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 computationMon, 21 Jan 2019 09:41:39 +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/2019/Jan/21/t1548060124jgl9uktdqo6yhid.htm/, Retrieved Sat, 04 May 2024 10:05:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=316683, Retrieved Sat, 04 May 2024 10:05:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact49
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2019-01-21 08:41:39] [f5309fd35450bf354bd8724b37fb349a] [Current]
Feedback Forum

Post a new message
Dataseries X:
3035
2552
2704
2554
2014
1655
1721
1524
1596
2074
2199
2512
2933
2889
2938
2497
1870
1726
1607
1545
1396
1787
2076
2837
2787
3891
3179
2011
1636
1580
1489
1300
1356
1653
2013
2823
3102
2294
2385
2444
1748
1554
1498
1361
1346
1564
1640
2293
2815
3137
2679
1969
1870
1633
1529
1366
1357
1570
1535
2491
3084
2605
2573
2143
1693
1504
1461
1354
1333
1492
1781
1915




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316683&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=316683&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316683&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0041715932597097
beta0.464506342250138
gamma0.154038316998336

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0041715932597097 \tabularnewline
beta & 0.464506342250138 \tabularnewline
gamma & 0.154038316998336 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316683&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]0.0041715932597097[/C][/ROW]
[ROW][C]beta[/C][C]0.464506342250138[/C][/ROW]
[ROW][C]gamma[/C][C]0.154038316998336[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316683&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316683&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
alpha0.0041715932597097
beta0.464506342250138
gamma0.154038316998336







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1329332914.9183468933518.0816531066539
1428892872.5857467408916.4142532591113
1529382927.5397215883910.4602784116091
1624972508.18254092205-11.182540922046
1718701890.78919838221-20.7891983822105
1817261736.02025923863-10.0202592386347
1916071718.67191402893-111.671914028932
2015451512.4923866124532.5076133875457
2113961564.79342809842-168.793428098423
2217872022.45830382237-235.458303822372
2320762147.44038245984-71.4403824598407
2428372451.4073439586385.592656041404
2527872864.51905974239-77.5190597423875
2638912821.234565025131069.76543497487
2731792879.72537535363299.27462464637
2820112466.53692218686-455.536922186855
2916361856.48211937403-220.482119374035
3015801705.08697323922-125.086973239217
3114891671.97292262546-182.972922625461
3213001490.47841151884-190.478411518841
3313561509.76497392601-153.764973926008
3416531947.76244673934-294.76244673934
3520132093.45974688607-80.4597468860661
3628232458.42381854697364.576181453026
3731022791.58562826597310.414371734026
3822942921.83790745205-627.837907452052
3923852852.22595677244-467.225956772444
4024442329.11704254828114.882957451723
4117481770.22388665529-22.2238866552905
4215541635.8494053106-81.8494053105956
4314981593.0909729481-95.0909729481
4413611414.59114744148-53.5911474414827
4513461437.68361173733-91.683611737333
