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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 computationFri, 20 May 2011 06:19:33 +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/2011/May/20/t13058721655llv3399k11piof.htm/, Retrieved Mon, 13 May 2024 01:12:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122414, Retrieved Mon, 13 May 2024 01:12:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKEYWORD: KDGP2W102
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2011-05-20 06:19:33] [be417f314f65e9d8a38b0902dfa3287c] [Current]
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Dataseries X:
32819
32700
32242
32810
33865
32226
31077
31293
30236
30160
32436
30695
27525
26434
25739
25204
24977
24320
22680
22052
21467
21383
21777
21928
21814
22937
23595
20830
19650
19195
19644
18483
18079
19178
18391
18441
18584
20108
20148
19394
17745
17696
17032
16438
15683
15594
15713
15937
16171
15928
16348
15579
15305
15648
14954
15137
15839
16050
15168
17064
16005
14886
14931
14544
13812
13031
12574
11964
11451
11346
11353
10702
10646
10556
10463
10407
10625
10872
10805
10653
10574
10431
10383
10296
10872
10635
10297
10570
10662
10709
10413
10846
10371
9924
9828




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122414&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122414&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'Herman Ole Andreas Wold' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.7808136475473
beta0.040561130325825
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.7808136475473 \tabularnewline
beta & 0.040561130325825 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122414&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]0.7808136475473[/C][/ROW]
[ROW][C]beta[/C][C]0.040561130325825[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122414&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
alpha0.7808136475473
beta0.040561130325825
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132752531358.874732906-3833.874732906
142643427197.8825910096-763.882591009551
152573925821.2895271255-82.2895271254602
162520425114.954130642589.0458693575347
172497724931.969893641845.0301063582083
182432024285.627015791734.3729842083449
192268022733.0931941151-53.0931941150629
202205222554.7914222584-502.791422258426
212146720786.8103882778680.189611722151
222138321000.8924940857382.107505914311
232177723445.7046297082-1668.70462970819
242192820231.86564406671696.13435593329
252181417409.26524382284404.73475617721
262293720488.93636303642448.06363696365
272359522006.33933664331588.6606633567
282083022931.8478594936-2101.84785949362
291965021248.7379665465-1598.73796654655
301919519484.725111246-289.725111246014
311964417817.83773550821826.16226449177
321848319225.7119192389-742.711919238936
331807917739.4878990857339.512100914253
341917817821.2362500451356.76374995496
351839120807.438705644-2416.43870564398
361844117953.4797374407487.520262559286
371858414948.78177009323635.21822990683
382010817142.27373282372965.72626717628
392014819035.44553430741112.55446569259
401939418925.156313981468.843686019038
411774519585.8294210866-1840.8294210866
421769618138.3159405732-442.315940573171
431703217029.83447631942.16552368057819
441643816606.4550023145-168.455002314546
451568315980.0245178406-297.024517840551
461559415941.761680242-347.761680241987
471571316870.0670596217-1157.06705962173
481593715775.8901210466161.109878953383
491617113335.86055457912835.13944542092
501592814862.15918652441065.84081347562
