/C][C]6213[/C][C]6164.00483966486[/C][C]48.9951603351428[/C][/ROW]
[ROW][C]27[/C][C]6174[/C][C]6212.9972427925[/C][C]-38.9972427925022[/C][/ROW]
[ROW][C]28[/C][C]6154[/C][C]6174.0021945737[/C][C]-20.002194573698[/C][/ROW]
[ROW][C]29[/C][C]6091[/C][C]6154.00112562548[/C][C]-63.0011256254802[/C][/ROW]
[ROW][C]30[/C][C]6096[/C][C]6091.00354539458[/C][C]4.99645460541979[/C][/ROW]
[ROW][C]31[/C][C]6046[/C][C]6095.99971882402[/C][C]-49.9997188240222[/C][/ROW]
[ROW][C]32[/C][C]6001[/C][C]6046.00281373913[/C][C]-45.0028137391264[/C][/ROW]
[ROW][C]33[/C][C]5979[/C][C]6001.0025325378[/C][C]-22.0025325377983[/C][/ROW]
[ROW][C]34[/C][C]5921[/C][C]5979.0012381947[/C][C]-58.0012381946963[/C][/ROW]
[ROW][C]35[/C][C]5863[/C][C]5921.00326402542[/C][C]-58.0032640254203[/C][/ROW]
[ROW][C]36[/C][C]5818[/C][C]5863.00326413942[/C][C]-45.0032641394246[/C][/ROW]
[ROW][C]37[/C][C]5758[/C][C]5818.00253256314[/C][C]-60.002532563145[/C][/ROW]
[ROW][C]38[/C][C]5786[/C][C]5758.00337664846[/C][C]27.9966233515406[/C][/ROW]
[ROW][C]39[/C][C]5734[/C][C]5785.99842448725[/C][C]-51.9984244872494[/C][/ROW]
[ROW][C]40[/C][C]5678[/C][C]5734.00292621649[/C][C]-56.0029262164853[/C][/ROW]
[ROW][C]41[/C][C]5610[/C][C]5678.00315157022[/C][C]-68.0031515702167[/C][/ROW]
[ROW][C]42[/C][C]5578[/C][C]5610.00382688409[/C][C]-32.0038268840863[/C][/ROW]
[ROW][C]43[/C][C]5589[/C][C]5578.00180101853[/C][C]10.9981989814742[/C][/ROW]
[ROW][C]44[/C][C]5553[/C][C]5588.99938107526[/C][C]-35.999381075263[/C][/ROW]
[ROW][C]45[/C][C]5533[/C][C]5553.00202586873[/C][C]-20.0020258687337[/C][/ROW]
[ROW][C]46[/C][C]5521[/C][C]5533.00112561599[/C][C]-12.001125615986[/C][/ROW]
[ROW][C]47[/C][C]5464[/C][C]5521.00067536453[/C][C]-57.0006753645321[/C][/ROW]
[ROW][C]48[/C][C]5419[/C][C]5464.00320771865[/C][C]-45.0032077186488[/C][/ROW]
[ROW][C]49[/C][C]5346[/C][C]5419.00253255997[/C][C]-73.002532559969[/C][/ROW]
[ROW][C]50[/C][C]5296[/C][C]5346.00410822475[/C][C]-50.0041082247462[/C][/ROW]
[ROW][C]51[/C][C]5255[/C][C]5296.00281398614[/C][C]-41.0028139861397[/C][/ROW]
[ROW][C]52[/C][C]5235[/C][C]5255.00230743742[/C][C]-20.0023074374167[/C][/ROW]
[ROW][C]53[/C][C]5164[/C][C]5235.00112563183[/C][C]-71.0011256318303[/C][/ROW]
[ROW][C]54[/C][C]5164[/C][C]5164.00399559537[/C][C]-0.0039955953734534[/C][/ROW]
[ROW][C]55[/C][C]5172[/C][C]5164.00000022485[/C][C]7.99999977514744[/C][/ROW]
[ROW][C]56[/C][C]5093[/C][C]5171.99954979922[/C][C]-78.9995497992204[/C][/ROW]
[ROW][C]57[/C][C]5070[/C][C]5093.00444570749[/C][C]-23.0044457074855[/C][/ROW]
[ROW][C]58[/C][C]5108[/C][C]5070.00129457746[/C][C]37.9987054225403[/C][/ROW]
[ROW][C]59[/C][C]5051[/C][C]5107.99786161909[/C][C]-56.9978616190901[/C][/ROW]
[ROW][C]60[/C][C]5021[/C][C]5051.0032075603[/C][C]-30.0032075603049[/C][/ROW]
[ROW][C]61[/C][C]5001[/C][C]5021.00168843348[/C][C]-20.0016884334755[/C][/ROW]
[ROW][C]62[/C][C]4918[/C][C]5001.001125597[/C][C]-83.0011255969966[/C][/ROW]
[ROW][C]63[/C][C]4886[/C][C]4918.00467089656[/C][C]-32.0046708965592[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299323&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299323&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
