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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 05 Jan 2015 08:43:08 +0000
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/Jan/05/t1420447461mrh8fleu68rvyox.htm/, Retrieved Tue, 14 May 2024 20:05:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271939, Retrieved Tue, 14 May 2024 20:05:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-01-05 08:43:08] [062c419fa600f620f2df94d64c8876ba] [Current]
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Dataseries X:
53
47
49
44
48
51
47
44
33
47
41
36
46
24
17
22
30
24
18
24
24
28
19
22
26
14
16
21
15
23
29
17
24
18
22
8
26
22
34
25
20
35
38
24
14
25
31
17
32
27
30
19
36
27
28
38
26
25
30
27
30
50
48
34
41
26
39
33
38
28
36
20
39
22
32
32
31
28
44
40
32
35
32
31
41
23
36
36
42
36
64
30
25
51
38
27




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271939&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271939&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271939&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.301396644055029
beta0.177238257885777
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.301396644055029 \tabularnewline
beta & 0.177238257885777 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271939&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]0.301396644055029[/C][/ROW]
[ROW][C]beta[/C][C]0.177238257885777[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271939&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271939&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
alpha0.301396644055029
beta0.177238257885777
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
349418
44437.83852528143976.16147471856031
54834.452065130387313.5479348696127
65134.015576631567616.9844233684324
74735.522125419416911.4778745805831
84435.98215564958338.01784435041674
93335.8276497366906-2.82764973669064
104732.253298035945214.7467019640548
114134.76355126925476.23644873074527
123635.04198769329630.958012306703722
134633.780697168133612.2193028318664
142436.5662649499945-12.5662649499945
151731.2102682714102-14.2102682714102
162224.5996759590058-2.59967595900575
173021.34960507307748.65039492692258
182421.95236338363742.04763661636262
191820.6744552313156-2.67445523131559
202417.83045767605696.16954232394308
212417.98158218487036.01841781512973
222818.40865623220589.59134376779419
231920.4249583185231-1.4249583185231
242219.04486405473342.95513594526659
252619.14277595740626.85722404259382
261420.783070279124-6.78307027912404
271617.9498807277362-1.9498807277362
282116.46923757718184.53076242281816
291517.1838673944455-2.18386739444554
302315.75807027115557.24192972884447
312917.560033529329411.4399664706706
321721.2383827264749-4.23838272647489
332419.96491985606864.03508014393136
341821.4006009407908-3.40060094079079
352220.41353594382371.58646405617634
36821.0143029496252-13.0143029496252
372616.5192365201289.48076347987196
382219.31056067748422.68943932251581
393420.198669727659813.8013302723402
402525.1731189035817-0.17311890358167
412025.9264681538611-5.92646815386113
423524.629191150154810.3708088498452
433828.79785714777939.2021428522207
442433.1058605531052-9.10586055310523
