## Free Statistics

of Irreproducible Research!

Author's title
Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 10 Nov 2012 09:57:27 -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/Nov/10/t1352559475sdniytaqo4roqgy.htm/, Retrieved Sat, 10 Dec 2022 06:40:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=187363, Retrieved Sat, 10 Dec 2022 06:40:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RM D  [Exponential Smoothing] [Single smoothing] [2012-11-10 14:54:36] [86dcce9422b96d4554cb918e531c1d5d]
- R         [Exponential Smoothing] [double smoothing] [2012-11-10 14:57:27] [c63d55528b56cf8bb48e0b5d1a959d8e] [Current]
-             [Exponential Smoothing] [Triple smoothing] [2012-11-10 14:59:32] [86dcce9422b96d4554cb918e531c1d5d]
-   P           [Exponential Smoothing] [Triple Smoothing ...] [2012-11-11 17:39:21] [74be16979710d4c4e7c6647856088456]
-  M              [Exponential Smoothing] [Triple Smoothing ...] [2012-11-11 17:40:47] [74be16979710d4c4e7c6647856088456]
-   P         [Exponential Smoothing] [Double Smoothing ...] [2012-11-11 17:31:29] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
236422
250580
279515
264417
283706
281288
271146
283944
269155
270899
276507
319957
250746
247772
280449
274925
296013
287881
279098
294763
261924
291596
287537
326201
255598
253086
285261
284747
300402
288854
295433
307256
273189
287540
290705
337006
268335
259060
293703
294262
312404
301014
309942
317079
293912
304060
301299
357634
281493
282478
319111
315223
328445
321081
328040
326362
313566
319768
324315
387243
293308
295109
339190
335678
345401
351002
351889
355773
333363
336214
343910
405788

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187363&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187363&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187363&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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'George Udny Yule' @ yule.wessa.net

 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.23686471684421 beta 0.331698570367038 gamma FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.23686471684421 \tabularnewline
beta & 0.331698570367038 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187363&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]0.23686471684421[/C][/ROW]
[ROW][C]beta[/C][C]0.331698570367038[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187363&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187363&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 Parameter Value alpha 0.23686471684421 beta 0.331698570367038 gamma FALSE

 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 279515 264738 14777 4 264417 283557.144645609 -19140.1446456088 5 283706 292838.717516783 -9132.71751678298 6 281288 303773.160281193 -22485.1602811932 7 271146 309778.273414608 -38632.2734146079 8 283944 308923.456765479 -24979.4567654789 9 269155 309339.932501821 -40184.9325018207 10 270899 302997.530296393 -32098.5302963932 11 276507 296048.604147738 -19541.6041477385 12 319957 290538.632099043 29418.3679009569 13 250746 298936.883115533 -48190.883115533 14 247772 285165.99459897 -37393.9945989696 15 280449 271014.548324914 9434.45167508634 16 274925 268696.351772981 6228.64822701865 17 296013 266108.1839853 29904.8160146998 18 287881 271477.617229378 