268276830-3
368416827.000168825313.9998311747031
467546840.99921215811-86.9992121581145
568696754.00489588928114.995104110724
668096868.99352863913-59.9935286391337
768366809.0033761417626.9966238582374
867666835.99848076232-69.9984807623196
967596766.00393917143-7.00393917143447
1067196759.00039414737-40.0003941473706
1167026719.00225102614-17.0022510261397
1266276702.00095680336-75.0009568033593
1366306627.004220686272.99577931373187
1466066629.99983141222-23.9998314122222
1565126606.00135059289-94.0013505928891
1665506512.0052899353137.9947100646905
1765786549.9978618439328.00213815607
1864996577.9984241769-78.9984241769034
1963716499.00444564414-128.004445644141
2063326371.00720346285-39.0072034628492
2162916332.00219513424-41.0021951342369
2263076291.0023074025915.9976925974097
2362526306.99909972827-54.9990997282657
2462506252.00309507978-2.00309507978182
2561646250.00011272437-86.000112724374
2662136164.0048396648648.9951603351428
2761746212.9972427925-38.9972427925022
2861546174.0021945737-20.002194573698
2960916154.00112562548-63.0011256254802
3060966091.003545394584.99645460541979
3160466095.99971882402-49.9997188240222
3260016046.00281373913-45.0028137391264
3359796001.0025325378-22.0025325377983
3459215979.0012381947-58.0012381946963
3558635921.00326402542-58.0032640254203
3658185863.00326413942-45.0032641394246
3757585818.00253256314-60.002532563145
3857865758.0033766484627.9966233515406
3957345785.99842448725-51.9984244872494
4056785734.00292621649-56.0029262164853
4156105678.00315157022-68.0031515702167
4255785610.00382688409-32.0038268840863
4355895578.0018010185310.9981989814742
4455535588.99938107526-35.999381075263
4555335553.00202586873-20.0020258687337
4655215533.00112561599-12.001125615986
4754645521.00067536453-57.0006753645321
4854195464.00320771865-45.0032077186488
4953465419.00253255997-73.002532559969
5052965346.00410822475-50.0041082247462
5152555296.00281398614-41.0028139861397
5252355255.00230743742-20.0023074374167
5351645235.00112563183-71.0011256318303
5451645164.00399559537-0.0039955953734534
5551725164.000000224857.99999977514744
5650935171.99954979922-78.9995497992204
5750705093.00444570749-23.0044457074855
5851085070.0012945774637.9987054225403
5950515107.99786161909-56.9978616190901
6050215051.0032075603-30.0032075603049
6150015021.00168843348-20.0016884334755
6249185001.001125597-83.0011255969966
6348864918.00467089656-32.0046708965592







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
644886.001801066024804.350607903024967.65299422903
654886.001801066024770.532825370685001.47077676136
664886.001801066024744.583091726275027.42051040577
674886.001801066024722.706307084995049.29729504705
684886.001801066024703.432402322155068.57119980989
694886.001801066024686.007420242745085.9961818893
704886.001801066024669.983469982585102.02013214946
714886.001801066024655.068723384925116.93487874712
724886.001801066024641.060474682645130.94312744941
734886.001801066024627.811134360895144.19246777116
744886.001801066024615.20928385625156.79431827584
