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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 computationMon, 21 Jan 2019 09:51:03 +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/t1548060670yvteiahbljgk5bu.htm/, Retrieved Sat, 04 May 2024 13:56:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=316832, Retrieved Sat, 04 May 2024 13:56:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2019-01-21 08:51:03] [1b2dfd293bc63642834dc6706d432f22] [Current]
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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 time4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316832&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=316832&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316832&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 time4 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.127971652247376
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.127971652247376 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316832&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.127971652247376[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316832&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316832&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
alpha1
beta0.127971652247376
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
327042069635
425542302.26199917708251.738000822916
520142184.47732707584-170.477327075844
616551622.6610618592332.3389381407683
717211267.79952920503453.200470794969
815241391.79634225195132.203657748048
915961211.71466276712384.285337232883
1020741332.89229230725741.107707692751
1121991905.73307015396293.266929846044
1225122068.26292371587443.737076284131
1329332438.04869053137494.951309468631
1428892922.38842738607-33.3884273860722
1529382874.1156551675463.8843448324646
1624972931.29104032849-434.291040328487
1718702434.71409834142-564.714098341418
1817261735.44670212928-9.44670212927986
1916071590.2377920495116.7622079504929
2015451473.3828794962571.6171205037542
2113961420.54784073631-24.5478407363107
2217871268.40641299818518.59358700182
2320761725.7716911717350.228308828304
2428372059.59098651626777.409013483742
2527872920.07730244378-133.077302443775
2638912853.047180173421037.95281982658
2731794089.87571748145-910.875717481452
2820113261.30944692334-1250.30944692334
2916361933.30528118005-297.305281180054
3015801520.2586331255759.7413668744282
3114891471.9038345520117.0961654479909
3213001383.09165909148-83.0916590914831
3313561183.45828218957172.54171781043
3416531261.53873089937391.461269100629
3520131608.63467629703404.365323702966
3628232020.38197488285802.618025117153
3731022933.09432968062168.905670319385
3822943233.70946738534-939.709467385338
3923852305.4532942115379.5467057884657
4024442406.6330175821237.3669824178801
4117482470.41493206163-722.414932061635
4215541681.96629959753-127.966299597531
4314981471.5902408060526.4097591939474
4413611418.96994132556-57.9699413255573
4513461274.5514321534471.4485678465576
4615641268.69482343148295.305176568525
4716401524.48551479415115.514485205848
4822931615.26809432445677.73190567555
4928152354.99856607451460.001433925487
5031372935.86570961012201.13429038988
5126793283.60519707492-604.605197074916
5219692748.23287104789-779.232871047889
5318701938.51315305442-68.5131530544238
5416331830.74541165737-197.745411657372
5515291568.43960460324-39.4396046032405
5613661459.39245323818-93.3924532381805