4615641838.85435660062-274.854356600617
4716402009.42040154301-369.420401543009
4822932423.01813634408-130.018136344077
4928152729.0741854551985.9258145448111
5031372709.84065815913427.159341840867
5126792667.7578872565811.2421127434181
5219692251.23702623999-282.237026239991
5318701691.64944652884178.350553471156
5416331553.4793476907879.5206523092224
5515291510.0675806911818.9324193088191
5613661344.9314677042521.0685322957527
5713571360.98303141691-3.98303141691349
5815701717.3140794361-147.314079436101
5915351866.38083400405-331.380834004046
6024912296.19924002635194.800759973647
6130842621.72927128874462.270728711258
6226052655.6163506714-50.6163506713951
6325732552.2237822540920.7762177459103
6421432110.7900535030732.2099464969306
6516931644.6502501121648.3497498878448
6615041497.548379521556.45162047845224
6714611446.7835506198614.2164493801411
6813541289.0990271927364.9009728072683
6913331300.9771978345332.022802165473
7014921621.01006721921-129.010067219215
7117811736.7408109674544.2591890325455
7219152228.09945837313-313.099458373127

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2933 & 2914.91834689335 & 18.0816531066539 \tabularnewline
14 & 2889 & 2872.58574674089 & 16.4142532591113 \tabularnewline
15 & 2938 & 2927.53972158839 & 10.4602784116091 \tabularnewline
16 & 2497 & 2508.18254092205 & -11.182540922046 \tabularnewline
17 & 1870 & 1890.78919838221 & -20.7891983822105 \tabularnewline
18 & 1726 & 1736.02025923863 & -10.0202592386347 \tabularnewline
19 & 1607 & 1718.67191402893 & -111.671914028932 \tabularnewline
20 & 1545 & 1512.49238661245 & 32.5076133875457 \tabularnewline
21 & 1396 & 1564.79342809842 & -168.793428098423 \tabularnewline
22 & 1787 & 2022.45830382237 & -235.458303822372 \tabularnewline
23 & 2076 & 2147.44038245984 & -71.4403824598407 \tabularnewline
24 & 2837 & 2451.4073439586 & 385.592656041404 \tabularnewline
25 & 2787 & 2864.51905974239 & -77.5190597423875 \tabularnewline
26 & 3891 & 2821.23456502513 & 1069.76543497487 \tabularnewline
27 & 3179 & 2879.72537535363 & 299.27462464637 \tabularnewline
28 & 2011 & 2466.53692218686 & -455.536922186855 \tabularnewline
29 & 1636 & 1856.48211937403 & -220.482119374035 \tabularnewline
30 & 1580 & 1705.08697323922 & -125.086973239217 \tabularnewline
31 & 1489 & 1671.97292262546 & -182.972922625461 \tabularnewline
32 & 1300 & 1490.47841151884 & -190.478411518841 \tabularnewline
33 & 1356 & 1509.76497392601 & -153.764973926008 \tabularnewline
34 & 1653 & 1947.76244673934 & -294.76244673934 \tabularnewline
35 & 2013 & 2093.45974688607 & -80.4597468860661 \tabularnewline
36 & 2823 & 2458.42381854697 & 364.576181453026 \tabularnewline
37 & 3102 & 2791.58562826597 & 310.414371734026 \tabularnewline
38 & 2294 & 2921.83790745205 & -627.837907452052 \tabularnewline
39 & 2385 & 2852.22595677244 & -467.225956772444 \tabularnewline
40 & 2444 & 2329.11704254828 & 114.882957451723 \tabularnewline
41 & 1748 & 1770.22388665529 & -22.2238866552905 \tabularnewline
42 & 1554 & 1635.8494053106 & -81.8494053105956 \tabularnewline
43 & 1498 & 1593.0909729481 & -95.0909729481 \tabularnewline
44 & 1361 & 1414.59114744148 & -53.5911474414827 \tabularnewline