16403.382770622 19 279098 274937.813169914 4160.18683008617 20 294763 275824.884231396 18938.1157686035 21 261924 281700.249216468 -19776.2492164684 22 291596 276851.772924334 14744.227075666 23 287537 281338.399306373 6198.60069362691 24 326201 284287.878040183 41913.1219598172 25 255598 298989.883827985 -43391.8838279846 26 253086 290076.943586409 -36990.9435864086 27 285261 279773.867330105 5487.13266989455 28 284747 279963.459905674 4783.54009432637 29 300402 280362.227910472 20039.7720895278 30 288854 285949.137546995 2904.86245300493 31 295433 287705.61999105 7727.38000894967 32 307256 291211.509071666 16044.4909283336 33 273189 297948.0068317 -24759.0068317 34 287540 293074.337725904 -5534.3377259039 35 290705 292319.49430483 -1614.49430483032 36 337006 292366.276401028 44639.7235989721 37 268335 306876.290597652 -38541.2905976519 38 259060 298655.557327004 -39595.5573270036 39 293703 287074.174073849 6628.82592615089 40 294262 286962.527798076 7299.47220192384 41 312404 287583.23661666 24820.7633833401 42 301014 294304.231101799 6709.76889820135 43 309942 297262.541035442 12679.4589645575 44 317079 302631.055691573 14447.9443084265 45 293912 309553.603707832 -15641.6037078321 46 304060 308120.074814132 -4060.07481413212 47 301299 309110.810791421 -7811.81079142075 48 357634 308599.136976208 49034.8630237915 49 281493 325404.990274379 -43911.990274379 50 282478 316744.949935482 -34266.9499354819 51 319111 307677.204315961 11433.795684039 52 315223 310332.679758538 4890.32024146238 53 328445 311822.457897926 16622.5421020737 54 321081 317397.180147054 3683.81985294586 55 328040 320196.604822978 7843.39517702215 56 326362 324597.523554949 1764.47644505074 57 313566 327697.191757479 -14131.1917574789 58 319768 325921.481947837 -6153.48194783728 59 324315 325551.945263853 -1236.94526385277 60 387243 326249.778719876 60993.2212801243 61 293308 346479.839329963 -53171.8393299626 62 295109 335490.636705062 -40381.6367050619 63 339190 324358.289971831 14831.710028169 64 335678 327469.330143811 8208.66985618934 65 345401 329656.541992533 15744.4580074673 66 351002 334865.72183154 16136.2781684598 67 351889 341435.50010981 10453.4998901895 68 355773 347480.536037643 8292.4639623572 69 333363 353665.21852325 -20302.2185232503 70 336214 351481.731269075 -15267.7312690752 71 343910 349291.186066799 -5381.18606679927 72 405788 349019.627246744 56768.3727532565

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 279515 & 264738 & 14777 \tabularnewline
4 & 264417 & 283557.144645609 & -19140.1446456088 \tabularnewline
5 & 283706 & 292838.717516783 & -9132.71751678298 \tabularnewline
6 & 281288 & 303773.160281193 & -22485.1602811932 \tabularnewline
7 & 271146 & 309778.273414608 & -38632.2734146079 \tabularnewline
8 & 283944 & 308923.456765479 & -24979.4567654789 \tabularnewline
9 & 269155 & 309339.932501821 & -40184.9325018207 \tabularnewline
10 & 270899 & 302997.530296393 & -32098.5302963932 \tabularnewline
11 & 276507 & 296048.604147738 & -19541.6041477385 \tabularnewline
12 & 319957 & 290538.632099043 & 29418.3679009569 \tabularnewline
13 & 250746 & 298936.883115533 & -48190.883115533 \tabularnewline
14 & 247772 & 285165.99459897 & -37393.9945989696 \tabularnewline
15 & 280449 & 271014.548324914 & 9434.45167508634 \tabularnewline