451431.4094670610002-17.4094670610002
462526.280397832204-1.28039783220402
473125.94417834825345.05582165174657
481727.7877511711011-10.7877511711011
493224.27985326154027.72014673845984
502726.76257631354260.23742368645738
513027.00271468901362.99728531098635
521928.2347781285326-9.23477812853257
533625.28682593575410.713174064246
542728.9234068077362-1.92340680773624
552828.6486181132958-0.648618113295786
563828.72339791178599.2766020882141
572632.2851527270532-6.28515272705317
582530.8209001905176-5.82090019051759
593029.1856250493490.814374950651025
602729.5937026767309-2.59370267673091
613028.83604409942931.16395590057067
625029.273108585852320.7268914141477
634836.713586330604511.2864136693955
643441.9116448786102-7.91164487861023
654140.90084072252990.0991592774701289
662642.3097630463163-16.3097630463163
673937.90183975398891.0981602460111
683338.7992687618257-5.79926876182574
693837.3080445825920.691955417408025
702837.8102171643884-9.81021716438838
713634.6230180258511.37698197414895
722034.881160186325-14.881160186325
733929.44421592511159.5557840748885
742231.8829452387704-9.88294523877039
753227.93496956152674.06503043847332
763228.40801687130653.59198312869346
773128.93036951411172.06963048588835
782829.1044478036053-1.10444780360532
794428.262871033647715.7371289663523
804033.33795092876426.66204907123578
813236.0337123057228-4.03371230572277
823535.2903301553499-0.290330155349878
833235.6596816712647-3.65968167126468
843134.8180253534316-3.81802535343162
854133.72468962326587.27531037673423
862336.3634879758763-13.3634879758763
873632.06795738801293.93204261198711
883633.19528752417632.80471247582373
894234.13266912152977.86733087847027
903637.0161719906293-1.01617199062927
916437.167933999575926.8320660004241
923047.1464040482136-17.1464040482136
932542.9539667791812-17.9539667791812
945137.559049572287713.4409504277123
953842.3444573995697-4.34445739956975
962741.5373263546772-14.5373263546772

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 49 & 41 & 8 \tabularnewline
4 & 44 & 37.8385252814397 & 6.16147471856031 \tabularnewline
5 & 48 & 34.4520651303873 & 13.5479348696127 \tabularnewline
6 & 51 & 34.0155766315676 & 16.9844233684324 \tabularnewline
7 & 47 & 35.5221254194169 & 11.4778745805831 \tabularnewline
8 & 44 & 35.9821556495833 & 8.01784435041674 \tabularnewline
9 & 33 & 35.8276497366906 & -2.82764973669064 \tabularnewline
10 & 47 & 32.2532980359452 & 14.7467019640548 \tabularnewline
11 & 41 & 34.7635512692547 & 6.23644873074527 \tabularnewline
12 & 36 & 35.0419876932963 & 0.958012306703722 \tabularnewline
13 & 46 & 33.7806971681336 & 12.2193028318664 \tabularnewline
14 & 24 & 36.5662649499945 & -12.5662649499945 \tabularnewline
15 & 17 & 31.2102682714102 & -14.2102682714102 \tabularnewline
16 & 22 & 24.5996759590058 & -2.59967595900575 \tabularnewline
17 & 30 & 21.3496050730774 & 8.65039492692258 \tabularnewline
18 & 24 & 21.9523633836374 & 2.04763661636262 \tabularnewline
19 & 18 & 20.6744552313156 & -2.67445523131559 \tabularnewline
20 & 24 & 17.8304576760569 & 6.16954232394308 \tabularnewline
21 & 24 & 17.9815821848703 & 6.01841781512973 \tabularnewline
22 & 28 & 18.4086562322058 & 9.59134376779419 \tabularnewline
