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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 09 Dec 2010 17:51:57 +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/2010/Dec/09/t1291916987kee0cx33571grc2.htm/, Retrieved Sun, 28 Apr 2024 21:14:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107301, Retrieved Sun, 28 Apr 2024 21:14:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Workshop 8 - trip...] [2010-12-09 17:51:57] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
9700
9081
9084
9743
8587
9731
9563
9998
9437
10038
9918
9252
9737
9035
9133
9487
8700
9627
8947
9283
8829
9947
9628
9318
9605
8640
9214
9567
8547
9185
9470
9123
9278
10170
9434
9655
9429
8739
9552
9687
9019
9672
9206
9069
9788
10312
10105
9863
9656
9295
9946
9701
9049
10190
9706
9765
9893
9994
10433
10073
10112
9266
9820
10097
9115
10411
9678
10408
10153
10368
10581
10597
10680
9738
9556




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107301&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107301&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107301&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.118633081220547
beta0.177857467177405
gamma0.5937606815085

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.118633081220547 \tabularnewline
beta & 0.177857467177405 \tabularnewline
gamma & 0.5937606815085 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107301&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]0.118633081220547[/C][/ROW]
[ROW][C]beta[/C][C]0.177857467177405[/C][/ROW]
[ROW][C]gamma[/C][C]0.5937606815085[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107301&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107301&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
alpha0.118633081220547
beta0.177857467177405
gamma0.5937606815085







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397379768.09802350428-31.0980235042771
1490359094.8206438525-59.8206438524921
1591339216.54027552891-83.5402755289124
1694879563.6832928337-76.6832928337008
1787008755.77177456493-55.7717745649261
1896279656.62261533747-29.6226153374682
1989479350.24224745979-403.242247459786
2092839699.77990897321-416.779908973213
2188299042.4175918722-213.417591872209
2299479575.42770895528371.572291044724
2396289462.01040501833165.989594981666
2493188775.37320289687542.626797103134
2596059309.96768879984295.032311200162
2686408661.11582635564-21.1158263556354
2792148776.59763276738437.402367232617
2895679201.70534380874365.294656191258
2985478479.071365477767.9286345223063
3091859432.79251990023-247.792519900235
3194708924.91458754528545.085412454724
3291239419.78785425682-296.787854256820
3392788925.53326165975352.46673834025
34101709886.2024401871283.797559812900
3594349707.32333142966-273.323331429661
3696559208.93877176675446.061228233255
3794299643.73599787529-214.73599787529
3887398799.4357954875-60.4357954874995
3995529179.84953180272372.150468197282
4096879587.748296431399.2517035687033
4190198700.58905330985318.410946690148
4296729546.74142131195125.25857868805
4392069533.8599186699-327.859918669908
4490699501.99459678781-432.99459678781
4597889345.86760799596442.132392004038
461031210297.647652282614.3523477174276
47101059805.97469658919299.025303410814
4898639774.7594553185788.2405446814264
4996569836.5490668885-180.549066888509
5092959093.02527743563201.974722564371
5199469752.46004416102193.539955838984
52970110014.0963668069-313.096366806853
5390499201.74952137105-152.749521371048
54101909890.02447533174299.975524668256
5597069663.5287347837642.4712652162380
5697659631.17664908248133.823350917515
57989310022.8239980114-129.823998011401
58999410693.3752773111-699.375277311072
591043310261.4369351175171.563064882548
601007310097.5339138071-24.5339138070922
61101129995.64352685936116.356473140644
6292669484.15197570541-218.151975705412
63982010077.0938250165-257.093825016538
64100979998.390460116198.6095398839061
6591159305.73915852747-190.739158527469
661041110212.5669742498198.433025750250
6796789823.26417307528-145.264173075282