45 & 1346 & 1437.68361173733 & -91.683611737333 \tabularnewline
46 & 1564 & 1838.85435660062 & -274.854356600617 \tabularnewline
47 & 1640 & 2009.42040154301 & -369.420401543009 \tabularnewline
48 & 2293 & 2423.01813634408 & -130.018136344077 \tabularnewline
49 & 2815 & 2729.07418545519 & 85.9258145448111 \tabularnewline
50 & 3137 & 2709.84065815913 & 427.159341840867 \tabularnewline
51 & 2679 & 2667.75788725658 & 11.2421127434181 \tabularnewline
52 & 1969 & 2251.23702623999 & -282.237026239991 \tabularnewline
53 & 1870 & 1691.64944652884 & 178.350553471156 \tabularnewline
54 & 1633 & 1553.47934769078 & 79.5206523092224 \tabularnewline
55 & 1529 & 1510.06758069118 & 18.9324193088191 \tabularnewline
56 & 1366 & 1344.93146770425 & 21.0685322957527 \tabularnewline
57 & 1357 & 1360.98303141691 & -3.98303141691349 \tabularnewline
58 & 1570 & 1717.3140794361 & -147.314079436101 \tabularnewline
59 & 1535 & 1866.38083400405 & -331.380834004046 \tabularnewline
60 & 2491 & 2296.19924002635 & 194.800759973647 \tabularnewline
61 & 3084 & 2621.72927128874 & 462.270728711258 \tabularnewline
62 & 2605 & 2655.6163506714 & -50.6163506713951 \tabularnewline
63 & 2573 & 2552.22378225409 & 20.7762177459103 \tabularnewline
64 & 2143 & 2110.79005350307 & 32.2099464969306 \tabularnewline
65 & 1693 & 1644.65025011216 & 48.3497498878448 \tabularnewline
66 & 1504 & 1497.54837952155 & 6.45162047845224 \tabularnewline
67 & 1461 & 1446.78355061986 & 14.2164493801411 \tabularnewline
68 & 1354 & 1289.09902719273 & 64.9009728072683 \tabularnewline
69 & 1333 & 1300.97719783453 & 32.022802165473 \tabularnewline
70 & 1492 & 1621.01006721921 & -129.010067219215 \tabularnewline
71 & 1781 & 1736.74081096745 & 44.2591890325455 \tabularnewline
72 & 1915 & 2228.09945837313 & -313.099458373127 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316683&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]2933[/C][C]2914.91834689335[/C][C]18.0816531066539[/C][/ROW]
[ROW][C]14[/C][C]2889[/C][C]2872.58574674089[/C][C]16.4142532591113[/C][/ROW]
[ROW][C]15[/C][C]2938[/C][C]2927.53972158839[/C][C]10.4602784116091[/C][/ROW]
[ROW][C]16[/C][C]2497[/C][C]2508.18254092205[/C][C]-11.182540922046[/C][/ROW]
[ROW][C]17[/C][C]1870[/C][C]1890.78919838221[/C][C]-20.7891983822105[/C][/ROW]
[ROW][C]18[/C][C]1726[/C][C]1736.02025923863[/C][C]-10.0202592386347[/C][/ROW]
[ROW][C]19[/C][C]1607[/C][C]1718.67191402893[/C][C]-111.671914028932[/C][/ROW]
[ROW][C]20[/C][C]1545[/C][C]1512.49238661245[/C][C]32.5076133875457[/C][/ROW]
[ROW][C]21[/C][C]1396[/C][C]1564.79342809842[/C][C]-168.793428098423[/C][/ROW]
[ROW][C]22[/C][C]1787[/C][C]2022.45830382237[/C][C]-235.458303822372[/C][/ROW]
[ROW][C]23[/C][C]2076[/C][C]2147.44038245984[/C][C]-71.4403824598407[/C][/ROW]
[ROW][C]24[/C][C]2837[/C][C]2451.4073439586[/C][C]385.592656041404[/C][/ROW]
[ROW][C]25[/C][C]2787[/C][C]2864.51905974239[/C][C]-77.5190597423875[/C][/ROW]
[ROW][C]26[/C][C]3891[/C][C]2821.23456502513[/C][C]1069.76543497487[/C][/ROW]
[ROW][C]27[/C][C]3179[/C][C]2879.72537535363[/C][C]299.27462464637[/C][/ROW]
[ROW][C]28[/C][C]2011[/C][C]2466.53692218686[/C][C]-455.536922186855[/C][/ROW]