511634814909.77646184311438.2235381569
521557914967.0875748674611.912425132628
531530515292.15906196712.8409380329704
541564815716.1959526223-68.1959526222818
551495415126.7495756887-172.749575688729
561513714653.3494573534483.650542646583
571583914652.51697077351186.48302922649
581605015953.06564940696.9343505939833
591516817256.8803628696-2088.88036286957
601706415900.21940874511163.78059125491
611600515037.1170064064967.882993593596
621488614866.410315447919.5896845520765
631493114294.3662643574636.633735642563
641454413634.9267262377909.073273762297
651381214160.3861779665-348.3861779665
661303114372.8385288407-1341.83852884072
671257412813.8894900441-239.889490044112
681196412477.7047619744-513.704761974364
691145111866.353210407-415.353210407
701134611640.7991209495-294.799120949516
711135312110.6828020543-757.682802054263
721070212499.5784613486-1797.57846134858
73106469180.680648500361465.31935149964
74105569105.69248581391450.3075141861
75104639746.49827189377716.50172810623
76104079172.143450018421234.85654998158
77106259649.68642771466975.313572285339
781087210693.1983367089178.801663291084
791080510626.5257435152178.474256484846
801065310633.646073911719.3539260883153
811057410553.611178337320.3888216627056
821043110802.0543132899-371.0543132899
831038311215.8641475573-832.864147557331
841029611420.6702388144-1124.67023881438
85108729466.226472512881405.77352748712
86106359463.423323756891171.57667624311
87102979838.89405343477458.105946565227
88105709281.355009887711288.64499011229
89106629850.67040216997811.329597830034
901070910693.025306295115.9746937049349
911041310595.4550488185-182.455048818514
921084610370.7605878589475.239412141114
931037110746.2330825674-375.233082567447
94992410686.7595721945-762.759572194485
95982810767.8819375799-939.881937579938

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 27525 & 31358.874732906 & -3833.874732906 \tabularnewline
14 & 26434 & 27197.8825910096 & -763.882591009551 \tabularnewline
15 & 25739 & 25821.2895271255 & -82.2895271254602 \tabularnewline
16 & 25204 & 25114.9541306425 & 89.0458693575347 \tabularnewline
17 & 24977 & 24931.9698936418 & 45.0301063582083 \tabularnewline
18 & 24320 & 24285.6270157917 & 34.3729842083449 \tabularnewline
19 & 22680 & 22733.0931941151 & -53.0931941150629 \tabularnewline
20 & 22052 & 22554.7914222584 & -502.791422258426 \tabularnewline
21 & 21467 & 20786.8103882778 & 680.189611722151 \tabularnewline
22 & 21383 & 21000.8924940857 & 382.107505914311 \tabularnewline
23 & 21777 & 23445.7046297082 & -1668.70462970819 \tabularnewline
24 & 21928 & 20231.8656440667 & 1696.13435593329 \tabularnewline
25 & 21814 & 17409.2652438228 & 4404.73475617721 \tabularnewline
26 & 22937 & 20488.9363630364 & 2448.06363696365 \tabularnewline
27 & 23595 & 22006.3393366433 & 1588.6606633567 \tabularnewline
28 & 20830 & 22931.8478594936 & -2101.84785949362 \tabularnewline
29 & 19650 & 21248.7379665465 & -1598.73796654655 \tabularnewline
30 & 19195 & 19484.725111246 & -289.725111246014 \tabularnewline
31 & 19644 & 17817.8377355082 & 1826.16226449177 \tabularnewline
32 & 18483 & 19225.7119192389 & -742.711919238936 \tabularnewline
33 & 18079 & 17739.4878990857 & 339.512100914253 \tabularnewline
34 & 19178 & 17821.236250045 & 1356.76374995496 \tabularnewline
35 & 18391 & 20807.438705644 & -2416.43870564398 \tabularnewline
36 & 18441 & 17953.4797374407 & 487.520262559286 \tabularnewline
37 & 18584 & 14948.7817700932 & 3635.21822990683 \tabularnewline