23 & 19 & 20.4249583185231 & -1.4249583185231 \tabularnewline
24 & 22 & 19.0448640547334 & 2.95513594526659 \tabularnewline
25 & 26 & 19.1427759574062 & 6.85722404259382 \tabularnewline
26 & 14 & 20.783070279124 & -6.78307027912404 \tabularnewline
27 & 16 & 17.9498807277362 & -1.9498807277362 \tabularnewline
28 & 21 & 16.4692375771818 & 4.53076242281816 \tabularnewline
29 & 15 & 17.1838673944455 & -2.18386739444554 \tabularnewline
30 & 23 & 15.7580702711555 & 7.24192972884447 \tabularnewline
31 & 29 & 17.5600335293294 & 11.4399664706706 \tabularnewline
32 & 17 & 21.2383827264749 & -4.23838272647489 \tabularnewline
33 & 24 & 19.9649198560686 & 4.03508014393136 \tabularnewline
34 & 18 & 21.4006009407908 & -3.40060094079079 \tabularnewline
35 & 22 & 20.4135359438237 & 1.58646405617634 \tabularnewline
36 & 8 & 21.0143029496252 & -13.0143029496252 \tabularnewline
37 & 26 & 16.519236520128 & 9.48076347987196 \tabularnewline
38 & 22 & 19.3105606774842 & 2.68943932251581 \tabularnewline
39 & 34 & 20.1986697276598 & 13.8013302723402 \tabularnewline
40 & 25 & 25.1731189035817 & -0.17311890358167 \tabularnewline
41 & 20 & 25.9264681538611 & -5.92646815386113 \tabularnewline
42 & 35 & 24.6291911501548 & 10.3708088498452 \tabularnewline
43 & 38 & 28.7978571477793 & 9.2021428522207 \tabularnewline
44 & 24 & 33.1058605531052 & -9.10586055310523 \tabularnewline
45 & 14 & 31.4094670610002 & -17.4094670610002 \tabularnewline
46 & 25 & 26.280397832204 & -1.28039783220402 \tabularnewline
47 & 31 & 25.9441783482534 & 5.05582165174657 \tabularnewline
48 & 17 & 27.7877511711011 & -10.7877511711011 \tabularnewline
49 & 32 & 24.2798532615402 & 7.72014673845984 \tabularnewline
50 & 27 & 26.7625763135426 & 0.23742368645738 \tabularnewline
51 & 30 & 27.0027146890136 & 2.99728531098635 \tabularnewline
52 & 19 & 28.2347781285326 & -9.23477812853257 \tabularnewline
53 & 36 & 25.286825935754 & 10.713174064246 \tabularnewline
54 & 27 & 28.9234068077362 & -1.92340680773624 \tabularnewline
55 & 28 & 28.6486181132958 & -0.648618113295786 \tabularnewline
56 & 38 & 28.7233979117859 & 9.2766020882141 \tabularnewline
57 & 26 & 32.2851527270532 & -6.28515272705317 \tabularnewline
58 & 25 & 30.8209001905176 & -5.82090019051759 \tabularnewline
59 & 30 & 29.185625049349 & 0.814374950651025 \tabularnewline
60 & 27 & 29.5937026767309 & -2.59370267673091 \tabularnewline
61 & 30 & 28.8360440994293 & 1.16395590057067 \tabularnewline
62 & 50 & 29.2731085858523 & 20.7268914141477 \tabularnewline
63 & 48 & 36.7135863306045 & 11.2864136693955 \tabularnewline
64 & 34 & 41.9116448786102 & -7.91164487861023 \tabularnewline
65 & 41 & 40.9008407225299 & 0.0991592774701289 \tabularnewline
66 & 26 & 42.3097630463163 & -16.3097630463163 \tabularnewline
67 & 39 & 37.9018397539889 & 1.0981602460111 \tabularnewline
68 & 33 & 38.7992687618257 & -5.79926876182574 \tabularnewline
69 & 38 & 37.308044582592 & 0.691955417408025 \tabularnewline
70 & 28 & 37.8102171643884 & -9.81021716438838 \tabularnewline
71 & 36 & 34.623018025851 & 1.37698197414895 \tabularnewline
72 & 20 & 34.881160186325 & -14.881160186325 \tabularnewline
73 & 39 & 29.4442159251115 & 9.5557840748885 \tabularnewline