16 & 274925 & 268696.351772981 & 6228.64822701865 \tabularnewline
17 & 296013 & 266108.1839853 & 29904.8160146998 \tabularnewline
18 & 287881 & 271477.617229378 & 16403.382770622 \tabularnewline
19 & 279098 & 274937.813169914 & 4160.18683008617 \tabularnewline
20 & 294763 & 275824.884231396 & 18938.1157686035 \tabularnewline
21 & 261924 & 281700.249216468 & -19776.2492164684 \tabularnewline
22 & 291596 & 276851.772924334 & 14744.227075666 \tabularnewline
23 & 287537 & 281338.399306373 & 6198.60069362691 \tabularnewline
24 & 326201 & 284287.878040183 & 41913.1219598172 \tabularnewline
25 & 255598 & 298989.883827985 & -43391.8838279846 \tabularnewline
26 & 253086 & 290076.943586409 & -36990.9435864086 \tabularnewline
27 & 285261 & 279773.867330105 & 5487.13266989455 \tabularnewline
28 & 284747 & 279963.459905674 & 4783.54009432637 \tabularnewline
29 & 300402 & 280362.227910472 & 20039.7720895278 \tabularnewline
30 & 288854 & 285949.137546995 & 2904.86245300493 \tabularnewline
31 & 295433 & 287705.61999105 & 7727.38000894967 \tabularnewline
32 & 307256 & 291211.509071666 & 16044.4909283336 \tabularnewline
33 & 273189 & 297948.0068317 & -24759.0068317 \tabularnewline
34 & 287540 & 293074.337725904 & -5534.3377259039 \tabularnewline
35 & 290705 & 292319.49430483 & -1614.49430483032 \tabularnewline
36 & 337006 & 292366.276401028 & 44639.7235989721 \tabularnewline
37 & 268335 & 306876.290597652 & -38541.2905976519 \tabularnewline
38 & 259060 & 298655.557327004 & -39595.5573270036 \tabularnewline
39 & 293703 & 287074.174073849 & 6628.82592615089 \tabularnewline
40 & 294262 & 286962.527798076 & 7299.47220192384 \tabularnewline
41 & 312404 & 287583.23661666 & 24820.7633833401 \tabularnewline
42 & 301014 & 294304.231101799 & 6709.76889820135 \tabularnewline
43 & 309942 & 297262.541035442 & 12679.4589645575 \tabularnewline
44 & 317079 & 302631.055691573 & 14447.9443084265 \tabularnewline
45 & 293912 & 309553.603707832 & -15641.6037078321 \tabularnewline
46 & 304060 & 308120.074814132 & -4060.07481413212 \tabularnewline
47 & 301299 & 309110.810791421 & -7811.81079142075 \tabularnewline
48 & 357634 & 308599.136976208 & 49034.8630237915 \tabularnewline
49 & 281493 & 325404.990274379 & -43911.990274379 \tabularnewline
50 & 282478 & 316744.949935482 & -34266.9499354819 \tabularnewline
51 & 319111 & 307677.204315961 & 11433.795684039 \tabularnewline
52 & 315223 & 310332.679758538 & 4890.32024146238 \tabularnewline
53 & 328445 & 311822.457897926 & 16622.5421020737 \tabularnewline
54 & 321081 & 317397.180147054 & 3683.81985294586 \tabularnewline
55 & 328040 & 320196.604822978 & 7843.39517702215 \tabularnewline
56 & 326362 & 324597.523554949 & 1764.47644505074 \tabularnewline
57 & 313566 & 327697.191757479 & -14131.1917574789 \tabularnewline
58 & 319768 & 325921.481947837 & -6153.48194783728 \tabularnewline
59 & 324315 & 325551.945263853 & -1236.94526385277 \tabularnewline
60 & 387243 & 326249.778719876 & 60993.2212801243 \tabularnewline
61 & 293308 & 346479.839329963 & -53171.8393299626 \tabularnewline
62 & 295109 & 335490.636705062 & -40381.6367050619 \tabularnewline
63 & 339190 & 324358.289971831 & 14831.710028169 \tabularnewline
64 & 335678 & 327469.330143811 & 8208.66985618934 \tabularnewline
65 & 345401 & 329656.541992533 & 15744.4580074673 \tabularnewline
66 & 351002 & 334865.72183154 & 16136.2781684598 \tabularnewline