[ROW][C]29[/C][C]1636[/C][C]1856.48211937403[/C][C]-220.482119374035[/C][/ROW]
[ROW][C]30[/C][C]1580[/C][C]1705.08697323922[/C][C]-125.086973239217[/C][/ROW]
[ROW][C]31[/C][C]1489[/C][C]1671.97292262546[/C][C]-182.972922625461[/C][/ROW]
[ROW][C]32[/C][C]1300[/C][C]1490.47841151884[/C][C]-190.478411518841[/C][/ROW]
[ROW][C]33[/C][C]1356[/C][C]1509.76497392601[/C][C]-153.764973926008[/C][/ROW]
[ROW][C]34[/C][C]1653[/C][C]1947.76244673934[/C][C]-294.76244673934[/C][/ROW]
[ROW][C]35[/C][C]2013[/C][C]2093.45974688607[/C][C]-80.4597468860661[/C][/ROW]
[ROW][C]36[/C][C]2823[/C][C]2458.42381854697[/C][C]364.576181453026[/C][/ROW]
[ROW][C]37[/C][C]3102[/C][C]2791.58562826597[/C][C]310.414371734026[/C][/ROW]
[ROW][C]38[/C][C]2294[/C][C]2921.83790745205[/C][C]-627.837907452052[/C][/ROW]
[ROW][C]39[/C][C]2385[/C][C]2852.22595677244[/C][C]-467.225956772444[/C][/ROW]
[ROW][C]40[/C][C]2444[/C][C]2329.11704254828[/C][C]114.882957451723[/C][/ROW]
[ROW][C]41[/C][C]1748[/C][C]1770.22388665529[/C][C]-22.2238866552905[/C][/ROW]
[ROW][C]42[/C][C]1554[/C][C]1635.8494053106[/C][C]-81.8494053105956[/C][/ROW]
[ROW][C]43[/C][C]1498[/C][C]1593.0909729481[/C][C]-95.0909729481[/C][/ROW]
[ROW][C]44[/C][C]1361[/C][C]1414.59114744148[/C][C]-53.5911474414827[/C][/ROW]
[ROW][C]45[/C][C]1346[/C][C]1437.68361173733[/C][C]-91.683611737333[/C][/ROW]
[ROW][C]46[/C][C]1564[/C][C]1838.85435660062[/C][C]-274.854356600617[/C][/ROW]
[ROW][C]47[/C][C]1640[/C][C]2009.42040154301[/C][C]-369.420401543009[/C][/ROW]
[ROW][C]48[/C][C]2293[/C][C]2423.01813634408[/C][C]-130.018136344077[/C][/ROW]
[ROW][C]49[/C][C]2815[/C][C]2729.07418545519[/C][C]85.9258145448111[/C][/ROW]
[ROW][C]50[/C][C]3137[/C][C]2709.84065815913[/C][C]427.159341840867[/C][/ROW]
[ROW][C]51[/C][C]2679[/C][C]2667.75788725658[/C][C]11.2421127434181[/C][/ROW]
[ROW][C]52[/C][C]1969[/C][C]2251.23702623999[/C][C]-282.237026239991[/C][/ROW]
[ROW][C]53[/C][C]1870[/C][C]1691.64944652884[/C][C]178.350553471156[/C][/ROW]
[ROW][C]54[/C][C]1633[/C][C]1553.47934769078[/C][C]79.5206523092224[/C][/ROW]
[ROW][C]55[/C][C]1529[/C][C]1510.06758069118[/C][C]18.9324193088191[/C][/ROW]
[ROW][C]56[/C][C]1366[/C][C]1344.93146770425[/C][C]21.0685322957527[/C][/ROW]
[ROW][C]57[/C][C]1357[/C][C]1360.98303141691[/C][C]-3.98303141691349[/C][/ROW]
[ROW][C]58[/C][C]1570[/C][C]1717.3140794361[/C][C]-147.314079436101[/C][/ROW]
[ROW][C]59[/C][C]1535[/C][C]1866.38083400405[/C][C]-331.380834004046[/C][/ROW]
[ROW][C]60[/C][C]2491[/C][C]2296.19924002635[/C][C]194.800759973647[/C][/ROW]
[ROW][C]61[/C][C]3084[/C][C]2621.72927128874[/C][C]462.270728711258[/C][/ROW]
[ROW][C]62[/C][C]2605[/C][C]2655.6163506714[/C][C]-50.6163506713951[/C][/ROW]
[ROW][C]63[/C][C]2573[/C][C]2552.22378225409[/C][C]20.7762177459103[/C][/ROW]
[ROW][C]64[/C][C]2143[/C][C]2110.79005350307[/C][C]32.2099464969306[/C][/ROW]
[ROW][C]65[/C][C]1693[/C][C]1644.65025011216[/C][C]48.3497498878448[/C][/ROW]
[ROW][C]66[/C][C]1504[/C][C]1497.54837952155[/C][C]6.45162047845224[/C][/ROW]
[ROW][C]67[/C][C]1461[/C][C]1446.78355061986[/C][C]14.2164493801411[/C][/ROW]
[ROW][C]68[/C][C]1354[/C][C]1289.09902719273[/C][C]64.9009728072683[/C][/ROW]
[ROW][C]69[/C][C]1333[/C][C]1300.97719783453[/C][C]32.022802165473[/C][/ROW]
