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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 09:23:39 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/17/t1355754235xkcl2jqq6eu57c8.htm/, Retrieved Fri, 29 Mar 2024 13:10:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200956, Retrieved Fri, 29 Mar 2024 13:10:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact238
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [] [2012-12-17 14:08:52] [b98453cac15ba1066b407e146608df68]
- RMP     [Exponential Smoothing] [] [2012-12-17 14:23:39] [d76b387543b13b5e3afd8ff9e5fdc89f] [Current]
- RMP       [Decomposition by Loess] [loes decompostion...] [2012-12-18 19:44:38] [cf3404f2aa5ecb19248d89bb206f05c1]
- R P       [Exponential Smoothing] [] [2013-01-15 15:05:40] [391561951b5d7f721cfaa4f5575ab127]
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Dataseries X:
164
96
73
49
39
59
169
169
210
278
298
245
200
188
90
79
78
91
167
169
289
247
275
203
223
104
107
85
75
99
135
211
335
488
326
346
261
224
141
148
145
223
272
445
560
612
467
404
518
404
300
210
196
186
247
343
464
680
711
610
513
292
273
322
189
257
324
404
677
858
895
664
628
308
324
248
272




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200956&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200956&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200956&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 time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.218080460096599
beta0.0173054151884953
gamma0.462793140010703

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.218080460096599 \tabularnewline
beta & 0.0173054151884953 \tabularnewline
gamma & 0.462793140010703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200956&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]0.218080460096599[/C][/ROW]
[ROW][C]beta[/C][C]0.0173054151884953[/C][/ROW]
[ROW][C]gamma[/C][C]0.462793140010703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200956&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200956&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
alpha0.218080460096599
beta0.0173054151884953
gamma0.462793140010703







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13200178.99624092635321.0037590736465
14188174.63835996249413.3616400375056
159084.38449121170785.61550878829223
167975.16157623332043.83842376667964
177876.85450827644111.14549172355892
189192.3808522909257-1.38085229092569
19167194.212808684525-27.2128086845248
20169184.008879972974-15.0088799729745
21289220.73159307239668.2684069276037
22247311.630510329539-64.630510329539
23275316.844391419137-41.844391419137
24203251.199669254532-48.1996692545315
25223205.1304972848517.8695027151497
26104195.805258677003-91.8052586770035
2710783.039923941585723.9600760584143
288576.91262573350648.08737426649361
297578.3961139894838-3.39611398948384
309991.85112901380267.14887098619738
31135187.381718260067-52.3817182600668
32211175.62566487090935.3743351290908
33335254.63550059062880.3644994093723
34488299.743136835132188.256863164868
35326374.415309851575-48.4153098515753
36346289.70118663462456.2988133653756
37261286.175603215236-25.1756032152355
38224206.86591188645317.1340881135471
39141134.8710637987656.12893620123523
40148112.16674567522235.8332543247782
41145113.54982161515931.4501783848409
42223148.92641455750574.0735854424945