74 & 22 & 31.8829452387704 & -9.88294523877039 \tabularnewline
75 & 32 & 27.9349695615267 & 4.06503043847332 \tabularnewline
76 & 32 & 28.4080168713065 & 3.59198312869346 \tabularnewline
77 & 31 & 28.9303695141117 & 2.06963048588835 \tabularnewline
78 & 28 & 29.1044478036053 & -1.10444780360532 \tabularnewline
79 & 44 & 28.2628710336477 & 15.7371289663523 \tabularnewline
80 & 40 & 33.3379509287642 & 6.66204907123578 \tabularnewline
81 & 32 & 36.0337123057228 & -4.03371230572277 \tabularnewline
82 & 35 & 35.2903301553499 & -0.290330155349878 \tabularnewline
83 & 32 & 35.6596816712647 & -3.65968167126468 \tabularnewline
84 & 31 & 34.8180253534316 & -3.81802535343162 \tabularnewline
85 & 41 & 33.7246896232658 & 7.27531037673423 \tabularnewline
86 & 23 & 36.3634879758763 & -13.3634879758763 \tabularnewline
87 & 36 & 32.0679573880129 & 3.93204261198711 \tabularnewline
88 & 36 & 33.1952875241763 & 2.80471247582373 \tabularnewline
89 & 42 & 34.1326691215297 & 7.86733087847027 \tabularnewline
90 & 36 & 37.0161719906293 & -1.01617199062927 \tabularnewline
91 & 64 & 37.1679339995759 & 26.8320660004241 \tabularnewline
92 & 30 & 47.1464040482136 & -17.1464040482136 \tabularnewline
93 & 25 & 42.9539667791812 & -17.9539667791812 \tabularnewline
94 & 51 & 37.5590495722877 & 13.4409504277123 \tabularnewline
95 & 38 & 42.3444573995697 & -4.34445739956975 \tabularnewline
96 & 27 & 41.5373263546772 & -14.5373263546772 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271939&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]49[/C][C]41[/C][C]8[/C][/ROW]
[ROW][C]4[/C][C]44[/C][C]37.8385252814397[/C][C]6.16147471856031[/C][/ROW]
[ROW][C]5[/C][C]48[/C][C]34.4520651303873[/C][C]13.5479348696127[/C][/ROW]
[ROW][C]6[/C][C]51[/C][C]34.0155766315676[/C][C]16.9844233684324[/C][/ROW]
[ROW][C]7[/C][C]47[/C][C]35.5221254194169[/C][C]11.4778745805831[/C][/ROW]
[ROW][C]8[/C][C]44[/C][C]35.9821556495833[/C][C]8.01784435041674[/C][/ROW]
[ROW][C]9[/C][C]33[/C][C]35.8276497366906[/C][C]-2.82764973669064[/C][/ROW]
[ROW][C]10[/C][C]47[/C][C]32.2532980359452[/C][C]14.7467019640548[/C][/ROW]
[ROW][C]11[/C][C]41[/C][C]34.7635512692547[/C][C]6.23644873074527[/C][/ROW]
[ROW][C]12[/C][C]36[/C][C]35.0419876932963[/C][C]0.958012306703722[/C][/ROW]
[ROW][C]13[/C][C]46[/C][C]33.7806971681336[/C][C]12.2193028318664[/C][/ROW]
[ROW][C]14[/C][C]24[/C][C]36.5662649499945[/C][C]-12.5662649499945[/C][/ROW]
[ROW][C]15[/C][C]17[/C][C]31.2102682714102[/C][C]-14.2102682714102[/C][/ROW]
[ROW][C]16[/C][C]22[/C][C]24.5996759590058[/C][C]-2.59967595900575[/C][/ROW]
[ROW][C]17[/C][C]30[/C][C]21.3496050730774[/C][C]8.65039492692258[/C][/ROW]
[ROW][C]18[/C][C]24[/C][C]21.9523633836374[/C][C]2.04763661636262[/C][/ROW]
[ROW][C]19[/C][C]18[/C][C]20.6744552313156[/C][C]-2.67445523131559[/C][/ROW]
[ROW][C]20[/C][C]24[/C][C]17.8304576760569[/C][C]6.16954232394308[/C][/ROW]
[ROW][C]21[/C][C]24[/C][C]17.9815821848703[/C][C]6.01841781512973[/C][/ROW]
[ROW][C]22[/C][C]28[/C][C]18.4086562322058[/C][C]9.59134376779419[/C][/ROW]
[ROW][C]23[/C][C]19[/C][C]20.4249583185231[/C][C]-1.4249583185231[/C][/ROW]
[ROW][C]24[/C][C]22[/C][C]19.0448640547334[/C][C]2.95513594526659[/C][/ROW]