38 & 20108 & 17142.2737328237 & 2965.72626717628 \tabularnewline
39 & 20148 & 19035.4455343074 & 1112.55446569259 \tabularnewline
40 & 19394 & 18925.156313981 & 468.843686019038 \tabularnewline
41 & 17745 & 19585.8294210866 & -1840.8294210866 \tabularnewline
42 & 17696 & 18138.3159405732 & -442.315940573171 \tabularnewline
43 & 17032 & 17029.8344763194 & 2.16552368057819 \tabularnewline
44 & 16438 & 16606.4550023145 & -168.455002314546 \tabularnewline
45 & 15683 & 15980.0245178406 & -297.024517840551 \tabularnewline
46 & 15594 & 15941.761680242 & -347.761680241987 \tabularnewline
47 & 15713 & 16870.0670596217 & -1157.06705962173 \tabularnewline
48 & 15937 & 15775.8901210466 & 161.109878953383 \tabularnewline
49 & 16171 & 13335.8605545791 & 2835.13944542092 \tabularnewline
50 & 15928 & 14862.1591865244 & 1065.84081347562 \tabularnewline
51 & 16348 & 14909.7764618431 & 1438.2235381569 \tabularnewline
52 & 15579 & 14967.0875748674 & 611.912425132628 \tabularnewline
53 & 15305 & 15292.159061967 & 12.8409380329704 \tabularnewline
54 & 15648 & 15716.1959526223 & -68.1959526222818 \tabularnewline
55 & 14954 & 15126.7495756887 & -172.749575688729 \tabularnewline
56 & 15137 & 14653.3494573534 & 483.650542646583 \tabularnewline
57 & 15839 & 14652.5169707735 & 1186.48302922649 \tabularnewline
58 & 16050 & 15953.065649406 & 96.9343505939833 \tabularnewline
59 & 15168 & 17256.8803628696 & -2088.88036286957 \tabularnewline
60 & 17064 & 15900.2194087451 & 1163.78059125491 \tabularnewline
61 & 16005 & 15037.1170064064 & 967.882993593596 \tabularnewline
62 & 14886 & 14866.4103154479 & 19.5896845520765 \tabularnewline
63 & 14931 & 14294.3662643574 & 636.633735642563 \tabularnewline
64 & 14544 & 13634.9267262377 & 909.073273762297 \tabularnewline
65 & 13812 & 14160.3861779665 & -348.3861779665 \tabularnewline
66 & 13031 & 14372.8385288407 & -1341.83852884072 \tabularnewline
67 & 12574 & 12813.8894900441 & -239.889490044112 \tabularnewline
68 & 11964 & 12477.7047619744 & -513.704761974364 \tabularnewline
69 & 11451 & 11866.353210407 & -415.353210407 \tabularnewline
70 & 11346 & 11640.7991209495 & -294.799120949516 \tabularnewline
71 & 11353 & 12110.6828020543 & -757.682802054263 \tabularnewline
72 & 10702 & 12499.5784613486 & -1797.57846134858 \tabularnewline
73 & 10646 & 9180.68064850036 & 1465.31935149964 \tabularnewline
74 & 10556 & 9105.6924858139 & 1450.3075141861 \tabularnewline
75 & 10463 & 9746.49827189377 & 716.50172810623 \tabularnewline
76 & 10407 & 9172.14345001842 & 1234.85654998158 \tabularnewline
77 & 10625 & 9649.68642771466 & 975.313572285339 \tabularnewline
78 & 10872 & 10693.1983367089 & 178.801663291084 \tabularnewline
79 & 10805 & 10626.5257435152 & 178.474256484846 \tabularnewline
80 & 10653 & 10633.6460739117 & 19.3539260883153 \tabularnewline
81 & 10574 & 10553.6111783373 & 20.3888216627056 \tabularnewline
82 & 10431 & 10802.0543132899 & -371.0543132899 \tabularnewline
83 & 10383 & 11215.8641475573 & -832.864147557331 \tabularnewline
84 & 10296 & 11420.6702388144 & -1124.67023881438 \tabularnewline
85 & 10872 & 9466.22647251288 & 1405.77352748712 \tabularnewline
86 & 10635 & 9463.42332375689 & 1171.57667624311 \tabularnewline
87 & 10297 & 9838.89405343477 & 458.105946565227 \tabularnewline
88 & 10570 & 9281.35500988771 & 1288.64499011229 \tabularnewline
89 & 10662 & 9850.67040216997 & 811.329597830034 \tabularnewline
90 & 10709 & 10693.0253062951 & 15.9746937049349 \tabularnewline
91 & 10413 & 10595.4550488185 & -182.455048818514 \tabularnewline