43272288.063668817784-16.0636688177838
44445341.325160023508103.674839976492
45560524.15744017202335.8425598279771
46612636.281411050963-24.2814110509629
47467550.340424535747-83.3404245357469
48404475.521642588138-71.5216425881379
49518395.133554478984122.866445521016
50404331.11212862318672.887871376814
51300219.58964171321680.4103582867844
52210213.190103539809-3.19010353980923
53196198.80019114449-2.8001911444903
54186260.418255421333-74.4182554213334
55247358.830883054141-111.830883054141
56343451.220925741842-108.220925741842
57464570.831096638769-106.831096638769
58680628.93555826529251.064441734708
59711532.952413008262178.047586991738
60610510.49234621689999.5076537831013
61513535.170082504436-22.1700825044355
62292404.647584147747-112.647584147747
63273250.4635186848722.53648131513
64322202.937201096688119.062798903312
65189213.953717654589-24.9537176545893
66257244.67828646518712.3217135348127
67324358.811501378948-34.8115013789479
68404489.4700262312-85.4700262311998
69677642.77069910480534.2293008951946
70858826.88943691033831.1105630896617
71895750.677946511787144.322053488213
72664669.883859986125-5.88385998612466
73628619.838937180898.1610628191097
74308429.723020645643-121.723020645643
75324306.9444375733617.0555624266399
76248284.098358932824-36.0983589328243
77272207.51375652696764.4862434730326

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 200 & 178.996240926353 & 21.0037590736465 \tabularnewline
14 & 188 & 174.638359962494 & 13.3616400375056 \tabularnewline
15 & 90 & 84.3844912117078 & 5.61550878829223 \tabularnewline
16 & 79 & 75.1615762333204 & 3.83842376667964 \tabularnewline
17 & 78 & 76.8545082764411 & 1.14549172355892 \tabularnewline
18 & 91 & 92.3808522909257 & -1.38085229092569 \tabularnewline
19 & 167 & 194.212808684525 & -27.2128086845248 \tabularnewline
20 & 169 & 184.008879972974 & -15.0088799729745 \tabularnewline
21 & 289 & 220.731593072396 & 68.2684069276037 \tabularnewline
22 & 247 & 311.630510329539 & -64.630510329539 \tabularnewline
23 & 275 & 316.844391419137 & -41.844391419137 \tabularnewline
24 & 203 & 251.199669254532 & -48.1996692545315 \tabularnewline
25 & 223 & 205.13049728485 & 17.8695027151497 \tabularnewline
26 & 104 & 195.805258677003 & -91.8052586770035 \tabularnewline
27 & 107 & 83.0399239415857 & 23.9600760584143 \tabularnewline
28 & 85 & 76.9126257335064 & 8.08737426649361 \tabularnewline
29 & 75 & 78.3961139894838 & -3.39611398948384 \tabularnewline
30 & 99 & 91.8511290138026 & 7.14887098619738 \tabularnewline
31 & 135 & 187.381718260067 & -52.3817182600668 \tabularnewline
32 & 211 & 175.625664870909 & 35.3743351290908 \tabularnewline
33 & 335 & 254.635500590628 & 80.3644994093723 \tabularnewline
34 & 488 & 299.743136835132 & 188.256863164868 \tabularnewline
35 & 326 & 374.415309851575 & -48.4153098515753 \tabularnewline
36 & 346 & 289.701186634624 & 56.2988133653756 \tabularnewline
37 & 261 & 286.175603215236 & -25.1756032152355 \tabularnewline
38 & 224 & 206.865911886453 & 17.1340881135471 \tabularnewline
39 & 141 & 134.871063798765 & 6.12893620123523 \tabularnewline
40 & 148 & 112.166745675222 & 35.8332543247782 \tabularnewline
41 & 145 & 113.549821615159 & 31.4501783848409 \tabularnewline
42 & 223 & 148.926414557505 & 74.0735854424945 \tabularnewline
43 & 272 & 288.063668817784 & -16.0636688177838 \tabularnewline