[ROW][C]25[/C][C]26[/C][C]19.1427759574062[/C][C]6.85722404259382[/C][/ROW]
[ROW][C]26[/C][C]14[/C][C]20.783070279124[/C][C]-6.78307027912404[/C][/ROW]
[ROW][C]27[/C][C]16[/C][C]17.9498807277362[/C][C]-1.9498807277362[/C][/ROW]
[ROW][C]28[/C][C]21[/C][C]16.4692375771818[/C][C]4.53076242281816[/C][/ROW]
[ROW][C]29[/C][C]15[/C][C]17.1838673944455[/C][C]-2.18386739444554[/C][/ROW]
[ROW][C]30[/C][C]23[/C][C]15.7580702711555[/C][C]7.24192972884447[/C][/ROW]
[ROW][C]31[/C][C]29[/C][C]17.5600335293294[/C][C]11.4399664706706[/C][/ROW]
[ROW][C]32[/C][C]17[/C][C]21.2383827264749[/C][C]-4.23838272647489[/C][/ROW]
[ROW][C]33[/C][C]24[/C][C]19.9649198560686[/C][C]4.03508014393136[/C][/ROW]
[ROW][C]34[/C][C]18[/C][C]21.4006009407908[/C][C]-3.40060094079079[/C][/ROW]
[ROW][C]35[/C][C]22[/C][C]20.4135359438237[/C][C]1.58646405617634[/C][/ROW]
[ROW][C]36[/C][C]8[/C][C]21.0143029496252[/C][C]-13.0143029496252[/C][/ROW]
[ROW][C]37[/C][C]26[/C][C]16.519236520128[/C][C]9.48076347987196[/C][/ROW]
[ROW][C]38[/C][C]22[/C][C]19.3105606774842[/C][C]2.68943932251581[/C][/ROW]
[ROW][C]39[/C][C]34[/C][C]20.1986697276598[/C][C]13.8013302723402[/C][/ROW]
[ROW][C]40[/C][C]25[/C][C]25.1731189035817[/C][C]-0.17311890358167[/C][/ROW]
[ROW][C]41[/C][C]20[/C][C]25.9264681538611[/C][C]-5.92646815386113[/C][/ROW]
[ROW][C]42[/C][C]35[/C][C]24.6291911501548[/C][C]10.3708088498452[/C][/ROW]
[ROW][C]43[/C][C]38[/C][C]28.7978571477793[/C][C]9.2021428522207[/C][/ROW]
[ROW][C]44[/C][C]24[/C][C]33.1058605531052[/C][C]-9.10586055310523[/C][/ROW]
[ROW][C]45[/C][C]14[/C][C]31.4094670610002[/C][C]-17.4094670610002[/C][/ROW]
[ROW][C]46[/C][C]25[/C][C]26.280397832204[/C][C]-1.28039783220402[/C][/ROW]
[ROW][C]47[/C][C]31[/C][C]25.9441783482534[/C][C]5.05582165174657[/C][/ROW]
[ROW][C]48[/C][C]17[/C][C]27.7877511711011[/C][C]-10.7877511711011[/C][/ROW]
[ROW][C]49[/C][C]32[/C][C]24.2798532615402[/C][C]7.72014673845984[/C][/ROW]
[ROW][C]50[/C][C]27[/C][C]26.7625763135426[/C][C]0.23742368645738[/C][/ROW]
[ROW][C]51[/C][C]30[/C][C]27.0027146890136[/C][C]2.99728531098635[/C][/ROW]
[ROW][C]52[/C][C]19[/C][C]28.2347781285326[/C][C]-9.23477812853257[/C][/ROW]
[ROW][C]53[/C][C]36[/C][C]25.286825935754[/C][C]10.713174064246[/C][/ROW]
[ROW][C]54[/C][C]27[/C][C]28.9234068077362[/C][C]-1.92340680773624[/C][/ROW]
[ROW][C]55[/C][C]28[/C][C]28.6486181132958[/C][C]-0.648618113295786[/C][/ROW]
[ROW][C]56[/C][C]38[/C][C]28.7233979117859[/C][C]9.2766020882141[/C][/ROW]
[ROW][C]57[/C][C]26[/C][C]32.2851527270532[/C][C]-6.28515272705317[/C][/ROW]
[ROW][C]58[/C][C]25[/C][C]30.8209001905176[/C][C]-5.82090019051759[/C][/ROW]
[ROW][C]59[/C][C]30[/C][C]29.185625049349[/C][C]0.814374950651025[/C][/ROW]
[ROW][C]60[/C][C]27[/C][C]29.5937026767309[/C][C]-2.59370267673091[/C][/ROW]
[ROW][C]61[/C][C]30[/C][C]28.8360440994293[/C][C]1.16395590057067[/C][/ROW]
[ROW][C]62[/C][C]50[/C][C]29.2731085858523[/C][C]20.7268914141477[/C][/ROW]
[ROW][C]63[/C][C]48[/C][C]36.7135863306045[/C][C]11.2864136693955[/C][/ROW]
[ROW][C]64[/C][C]34[/C][C]41.9116448786102[/C][C]-7.91164487861023[/C][/ROW]
[ROW][C]65[/C][C]41[/C][C]40.9008407225299[/C][C]0.0991592774701289[/C][/ROW]
[ROW][C]66[/C][C]26[/C][C]42.3097630463163[/C][C]-16.3097630463163[/C][/ROW]
