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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 20 Apr 2015 22:05:03 +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/2015/Apr/20/t14295639600lh4k2qzmv2zb5u.htm/, Retrieved Thu, 09 May 2024 07:23:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278771, Retrieved Thu, 09 May 2024 07:23:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-20 21:05:03] [4fa22ecf638daf61dea82ccfb30e12bf] [Current]
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Dataseries X:
2201
1239
966
1001
1079
909
1038
817
817
926
555
156
1604
610
635
623
744
939
993
634
858
849
458
109
1538
739
855
834
1004
1355
968
811
1121
960
973
233
1662
894
966
859
946
1156
895
952
1078
689
621
587
1425
1022
1406
776
1105
2244
679
665
704
449
560
229
1158
908
1104
731
989
1308
757
896
917
844
815
401




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278771&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]1 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=278771&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278771&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.353448151874362
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.353448151874362 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278771&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]0.353448151874362[/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=278771&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278771&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
alpha0.353448151874362
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
212392201-962
39661860.98287789686-894.982877896864
410011544.65283374502-543.652833745019
510791352.49974439658-273.499744396582
69091255.8317652015-346.8317652015
710381133.24471877971-95.244718779707
88171099.58064895123-282.580648951226
9817999.703040823957-182.703040823957
10926935.126988702904-9.12698870290353
11555931.901071413684-376.901071413684
12156798.68608428305-642.68608428305
131604571.5298755578351032.47012444216
14610936.454532907411-326.454532907411
15635821.069781580279-186.069781580279
16623755.303761161063-132.303761161063
17744708.54124129265835.4587587073418
18939721.074074025527217.925925974473
19993798.099589806714194.900410193286
20634866.986779589086-232.986779589086
21858784.63803293216473.3619670678358
22849810.56768461015938.4323153898413
23458824.151515456951-366.151515456951
24109694.735939012695-585.735939012695
251538487.7086538822631050.29134611774
26739858.932189097214-119.932189097214
27855816.54237851055738.457621489443
28834830.1351537514843.86484624851562
291004831.501176515301172.498823484699
301355892.47056687647462.52943312353
319681055.95074020148-87.9507402014779
328111024.86471362128-213.864713621283
331121949.274625840701171.725374159299
349601009.97064196724-49.9706419672386
35973992.308610915943-19.3086109159428
36233985.484018072442-752.484018072442
371662719.519932569743942.480067430257
388941052.63777058139-158.637770581392
39966996.56754375193-30.5675437519299
40859985.763501905471-126.763501905471
41946940.959176431865.04082356813956
421156942.740846205944213.259153794056
438951018.11689998474-123.116899984744
44952974.601459220635-22.6014592206353
451078966.613015229438111.386984770562
466891005.98253913945-316.982539139451
47621893.945646504169-272.945646504169
48587797.473512185118-210.473512185118
491425723.082038284782701.917961715218
501022971.17364462044550.8263553795548
511406989.138125995858416.861874004142