67 & 351889 & 341435.50010981 & 10453.4998901895 \tabularnewline
68 & 355773 & 347480.536037643 & 8292.4639623572 \tabularnewline
69 & 333363 & 353665.21852325 & -20302.2185232503 \tabularnewline
70 & 336214 & 351481.731269075 & -15267.7312690752 \tabularnewline
71 & 343910 & 349291.186066799 & -5381.18606679927 \tabularnewline
72 & 405788 & 349019.627246744 & 56768.3727532565 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187363&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]279515[/C][C]264738[/C][C]14777[/C][/ROW]
[ROW][C]4[/C][C]264417[/C][C]283557.144645609[/C][C]-19140.1446456088[/C][/ROW]
[ROW][C]5[/C][C]283706[/C][C]292838.717516783[/C][C]-9132.71751678298[/C][/ROW]
[ROW][C]6[/C][C]281288[/C][C]303773.160281193[/C][C]-22485.1602811932[/C][/ROW]
[ROW][C]7[/C][C]271146[/C][C]309778.273414608[/C][C]-38632.2734146079[/C][/ROW]
[ROW][C]8[/C][C]283944[/C][C]308923.456765479[/C][C]-24979.4567654789[/C][/ROW]
[ROW][C]9[/C][C]269155[/C][C]309339.932501821[/C][C]-40184.9325018207[/C][/ROW]
[ROW][C]10[/C][C]270899[/C][C]302997.530296393[/C][C]-32098.5302963932[/C][/ROW]
[ROW][C]11[/C][C]276507[/C][C]296048.604147738[/C][C]-19541.6041477385[/C][/ROW]
[ROW][C]12[/C][C]319957[/C][C]290538.632099043[/C][C]29418.3679009569[/C][/ROW]
[ROW][C]13[/C][C]250746[/C][C]298936.883115533[/C][C]-48190.883115533[/C][/ROW]
[ROW][C]14[/C][C]247772[/C][C]285165.99459897[/C][C]-37393.9945989696[/C][/ROW]
[ROW][C]15[/C][C]280449[/C][C]271014.548324914[/C][C]9434.45167508634[/C][/ROW]
[ROW][C]16[/C][C]274925[/C][C]268696.351772981[/C][C]6228.64822701865[/C][/ROW]
[ROW][C]17[/C][C]296013[/C][C]266108.1839853[/C][C]29904.8160146998[/C][/ROW]
[ROW][C]18[/C][C]287881[/C][C]271477.617229378[/C][C]16403.382770622[/C][/ROW]
[ROW][C]19[/C][C]279098[/C][C]274937.813169914[/C][C]4160.18683008617[/C][/ROW]
[ROW][C]20[/C][C]294763[/C][C]275824.884231396[/C][C]18938.1157686035[/C][/ROW]
[ROW][C]21[/C][C]261924[/C][C]281700.249216468[/C][C]-19776.2492164684[/C][/ROW]
[ROW][C]22[/C][C]291596[/C][C]276851.772924334[/C][C]14744.227075666[/C][/ROW]
[ROW][C]23[/C][C]287537[/C][C]281338.399306373[/C][C]6198.60069362691[/C][/ROW]
[ROW][C]24[/C][C]326201[/C][C]284287.878040183[/C][C]41913.1219598172[/C][/ROW]
[ROW][C]25[/C][C]255598[/C][C]298989.883827985[/C][C]-43391.8838279846[/C][/ROW]
[ROW][C]26[/C][C]253086[/C][C]290076.943586409[/C][C]-36990.9435864086[/C][/ROW]
[ROW][C]27[/C][C]285261[/C][C]279773.867330105[/C][C]5487.13266989455[/C][/ROW]
[ROW][C]28[/C][C]284747[/C][C]279963.459905674[/C][C]4783.54009432637[/C][/ROW]
[ROW][C]29[/C][C]300402[/C][C]280362.227910472[/C][C]20039.7720895278[/C][/ROW]
[ROW][C]30[/C][C]288854[/C][C]285949.137546995[/C][C]2904.86245300493[/C][/ROW]
[ROW][C]31[/C][C]295433[/C][C]287705.61999105[/C][C]7727.38000894967[/C][/ROW]
[ROW][C]32[/C][C]307256[/C][C]291211.509071666[/C][C]16044.4909283336[/C][/ROW]
[ROW][C]33[/C][C]273189[/C][C]297948.0068317[/C][C]-24759.0068317[/C][/ROW]
[ROW][C]34[/C][C]287540[/C][C]293074.337725904[/C][C]-5534.3377259039[/C][/ROW]
[ROW][C]35[/C][C]290705[/C][C]292319.49430483[/C][C]-1614.49430483032[/C][/ROW]
[ROW][C]36[/C][C]337006[/C][C]292366.276401028[/C][C]44639.7235989721[/C][/ROW]
[ROW][C]37[/C][C]268335[/C][C]306876.290597652[/C][C]-38541.2905976519[/C][/ROW]
[ROW][C]38[/C][C]259060[/C][C]298655.557327004[/C][C]-39595.5573270036[/C][/ROW]