44 & 445 & 341.325160023508 & 103.674839976492 \tabularnewline
45 & 560 & 524.157440172023 & 35.8425598279771 \tabularnewline
46 & 612 & 636.281411050963 & -24.2814110509629 \tabularnewline
47 & 467 & 550.340424535747 & -83.3404245357469 \tabularnewline
48 & 404 & 475.521642588138 & -71.5216425881379 \tabularnewline
49 & 518 & 395.133554478984 & 122.866445521016 \tabularnewline
50 & 404 & 331.112128623186 & 72.887871376814 \tabularnewline
51 & 300 & 219.589641713216 & 80.4103582867844 \tabularnewline
52 & 210 & 213.190103539809 & -3.19010353980923 \tabularnewline
53 & 196 & 198.80019114449 & -2.8001911444903 \tabularnewline
54 & 186 & 260.418255421333 & -74.4182554213334 \tabularnewline
55 & 247 & 358.830883054141 & -111.830883054141 \tabularnewline
56 & 343 & 451.220925741842 & -108.220925741842 \tabularnewline
57 & 464 & 570.831096638769 & -106.831096638769 \tabularnewline
58 & 680 & 628.935558265292 & 51.064441734708 \tabularnewline
59 & 711 & 532.952413008262 & 178.047586991738 \tabularnewline
60 & 610 & 510.492346216899 & 99.5076537831013 \tabularnewline
61 & 513 & 535.170082504436 & -22.1700825044355 \tabularnewline
62 & 292 & 404.647584147747 & -112.647584147747 \tabularnewline
63 & 273 & 250.46351868487 & 22.53648131513 \tabularnewline
64 & 322 & 202.937201096688 & 119.062798903312 \tabularnewline
65 & 189 & 213.953717654589 & -24.9537176545893 \tabularnewline
66 & 257 & 244.678286465187 & 12.3217135348127 \tabularnewline
67 & 324 & 358.811501378948 & -34.8115013789479 \tabularnewline
68 & 404 & 489.4700262312 & -85.4700262311998 \tabularnewline
69 & 677 & 642.770699104805 & 34.2293008951946 \tabularnewline
70 & 858 & 826.889436910338 & 31.1105630896617 \tabularnewline
71 & 895 & 750.677946511787 & 144.322053488213 \tabularnewline
72 & 664 & 669.883859986125 & -5.88385998612466 \tabularnewline
73 & 628 & 619.83893718089 & 8.1610628191097 \tabularnewline
74 & 308 & 429.723020645643 & -121.723020645643 \tabularnewline
75 & 324 & 306.94443757336 & 17.0555624266399 \tabularnewline
76 & 248 & 284.098358932824 & -36.0983589328243 \tabularnewline
77 & 272 & 207.513756526967 & 64.4862434730326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200956&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]200[/C][C]178.996240926353[/C][C]21.0037590736465[/C][/ROW]
[ROW][C]14[/C][C]188[/C][C]174.638359962494[/C][C]13.3616400375056[/C][/ROW]
[ROW][C]15[/C][C]90[/C][C]84.3844912117078[/C][C]5.61550878829223[/C][/ROW]
[ROW][C]16[/C][C]79[/C][C]75.1615762333204[/C][C]3.83842376667964[/C][/ROW]
[ROW][C]17[/C][C]78[/C][C]76.8545082764411[/C][C]1.14549172355892[/C][/ROW]
[ROW][C]18[/C][C]91[/C][C]92.3808522909257[/C][C]-1.38085229092569[/C][/ROW]
[ROW][C]19[/C][C]167[/C][C]194.212808684525[/C][C]-27.2128086845248[/C][/ROW]
[ROW][C]20[/C][C]169[/C][C]184.008879972974[/C][C]-15.0088799729745[/C][/ROW]
[ROW][C]21[/C][C]289[/C][C]220.731593072396[/C][C]68.2684069276037[/C][/ROW]
[ROW][C]22[/C][C]247[/C][C]311.630510329539[/C][C]-64.630510329539[/C][/ROW]
[ROW][C]23[/C][C]275[/C][C]316.844391419137[/C][C]-41.844391419137[/C][/ROW]
[ROW][C]24[/C][C]203[/C][C]251.199669254532[/C][C]-48.1996692545315[/C][/ROW]
[ROW][C]25[/C][C]223[/C][C]205.13049728485[/C][C]17.8695027151497[/C][/ROW]
[ROW][C]26[/C][C]104[/C][C]195.805258677003[/C][C]-91.8052586770035[/C][/ROW]
[ROW][C]27[/C][C]107[/C][C]83.0399239415857[/C][C]23.9600760584143[/C][/ROW]