527761136.47718494951-360.477184949506
5311051009.0671901362395.9328098637698
5422441042.974464486691201.02553551331
556791467.47472036779-788.474720367789
566651188.78978765414-523.789787654139
577041003.65725523712-299.657255237119
58449897.743952177815-448.743952177815
59560739.136231615769-179.136231615769
60229675.820861617438-446.820861617438
611158517.892853859844640.107146140156
62908744.137541664655163.862458335345
631104802.054424724872301.945575275128
64731908.776530272507-177.776530272507
65989845.941744201053143.058255798947
661308896.505420323561411.494579676439
677571041.94741901652-284.947419016516
68896941.233280383759-45.2332803837587
69917925.245661028904-8.24566102890435
70844922.331247377256-78.3312473772557
71815894.645212757751-79.6452127577513
72401866.494759502884-465.494759502884

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1239 & 2201 & -962 \tabularnewline
3 & 966 & 1860.98287789686 & -894.982877896864 \tabularnewline
4 & 1001 & 1544.65283374502 & -543.652833745019 \tabularnewline
5 & 1079 & 1352.49974439658 & -273.499744396582 \tabularnewline
6 & 909 & 1255.8317652015 & -346.8317652015 \tabularnewline
7 & 1038 & 1133.24471877971 & -95.244718779707 \tabularnewline
8 & 817 & 1099.58064895123 & -282.580648951226 \tabularnewline
9 & 817 & 999.703040823957 & -182.703040823957 \tabularnewline
10 & 926 & 935.126988702904 & -9.12698870290353 \tabularnewline
11 & 555 & 931.901071413684 & -376.901071413684 \tabularnewline
12 & 156 & 798.68608428305 & -642.68608428305 \tabularnewline
13 & 1604 & 571.529875557835 & 1032.47012444216 \tabularnewline
14 & 610 & 936.454532907411 & -326.454532907411 \tabularnewline
15 & 635 & 821.069781580279 & -186.069781580279 \tabularnewline
16 & 623 & 755.303761161063 & -132.303761161063 \tabularnewline
17 & 744 & 708.541241292658 & 35.4587587073418 \tabularnewline
18 & 939 & 721.074074025527 & 217.925925974473 \tabularnewline
19 & 993 & 798.099589806714 & 194.900410193286 \tabularnewline
20 & 634 & 866.986779589086 & -232.986779589086 \tabularnewline
21 & 858 & 784.638032932164 & 73.3619670678358 \tabularnewline
22 & 849 & 810.567684610159 & 38.4323153898413 \tabularnewline
23 & 458 & 824.151515456951 & -366.151515456951 \tabularnewline
24 & 109 & 694.735939012695 & -585.735939012695 \tabularnewline
25 & 1538 & 487.708653882263 & 1050.29134611774 \tabularnewline
26 & 739 & 858.932189097214 & -119.932189097214 \tabularnewline
27 & 855 & 816.542378510557 & 38.457621489443 \tabularnewline
28 & 834 & 830.135153751484 & 3.86484624851562 \tabularnewline
29 & 1004 & 831.501176515301 & 172.498823484699 \tabularnewline
30 & 1355 & 892.47056687647 & 462.52943312353 \tabularnewline
31 & 968 & 1055.95074020148 & -87.9507402014779 \tabularnewline
32 & 811 & 1024.86471362128 & -213.864713621283 \tabularnewline
33 & 1121 & 949.274625840701 & 171.725374159299 \tabularnewline
34 & 960 & 1009.97064196724 & -49.9706419672386 \tabularnewline
35 & 973 & 992.308610915943 & -19.3086109159428 \tabularnewline
36 & 233 & 985.484018072442 & -752.484018072442 \tabularnewline
37 & 1662 & 719.519932569743 & 942.480067430257 \tabularnewline
38 & 894 & 1052.63777058139 & -158.637770581392 \tabularnewline
39 & 966 & 996.56754375193 & -30.5675437519299 \tabularnewline
40 & 859 & 985.763501905471 & -126.763501905471 \tabularnewline
41 & 946 & 940.95917643186 & 5.04082356813956 \tabularnewline
42 & 1156 & 942.740846205944 & 213.259153794056 \tabularnewline
43 & 895 & 1018.11689998474 & -123.116899984744 \tabularnewline