[ROW][C]67[/C][C]39[/C][C]37.9018397539889[/C][C]1.0981602460111[/C][/ROW]
[ROW][C]68[/C][C]33[/C][C]38.7992687618257[/C][C]-5.79926876182574[/C][/ROW]
[ROW][C]69[/C][C]38[/C][C]37.308044582592[/C][C]0.691955417408025[/C][/ROW]
[ROW][C]70[/C][C]28[/C][C]37.8102171643884[/C][C]-9.81021716438838[/C][/ROW]
[ROW][C]71[/C][C]36[/C][C]34.623018025851[/C][C]1.37698197414895[/C][/ROW]
[ROW][C]72[/C][C]20[/C][C]34.881160186325[/C][C]-14.881160186325[/C][/ROW]
[ROW][C]73[/C][C]39[/C][C]29.4442159251115[/C][C]9.5557840748885[/C][/ROW]
[ROW][C]74[/C][C]22[/C][C]31.8829452387704[/C][C]-9.88294523877039[/C][/ROW]
[ROW][C]75[/C][C]32[/C][C]27.9349695615267[/C][C]4.06503043847332[/C][/ROW]
[ROW][C]76[/C][C]32[/C][C]28.4080168713065[/C][C]3.59198312869346[/C][/ROW]
[ROW][C]77[/C][C]31[/C][C]28.9303695141117[/C][C]2.06963048588835[/C][/ROW]
[ROW][C]78[/C][C]28[/C][C]29.1044478036053[/C][C]-1.10444780360532[/C][/ROW]
[ROW][C]79[/C][C]44[/C][C]28.2628710336477[/C][C]15.7371289663523[/C][/ROW]
[ROW][C]80[/C][C]40[/C][C]33.3379509287642[/C][C]6.66204907123578[/C][/ROW]
[ROW][C]81[/C][C]32[/C][C]36.0337123057228[/C][C]-4.03371230572277[/C][/ROW]
[ROW][C]82[/C][C]35[/C][C]35.2903301553499[/C][C]-0.290330155349878[/C][/ROW]
[ROW][C]83[/C][C]32[/C][C]35.6596816712647[/C][C]-3.65968167126468[/C][/ROW]
[ROW][C]84[/C][C]31[/C][C]34.8180253534316[/C][C]-3.81802535343162[/C][/ROW]
[ROW][C]85[/C][C]41[/C][C]33.7246896232658[/C][C]7.27531037673423[/C][/ROW]
[ROW][C]86[/C][C]23[/C][C]36.3634879758763[/C][C]-13.3634879758763[/C][/ROW]
[ROW][C]87[/C][C]36[/C][C]32.0679573880129[/C][C]3.93204261198711[/C][/ROW]
[ROW][C]88[/C][C]36[/C][C]33.1952875241763[/C][C]2.80471247582373[/C][/ROW]
[ROW][C]89[/C][C]42[/C][C]34.1326691215297[/C][C]7.86733087847027[/C][/ROW]
[ROW][C]90[/C][C]36[/C][C]37.0161719906293[/C][C]-1.01617199062927[/C][/ROW]
[ROW][C]91[/C][C]64[/C][C]37.1679339995759[/C][C]26.8320660004241[/C][/ROW]
[ROW][C]92[/C][C]30[/C][C]47.1464040482136[/C][C]-17.1464040482136[/C][/ROW]
[ROW][C]93[/C][C]25[/C][C]42.9539667791812[/C][C]-17.9539667791812[/C][/ROW]
[ROW][C]94[/C][C]51[/C][C]37.5590495722877[/C][C]13.4409504277123[/C][/ROW]
[ROW][C]95[/C][C]38[/C][C]42.3444573995697[/C][C]-4.34445739956975[/C][/ROW]
[ROW][C]96[/C][C]27[/C][C]41.5373263546772[/C][C]-14.5373263546772[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271939&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271939&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
349418
44437.83852528143976.16147471856031
54834.452065130387313.5479348696127
65134.015576631567616.9844233684324
74735.522125419416911.4778745805831
84435.98215564958338.01784435041674
93335.8276497366906-2.82764973669064
104732.253298035945214.7467019640548
114134.76355126925476.23644873074527
123635.04198769329630.958012306703722
134633.780697168133612.2193028318664
142436.5662649499945-12.5662649499945
151731.2102682714102-14.2102682714102
162224.5996759590058-2.59967595900575
173021.34960507307748.65039492692258
182421.95236338363742.04763661636262
191820.6744552313156-2.67445523131559
202417.83045767605696.16954232394308
212417.98158218487036.01841781512973
222818.40865623220589.59134376779419
231920.4249583185231-1.4249583185231