[ROW][C]28[/C][C]85[/C][C]76.9126257335064[/C][C]8.08737426649361[/C][/ROW]
[ROW][C]29[/C][C]75[/C][C]78.3961139894838[/C][C]-3.39611398948384[/C][/ROW]
[ROW][C]30[/C][C]99[/C][C]91.8511290138026[/C][C]7.14887098619738[/C][/ROW]
[ROW][C]31[/C][C]135[/C][C]187.381718260067[/C][C]-52.3817182600668[/C][/ROW]
[ROW][C]32[/C][C]211[/C][C]175.625664870909[/C][C]35.3743351290908[/C][/ROW]
[ROW][C]33[/C][C]335[/C][C]254.635500590628[/C][C]80.3644994093723[/C][/ROW]
[ROW][C]34[/C][C]488[/C][C]299.743136835132[/C][C]188.256863164868[/C][/ROW]
[ROW][C]35[/C][C]326[/C][C]374.415309851575[/C][C]-48.4153098515753[/C][/ROW]
[ROW][C]36[/C][C]346[/C][C]289.701186634624[/C][C]56.2988133653756[/C][/ROW]
[ROW][C]37[/C][C]261[/C][C]286.175603215236[/C][C]-25.1756032152355[/C][/ROW]
[ROW][C]38[/C][C]224[/C][C]206.865911886453[/C][C]17.1340881135471[/C][/ROW]
[ROW][C]39[/C][C]141[/C][C]134.871063798765[/C][C]6.12893620123523[/C][/ROW]
[ROW][C]40[/C][C]148[/C][C]112.166745675222[/C][C]35.8332543247782[/C][/ROW]
[ROW][C]41[/C][C]145[/C][C]113.549821615159[/C][C]31.4501783848409[/C][/ROW]
[ROW][C]42[/C][C]223[/C][C]148.926414557505[/C][C]74.0735854424945[/C][/ROW]
[ROW][C]43[/C][C]272[/C][C]288.063668817784[/C][C]-16.0636688177838[/C][/ROW]
[ROW][C]44[/C][C]445[/C][C]341.325160023508[/C][C]103.674839976492[/C][/ROW]
[ROW][C]45[/C][C]560[/C][C]524.157440172023[/C][C]35.8425598279771[/C][/ROW]
[ROW][C]46[/C][C]612[/C][C]636.281411050963[/C][C]-24.2814110509629[/C][/ROW]
[ROW][C]47[/C][C]467[/C][C]550.340424535747[/C][C]-83.3404245357469[/C][/ROW]
[ROW][C]48[/C][C]404[/C][C]475.521642588138[/C][C]-71.5216425881379[/C][/ROW]
[ROW][C]49[/C][C]518[/C][C]395.133554478984[/C][C]122.866445521016[/C][/ROW]
[ROW][C]50[/C][C]404[/C][C]331.112128623186[/C][C]72.887871376814[/C][/ROW]
[ROW][C]51[/C][C]300[/C][C]219.589641713216[/C][C]80.4103582867844[/C][/ROW]
[ROW][C]52[/C][C]210[/C][C]213.190103539809[/C][C]-3.19010353980923[/C][/ROW]
[ROW][C]53[/C][C]196[/C][C]198.80019114449[/C][C]-2.8001911444903[/C][/ROW]
[ROW][C]54[/C][C]186[/C][C]260.418255421333[/C][C]-74.4182554213334[/C][/ROW]
[ROW][C]55[/C][C]247[/C][C]358.830883054141[/C][C]-111.830883054141[/C][/ROW]
[ROW][C]56[/C][C]343[/C][C]451.220925741842[/C][C]-108.220925741842[/C][/ROW]
[ROW][C]57[/C][C]464[/C][C]570.831096638769[/C][C]-106.831096638769[/C][/ROW]
[ROW][C]58[/C][C]680[/C][C]628.935558265292[/C][C]51.064441734708[/C][/ROW]
[ROW][C]59[/C][C]711[/C][C]532.952413008262[/C][C]178.047586991738[/C][/ROW]
[ROW][C]60[/C][C]610[/C][C]510.492346216899[/C][C]99.5076537831013[/C][/ROW]
[ROW][C]61[/C][C]513[/C][C]535.170082504436[/C][C]-22.1700825044355[/C][/ROW]
[ROW][C]62[/C][C]292[/C][C]404.647584147747[/C][C]-112.647584147747[/C][/ROW]
[ROW][C]63[/C][C]273[/C][C]250.46351868487[/C][C]22.53648131513[/C][/ROW]
[ROW][C]64[/C][C]322[/C][C]202.937201096688[/C][C]119.062798903312[/C][/ROW]
[ROW][C]65[/C][C]189[/C][C]213.953717654589[/C][C]-24.9537176545893[/C][/ROW]
[ROW][C]66[/C][C]257[/C][C]244.678286465187[/C][C]12.3217135348127[/C][/ROW]
[ROW][C]67[/C][C]324[/C][C]358.811501378948[/C][C]-34.8115013789479[/C][/ROW]
[ROW][C]68[/C][C]404[/C][C]489.4700262312[/C][C]-85.4700262311998[/C][/ROW]
[ROW][C]69[/C][C]677[/C][C]642.770699104805[/C][C]34.2293008951946[/C][/ROW]
[ROW][C]70[/C][C]858[/C][C]826.889436910338[/C][C]31.1105630896617[/C][/ROW]
[ROW][C]71[/C][C]895[/C][C]750.677946511787[/C][C]144.322053488213[/C][/ROW]