5713571284.4408666898572.5591333101452
5815701284.72637886519285.273621134808
5915351534.233315504410.766684495594973
6024911499.33142938606991.668570613941
6130842582.23689484932501.763105150681
6226053239.44834845223-634.448348452225
6325732679.25694503517-106.256945035175
6421432633.65906821627-490.659068216265
6516932140.86861656647-447.868616566472
6615041633.55412971471-129.554129714714
6714611427.9748736796533.025126320349
6813541389.20115366054-35.2011536605442
6913331277.6964038655955.3035961344094
7014921263.77369643813228.226303561867
7117811451.98019359126329.019806408744
7219151783.08540183949131.914598160505

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2704 & 2069 & 635 \tabularnewline
4 & 2554 & 2302.26199917708 & 251.738000822916 \tabularnewline
5 & 2014 & 2184.47732707584 & -170.477327075844 \tabularnewline
6 & 1655 & 1622.66106185923 & 32.3389381407683 \tabularnewline
7 & 1721 & 1267.79952920503 & 453.200470794969 \tabularnewline
8 & 1524 & 1391.79634225195 & 132.203657748048 \tabularnewline
9 & 1596 & 1211.71466276712 & 384.285337232883 \tabularnewline
10 & 2074 & 1332.89229230725 & 741.107707692751 \tabularnewline
11 & 2199 & 1905.73307015396 & 293.266929846044 \tabularnewline
12 & 2512 & 2068.26292371587 & 443.737076284131 \tabularnewline
13 & 2933 & 2438.04869053137 & 494.951309468631 \tabularnewline
14 & 2889 & 2922.38842738607 & -33.3884273860722 \tabularnewline
15 & 2938 & 2874.11565516754 & 63.8843448324646 \tabularnewline
16 & 2497 & 2931.29104032849 & -434.291040328487 \tabularnewline
17 & 1870 & 2434.71409834142 & -564.714098341418 \tabularnewline
18 & 1726 & 1735.44670212928 & -9.44670212927986 \tabularnewline
19 & 1607 & 1590.23779204951 & 16.7622079504929 \tabularnewline
20 & 1545 & 1473.38287949625 & 71.6171205037542 \tabularnewline
21 & 1396 & 1420.54784073631 & -24.5478407363107 \tabularnewline
22 & 1787 & 1268.40641299818 & 518.59358700182 \tabularnewline
23 & 2076 & 1725.7716911717 & 350.228308828304 \tabularnewline
24 & 2837 & 2059.59098651626 & 777.409013483742 \tabularnewline
25 & 2787 & 2920.07730244378 & -133.077302443775 \tabularnewline
26 & 3891 & 2853.04718017342 & 1037.95281982658 \tabularnewline
27 & 3179 & 4089.87571748145 & -910.875717481452 \tabularnewline
28 & 2011 & 3261.30944692334 & -1250.30944692334 \tabularnewline
29 & 1636 & 1933.30528118005 & -297.305281180054 \tabularnewline
30 & 1580 & 1520.25863312557 & 59.7413668744282 \tabularnewline
31 & 1489 & 1471.90383455201 & 17.0961654479909 \tabularnewline
32 & 1300 & 1383.09165909148 & -83.0916590914831 \tabularnewline
33 & 1356 & 1183.45828218957 & 172.54171781043 \tabularnewline
34 & 1653 & 1261.53873089937 & 391.461269100629 \tabularnewline
35 & 2013 & 1608.63467629703 & 404.365323702966 \tabularnewline
36 & 2823 & 2020.38197488285 & 802.618025117153 \tabularnewline
37 & 3102 & 2933.09432968062 & 168.905670319385 \tabularnewline
38 & 2294 & 3233.70946738534 & -939.709467385338 \tabularnewline
39 & 2385 & 2305.45329421153 & 79.5467057884657 \tabularnewline
40 & 2444 & 2406.63301758212 & 37.3669824178801 \tabularnewline
41 & 1748 & 2470.41493206163 & -722.414932061635 \tabularnewline
42 & 1554 & 1681.96629959753 & -127.966299597531 \tabularnewline
43 & 1498 & 1471.59024080605 & 26.4097591939474 \tabularnewline
44 & 1361 & 1418.96994132556 & -57.9699413255573 \tabularnewline
45 & 1346 & 1274.55143215344 & 71.4485678465576 \tabularnewline