[ROW][C]39[/C][C]293703[/C][C]287074.174073849[/C][C]6628.82592615089[/C][/ROW]
[ROW][C]40[/C][C]294262[/C][C]286962.527798076[/C][C]7299.47220192384[/C][/ROW]
[ROW][C]41[/C][C]312404[/C][C]287583.23661666[/C][C]24820.7633833401[/C][/ROW]
[ROW][C]42[/C][C]301014[/C][C]294304.231101799[/C][C]6709.76889820135[/C][/ROW]
[ROW][C]43[/C][C]309942[/C][C]297262.541035442[/C][C]12679.4589645575[/C][/ROW]
[ROW][C]44[/C][C]317079[/C][C]302631.055691573[/C][C]14447.9443084265[/C][/ROW]
[ROW][C]45[/C][C]293912[/C][C]309553.603707832[/C][C]-15641.6037078321[/C][/ROW]
[ROW][C]46[/C][C]304060[/C][C]308120.074814132[/C][C]-4060.07481413212[/C][/ROW]
[ROW][C]47[/C][C]301299[/C][C]309110.810791421[/C][C]-7811.81079142075[/C][/ROW]
[ROW][C]48[/C][C]357634[/C][C]308599.136976208[/C][C]49034.8630237915[/C][/ROW]
[ROW][C]49[/C][C]281493[/C][C]325404.990274379[/C][C]-43911.990274379[/C][/ROW]
[ROW][C]50[/C][C]282478[/C][C]316744.949935482[/C][C]-34266.9499354819[/C][/ROW]
[ROW][C]51[/C][C]319111[/C][C]307677.204315961[/C][C]11433.795684039[/C][/ROW]
[ROW][C]52[/C][C]315223[/C][C]310332.679758538[/C][C]4890.32024146238[/C][/ROW]
[ROW][C]53[/C][C]328445[/C][C]311822.457897926[/C][C]16622.5421020737[/C][/ROW]
[ROW][C]54[/C][C]321081[/C][C]317397.180147054[/C][C]3683.81985294586[/C][/ROW]
[ROW][C]55[/C][C]328040[/C][C]320196.604822978[/C][C]7843.39517702215[/C][/ROW]
[ROW][C]56[/C][C]326362[/C][C]324597.523554949[/C][C]1764.47644505074[/C][/ROW]
[ROW][C]57[/C][C]313566[/C][C]327697.191757479[/C][C]-14131.1917574789[/C][/ROW]
[ROW][C]58[/C][C]319768[/C][C]325921.481947837[/C][C]-6153.48194783728[/C][/ROW]
[ROW][C]59[/C][C]324315[/C][C]325551.945263853[/C][C]-1236.94526385277[/C][/ROW]
[ROW][C]60[/C][C]387243[/C][C]326249.778719876[/C][C]60993.2212801243[/C][/ROW]
[ROW][C]61[/C][C]293308[/C][C]346479.839329963[/C][C]-53171.8393299626[/C][/ROW]
[ROW][C]62[/C][C]295109[/C][C]335490.636705062[/C][C]-40381.6367050619[/C][/ROW]
[ROW][C]63[/C][C]339190[/C][C]324358.289971831[/C][C]14831.710028169[/C][/ROW]
[ROW][C]64[/C][C]335678[/C][C]327469.330143811[/C][C]8208.66985618934[/C][/ROW]
[ROW][C]65[/C][C]345401[/C][C]329656.541992533[/C][C]15744.4580074673[/C][/ROW]
[ROW][C]66[/C][C]351002[/C][C]334865.72183154[/C][C]16136.2781684598[/C][/ROW]
[ROW][C]67[/C][C]351889[/C][C]341435.50010981[/C][C]10453.4998901895[/C][/ROW]
[ROW][C]68[/C][C]355773[/C][C]347480.536037643[/C][C]8292.4639623572[/C][/ROW]
[ROW][C]69[/C][C]333363[/C][C]353665.21852325[/C][C]-20302.2185232503[/C][/ROW]
[ROW][C]70[/C][C]336214[/C][C]351481.731269075[/C][C]-15267.7312690752[/C][/ROW]
[ROW][C]71[/C][C]343910[/C][C]349291.186066799[/C][C]-5381.18606679927[/C][/ROW]
[ROW][C]72[/C][C]405788[/C][C]349019.627246744[/C][C]56768.3727532565[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187363&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187363&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 t Observed Fitted Residuals 3 279515 264738 14777 4 264417 283557.144645609 -19140.1446456088 5 283706 292838.717516783 -9132.71751678298 6 281288 303773.160281193 -22485.1602811932 7 271146 309778.273414608 -38632.2734146079 8 283944 308923.456765479 -24979.4567654789 9 269155 309339.932501821 -40184.9325018207 10 270899 302997.530296393 -32098.5302963932 11 276507 296048.604147738 -19541.6041477385 