[ROW][C]70[/C][C]1492[/C][C]1621.01006721921[/C][C]-129.010067219215[/C][/ROW]
[ROW][C]71[/C][C]1781[/C][C]1736.74081096745[/C][C]44.2591890325455[/C][/ROW]
[ROW][C]72[/C][C]1915[/C][C]2228.09945837313[/C][C]-313.099458373127[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316683&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316683&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
1329332914.9183468933518.0816531066539
1428892872.5857467408916.4142532591113
1529382927.5397215883910.4602784116091
1624972508.18254092205-11.182540922046
1718701890.78919838221-20.7891983822105
1817261736.02025923863-10.0202592386347
1916071718.67191402893-111.671914028932
2015451512.4923866124532.5076133875457
2113961564.79342809842-168.793428098423
2217872022.45830382237-235.458303822372
2320762147.44038245984-71.4403824598407
2428372451.4073439586385.592656041404
2527872864.51905974239-77.5190597423875
2638912821.234565025131069.76543497487
2731792879.72537535363299.27462464637
2820112466.53692218686-455.536922186855
2916361856.48211937403-220.482119374035
3015801705.08697323922-125.086973239217
3114891671.97292262546-182.972922625461
3213001490.47841151884-190.478411518841
3313561509.76497392601-153.764973926008
3416531947.76244673934-294.76244673934
3520132093.45974688607-80.4597468860661
3628232458.42381854697364.576181453026
3731022791.58562826597310.414371734026
3822942921.83790745205-627.837907452052
3923852852.22595677244-467.225956772444
4024442329.11704254828114.882957451723
4117481770.22388665529-22.2238866552905
4215541635.8494053106-81.8494053105956
4314981593.0909729481-95.0909729481
4413611414.59114744148-53.5911474414827
4513461437.68361173733-91.683611737333
4615641838.85435660062-274.854356600617
4716402009.42040154301-369.420401543009
4822932423.01813634408-130.018136344077
4928152729.0741854551985.9258145448111
5031372709.84065815913427.159341840867
5126792667.7578872565811.2421127434181
5219692251.23702623999-282.237026239991
5318701691.64944652884178.350553471156
5416331553.4793476907879.5206523092224
5515291510.0675806911818.9324193088191
5613661344.9314677042521.0685322957527
5713571360.98303141691-3.98303141691349
5815701717.3140794361-147.314079436101
5915351866.38083400405-331.380834004046
6024912296.19924002635194.800759973647
6130842621.72927128874462.270728711258
6226052655.6163506714-50.6163506713951
6325732552.2237822540920.7762177459103
6421432110.7900535030732.2099464969306
6516931644.6502501121648.3497498878448
6615041497.548379521556.45162047845224
6714611446.7835506198614.2164493801411
6813541289.0990271927364.9009728072683
6913331300.9771978345332.022802165473
7014921621.01006721921-129.010067219215
7117811736.7408109674544.2591890325455
7219152228.09945837313-313.099458373127







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
732576.857757663282498.02627379282655.68924153376
742531.40779754112452.518694010982610.29690107122
752442.5651479352363.584337743722521.54595812628
762021.64849288281942.60994503472100.68704073089
771577.995001384571498.933466021961657.05653674717
781430.629668660021351.469523514151509.78981380588
791382.734660631811303.403684021481462.06563724214