68104089796.48237564632611.517624353677
691015310096.942566585956.057433414142
701036810485.5241309133-117.524130913331
711058110584.7066133174-3.70661331736665
721059710300.0046737778296.99532622221
731068010319.3889237420360.611076258041
7497389676.3721946804161.6278053195856
75955610302.5828340882-746.582834088236

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9737 & 9768.09802350428 & -31.0980235042771 \tabularnewline
14 & 9035 & 9094.8206438525 & -59.8206438524921 \tabularnewline
15 & 9133 & 9216.54027552891 & -83.5402755289124 \tabularnewline
16 & 9487 & 9563.6832928337 & -76.6832928337008 \tabularnewline
17 & 8700 & 8755.77177456493 & -55.7717745649261 \tabularnewline
18 & 9627 & 9656.62261533747 & -29.6226153374682 \tabularnewline
19 & 8947 & 9350.24224745979 & -403.242247459786 \tabularnewline
20 & 9283 & 9699.77990897321 & -416.779908973213 \tabularnewline
21 & 8829 & 9042.4175918722 & -213.417591872209 \tabularnewline
22 & 9947 & 9575.42770895528 & 371.572291044724 \tabularnewline
23 & 9628 & 9462.01040501833 & 165.989594981666 \tabularnewline
24 & 9318 & 8775.37320289687 & 542.626797103134 \tabularnewline
25 & 9605 & 9309.96768879984 & 295.032311200162 \tabularnewline
26 & 8640 & 8661.11582635564 & -21.1158263556354 \tabularnewline
27 & 9214 & 8776.59763276738 & 437.402367232617 \tabularnewline
28 & 9567 & 9201.70534380874 & 365.294656191258 \tabularnewline
29 & 8547 & 8479.0713654777 & 67.9286345223063 \tabularnewline
30 & 9185 & 9432.79251990023 & -247.792519900235 \tabularnewline
31 & 9470 & 8924.91458754528 & 545.085412454724 \tabularnewline
32 & 9123 & 9419.78785425682 & -296.787854256820 \tabularnewline
33 & 9278 & 8925.53326165975 & 352.46673834025 \tabularnewline
34 & 10170 & 9886.2024401871 & 283.797559812900 \tabularnewline
35 & 9434 & 9707.32333142966 & -273.323331429661 \tabularnewline
36 & 9655 & 9208.93877176675 & 446.061228233255 \tabularnewline
37 & 9429 & 9643.73599787529 & -214.73599787529 \tabularnewline
38 & 8739 & 8799.4357954875 & -60.4357954874995 \tabularnewline
39 & 9552 & 9179.84953180272 & 372.150468197282 \tabularnewline
40 & 9687 & 9587.7482964313 & 99.2517035687033 \tabularnewline
41 & 9019 & 8700.58905330985 & 318.410946690148 \tabularnewline
42 & 9672 & 9546.74142131195 & 125.25857868805 \tabularnewline
43 & 9206 & 9533.8599186699 & -327.859918669908 \tabularnewline
44 & 9069 & 9501.99459678781 & -432.99459678781 \tabularnewline
45 & 9788 & 9345.86760799596 & 442.132392004038 \tabularnewline
46 & 10312 & 10297.6476522826 & 14.3523477174276 \tabularnewline
47 & 10105 & 9805.97469658919 & 299.025303410814 \tabularnewline
48 & 9863 & 9774.75945531857 & 88.2405446814264 \tabularnewline
49 & 9656 & 9836.5490668885 & -180.549066888509 \tabularnewline
50 & 9295 & 9093.02527743563 & 201.974722564371 \tabularnewline
51 & 9946 & 9752.46004416102 & 193.539955838984 \tabularnewline
52 & 9701 & 10014.0963668069 & -313.096366806853 \tabularnewline
53 & 9049 & 9201.74952137105 & -152.749521371048 \tabularnewline
54 & 10190 & 9890.02447533174 & 299.975524668256 \tabularnewline
55 & 9706 & 9663.52873478376 & 42.4712652162380 \tabularnewline
56 & 9765 & 9631.17664908248 & 133.823350917515 \tabularnewline
57 & 9893 & 10022.8239980114 & -129.823998011401 \tabularnewline
58 & 9994 & 10693.3752773111 & -699.375277311072 \tabularnewline
59 & 10433 & 10261.4369351175 & 171.563064882548 \tabularnewline
60 & 10073 & 10097.5339138071 & -24.5339138070922 \tabularnewline
61 & 10112 & 9995.64352685936 & 116.356473140644 \tabularnewline
62 & 9266 & 9484.15197570541 & -218.151975705412 \tabularnewline
63 & 9820 & 10077.0938250165 & -257.093825016538 \tabularnewline
64 & 10097 & 9998.3904601161 & 98.6095398839061 \tabularnewline
65 & 9115 & 9305.73915852747 & -190.739158527469 \tabularnewline
66 & 10411 & 10212.5669742498 & 198.433025750250 \tabularnewline
67 & 9678 & 9823.26417307528 & -145.264173075282 \tabularnewline
68 & 10408 & 9796.48237564632 & 611.517624353677 \tabularnewline
69 & 10153 & 10096.9425665859 & 56.057433414142 \tabularnewline