92 & 10846 & 10370.7605878589 & 475.239412141114 \tabularnewline
93 & 10371 & 10746.2330825674 & -375.233082567447 \tabularnewline
94 & 9924 & 10686.7595721945 & -762.759572194485 \tabularnewline
95 & 9828 & 10767.8819375799 & -939.881937579938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122414&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]27525[/C][C]31358.874732906[/C][C]-3833.874732906[/C][/ROW]
[ROW][C]14[/C][C]26434[/C][C]27197.8825910096[/C][C]-763.882591009551[/C][/ROW]
[ROW][C]15[/C][C]25739[/C][C]25821.2895271255[/C][C]-82.2895271254602[/C][/ROW]
[ROW][C]16[/C][C]25204[/C][C]25114.9541306425[/C][C]89.0458693575347[/C][/ROW]
[ROW][C]17[/C][C]24977[/C][C]24931.9698936418[/C][C]45.0301063582083[/C][/ROW]
[ROW][C]18[/C][C]24320[/C][C]24285.6270157917[/C][C]34.3729842083449[/C][/ROW]
[ROW][C]19[/C][C]22680[/C][C]22733.0931941151[/C][C]-53.0931941150629[/C][/ROW]
[ROW][C]20[/C][C]22052[/C][C]22554.7914222584[/C][C]-502.791422258426[/C][/ROW]
[ROW][C]21[/C][C]21467[/C][C]20786.8103882778[/C][C]680.189611722151[/C][/ROW]
[ROW][C]22[/C][C]21383[/C][C]21000.8924940857[/C][C]382.107505914311[/C][/ROW]
[ROW][C]23[/C][C]21777[/C][C]23445.7046297082[/C][C]-1668.70462970819[/C][/ROW]
[ROW][C]24[/C][C]21928[/C][C]20231.8656440667[/C][C]1696.13435593329[/C][/ROW]
[ROW][C]25[/C][C]21814[/C][C]17409.2652438228[/C][C]4404.73475617721[/C][/ROW]
[ROW][C]26[/C][C]22937[/C][C]20488.9363630364[/C][C]2448.06363696365[/C][/ROW]
[ROW][C]27[/C][C]23595[/C][C]22006.3393366433[/C][C]1588.6606633567[/C][/ROW]
[ROW][C]28[/C][C]20830[/C][C]22931.8478594936[/C][C]-2101.84785949362[/C][/ROW]
[ROW][C]29[/C][C]19650[/C][C]21248.7379665465[/C][C]-1598.73796654655[/C][/ROW]
[ROW][C]30[/C][C]19195[/C][C]19484.725111246[/C][C]-289.725111246014[/C][/ROW]
[ROW][C]31[/C][C]19644[/C][C]17817.8377355082[/C][C]1826.16226449177[/C][/ROW]
[ROW][C]32[/C][C]18483[/C][C]19225.7119192389[/C][C]-742.711919238936[/C][/ROW]
[ROW][C]33[/C][C]18079[/C][C]17739.4878990857[/C][C]339.512100914253[/C][/ROW]
[ROW][C]34[/C][C]19178[/C][C]17821.236250045[/C][C]1356.76374995496[/C][/ROW]
[ROW][C]35[/C][C]18391[/C][C]20807.438705644[/C][C]-2416.43870564398[/C][/ROW]
[ROW][C]36[/C][C]18441[/C][C]17953.4797374407[/C][C]487.520262559286[/C][/ROW]
[ROW][C]37[/C][C]18584[/C][C]14948.7817700932[/C][C]3635.21822990683[/C][/ROW]
[ROW][C]38[/C][C]20108[/C][C]17142.2737328237[/C][C]2965.72626717628[/C][/ROW]
[ROW][C]39[/C][C]20148[/C][C]19035.4455343074[/C][C]1112.55446569259[/C][/ROW]
[ROW][C]40[/C][C]19394[/C][C]18925.156313981[/C][C]468.843686019038[/C][/ROW]
[ROW][C]41[/C][C]17745[/C][C]19585.8294210866[/C][C]-1840.8294210866[/C][/ROW]
[ROW][C]42[/C][C]17696[/C][C]18138.3159405732[/C][C]-442.315940573171[/C][/ROW]
[ROW][C]43[/C][C]17032[/C][C]17029.8344763194[/C][C]2.16552368057819[/C][/ROW]
[ROW][C]44[/C][C]16438[/C][C]16606.4550023145[/C][C]-168.455002314546[/C][/ROW]
[ROW][C]45[/C][C]15683[/C][C]15980.0245178406[/C][C]-297.024517840551[/C][/ROW]
[ROW][C]46[/C][C]15594[/C][C]15941.761680242[/C][C]-347.761680241987[/C][/ROW]
[ROW][C]47[/C][C]15713[/C][C]16870.0670596217[/C][C]-1157.06705962173[/C][/ROW]
[ROW][C]48[/C][C]15937[/C][C]15775.8901210466[/C][C]161.109878953383[/C][/ROW]
[ROW][C]49[/C][C]16171[/C][C]13335.8605545791[/C][C]2835.13944542092[/C][/ROW]
[ROW][C]50[/C][C]15928[/C][C]14862.1591865244[/C][C]1065.84081347562[/C][/ROW]
[ROW][C]51[/C][C]16348[/C][C]14909.7764618431[/C][C]1438.2235381569[/C][/ROW]
[ROW][C]52[/C][C]15579[/C][C]14967.0875748674[/C][C]611.912425132628[/C][/ROW]