44 & 952 & 974.601459220635 & -22.6014592206353 \tabularnewline
45 & 1078 & 966.613015229438 & 111.386984770562 \tabularnewline
46 & 689 & 1005.98253913945 & -316.982539139451 \tabularnewline
47 & 621 & 893.945646504169 & -272.945646504169 \tabularnewline
48 & 587 & 797.473512185118 & -210.473512185118 \tabularnewline
49 & 1425 & 723.082038284782 & 701.917961715218 \tabularnewline
50 & 1022 & 971.173644620445 & 50.8263553795548 \tabularnewline
51 & 1406 & 989.138125995858 & 416.861874004142 \tabularnewline
52 & 776 & 1136.47718494951 & -360.477184949506 \tabularnewline
53 & 1105 & 1009.06719013623 & 95.9328098637698 \tabularnewline
54 & 2244 & 1042.97446448669 & 1201.02553551331 \tabularnewline
55 & 679 & 1467.47472036779 & -788.474720367789 \tabularnewline
56 & 665 & 1188.78978765414 & -523.789787654139 \tabularnewline
57 & 704 & 1003.65725523712 & -299.657255237119 \tabularnewline
58 & 449 & 897.743952177815 & -448.743952177815 \tabularnewline
59 & 560 & 739.136231615769 & -179.136231615769 \tabularnewline
60 & 229 & 675.820861617438 & -446.820861617438 \tabularnewline
61 & 1158 & 517.892853859844 & 640.107146140156 \tabularnewline
62 & 908 & 744.137541664655 & 163.862458335345 \tabularnewline
63 & 1104 & 802.054424724872 & 301.945575275128 \tabularnewline
64 & 731 & 908.776530272507 & -177.776530272507 \tabularnewline
65 & 989 & 845.941744201053 & 143.058255798947 \tabularnewline
66 & 1308 & 896.505420323561 & 411.494579676439 \tabularnewline
67 & 757 & 1041.94741901652 & -284.947419016516 \tabularnewline
68 & 896 & 941.233280383759 & -45.2332803837587 \tabularnewline
69 & 917 & 925.245661028904 & -8.24566102890435 \tabularnewline
70 & 844 & 922.331247377256 & -78.3312473772557 \tabularnewline
71 & 815 & 894.645212757751 & -79.6452127577513 \tabularnewline
72 & 401 & 866.494759502884 & -465.494759502884 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278771&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]1239[/C][C]2201[/C][C]-962[/C][/ROW]
[ROW][C]3[/C][C]966[/C][C]1860.98287789686[/C][C]-894.982877896864[/C][/ROW]
[ROW][C]4[/C][C]1001[/C][C]1544.65283374502[/C][C]-543.652833745019[/C][/ROW]
[ROW][C]5[/C][C]1079[/C][C]1352.49974439658[/C][C]-273.499744396582[/C][/ROW]
[ROW][C]6[/C][C]909[/C][C]1255.8317652015[/C][C]-346.8317652015[/C][/ROW]
[ROW][C]7[/C][C]1038[/C][C]1133.24471877971[/C][C]-95.244718779707[/C][/ROW]
[ROW][C]8[/C][C]817[/C][C]1099.58064895123[/C][C]-282.580648951226[/C][/ROW]
[ROW][C]9[/C][C]817[/C][C]999.703040823957[/C][C]-182.703040823957[/C][/ROW]
[ROW][C]10[/C][C]926[/C][C]935.126988702904[/C][C]-9.12698870290353[/C][/ROW]
[ROW][C]11[/C][C]555[/C][C]931.901071413684[/C][C]-376.901071413684[/C][/ROW]
[ROW][C]12[/C][C]156[/C][C]798.68608428305[/C][C]-642.68608428305[/C][/ROW]
[ROW][C]13[/C][C]1604[/C][C]571.529875557835[/C][C]1032.47012444216[/C][/ROW]
[ROW][C]14[/C][C]610[/C][C]936.454532907411[/C][C]-326.454532907411[/C][/ROW]
[ROW][C]15[/C][C]635[/C][C]821.069781580279[/C][C]-186.069781580279[/C][/ROW]
[ROW][C]16[/C][C]623[/C][C]755.303761161063[/C][C]-132.303761161063[/C][/ROW]
[ROW][C]17[/C][C]744[/C][C]708.541241292658[/C][C]35.4587587073418[/C][/ROW]
[ROW][C]18[/C][C]939[/C][C]721.074074025527[/C][C]217.925925974473[/C][/ROW]
[ROW][C]19[/C][C]993[/C][C]798.099589806714[/C][C]194.900410193286[/C][/ROW]
[ROW][C]20[/C][C]634[/C][C]866.986779589086[/C][C]-232.986779589086[/C][/ROW]
[ROW][C]21[/C][C]858[/C][C]784.638032932164[/C][C]73.3619670678358[/C][/ROW]