70 & 10368 & 10485.5241309133 & -117.524130913331 \tabularnewline
71 & 10581 & 10584.7066133174 & -3.70661331736665 \tabularnewline
72 & 10597 & 10300.0046737778 & 296.99532622221 \tabularnewline
73 & 10680 & 10319.3889237420 & 360.611076258041 \tabularnewline
74 & 9738 & 9676.37219468041 & 61.6278053195856 \tabularnewline
75 & 9556 & 10302.5828340882 & -746.582834088236 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107301&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]9737[/C][C]9768.09802350428[/C][C]-31.0980235042771[/C][/ROW]
[ROW][C]14[/C][C]9035[/C][C]9094.8206438525[/C][C]-59.8206438524921[/C][/ROW]
[ROW][C]15[/C][C]9133[/C][C]9216.54027552891[/C][C]-83.5402755289124[/C][/ROW]
[ROW][C]16[/C][C]9487[/C][C]9563.6832928337[/C][C]-76.6832928337008[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]8755.77177456493[/C][C]-55.7717745649261[/C][/ROW]
[ROW][C]18[/C][C]9627[/C][C]9656.62261533747[/C][C]-29.6226153374682[/C][/ROW]
[ROW][C]19[/C][C]8947[/C][C]9350.24224745979[/C][C]-403.242247459786[/C][/ROW]
[ROW][C]20[/C][C]9283[/C][C]9699.77990897321[/C][C]-416.779908973213[/C][/ROW]
[ROW][C]21[/C][C]8829[/C][C]9042.4175918722[/C][C]-213.417591872209[/C][/ROW]
[ROW][C]22[/C][C]9947[/C][C]9575.42770895528[/C][C]371.572291044724[/C][/ROW]
[ROW][C]23[/C][C]9628[/C][C]9462.01040501833[/C][C]165.989594981666[/C][/ROW]
[ROW][C]24[/C][C]9318[/C][C]8775.37320289687[/C][C]542.626797103134[/C][/ROW]
[ROW][C]25[/C][C]9605[/C][C]9309.96768879984[/C][C]295.032311200162[/C][/ROW]
[ROW][C]26[/C][C]8640[/C][C]8661.11582635564[/C][C]-21.1158263556354[/C][/ROW]
[ROW][C]27[/C][C]9214[/C][C]8776.59763276738[/C][C]437.402367232617[/C][/ROW]
[ROW][C]28[/C][C]9567[/C][C]9201.70534380874[/C][C]365.294656191258[/C][/ROW]
[ROW][C]29[/C][C]8547[/C][C]8479.0713654777[/C][C]67.9286345223063[/C][/ROW]
[ROW][C]30[/C][C]9185[/C][C]9432.79251990023[/C][C]-247.792519900235[/C][/ROW]
[ROW][C]31[/C][C]9470[/C][C]8924.91458754528[/C][C]545.085412454724[/C][/ROW]
[ROW][C]32[/C][C]9123[/C][C]9419.78785425682[/C][C]-296.787854256820[/C][/ROW]
[ROW][C]33[/C][C]9278[/C][C]8925.53326165975[/C][C]352.46673834025[/C][/ROW]
[ROW][C]34[/C][C]10170[/C][C]9886.2024401871[/C][C]283.797559812900[/C][/ROW]
[ROW][C]35[/C][C]9434[/C][C]9707.32333142966[/C][C]-273.323331429661[/C][/ROW]
[ROW][C]36[/C][C]9655[/C][C]9208.93877176675[/C][C]446.061228233255[/C][/ROW]
[ROW][C]37[/C][C]9429[/C][C]9643.73599787529[/C][C]-214.73599787529[/C][/ROW]
[ROW][C]38[/C][C]8739[/C][C]8799.4357954875[/C][C]-60.4357954874995[/C][/ROW]
[ROW][C]39[/C][C]9552[/C][C]9179.84953180272[/C][C]372.150468197282[/C][/ROW]
[ROW][C]40[/C][C]9687[/C][C]9587.7482964313[/C][C]99.2517035687033[/C][/ROW]
[ROW][C]41[/C][C]9019[/C][C]8700.58905330985[/C][C]318.410946690148[/C][/ROW]
[ROW][C]42[/C][C]9672[/C][C]9546.74142131195[/C][C]125.25857868805[/C][/ROW]
[ROW][C]43[/C][C]9206[/C][C]9533.8599186699[/C][C]-327.859918669908[/C][/ROW]
[ROW][C]44[/C][C]9069[/C][C]9501.99459678781[/C][C]-432.99459678781[/C][/ROW]
[ROW][C]45[/C][C]9788[/C][C]9345.86760799596[/C][C]442.132392004038[/C][/ROW]
[ROW][C]46[/C][C]10312[/C][C]10297.6476522826[/C][C]14.3523477174276[/C][/ROW]
[ROW][C]47[/C][C]10105[/C][C]9805.97469658919[/C][C]299.025303410814[/C][/ROW]
[ROW][C]48[/C][C]9863[/C][C]9774.75945531857[/C][C]88.2405446814264[/C][/ROW]
[ROW][C]49[/C][C]9656[/C][C]9836.5490668885[/C][C]-180.549066888509[/C][/ROW]
[ROW][C]50[/C][C]9295[/C][C]9093.02527743563[/C][C]201.974722564371[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]9752.46004416102[/C][C]193.539955838984[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]10014.0963668069[/C][C]-313.096366806853[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]9201.74952137105[/C][C]-152.749521371048[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]9890.02447533174[/C][C]299.975524668256[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]9663.52873478376[/C][C]42.4712652162380[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]9631.17664908248[/C][C]133.823350917515[