754886.001801066024603.168361777075168.83524035498

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
64 & 4886.00180106602 & 4804.35060790302 & 4967.65299422903 \tabularnewline
65 & 4886.00180106602 & 4770.53282537068 & 5001.47077676136 \tabularnewline
66 & 4886.00180106602 & 4744.58309172627 & 5027.42051040577 \tabularnewline
67 & 4886.00180106602 & 4722.70630708499 & 5049.29729504705 \tabularnewline
68 & 4886.00180106602 & 4703.43240232215 & 5068.57119980989 \tabularnewline
69 & 4886.00180106602 & 4686.00742024274 & 5085.9961818893 \tabularnewline
70 & 4886.00180106602 & 4669.98346998258 & 5102.02013214946 \tabularnewline
71 & 4886.00180106602 & 4655.06872338492 & 5116.93487874712 \tabularnewline
72 & 4886.00180106602 & 4641.06047468264 & 5130.94312744941 \tabularnewline
73 & 4886.00180106602 & 4627.81113436089 & 5144.19246777116 \tabularnewline
74 & 4886.00180106602 & 4615.2092838562 & 5156.79431827584 \tabularnewline
75 & 4886.00180106602 & 4603.16836177707 & 5168.83524035498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299323&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]64[/C][C]4886.00180106602[/C][C]4804.35060790302[/C][C]4967.65299422903[/C][/ROW]
[ROW][C]65[/C][C]4886.00180106602[/C][C]4770.53282537068[/C][C]5001.47077676136[/C][/ROW]
[ROW][C]66[/C][C]4886.00180106602[/C][C]4744.58309172627[/C][C]5027.42051040577[/C][/ROW]
[ROW][C]67[/C][C]4886.00180106602[/C][C]4722.70630708499[/C][C]5049.29729504705[/C][/ROW]
[ROW][C]68[/C][C]4886.00180106602[/C][C]4703.43240232215[/C][C]5068.57119980989[/C][/ROW]
[ROW][C]69[/C][C]4886.00180106602[/C][C]4686.00742024274[/C][C]5085.9961818893[/C][/ROW]
[ROW][C]70[/C][C]4886.00180106602[/C][C]4669.98346998258[/C][C]5102.02013214946[/C][/ROW]
[ROW][C]71[/C][C]4886.00180106602[/C][C]4655.06872338492[/C][C]5116.93487874712[/C][/ROW]
[ROW][C]72[/C][C]4886.00180106602[/C][C]4641.06047468264[/C][C]5130.94312744941[/C][/ROW]
[ROW][C]73[/C][C]4886.00180106602[/C][C]4627.81113436089[/C][C]5144.19246777116[/C][/ROW]
[ROW][C]74[/C][C]4886.00180106602[/C][C]4615.2092838562[/C][C]5156.79431827584[/C][/ROW]
[ROW][C]75[/C][C]4886.00180106602[/C][C]4603.16836177707[/C][C]5168.83524035498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299323&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299323&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
644886.001801066024804.350607903024967.65299422903
654886.001801066024770.532825370685001.47077676136
664886.001801066024744.583091726275027.42051040577
674886.001801066024722.706307084995049.29729504705
684886.001801066024703.432402322155068.57119980989
694886.001801066024686.007420242745085.9961818893
704886.001801066024669.983469982585102.02013214946
714886.001801066024655.068723384925116.93487874712
724886.001801066024641.060474682645130.94312744941
734886.001801066024627.811134360895144.19246777116
744886.001801066024615.20928385625156.79431827584
754886.001801066024603.168361777075168.83524035498



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; 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')