[ROW][C]53[/C][C]15305[/C][C]15292.159061967[/C][C]12.8409380329704[/C][/ROW]
[ROW][C]54[/C][C]15648[/C][C]15716.1959526223[/C][C]-68.1959526222818[/C][/ROW]
[ROW][C]55[/C][C]14954[/C][C]15126.7495756887[/C][C]-172.749575688729[/C][/ROW]
[ROW][C]56[/C][C]15137[/C][C]14653.3494573534[/C][C]483.650542646583[/C][/ROW]
[ROW][C]57[/C][C]15839[/C][C]14652.5169707735[/C][C]1186.48302922649[/C][/ROW]
[ROW][C]58[/C][C]16050[/C][C]15953.065649406[/C][C]96.9343505939833[/C][/ROW]
[ROW][C]59[/C][C]15168[/C][C]17256.8803628696[/C][C]-2088.88036286957[/C][/ROW]
[ROW][C]60[/C][C]17064[/C][C]15900.2194087451[/C][C]1163.78059125491[/C][/ROW]
[ROW][C]61[/C][C]16005[/C][C]15037.1170064064[/C][C]967.882993593596[/C][/ROW]
[ROW][C]62[/C][C]14886[/C][C]14866.4103154479[/C][C]19.5896845520765[/C][/ROW]
[ROW][C]63[/C][C]14931[/C][C]14294.3662643574[/C][C]636.633735642563[/C][/ROW]
[ROW][C]64[/C][C]14544[/C][C]13634.9267262377[/C][C]909.073273762297[/C][/ROW]
[ROW][C]65[/C][C]13812[/C][C]14160.3861779665[/C][C]-348.3861779665[/C][/ROW]
[ROW][C]66[/C][C]13031[/C][C]14372.8385288407[/C][C]-1341.83852884072[/C][/ROW]
[ROW][C]67[/C][C]12574[/C][C]12813.8894900441[/C][C]-239.889490044112[/C][/ROW]
[ROW][C]68[/C][C]11964[/C][C]12477.7047619744[/C][C]-513.704761974364[/C][/ROW]
[ROW][C]69[/C][C]11451[/C][C]11866.353210407[/C][C]-415.353210407[/C][/ROW]
[ROW][C]70[/C][C]11346[/C][C]11640.7991209495[/C][C]-294.799120949516[/C][/ROW]
[ROW][C]71[/C][C]11353[/C][C]12110.6828020543[/C][C]-757.682802054263[/C][/ROW]
[ROW][C]72[/C][C]10702[/C][C]12499.5784613486[/C][C]-1797.57846134858[/C][/ROW]
[ROW][C]73[/C][C]10646[/C][C]9180.68064850036[/C][C]1465.31935149964[/C][/ROW]
[ROW][C]74[/C][C]10556[/C][C]9105.6924858139[/C][C]1450.3075141861[/C][/ROW]
[ROW][C]75[/C][C]10463[/C][C]9746.49827189377[/C][C]716.50172810623[/C][/ROW]
[ROW][C]76[/C][C]10407[/C][C]9172.14345001842[/C][C]1234.85654998158[/C][/ROW]
[ROW][C]77[/C][C]10625[/C][C]9649.68642771466[/C][C]975.313572285339[/C][/ROW]
[ROW][C]78[/C][C]10872[/C][C]10693.1983367089[/C][C]178.801663291084[/C][/ROW]
[ROW][C]79[/C][C]10805[/C][C]10626.5257435152[/C][C]178.474256484846[/C][/ROW]
[ROW][C]80[/C][C]10653[/C][C]10633.6460739117[/C][C]19.3539260883153[/C][/ROW]
[ROW][C]81[/C][C]10574[/C][C]10553.6111783373[/C][C]20.3888216627056[/C][/ROW]
[ROW][C]82[/C][C]10431[/C][C]10802.0543132899[/C][C]-371.0543132899[/C][/ROW]
[ROW][C]83[/C][C]10383[/C][C]11215.8641475573[/C][C]-832.864147557331[/C][/ROW]
[ROW][C]84[/C][C]10296[/C][C]11420.6702388144[/C][C]-1124.67023881438[/C][/ROW]
[ROW][C]85[/C][C]10872[/C][C]9466.22647251288[/C][C]1405.77352748712[/C][/ROW]
[ROW][C]86[/C][C]10635[/C][C]9463.42332375689[/C][C]1171.57667624311[/C][/ROW]
[ROW][C]87[/C][C]10297[/C][C]9838.89405343477[/C][C]458.105946565227[/C][/ROW]
[ROW][C]88[/C][C]10570[/C][C]9281.35500988771[/C][C]1288.64499011229[/C][/ROW]
[ROW][C]89[/C][C]10662[/C][C]9850.67040216997[/C][C]811.329597830034[/C][/ROW]
[ROW][C]90[/C][C]10709[/C][C]10693.0253062951[/C][C]15.9746937049349[/C][/ROW]
[ROW][C]91[/C][C]10413[/C][C]10595.4550488185[/C][C]-182.455048818514[/C][/ROW]
[ROW][C]92[/C][C]10846[/C][C]10370.7605878589[/C][C]475.239412141114[/C][/ROW]
[ROW][C]93[/C][C]10371[/C][C]10746.2330825674[/C][C]-375.233082567447[/C][/ROW]
[ROW][C]94[/C][C]9924[/C][C]10686.7595721945[/C][C]-762.759572194485[/C][/ROW]
[ROW][C]95[/C][C]9828[/C][C]10767.8819375799[/C][C]-939.881937579938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122414&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122414&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