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]10022.8239980114[/C][C]-129.823998011401[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]10693.3752773111[/C][C]-699.375277311072[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]10261.4369351175[/C][C]171.563064882548[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]10097.5339138071[/C][C]-24.5339138070922[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]9995.64352685936[/C][C]116.356473140644[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]9484.15197570541[/C][C]-218.151975705412[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]10077.0938250165[/C][C]-257.093825016538[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9998.3904601161[/C][C]98.6095398839061[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9305.73915852747[/C][C]-190.739158527469[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]10212.5669742498[/C][C]198.433025750250[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9823.26417307528[/C][C]-145.264173075282[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]9796.48237564632[/C][C]611.517624353677[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]10096.9425665859[/C][C]56.057433414142[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10485.5241309133[/C][C]-117.524130913331[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10584.7066133174[/C][C]-3.70661331736665[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10300.0046737778[/C][C]296.99532622221[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10319.3889237420[/C][C]360.611076258041[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]9676.37219468041[/C][C]61.6278053195856[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]10302.5828340882[/C][C]-746.582834088236[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107301&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107301&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
1397379768.09802350428-31.0980235042771
1490359094.8206438525-59.8206438524921
1591339216.54027552891-83.5402755289124
1694879563.6832928337-76.6832928337008
1787008755.77177456493-55.7717745649261
1896279656.62261533747-29.6226153374682
1989479350.24224745979-403.242247459786
2092839699.77990897321-416.779908973213
2188299042.4175918722-213.417591872209
2299479575.42770895528371.572291044724
2396289462.01040501833165.989594981666
2493188775.37320289687542.626797103134
2596059309.96768879984295.032311200162
2686408661.11582635564-21.1158263556354
2792148776.59763276738437.402367232617
2895679201.70534380874365.294656191258
2985478479.071365477767.9286345223063
3091859432.79251990023-247.792519900235
3194708924.91458754528545.085412454724
3291239419.78785425682-296.787854256820
3392788925.53326165975352.46673834025
34101709886.2024401871283.797559812900
3594349707.32333142966-273.323331429661
3696559208.93877176675446.061228233255
3794299643.73599787529-214.73599787529
3887398799.4357954875-60.4357954874995
3995529179.84953180272372.150468197282
4096879587.748296431399.2517035687033
4190198700.58905330985318.410946690148
4296729546.74142131195125.25857868805
4392069533.8599186699-327.859918669908
4490699501.99459678781-432.99459678781
4597889345.86760799596442.132392004038
461031210297.647652282614.3523477174276
47101059805.97469658919299.025303410814
4898639774.7594553185788.2405446814264
4996569836.5490668885-180.549066888509
5092959093.02527743563201.974722564371
5199469752.46004416102193.539955838984
52970110014.0963668069-313.096366806853
5390499201.74952137105-152.749521371048
54101909890.02447533174299.975524668256
5597069663.5287347837642.4712652162380
5697659631.17664908248133.823350917515
57989310022.8239980114-129.823998011401
58999410693.3752773111-699.375277311072
591043310261.4369351175171.563064882548
601007310097.5339138071-24.5339138070922
61101129995.64352685936116.356473140644
6292669484.15197570541-218.151975705412
63982010077.0938250165-257.093825016538
64100979998.390460116198.6095398839061
6591159305.73915852747-190.739158527469