242219.04486405473342.95513594526659
252619.14277595740626.85722404259382
261420.783070279124-6.78307027912404
271617.9498807277362-1.9498807277362
282116.46923757718184.53076242281816
291517.1838673944455-2.18386739444554
302315.75807027115557.24192972884447
312917.560033529329411.4399664706706
321721.2383827264749-4.23838272647489
332419.96491985606864.03508014393136
341821.4006009407908-3.40060094079079
352220.41353594382371.58646405617634
36821.0143029496252-13.0143029496252
372616.5192365201289.48076347987196
382219.31056067748422.68943932251581
393420.198669727659813.8013302723402
402525.1731189035817-0.17311890358167
412025.9264681538611-5.92646815386113
423524.629191150154810.3708088498452
433828.79785714777939.2021428522207
442433.1058605531052-9.10586055310523
451431.4094670610002-17.4094670610002
462526.280397832204-1.28039783220402
473125.94417834825345.05582165174657
481727.7877511711011-10.7877511711011
493224.27985326154027.72014673845984
502726.76257631354260.23742368645738
513027.00271468901362.99728531098635
521928.2347781285326-9.23477812853257
533625.28682593575410.713174064246
542728.9234068077362-1.92340680773624
552828.6486181132958-0.648618113295786
563828.72339791178599.2766020882141
572632.2851527270532-6.28515272705317
582530.8209001905176-5.82090019051759
593029.1856250493490.814374950651025
602729.5937026767309-2.59370267673091
613028.83604409942931.16395590057067
625029.273108585852320.7268914141477
634836.713586330604511.2864136693955
643441.9116448786102-7.91164487861023
654140.90084072252990.0991592774701289
662642.3097630463163-16.3097630463163
673937.90183975398891.0981602460111
683338.7992687618257-5.79926876182574
693837.3080445825920.691955417408025
702837.8102171643884-9.81021716438838
713634.6230180258511.37698197414895
722034.881160186325-14.881160186325
733929.44421592511159.5557840748885
742231.8829452387704-9.88294523877039
753227.93496956152674.06503043847332
763228.40801687130653.59198312869346
773128.93036951411172.06963048588835
782829.1044478036053-1.10444780360532
794428.262871033647715.7371289663523
804033.33795092876426.66204907123578
813236.0337123057228-4.03371230572277
823535.2903301553499-0.290330155349878
833235.6596816712647-3.65968167126468
843134.8180253534316-3.81802535343162
854133.72468962326587.27531037673423
862336.3634879758763-13.3634879758763
873632.06795738801293.93204261198711
883633.19528752417632.80471247582373
894234.13266912152977.86733087847027
903637.0161719906293-1.01617199062927
916437.167933999575926.8320660004241
923047.1464040482136-17.1464040482136
932542.9539667791812-17.9539667791812
945137.559049572287713.4409504277123
953842.3444573995697-4.34445739956975
962741.5373263546772-14.5373263546772







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9736.881529142468719.202529053763454.560529231174
9836.607233307092717.848371682791455.366094931394
9936.332937471716616.233619342132956.4322556013003
10036.058641636340514.365465135840557.7518181368406
10135.784345800964512.25749720825259.3111943936769
10235.51004996558849.926413664551461.0936862666254
10335.23575413021237.3896198426377463.081888417787
10434.96145829483634.6637584996383265.2591580900342