[ROW][C]22[/C][C]849[/C][C]810.567684610159[/C][C]38.4323153898413[/C][/ROW]
[ROW][C]23[/C][C]458[/C][C]824.151515456951[/C][C]-366.151515456951[/C][/ROW]
[ROW][C]24[/C][C]109[/C][C]694.735939012695[/C][C]-585.735939012695[/C][/ROW]
[ROW][C]25[/C][C]1538[/C][C]487.708653882263[/C][C]1050.29134611774[/C][/ROW]
[ROW][C]26[/C][C]739[/C][C]858.932189097214[/C][C]-119.932189097214[/C][/ROW]
[ROW][C]27[/C][C]855[/C][C]816.542378510557[/C][C]38.457621489443[/C][/ROW]
[ROW][C]28[/C][C]834[/C][C]830.135153751484[/C][C]3.86484624851562[/C][/ROW]
[ROW][C]29[/C][C]1004[/C][C]831.501176515301[/C][C]172.498823484699[/C][/ROW]
[ROW][C]30[/C][C]1355[/C][C]892.47056687647[/C][C]462.52943312353[/C][/ROW]
[ROW][C]31[/C][C]968[/C][C]1055.95074020148[/C][C]-87.9507402014779[/C][/ROW]
[ROW][C]32[/C][C]811[/C][C]1024.86471362128[/C][C]-213.864713621283[/C][/ROW]
[ROW][C]33[/C][C]1121[/C][C]949.274625840701[/C][C]171.725374159299[/C][/ROW]
[ROW][C]34[/C][C]960[/C][C]1009.97064196724[/C][C]-49.9706419672386[/C][/ROW]
[ROW][C]35[/C][C]973[/C][C]992.308610915943[/C][C]-19.3086109159428[/C][/ROW]
[ROW][C]36[/C][C]233[/C][C]985.484018072442[/C][C]-752.484018072442[/C][/ROW]
[ROW][C]37[/C][C]1662[/C][C]719.519932569743[/C][C]942.480067430257[/C][/ROW]
[ROW][C]38[/C][C]894[/C][C]1052.63777058139[/C][C]-158.637770581392[/C][/ROW]
[ROW][C]39[/C][C]966[/C][C]996.56754375193[/C][C]-30.5675437519299[/C][/ROW]
[ROW][C]40[/C][C]859[/C][C]985.763501905471[/C][C]-126.763501905471[/C][/ROW]
[ROW][C]41[/C][C]946[/C][C]940.95917643186[/C][C]5.04082356813956[/C][/ROW]
[ROW][C]42[/C][C]1156[/C][C]942.740846205944[/C][C]213.259153794056[/C][/ROW]
[ROW][C]43[/C][C]895[/C][C]1018.11689998474[/C][C]-123.116899984744[/C][/ROW]
[ROW][C]44[/C][C]952[/C][C]974.601459220635[/C][C]-22.6014592206353[/C][/ROW]
[ROW][C]45[/C][C]1078[/C][C]966.613015229438[/C][C]111.386984770562[/C][/ROW]
[ROW][C]46[/C][C]689[/C][C]1005.98253913945[/C][C]-316.982539139451[/C][/ROW]
[ROW][C]47[/C][C]621[/C][C]893.945646504169[/C][C]-272.945646504169[/C][/ROW]
[ROW][C]48[/C][C]587[/C][C]797.473512185118[/C][C]-210.473512185118[/C][/ROW]
[ROW][C]49[/C][C]1425[/C][C]723.082038284782[/C][C]701.917961715218[/C][/ROW]
[ROW][C]50[/C][C]1022[/C][C]971.173644620445[/C][C]50.8263553795548[/C][/ROW]
[ROW][C]51[/C][C]1406[/C][C]989.138125995858[/C][C]416.861874004142[/C][/ROW]
[ROW][C]52[/C][C]776[/C][C]1136.47718494951[/C][C]-360.477184949506[/C][/ROW]
[ROW][C]53[/C][C]1105[/C][C]1009.06719013623[/C][C]95.9328098637698[/C][/ROW]
[ROW][C]54[/C][C]2244[/C][C]1042.97446448669[/C][C]1201.02553551331[/C][/ROW]
[ROW][C]55[/C][C]679[/C][C]1467.47472036779[/C][C]-788.474720367789[/C][/ROW]
[ROW][C]56[/C][C]665[/C][C]1188.78978765414[/C][C]-523.789787654139[/C][/ROW]
[ROW][C]57[/C][C]704[/C][C]1003.65725523712[/C][C]-299.657255237119[/C][/ROW]
[ROW][C]58[/C][C]449[/C][C]897.743952177815[/C][C]-448.743952177815[/C][/ROW]
[ROW][C]59[/C][C]560[/C][C]739.136231615769[/C][C]-179.136231615769[/C][/ROW]
[ROW][C]60[/C][C]229[/C][C]675.820861617438[/C][C]-446.820861617438[/C][/ROW]
[ROW][C]61[/C][C]1158[/C][C]517.892853859844[/C][C]640.107146140156[/C][/ROW]
[ROW][C]62[/C][C]908[/C][C]744.137541664655[/C][C]163.862458335345[/C][/ROW]
[ROW][C]63[/C][C]1104[/C][C]802.054424724872[/C][C]301.945575275128[/C][/ROW]
[ROW][C]64[/C][C]731[/C][C]908.776530272507[/C][C]-177.776530272507[/C][/ROW]
[ROW][C]65[/C][C]989[/C][C]845.941744201053[/C][C]143.058255798947[/C][/ROW]
[ROW][C]66[/C][C]1308[/C][C]896.505420323561[/C][C]411.494579676439[/C][/ROW]