12 319957 290538.632099043 29418.3679009569 13 250746 298936.883115533 -48190.883115533 14 247772 285165.99459897 -37393.9945989696 15 280449 271014.548324914 9434.45167508634 16 274925 268696.351772981 6228.64822701865 17 296013 266108.1839853 29904.8160146998 18 287881 271477.617229378 16403.382770622 19 279098 274937.813169914 4160.18683008617 20 294763 275824.884231396 18938.1157686035 21 261924 281700.249216468 -19776.2492164684 22 291596 276851.772924334 14744.227075666 23 287537 281338.399306373 6198.60069362691 24 326201 284287.878040183 41913.1219598172 25 255598 298989.883827985 -43391.8838279846 26 253086 290076.943586409 -36990.9435864086 27 285261 279773.867330105 5487.13266989455 28 284747 279963.459905674 4783.54009432637 29 300402 280362.227910472 20039.7720895278 30 288854 285949.137546995 2904.86245300493 31 295433 287705.61999105 7727.38000894967 32 307256 291211.509071666 16044.4909283336 33 273189 297948.0068317 -24759.0068317 34 287540 293074.337725904 -5534.3377259039 35 290705 292319.49430483 -1614.49430483032 36 337006 292366.276401028 44639.7235989721 37 268335 306876.290597652 -38541.2905976519 38 259060 298655.557327004 -39595.5573270036 39 293703 287074.174073849 6628.82592615089 40 294262 286962.527798076 7299.47220192384 41 312404 287583.23661666 24820.7633833401 42 301014 294304.231101799 6709.76889820135 43 309942 297262.541035442 12679.4589645575 44 317079 302631.055691573 14447.9443084265 45 293912 309553.603707832 -15641.6037078321 46 304060 308120.074814132 -4060.07481413212 47 301299 309110.810791421 -7811.81079142075 48 357634 308599.136976208 49034.8630237915 49 281493 325404.990274379 -43911.990274379 50 282478 316744.949935482 -34266.9499354819 51 319111 307677.204315961 11433.795684039 52 315223 310332.679758538 4890.32024146238 53 328445 311822.457897926 16622.5421020737 54 321081 317397.180147054 3683.81985294586 55 328040 320196.604822978 7843.39517702215 56 326362 324597.523554949 1764.47644505074 57 313566 327697.191757479 -14131.1917574789 58 319768 325921.481947837 -6153.48194783728 59 324315 325551.945263853 -1236.94526385277 60 387243 326249.778719876 60993.2212801243 61 293308 346479.839329963 -53171.8393299626 62 295109 335490.636705062 -40381.6367050619 63 339190 324358.289971831 14831.710028169 64 335678 327469.330143811 8208.66985618934 65 345401 329656.541992533 15744.4580074673 66 351002 334865.72183154 16136.2781684598 67 351889 341435.50010981 10453.4998901895 68 355773 347480.536037643 8292.4639623572 69 333363 353665.21852325 -20302.2185232503 70 336214 351481.731269075 -15267.7312690752 71 343910 349291.186066799 -5381.18606679927 72 405788 349019.627246744 56768.3727532565

 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 367929.265874365 317722.828688937 418135.703059792 74 373392.479964079 320747.55066839 426037.409259769 75 378855.694053794 322617.006047813 435094.382059775 76 384318.908143509 323280.309899035 445357.506387982 77 389782.122233223 322764.440102795 456799.804363651 78 395245.336322938 321144.813027708 469345.859618168 79 400708.550412652 318517.408702223 482899.692123082 80 406171.764502367 314979.779197821 497363.749806913 81 411634.978592082 310621.164816306 512648.792367858 82 417098.192681796 305518.890204007 528677.495159585 83 422561.406771511 299738.165957603 545384.647585419 84 428024.620861225 293333.367997985 562715.873724466