46 & 1564 & 1268.69482343148 & 295.305176568525 \tabularnewline
47 & 1640 & 1524.48551479415 & 115.514485205848 \tabularnewline
48 & 2293 & 1615.26809432445 & 677.73190567555 \tabularnewline
49 & 2815 & 2354.99856607451 & 460.001433925487 \tabularnewline
50 & 3137 & 2935.86570961012 & 201.13429038988 \tabularnewline
51 & 2679 & 3283.60519707492 & -604.605197074916 \tabularnewline
52 & 1969 & 2748.23287104789 & -779.232871047889 \tabularnewline
53 & 1870 & 1938.51315305442 & -68.5131530544238 \tabularnewline
54 & 1633 & 1830.74541165737 & -197.745411657372 \tabularnewline
55 & 1529 & 1568.43960460324 & -39.4396046032405 \tabularnewline
56 & 1366 & 1459.39245323818 & -93.3924532381805 \tabularnewline
57 & 1357 & 1284.44086668985 & 72.5591333101452 \tabularnewline
58 & 1570 & 1284.72637886519 & 285.273621134808 \tabularnewline
59 & 1535 & 1534.23331550441 & 0.766684495594973 \tabularnewline
60 & 2491 & 1499.33142938606 & 991.668570613941 \tabularnewline
61 & 3084 & 2582.23689484932 & 501.763105150681 \tabularnewline
62 & 2605 & 3239.44834845223 & -634.448348452225 \tabularnewline
63 & 2573 & 2679.25694503517 & -106.256945035175 \tabularnewline
64 & 2143 & 2633.65906821627 & -490.659068216265 \tabularnewline
65 & 1693 & 2140.86861656647 & -447.868616566472 \tabularnewline
66 & 1504 & 1633.55412971471 & -129.554129714714 \tabularnewline
67 & 1461 & 1427.97487367965 & 33.025126320349 \tabularnewline
68 & 1354 & 1389.20115366054 & -35.2011536605442 \tabularnewline
69 & 1333 & 1277.69640386559 & 55.3035961344094 \tabularnewline
70 & 1492 & 1263.77369643813 & 228.226303561867 \tabularnewline
71 & 1781 & 1451.98019359126 & 329.019806408744 \tabularnewline
72 & 1915 & 1783.08540183949 & 131.914598160505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316832&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]2704[/C][C]2069[/C][C]635[/C][/ROW]
[ROW][C]4[/C][C]2554[/C][C]2302.26199917708[/C][C]251.738000822916[/C][/ROW]
[ROW][C]5[/C][C]2014[/C][C]2184.47732707584[/C][C]-170.477327075844[/C][/ROW]
[ROW][C]6[/C][C]1655[/C][C]1622.66106185923[/C][C]32.3389381407683[/C][/ROW]
[ROW][C]7[/C][C]1721[/C][C]1267.79952920503[/C][C]453.200470794969[/C][/ROW]
[ROW][C]8[/C][C]1524[/C][C]1391.79634225195[/C][C]132.203657748048[/C][/ROW]
[ROW][C]9[/C][C]1596[/C][C]1211.71466276712[/C][C]384.285337232883[/C][/ROW]
[ROW][C]10[/C][C]2074[/C][C]1332.89229230725[/C][C]741.107707692751[/C][/ROW]
[ROW][C]11[/C][C]2199[/C][C]1905.73307015396[/C][C]293.266929846044[/C][/ROW]
[ROW][C]12[/C][C]2512[/C][C]2068.26292371587[/C][C]443.737076284131[/C][/ROW]
[ROW][C]13[/C][C]2933[/C][C]2438.04869053137[/C][C]494.951309468631[/C][/ROW]
[ROW][C]14[/C][C]2889[/C][C]2922.38842738607[/C][C]-33.3884273860722[/C][/ROW]
[ROW][C]15[/C][C]2938[/C][C]2874.11565516754[/C][C]63.8843448324646[/C][/ROW]
[ROW][C]16[/C][C]2497[/C][C]2931.29104032849[/C][C]-434.291040328487[/C][/ROW]
[ROW][C]17[/C][C]1870[/C][C]2434.71409834142[/C][C]-564.714098341418[/C][/ROW]
[ROW][C]18[/C][C]1726[/C][C]1735.44670212928[/C][C]-9.44670212927986[/C][/ROW]
[ROW][C]19[/C][C]1607[/C][C]1590.23779204951[/C][C]16.7622079504929[/C][/ROW]
[ROW][C]20[/C][C]1545[/C][C]1473.38287949625[/C][C]71.6171205037542[/C][/ROW]
[ROW][C]21[/C][C]1396[/C][C]1420.54784073631[/C][C]-24.5478407363107[/C][/ROW]
[ROW][C]22[/C][C]1787[/C][C]1268.40641299818[/C][C]518.59358700182[/C][/ROW]
[ROW][C]23[/C][C]2076[/C][C]1725.7716911717[/C][C]350.228308828304[/C][/ROW]
[ROW][C]24[/C][C]2837[/C][C]2059.59098651626[/C][C]777.409013483742[/C][/ROW]