132752531358.874732906-3833.874732906
142643427197.8825910096-763.882591009551
152573925821.2895271255-82.2895271254602
162520425114.954130642589.0458693575347
172497724931.969893641845.0301063582083
182432024285.627015791734.3729842083449
192268022733.0931941151-53.0931941150629
202205222554.7914222584-502.791422258426
212146720786.8103882778680.189611722151
222138321000.8924940857382.107505914311
232177723445.7046297082-1668.70462970819
242192820231.86564406671696.13435593329
252181417409.26524382284404.73475617721
262293720488.93636303642448.06363696365
272359522006.33933664331588.6606633567
282083022931.8478594936-2101.84785949362
291965021248.7379665465-1598.73796654655
301919519484.725111246-289.725111246014
311964417817.83773550821826.16226449177
321848319225.7119192389-742.711919238936
331807917739.4878990857339.512100914253
341917817821.2362500451356.76374995496
351839120807.438705644-2416.43870564398
361844117953.4797374407487.520262559286
371858414948.78177009323635.21822990683
382010817142.27373282372965.72626717628
392014819035.44553430741112.55446569259
401939418925.156313981468.843686019038
411774519585.8294210866-1840.8294210866
421769618138.3159405732-442.315940573171
431703217029.83447631942.16552368057819
441643816606.4550023145-168.455002314546
451568315980.0245178406-297.024517840551
461559415941.761680242-347.761680241987
471571316870.0670596217-1157.06705962173
481593715775.8901210466161.109878953383
491617113335.86055457912835.13944542092
501592814862.15918652441065.84081347562
511634814909.77646184311438.2235381569
521557914967.0875748674611.912425132628
531530515292.15906196712.8409380329704
541564815716.1959526223-68.1959526222818
551495415126.7495756887-172.749575688729
561513714653.3494573534483.650542646583
571583914652.51697077351186.48302922649
581605015953.06564940696.9343505939833
591516817256.8803628696-2088.88036286957
601706415900.21940874511163.78059125491
611600515037.1170064064967.882993593596
621488614866.410315447919.5896845520765
631493114294.3662643574636.633735642563
641454413634.9267262377909.073273762297
651381214160.3861779665-348.3861779665
661303114372.8385288407-1341.83852884072
671257412813.8894900441-239.889490044112
681196412477.7047619744-513.704761974364
691145111866.353210407-415.353210407
701134611640.7991209495-294.799120949516
711135312110.6828020543-757.682802054263
721070212499.5784613486-1797.57846134858
73106469180.680648500361465.31935149964
74105569105.69248581391450.3075141861
75104639746.49827189377716.50172810623
76104079172.143450018421234.85654998158
77106259649.68642771466975.313572285339
781087210693.1983367089178.801663291084
791080510626.5257435152178.474256484846
801065310633.646073911719.3539260883153
811057410553.611178337320.3888216627056
821043110802.0543132899-371.0543132899
831038311215.8641475573-832.864147557331
841029611420.6702388144-1124.67023881438
85108729466.226472512881405.77352748712
86106359463.423323756891171.57667624311
87102979838.89405343477458.105946565227
88105709281.355009887711288.64499011229
89106629850.67040216997811.329597830034
901070910693.025306295115.9746937049349
911041310595.4550488185-182.455048818514
921084610370.7605878589475.239412141114
931037110746.2330825674-375.233082567447
94992410686.7595721945-762.759572194485
95982810767.8819375799-939.881937579938







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9610896.16159465478345.2587971590213447.0643921503
9710481.12794446667194.3901247352913767.8657641979