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 367929.265874365 & 317722.828688937 & 418135.703059792 \tabularnewline
74 & 373392.479964079 & 320747.55066839 & 426037.409259769 \tabularnewline
75 & 378855.694053794 & 322617.006047813 & 435094.382059775 \tabularnewline
76 & 384318.908143509 & 323280.309899035 & 445357.506387982 \tabularnewline
77 & 389782.122233223 & 322764.440102795 & 456799.804363651 \tabularnewline
78 & 395245.336322938 & 321144.813027708 & 469345.859618168 \tabularnewline
79 & 400708.550412652 & 318517.408702223 & 482899.692123082 \tabularnewline
80 & 406171.764502367 & 314979.779197821 & 497363.749806913 \tabularnewline
81 & 411634.978592082 & 310621.164816306 & 512648.792367858 \tabularnewline
82 & 417098.192681796 & 305518.890204007 & 528677.495159585 \tabularnewline
83 & 422561.406771511 & 299738.165957603 & 545384.647585419 \tabularnewline
84 & 428024.620861225 & 293333.367997985 & 562715.873724466 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187363&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]367929.265874365[/C][C]317722.828688937[/C][C]418135.703059792[/C][/ROW]
[ROW][C]74[/C][C]373392.479964079[/C][C]320747.55066839[/C][C]426037.409259769[/C][/ROW]
[ROW][C]75[/C][C]378855.694053794[/C][C]322617.006047813[/C][C]435094.382059775[/C][/ROW]
[ROW][C]76[/C][C]384318.908143509[/C][C]323280.309899035[/C][C]445357.506387982[/C][/ROW]
[ROW][C]77[/C][C]389782.122233223[/C][C]322764.440102795[/C][C]456799.804363651[/C][/ROW]
[ROW][C]78[/C][C]395245.336322938[/C][C]321144.813027708[/C][C]469345.859618168[/C][/ROW]
[ROW][C]79[/C][C]400708.550412652[/C][C]318517.408702223[/C][C]482899.692123082[/C][/ROW]
[ROW][C]80[/C][C]406171.764502367[/C][C]314979.779197821[/C][C]497363.749806913[/C][/ROW]
[ROW][C]81[/C][C]411634.978592082[/C][C]310621.164816306[/C][C]512648.792367858[/C][/ROW]
[ROW][C]82[/C][C]417098.192681796[/C][C]305518.890204007[/C][C]528677.495159585[/C][/ROW]
[ROW][C]83[/C][C]422561.406771511[/C][C]299738.165957603[/C][C]545384.647585419[/C][/ROW]
[ROW][C]84[/C][C]428024.620861225[/C][C]293333.367997985[/C][C]562715.873724466[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187363&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187363&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 t Forecast 95% Lower Bound 95% Upper Bound 73 367929.265874365 317722.828688937 418135.703059792 74 373392.479964079 320747.55066839 426037.409259769 75 378855.694053794 322617.006047813 435094.382059775 76 384318.908143509 323280.309899035 445357.506387982 77 389782.122233223 322764.440102795 456799.804363651 78 395245.336322938 321144.813027708 469345.859618168 79 400708.550412652 318517.408702223 482899.692123082 80 406171.764502367 314979.779197821 497363.749806913 81 411634.978592082 310621.164816306 512648.792367858 82 417098.192681796 305518.890204007 528677.495159585 83 422561.406771511 299738.165957603 545384.647585419 84 428024.620861225 293333.367997985 562715.873724466

par1 <- as.numeric(par1)if (par2 == 'Single') K <- 1if (par2 == 'Double') K <- 2if (par2 == 'Triple') K <- par1nx <- length(x)nxmK <- nx - Kx <- 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)fitmyresid <- 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')