[ROW][C]25[/C][C]2787[/C][C]2920.07730244378[/C][C]-133.077302443775[/C][/ROW]
[ROW][C]26[/C][C]3891[/C][C]2853.04718017342[/C][C]1037.95281982658[/C][/ROW]
[ROW][C]27[/C][C]3179[/C][C]4089.87571748145[/C][C]-910.875717481452[/C][/ROW]
[ROW][C]28[/C][C]2011[/C][C]3261.30944692334[/C][C]-1250.30944692334[/C][/ROW]
[ROW][C]29[/C][C]1636[/C][C]1933.30528118005[/C][C]-297.305281180054[/C][/ROW]
[ROW][C]30[/C][C]1580[/C][C]1520.25863312557[/C][C]59.7413668744282[/C][/ROW]
[ROW][C]31[/C][C]1489[/C][C]1471.90383455201[/C][C]17.0961654479909[/C][/ROW]
[ROW][C]32[/C][C]1300[/C][C]1383.09165909148[/C][C]-83.0916590914831[/C][/ROW]
[ROW][C]33[/C][C]1356[/C][C]1183.45828218957[/C][C]172.54171781043[/C][/ROW]
[ROW][C]34[/C][C]1653[/C][C]1261.53873089937[/C][C]391.461269100629[/C][/ROW]
[ROW][C]35[/C][C]2013[/C][C]1608.63467629703[/C][C]404.365323702966[/C][/ROW]
[ROW][C]36[/C][C]2823[/C][C]2020.38197488285[/C][C]802.618025117153[/C][/ROW]
[ROW][C]37[/C][C]3102[/C][C]2933.09432968062[/C][C]168.905670319385[/C][/ROW]
[ROW][C]38[/C][C]2294[/C][C]3233.70946738534[/C][C]-939.709467385338[/C][/ROW]
[ROW][C]39[/C][C]2385[/C][C]2305.45329421153[/C][C]79.5467057884657[/C][/ROW]
[ROW][C]40[/C][C]2444[/C][C]2406.63301758212[/C][C]37.3669824178801[/C][/ROW]
[ROW][C]41[/C][C]1748[/C][C]2470.41493206163[/C][C]-722.414932061635[/C][/ROW]
[ROW][C]42[/C][C]1554[/C][C]1681.96629959753[/C][C]-127.966299597531[/C][/ROW]
[ROW][C]43[/C][C]1498[/C][C]1471.59024080605[/C][C]26.4097591939474[/C][/ROW]
[ROW][C]44[/C][C]1361[/C][C]1418.96994132556[/C][C]-57.9699413255573[/C][/ROW]
[ROW][C]45[/C][C]1346[/C][C]1274.55143215344[/C][C]71.4485678465576[/C][/ROW]
[ROW][C]46[/C][C]1564[/C][C]1268.69482343148[/C][C]295.305176568525[/C][/ROW]
[ROW][C]47[/C][C]1640[/C][C]1524.48551479415[/C][C]115.514485205848[/C][/ROW]
[ROW][C]48[/C][C]2293[/C][C]1615.26809432445[/C][C]677.73190567555[/C][/ROW]
[ROW][C]49[/C][C]2815[/C][C]2354.99856607451[/C][C]460.001433925487[/C][/ROW]
[ROW][C]50[/C][C]3137[/C][C]2935.86570961012[/C][C]201.13429038988[/C][/ROW]
[ROW][C]51[/C][C]2679[/C][C]3283.60519707492[/C][C]-604.605197074916[/C][/ROW]
[ROW][C]52[/C][C]1969[/C][C]2748.23287104789[/C][C]-779.232871047889[/C][/ROW]
[ROW][C]53[/C][C]1870[/C][C]1938.51315305442[/C][C]-68.5131530544238[/C][/ROW]
[ROW][C]54[/C][C]1633[/C][C]1830.74541165737[/C][C]-197.745411657372[/C][/ROW]
[ROW][C]55[/C][C]1529[/C][C]1568.43960460324[/C][C]-39.4396046032405[/C][/ROW]
[ROW][C]56[/C][C]1366[/C][C]1459.39245323818[/C][C]-93.3924532381805[/C][/ROW]
[ROW][C]57[/C][C]1357[/C][C]1284.44086668985[/C][C]72.5591333101452[/C][/ROW]
[ROW][C]58[/C][C]1570[/C][C]1284.72637886519[/C][C]285.273621134808[/C][/ROW]
[ROW][C]59[/C][C]1535[/C][C]1534.23331550441[/C][C]0.766684495594973[/C][/ROW]
[ROW][C]60[/C][C]2491[/C][C]1499.33142938606[/C][C]991.668570613941[/C][/ROW]
[ROW][C]61[/C][C]3084[/C][C]2582.23689484932[/C][C]501.763105150681[/C][/ROW]
[ROW][C]62[/C][C]2605[/C][C]3239.44834845223[/C][C]-634.448348452225[/C][/ROW]
[ROW][C]63[/C][C]2573[/C][C]2679.25694503517[/C][C]-106.256945035175[/C][/ROW]
[ROW][C]64[/C][C]2143[/C][C]2633.65906821627[/C][C]-490.659068216265[/C][/ROW]
[ROW][C]65[/C][C]1693[/C][C]2140.86861656647[/C][C]-447.868616566472[/C][/ROW]
[ROW][C]66[/C][C]1504[/C][C]1633.55412971471[/C][C]-129.554129714714[/C][/ROW]
[ROW][C]67[/C][C]1461[/C][C]1427.97487367965[/C][C]33.025126320349[/C][/ROW]