989391.436582611475462.1117614434813320.7614037795
998720.728268780654200.6615747670513240.7949627943
1007998.015206200992919.6367964937513076.3936159082
1017426.184247677181811.0778119921413041.2906833622
1027404.681889529171267.7009032233113541.662875835
1037194.61025294456546.12719505226813843.0933108368
1047205.7802815433353.029203059548314358.5313600271
1056957.95968357163-694.10881831501414610.0281854583
1067052.60894591557-1095.5376988007115200.7555906319
1077660.71488590755-981.58375633650116303.0135281516

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
96 & 10896.1615946547 & 8345.25879715902 & 13447.0643921503 \tabularnewline
97 & 10481.1279444666 & 7194.39012473529 & 13767.8657641979 \tabularnewline
98 & 9391.43658261147 & 5462.11176144348 & 13320.7614037795 \tabularnewline
99 & 8720.72826878065 & 4200.66157476705 & 13240.7949627943 \tabularnewline
100 & 7998.01520620099 & 2919.63679649375 & 13076.3936159082 \tabularnewline
101 & 7426.18424767718 & 1811.07781199214 & 13041.2906833622 \tabularnewline
102 & 7404.68188952917 & 1267.70090322331 & 13541.662875835 \tabularnewline
103 & 7194.61025294456 & 546.127195052268 & 13843.0933108368 \tabularnewline
104 & 7205.78028154333 & 53.0292030595483 & 14358.5313600271 \tabularnewline
105 & 6957.95968357163 & -694.108818315014 & 14610.0281854583 \tabularnewline
106 & 7052.60894591557 & -1095.53769880071 & 15200.7555906319 \tabularnewline
107 & 7660.71488590755 & -981.583756336501 & 16303.0135281516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122414&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]96[/C][C]10896.1615946547[/C][C]8345.25879715902[/C][C]13447.0643921503[/C][/ROW]
[ROW][C]97[/C][C]10481.1279444666[/C][C]7194.39012473529[/C][C]13767.8657641979[/C][/ROW]
[ROW][C]98[/C][C]9391.43658261147[/C][C]5462.11176144348[/C][C]13320.7614037795[/C][/ROW]
[ROW][C]99[/C][C]8720.72826878065[/C][C]4200.66157476705[/C][C]13240.7949627943[/C][/ROW]
[ROW][C]100[/C][C]7998.01520620099[/C][C]2919.63679649375[/C][C]13076.3936159082[/C][/ROW]
[ROW][C]101[/C][C]7426.18424767718[/C][C]1811.07781199214[/C][C]13041.2906833622[/C][/ROW]
[ROW][C]102[/C][C]7404.68188952917[/C][C]1267.70090322331[/C][C]13541.662875835[/C][/ROW]
[ROW][C]103[/C][C]7194.61025294456[/C][C]546.127195052268[/C][C]13843.0933108368[/C][/ROW]
[ROW][C]104[/C][C]7205.78028154333[/C][C]53.0292030595483[/C][C]14358.5313600271[/C][/ROW]
[ROW][C]105[/C][C]6957.95968357163[/C][C]-694.108818315014[/C][C]14610.0281854583[/C][/ROW]
[ROW][C]106[/C][C]7052.60894591557[/C][C]-1095.53769880071[/C][C]15200.7555906319[/C][/ROW]
[ROW][C]107[/C][C]7660.71488590755[/C][C]-981.583756336501[/C][C]16303.0135281516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122414&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122414&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
9610896.16159465478345.2587971590213447.0643921503
9710481.12794446667194.3901247352913767.8657641979
989391.436582611475462.1117614434813320.7614037795
998720.728268780654200.6615747670513240.7949627943
1007998.015206200992919.6367964937513076.3936159082
1017426.184247677181811.0778119921413041.2906833622
1027404.681889529171267.7009032233113541.662875835
1037194.61025294456546.12719505226813843.0933108368
1047205.7802815433353.029203059548314358.5313600271
1056957.95968357163-694.10881831501414610.0281854583
1067052.60894591557-1095.5376988007115200.7555906319
1077660.71488590755-981.58375633650116303.0135281516



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