[ROW][C]72[/C][C]664[/C][C]669.883859986125[/C][C]-5.88385998612466[/C][/ROW]
[ROW][C]73[/C][C]628[/C][C]619.83893718089[/C][C]8.1610628191097[/C][/ROW]
[ROW][C]74[/C][C]308[/C][C]429.723020645643[/C][C]-121.723020645643[/C][/ROW]
[ROW][C]75[/C][C]324[/C][C]306.94443757336[/C][C]17.0555624266399[/C][/ROW]
[ROW][C]76[/C][C]248[/C][C]284.098358932824[/C][C]-36.0983589328243[/C][/ROW]
[ROW][C]77[/C][C]272[/C][C]207.513756526967[/C][C]64.4862434730326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200956&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200956&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
13200178.99624092635321.0037590736465
14188174.63835996249413.3616400375056
159084.38449121170785.61550878829223
167975.16157623332043.83842376667964
177876.85450827644111.14549172355892
189192.3808522909257-1.38085229092569
19167194.212808684525-27.2128086845248
20169184.008879972974-15.0088799729745
21289220.73159307239668.2684069276037
22247311.630510329539-64.630510329539
23275316.844391419137-41.844391419137
24203251.199669254532-48.1996692545315
25223205.1304972848517.8695027151497
26104195.805258677003-91.8052586770035
2710783.039923941585723.9600760584143
288576.91262573350648.08737426649361
297578.3961139894838-3.39611398948384
309991.85112901380267.14887098619738
31135187.381718260067-52.3817182600668
32211175.62566487090935.3743351290908
33335254.63550059062880.3644994093723
34488299.743136835132188.256863164868
35326374.415309851575-48.4153098515753
36346289.70118663462456.2988133653756
37261286.175603215236-25.1756032152355
38224206.86591188645317.1340881135471
39141134.8710637987656.12893620123523
40148112.16674567522235.8332543247782
41145113.54982161515931.4501783848409
42223148.92641455750574.0735854424945
43272288.063668817784-16.0636688177838
44445341.325160023508103.674839976492
45560524.15744017202335.8425598279771
46612636.281411050963-24.2814110509629
47467550.340424535747-83.3404245357469
48404475.521642588138-71.5216425881379
49518395.133554478984122.866445521016
50404331.11212862318672.887871376814
51300219.58964171321680.4103582867844
52210213.190103539809-3.19010353980923
53196198.80019114449-2.8001911444903
54186260.418255421333-74.4182554213334
55247358.830883054141-111.830883054141
56343451.220925741842-108.220925741842
57464570.831096638769-106.831096638769
58680628.93555826529251.064441734708
59711532.952413008262178.047586991738
60610510.49234621689999.5076537831013
61513535.170082504436-22.1700825044355
62292404.647584147747-112.647584147747
63273250.4635186848722.53648131513
64322202.937201096688119.062798903312
65189213.953717654589-24.9537176545893
66257244.67828646518712.3217135348127
67324358.811501378948-34.8115013789479
68404489.4700262312-85.4700262311998
69677642.77069910480534.2293008951946
70858826.88943691033831.1105630896617
71895750.677946511787144.322053488213
72664669.883859986125-5.88385998612466
73628619.838937180898.1610628191097
74308429.723020645643-121.723020645643
75324306.9444375733617.0555624266399
76248284.098358932824-36.0983589328243
77272207.51375652696764.4862434730326







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
78276.417258799644198.681120881678354.15339671761
79379.342779008801291.705564802701466.979993214901
80511.887383402644408.64788264587615.126884159418
81761.825098419197626.312667511409897.337529326985