[ROW][C]68[/C][C]1354[/C][C]1389.20115366054[/C][C]-35.2011536605442[/C][/ROW]
[ROW][C]69[/C][C]1333[/C][C]1277.69640386559[/C][C]55.3035961344094[/C][/ROW]
[ROW][C]70[/C][C]1492[/C][C]1263.77369643813[/C][C]228.226303561867[/C][/ROW]
[ROW][C]71[/C][C]1781[/C][C]1451.98019359126[/C][C]329.019806408744[/C][/ROW]
[ROW][C]72[/C][C]1915[/C][C]1783.08540183949[/C][C]131.914598160505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316832&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316832&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
327042069635
425542302.26199917708251.738000822916
520142184.47732707584-170.477327075844
616551622.6610618592332.3389381407683
717211267.79952920503453.200470794969
815241391.79634225195132.203657748048
915961211.71466276712384.285337232883
1020741332.89229230725741.107707692751
1121991905.73307015396293.266929846044
1225122068.26292371587443.737076284131
1329332438.04869053137494.951309468631
1428892922.38842738607-33.3884273860722
1529382874.1156551675463.8843448324646
1624972931.29104032849-434.291040328487
1718702434.71409834142-564.714098341418
1817261735.44670212928-9.44670212927986
1916071590.2377920495116.7622079504929
2015451473.3828794962571.6171205037542
2113961420.54784073631-24.5478407363107
2217871268.40641299818518.59358700182
2320761725.7716911717350.228308828304
2428372059.59098651626777.409013483742
2527872920.07730244378-133.077302443775
2638912853.047180173421037.95281982658
2731794089.87571748145-910.875717481452
2820113261.30944692334-1250.30944692334
2916361933.30528118005-297.305281180054
3015801520.2586331255759.7413668744282
3114891471.9038345520117.0961654479909
3213001383.09165909148-83.0916590914831
3313561183.45828218957172.54171781043
3416531261.53873089937391.461269100629
3520131608.63467629703404.365323702966
3628232020.38197488285802.618025117153
3731022933.09432968062168.905670319385
3822943233.70946738534-939.709467385338
3923852305.4532942115379.5467057884657
4024442406.6330175821237.3669824178801
4117482470.41493206163-722.414932061635
4215541681.96629959753-127.966299597531
4314981471.5902408060526.4097591939474
4413611418.96994132556-57.9699413255573
4513461274.5514321534471.4485678465576
4615641268.69482343148295.305176568525
4716401524.48551479415115.514485205848
4822931615.26809432445677.73190567555
4928152354.99856607451460.001433925487
5031372935.86570961012201.13429038988
5126793283.60519707492-604.605197074916
5219692748.23287104789-779.232871047889
5318701938.51315305442-68.5131530544238
5416331830.74541165737-197.745411657372
5515291568.43960460324-39.4396046032405
5613661459.39245323818-93.3924532381805
5713571284.4408666898572.5591333101452
5815701284.72637886519285.273621134808
5915351534.233315504410.766684495594973
6024911499.33142938606991.668570613941
6130842582.23689484932501.763105150681
6226053239.44834845223-634.448348452225
6325732679.25694503517-106.256945035175
6421432633.65906821627-490.659068216265
6516932140.86861656647-447.868616566472
6615041633.55412971471-129.554129714714
6714611427.9748736796533.025126320349
6813541389.20115366054-35.2011536605442
6913331277.6964038655955.3035961344094
7014921263.77369643813228.226303561867
7117811451.98019359126329.019806408744
7219151783.08540183949131.914598160505







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731933.966730921641067.036449308172800.89701253512
741952.93346184329646.103981299423259.76294238715
751971.90019276493270.9234113348473672.87697419501