10534.68716245946021.7639720949092567.6103528240112
10634.4128666240842-1.2963550211019870.1220882692703
10734.1385707887081-4.5055816291606172.7827232065768
10833.864274953332-7.8536617597125975.5822116663767

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 36.8815291424687 & 19.2025290537634 & 54.560529231174 \tabularnewline
98 & 36.6072333070927 & 17.8483716827914 & 55.366094931394 \tabularnewline
99 & 36.3329374717166 & 16.2336193421329 & 56.4322556013003 \tabularnewline
100 & 36.0586416363405 & 14.3654651358405 & 57.7518181368406 \tabularnewline
101 & 35.7843458009645 & 12.257497208252 & 59.3111943936769 \tabularnewline
102 & 35.5100499655884 & 9.9264136645514 & 61.0936862666254 \tabularnewline
103 & 35.2357541302123 & 7.38961984263774 & 63.081888417787 \tabularnewline
104 & 34.9614582948363 & 4.66375849963832 & 65.2591580900342 \tabularnewline
105 & 34.6871624594602 & 1.76397209490925 & 67.6103528240112 \tabularnewline
106 & 34.4128666240842 & -1.29635502110198 & 70.1220882692703 \tabularnewline
107 & 34.1385707887081 & -4.50558162916061 & 72.7827232065768 \tabularnewline
108 & 33.864274953332 & -7.85366175971259 & 75.5822116663767 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271939&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]97[/C][C]36.8815291424687[/C][C]19.2025290537634[/C][C]54.560529231174[/C][/ROW]
[ROW][C]98[/C][C]36.6072333070927[/C][C]17.8483716827914[/C][C]55.366094931394[/C][/ROW]
[ROW][C]99[/C][C]36.3329374717166[/C][C]16.2336193421329[/C][C]56.4322556013003[/C][/ROW]
[ROW][C]100[/C][C]36.0586416363405[/C][C]14.3654651358405[/C][C]57.7518181368406[/C][/ROW]
[ROW][C]101[/C][C]35.7843458009645[/C][C]12.257497208252[/C][C]59.3111943936769[/C][/ROW]
[ROW][C]102[/C][C]35.5100499655884[/C][C]9.9264136645514[/C][C]61.0936862666254[/C][/ROW]
[ROW][C]103[/C][C]35.2357541302123[/C][C]7.38961984263774[/C][C]63.081888417787[/C][/ROW]
[ROW][C]104[/C][C]34.9614582948363[/C][C]4.66375849963832[/C][C]65.2591580900342[/C][/ROW]
[ROW][C]105[/C][C]34.6871624594602[/C][C]1.76397209490925[/C][C]67.6103528240112[/C][/ROW]
[ROW][C]106[/C][C]34.4128666240842[/C][C]-1.29635502110198[/C][C]70.1220882692703[/C][/ROW]
[ROW][C]107[/C][C]34.1385707887081[/C][C]-4.50558162916061[/C][C]72.7827232065768[/C][/ROW]
[ROW][C]108[/C][C]33.864274953332[/C][C]-7.85366175971259[/C][C]75.5822116663767[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271939&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271939&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
9736.881529142468719.202529053763454.560529231174
9836.607233307092717.848371682791455.366094931394
9936.332937471716616.233619342132956.4322556013003
10036.058641636340514.365465135840557.7518181368406
10135.784345800964512.25749720825259.3111943936769
10235.51004996558849.926413664551461.0936862666254
10335.23575413021237.3896198426377463.081888417787
10434.96145829483634.6637584996383265.2591580900342
10534.68716245946021.7639720949092567.6103528240112
10634.4128666240842-1.2963550211019870.1220882692703
10734.1385707887081-4.5055816291606172.7827232065768
10833.864274953332-7.8536617597125975.5822116663767



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')