801239.110181569691159.663581917911318.55678122146
811244.72620512471164.978043855741324.47436639366
821525.19468536271444.419563148021605.96980757738
831660.611873642451578.668415044861742.55533224004
842075.168921285452040.75297590852109.5848666624

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2576.85775766328 & 2498.0262737928 & 2655.68924153376 \tabularnewline
74 & 2531.4077975411 & 2452.51869401098 & 2610.29690107122 \tabularnewline
75 & 2442.565147935 & 2363.58433774372 & 2521.54595812628 \tabularnewline
76 & 2021.6484928828 & 1942.6099450347 & 2100.68704073089 \tabularnewline
77 & 1577.99500138457 & 1498.93346602196 & 1657.05653674717 \tabularnewline
78 & 1430.62966866002 & 1351.46952351415 & 1509.78981380588 \tabularnewline
79 & 1382.73466063181 & 1303.40368402148 & 1462.06563724214 \tabularnewline
80 & 1239.11018156969 & 1159.66358191791 & 1318.55678122146 \tabularnewline
81 & 1244.7262051247 & 1164.97804385574 & 1324.47436639366 \tabularnewline
82 & 1525.1946853627 & 1444.41956314802 & 1605.96980757738 \tabularnewline
83 & 1660.61187364245 & 1578.66841504486 & 1742.55533224004 \tabularnewline
84 & 2075.16892128545 & 2040.7529759085 & 2109.5848666624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316683&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]2576.85775766328[/C][C]2498.0262737928[/C][C]2655.68924153376[/C][/ROW]
[ROW][C]74[/C][C]2531.4077975411[/C][C]2452.51869401098[/C][C]2610.29690107122[/C][/ROW]
[ROW][C]75[/C][C]2442.565147935[/C][C]2363.58433774372[/C][C]2521.54595812628[/C][/ROW]
[ROW][C]76[/C][C]2021.6484928828[/C][C]1942.6099450347[/C][C]2100.68704073089[/C][/ROW]
[ROW][C]77[/C][C]1577.99500138457[/C][C]1498.93346602196[/C][C]1657.05653674717[/C][/ROW]
[ROW][C]78[/C][C]1430.62966866002[/C][C]1351.46952351415[/C][C]1509.78981380588[/C][/ROW]
[ROW][C]79[/C][C]1382.73466063181[/C][C]1303.40368402148[/C][C]1462.06563724214[/C][/ROW]
[ROW][C]80[/C][C]1239.11018156969[/C][C]1159.66358191791[/C][C]1318.55678122146[/C][/ROW]
[ROW][C]81[/C][C]1244.7262051247[/C][C]1164.97804385574[/C][C]1324.47436639366[/C][/ROW]
[ROW][C]82[/C][C]1525.1946853627[/C][C]1444.41956314802[/C][C]1605.96980757738[/C][/ROW]
[ROW][C]83[/C][C]1660.61187364245[/C][C]1578.66841504486[/C][C]1742.55533224004[/C][/ROW]
[ROW][C]84[/C][C]2075.16892128545[/C][C]2040.7529759085[/C][C]2109.5848666624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316683&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316683&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
732576.857757663282498.02627379282655.68924153376
742531.40779754112452.518694010982610.29690107122
752442.5651479352363.584337743722521.54595812628
762021.64849288281942.60994503472100.68704073089
771577.995001384571498.933466021961657.05653674717
781430.629668660021351.469523514151509.78981380588
791382.734660631811303.403684021481462.06563724214
801239.110181569691159.663581917911318.55678122146
811244.72620512471164.978043855741324.47436639366
821525.19468536271444.419563148021605.96980757738
831660.611873642451578.668415044861742.55533224004
842075.168921285452040.75297590852109.5848666624



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')