761990.86692368657-90.65673682256724072.39058419571
772009.83365460822-449.9785298781914469.64583909462
782028.80038552986-812.2811319337574869.88190299348
792047.7671164515-1180.322387245695275.85662014869
802066.73384737315-1555.661137276025689.12883202232
812085.70057829479-1939.210775823676110.61193241325
822104.66730921643-2331.510806214076540.84542464694
832123.63404013808-2732.872573838056980.14065411421
842142.60077105972-3143.46284420867428.66438632804

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1933.96673092164 & 1067.03644930817 & 2800.89701253512 \tabularnewline
74 & 1952.93346184329 & 646.10398129942 & 3259.76294238715 \tabularnewline
75 & 1971.90019276493 & 270.923411334847 & 3672.87697419501 \tabularnewline
76 & 1990.86692368657 & -90.6567368225672 & 4072.39058419571 \tabularnewline
77 & 2009.83365460822 & -449.978529878191 & 4469.64583909462 \tabularnewline
78 & 2028.80038552986 & -812.281131933757 & 4869.88190299348 \tabularnewline
79 & 2047.7671164515 & -1180.32238724569 & 5275.85662014869 \tabularnewline
80 & 2066.73384737315 & -1555.66113727602 & 5689.12883202232 \tabularnewline
81 & 2085.70057829479 & -1939.21077582367 & 6110.61193241325 \tabularnewline
82 & 2104.66730921643 & -2331.51080621407 & 6540.84542464694 \tabularnewline
83 & 2123.63404013808 & -2732.87257383805 & 6980.14065411421 \tabularnewline
84 & 2142.60077105972 & -3143.4628442086 & 7428.66438632804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316832&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]1933.96673092164[/C][C]1067.03644930817[/C][C]2800.89701253512[/C][/ROW]
[ROW][C]74[/C][C]1952.93346184329[/C][C]646.10398129942[/C][C]3259.76294238715[/C][/ROW]
[ROW][C]75[/C][C]1971.90019276493[/C][C]270.923411334847[/C][C]3672.87697419501[/C][/ROW]
[ROW][C]76[/C][C]1990.86692368657[/C][C]-90.6567368225672[/C][C]4072.39058419571[/C][/ROW]
[ROW][C]77[/C][C]2009.83365460822[/C][C]-449.978529878191[/C][C]4469.64583909462[/C][/ROW]
[ROW][C]78[/C][C]2028.80038552986[/C][C]-812.281131933757[/C][C]4869.88190299348[/C][/ROW]
[ROW][C]79[/C][C]2047.7671164515[/C][C]-1180.32238724569[/C][C]5275.85662014869[/C][/ROW]
[ROW][C]80[/C][C]2066.73384737315[/C][C]-1555.66113727602[/C][C]5689.12883202232[/C][/ROW]
[ROW][C]81[/C][C]2085.70057829479[/C][C]-1939.21077582367[/C][C]6110.61193241325[/C][/ROW]
[ROW][C]82[/C][C]2104.66730921643[/C][C]-2331.51080621407[/C][C]6540.84542464694[/C][/ROW]
[ROW][C]83[/C][C]2123.63404013808[/C][C]-2732.87257383805[/C][C]6980.14065411421[/C][/ROW]
[ROW][C]84[/C][C]2142.60077105972[/C][C]-3143.4628442086[/C][C]7428.66438632804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316832&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316832&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
731933.966730921641067.036449308172800.89701253512
741952.93346184329646.103981299423259.76294238715
751971.90019276493270.9234113348473672.87697419501
761990.86692368657-90.65673682256724072.39058419571
772009.83365460822-449.9785298781914469.64583909462
782028.80038552986-812.2811319337574869.88190299348
792047.7671164515-1180.322387245695275.85662014869
802066.73384737315-1555.661137276025689.12883202232
812085.70057829479-1939.210775823676110.61193241325
822104.66730921643-2331.510806214076540.84542464694
832123.63404013808-2732.872573838056980.14065411421
842142.60077105972-3143.46284420867428.66438632804



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