82962.962937770582797.30399042921128.62188511197
83912.083715338352749.8111085913121074.35632208539
84729.232971744311588.610706679794869.855236808829
85680.793824096317543.114120985261818.473527207372
86416.838116998216310.61017801567523.066055980761
87363.206261449792259.555013485212466.857509414371
88310.12676937191209.344477671202410.909061072618
89270.241023698426207.718910593908332.763136802945

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
78 & 276.417258799644 & 198.681120881678 & 354.15339671761 \tabularnewline
79 & 379.342779008801 & 291.705564802701 & 466.979993214901 \tabularnewline
80 & 511.887383402644 & 408.64788264587 & 615.126884159418 \tabularnewline
81 & 761.825098419197 & 626.312667511409 & 897.337529326985 \tabularnewline
82 & 962.962937770582 & 797.3039904292 & 1128.62188511197 \tabularnewline
83 & 912.083715338352 & 749.811108591312 & 1074.35632208539 \tabularnewline
84 & 729.232971744311 & 588.610706679794 & 869.855236808829 \tabularnewline
85 & 680.793824096317 & 543.114120985261 & 818.473527207372 \tabularnewline
86 & 416.838116998216 & 310.61017801567 & 523.066055980761 \tabularnewline
87 & 363.206261449792 & 259.555013485212 & 466.857509414371 \tabularnewline
88 & 310.12676937191 & 209.344477671202 & 410.909061072618 \tabularnewline
89 & 270.241023698426 & 207.718910593908 & 332.763136802945 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200956&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]78[/C][C]276.417258799644[/C][C]198.681120881678[/C][C]354.15339671761[/C][/ROW]
[ROW][C]79[/C][C]379.342779008801[/C][C]291.705564802701[/C][C]466.979993214901[/C][/ROW]
[ROW][C]80[/C][C]511.887383402644[/C][C]408.64788264587[/C][C]615.126884159418[/C][/ROW]
[ROW][C]81[/C][C]761.825098419197[/C][C]626.312667511409[/C][C]897.337529326985[/C][/ROW]
[ROW][C]82[/C][C]962.962937770582[/C][C]797.3039904292[/C][C]1128.62188511197[/C][/ROW]
[ROW][C]83[/C][C]912.083715338352[/C][C]749.811108591312[/C][C]1074.35632208539[/C][/ROW]
[ROW][C]84[/C][C]729.232971744311[/C][C]588.610706679794[/C][C]869.855236808829[/C][/ROW]
[ROW][C]85[/C][C]680.793824096317[/C][C]543.114120985261[/C][C]818.473527207372[/C][/ROW]
[ROW][C]86[/C][C]416.838116998216[/C][C]310.61017801567[/C][C]523.066055980761[/C][/ROW]
[ROW][C]87[/C][C]363.206261449792[/C][C]259.555013485212[/C][C]466.857509414371[/C][/ROW]
[ROW][C]88[/C][C]310.12676937191[/C][C]209.344477671202[/C][C]410.909061072618[/C][/ROW]
[ROW][C]89[/C][C]270.241023698426[/C][C]207.718910593908[/C][C]332.763136802945[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200956&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200956&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
78276.417258799644198.681120881678354.15339671761
79379.342779008801291.705564802701466.979993214901
80511.887383402644408.64788264587615.126884159418
81761.825098419197626.312667511409897.337529326985
82962.962937770582797.30399042921128.62188511197
83912.083715338352749.8111085913121074.35632208539
84729.232971744311588.610706679794869.855236808829
85680.793824096317543.114120985261818.473527207372
86416.838116998216310.61017801567523.066055980761
87363.206261449792259.555013485212466.857509414371
88310.12676937191209.344477671202410.909061072618
89270.241023698426207.718910593908332.763136802945



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