[ROW][C]67[/C][C]757[/C][C]1041.94741901652[/C][C]-284.947419016516[/C][/ROW]
[ROW][C]68[/C][C]896[/C][C]941.233280383759[/C][C]-45.2332803837587[/C][/ROW]
[ROW][C]69[/C][C]917[/C][C]925.245661028904[/C][C]-8.24566102890435[/C][/ROW]
[ROW][C]70[/C][C]844[/C][C]922.331247377256[/C][C]-78.3312473772557[/C][/ROW]
[ROW][C]71[/C][C]815[/C][C]894.645212757751[/C][C]-79.6452127577513[/C][/ROW]
[ROW][C]72[/C][C]401[/C][C]866.494759502884[/C][C]-465.494759502884[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278771&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278771&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
212392201-962
39661860.98287789686-894.982877896864
410011544.65283374502-543.652833745019
510791352.49974439658-273.499744396582
69091255.8317652015-346.8317652015
710381133.24471877971-95.244718779707
88171099.58064895123-282.580648951226
9817999.703040823957-182.703040823957
10926935.126988702904-9.12698870290353
11555931.901071413684-376.901071413684
12156798.68608428305-642.68608428305
131604571.5298755578351032.47012444216
14610936.454532907411-326.454532907411
15635821.069781580279-186.069781580279
16623755.303761161063-132.303761161063
17744708.54124129265835.4587587073418
18939721.074074025527217.925925974473
19993798.099589806714194.900410193286
20634866.986779589086-232.986779589086
21858784.63803293216473.3619670678358
22849810.56768461015938.4323153898413
23458824.151515456951-366.151515456951
24109694.735939012695-585.735939012695
251538487.7086538822631050.29134611774
26739858.932189097214-119.932189097214
27855816.54237851055738.457621489443
28834830.1351537514843.86484624851562
291004831.501176515301172.498823484699
301355892.47056687647462.52943312353
319681055.95074020148-87.9507402014779
328111024.86471362128-213.864713621283
331121949.274625840701171.725374159299
349601009.97064196724-49.9706419672386
35973992.308610915943-19.3086109159428
36233985.484018072442-752.484018072442
371662719.519932569743942.480067430257
388941052.63777058139-158.637770581392
39966996.56754375193-30.5675437519299
40859985.763501905471-126.763501905471
41946940.959176431865.04082356813956
421156942.740846205944213.259153794056
438951018.11689998474-123.116899984744
44952974.601459220635-22.6014592206353
451078966.613015229438111.386984770562
466891005.98253913945-316.982539139451
47621893.945646504169-272.945646504169
48587797.473512185118-210.473512185118
491425723.082038284782701.917961715218
501022971.17364462044550.8263553795548
511406989.138125995858416.861874004142
527761136.47718494951-360.477184949506
5311051009.0671901362395.9328098637698
5422441042.974464486691201.02553551331
556791467.47472036779-788.474720367789
566651188.78978765414-523.789787654139
577041003.65725523712-299.657255237119
58449897.743952177815-448.743952177815
59560739.136231615769-179.136231615769
60229675.820861617438-446.820861617438
611158517.892853859844640.107146140156
62908744.137541664655163.862458335345
631104802.054424724872301.945575275128
64731908.776530272507-177.776530272507
65989845.941744201053143.058255798947
661308896.505420323561411.494579676439
677571041.94741901652-284.947419016516
68896941.233280383759-45.2332803837587
69917925.245661028904-8.24566102890435
70844922.331247377256-78.3312473772557
71815894.645212757751-79.6452127577513
72401866.494759502884-465.494759502884







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73701.966497049389-124.9509754222151528.88396952099
74701.966497049389-175.0829272759431579.01592137472