661041110212.5669742498198.433025750250
6796789823.26417307528-145.264173075282
68104089796.48237564632611.517624353677
691015310096.942566585956.057433414142
701036810485.5241309133-117.524130913331
711058110584.7066133174-3.70661331736665
721059710300.0046737778296.99532622221
731068010319.3889237420360.611076258041
7497389676.3721946804161.6278053195856
75955610302.5828340882-746.582834088236







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7610362.08555931139787.7658812375510936.4052373851
779514.36163888498934.4621917131810094.2610860566
7810659.551959584410072.342060445911246.7618587228
7910074.73012016489478.2964894773110671.1637508523
8010472.17197759209864.4467995052611079.8971556787
8110407.44976107679786.2415776256311028.6579445278
8210695.407185713610058.433156512111332.381214915
8310867.439758852310212.357699186511522.5218185182
8410739.964142714810064.402840546511415.5254448832
8510750.562795536410052.149371485211448.9762195877
869893.84903239089170.2324824399510617.4655823417
8710074.04222420759322.9126966727210825.1717517423

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 10362.0855593113 & 9787.76588123755 & 10936.4052373851 \tabularnewline
77 & 9514.3616388849 & 8934.46219171318 & 10094.2610860566 \tabularnewline
78 & 10659.5519595844 & 10072.3420604459 & 11246.7618587228 \tabularnewline
79 & 10074.7301201648 & 9478.29648947731 & 10671.1637508523 \tabularnewline
80 & 10472.1719775920 & 9864.44679950526 & 11079.8971556787 \tabularnewline
81 & 10407.4497610767 & 9786.24157762563 & 11028.6579445278 \tabularnewline
82 & 10695.4071857136 & 10058.4331565121 & 11332.381214915 \tabularnewline
83 & 10867.4397588523 & 10212.3576991865 & 11522.5218185182 \tabularnewline
84 & 10739.9641427148 & 10064.4028405465 & 11415.5254448832 \tabularnewline
85 & 10750.5627955364 & 10052.1493714852 & 11448.9762195877 \tabularnewline
86 & 9893.8490323908 & 9170.23248243995 & 10617.4655823417 \tabularnewline
87 & 10074.0422242075 & 9322.91269667272 & 10825.1717517423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107301&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]76[/C][C]10362.0855593113[/C][C]9787.76588123755[/C][C]10936.4052373851[/C][/ROW]
[ROW][C]77[/C][C]9514.3616388849[/C][C]8934.46219171318[/C][C]10094.2610860566[/C][/ROW]
[ROW][C]78[/C][C]10659.5519595844[/C][C]10072.3420604459[/C][C]11246.7618587228[/C][/ROW]
[ROW][C]79[/C][C]10074.7301201648[/C][C]9478.29648947731[/C][C]10671.1637508523[/C][/ROW]
[ROW][C]80[/C][C]10472.1719775920[/C][C]9864.44679950526[/C][C]11079.8971556787[/C][/ROW]
[ROW][C]81[/C][C]10407.4497610767[/C][C]9786.24157762563[/C][C]11028.6579445278[/C][/ROW]
[ROW][C]82[/C][C]10695.4071857136[/C][C]10058.4331565121[/C][C]11332.381214915[/C][/ROW]
[ROW][C]83[/C][C]10867.4397588523[/C][C]10212.3576991865[/C][C]11522.5218185182[/C][/ROW]
[ROW][C]84[/C][C]10739.9641427148[/C][C]10064.4028405465[/C][C]11415.5254448832[/C][/ROW]
[ROW][C]85[/C][C]10750.5627955364[/C][C]10052.1493714852[/C][C]11448.9762195877[/C][/ROW]
[ROW][C]86[/C][C]9893.8490323908[/C][C]9170.23248243995[/C][C]10617.4655823417[/C][/ROW]
[ROW][C]87[/C][C]10074.0422242075[/C][C]9322.91269667272[/C][C]10825.1717517423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107301&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107301&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
7610362.08555931139787.7658812375510936.4052373851
779514.36163888498934.4621917131810094.2610860566
7810659.551959584410072.342060445911246.7618587228
7910074.73012016489478.2964894773110671.1637508523
8010472.17197759209864.4467995052611079.8971556787
8110407.44976107679786.2415776256311028.6579445278
8210695.407185713610058.433156512111332.381214915
8310867.439758852310212.357699186511522.5218185182
8410739.964142714810064.402840546511415.5254448832
8510750.562795536410052.149371485211448.9762195877
869893.84903239089170.2324824399510617.4655823417
8710074.04222420759322.9126966727210825.1717517423



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')