75701.966497049389-222.500310975631626.43330507441
76701.966497049389-267.6014817796031671.53447587838
77701.966497049389-310.6959600413771714.62895414015
78701.966497049389-352.029915862761755.96290996154
79701.966497049389-391.8029598574351795.73595395621
80701.966497049389-430.1796115835991834.11260568238
81701.966497049389-467.297372966011871.23036706479
82701.966497049389-503.2725597994831907.20555389826
83701.966497049389-538.2046083165311942.13760241531
84701.966497049389-572.1793176104161976.11231170919

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 701.966497049389 & -124.950975422215 & 1528.88396952099 \tabularnewline
74 & 701.966497049389 & -175.082927275943 & 1579.01592137472 \tabularnewline
75 & 701.966497049389 & -222.50031097563 & 1626.43330507441 \tabularnewline
76 & 701.966497049389 & -267.601481779603 & 1671.53447587838 \tabularnewline
77 & 701.966497049389 & -310.695960041377 & 1714.62895414015 \tabularnewline
78 & 701.966497049389 & -352.02991586276 & 1755.96290996154 \tabularnewline
79 & 701.966497049389 & -391.802959857435 & 1795.73595395621 \tabularnewline
80 & 701.966497049389 & -430.179611583599 & 1834.11260568238 \tabularnewline
81 & 701.966497049389 & -467.29737296601 & 1871.23036706479 \tabularnewline
82 & 701.966497049389 & -503.272559799483 & 1907.20555389826 \tabularnewline
83 & 701.966497049389 & -538.204608316531 & 1942.13760241531 \tabularnewline
84 & 701.966497049389 & -572.179317610416 & 1976.11231170919 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278771&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]701.966497049389[/C][C]-124.950975422215[/C][C]1528.88396952099[/C][/ROW]
[ROW][C]74[/C][C]701.966497049389[/C][C]-175.082927275943[/C][C]1579.01592137472[/C][/ROW]
[ROW][C]75[/C][C]701.966497049389[/C][C]-222.50031097563[/C][C]1626.43330507441[/C][/ROW]
[ROW][C]76[/C][C]701.966497049389[/C][C]-267.601481779603[/C][C]1671.53447587838[/C][/ROW]
[ROW][C]77[/C][C]701.966497049389[/C][C]-310.695960041377[/C][C]1714.62895414015[/C][/ROW]
[ROW][C]78[/C][C]701.966497049389[/C][C]-352.02991586276[/C][C]1755.96290996154[/C][/ROW]
[ROW][C]79[/C][C]701.966497049389[/C][C]-391.802959857435[/C][C]1795.73595395621[/C][/ROW]
[ROW][C]80[/C][C]701.966497049389[/C][C]-430.179611583599[/C][C]1834.11260568238[/C][/ROW]
[ROW][C]81[/C][C]701.966497049389[/C][C]-467.29737296601[/C][C]1871.23036706479[/C][/ROW]
[ROW][C]82[/C][C]701.966497049389[/C][C]-503.272559799483[/C][C]1907.20555389826[/C][/ROW]
[ROW][C]83[/C][C]701.966497049389[/C][C]-538.204608316531[/C][C]1942.13760241531[/C][/ROW]
[ROW][C]84[/C][C]701.966497049389[/C][C]-572.179317610416[/C][C]1976.11231170919[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278771&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278771&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
73701.966497049389-124.9509754222151528.88396952099
74701.966497049389-175.0829272759431579.01592137472
75701.966497049389-222.500310975631626.43330507441
76701.966497049389-267.6014817796031671.53447587838
77701.966497049389-310.6959600413771714.62895414015
78701.966497049389-352.029915862761755.96290996154
79701.966497049389-391.8029598574351795.73595395621
80701.966497049389-430.1796115835991834.11260568238
81701.966497049389-467.297372966011871.23036706479
82701.966497049389-503.2725597994831907.20555389826
83701.966497049389-538.2046083165311942.13760241531
84701.966497049389-572.1793176104161976.11231170919



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