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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 computationSat, 17 Dec 2016 11:19:56 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/17/t1481970014fhn0ehm3me16stz.htm/, Retrieved Thu, 02 May 2024 04:38:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300668, Retrieved Thu, 02 May 2024 04:38:59 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [N2983] [2016-12-17 10:19:56] [563c2945bc7c763925d38f2fb19cdb55] [Current]
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Dataseries X:
15283
14698
14664
14660
14605
14480
14412
14454
13915
13858
13768
13738
13647
13591
13589
13294
13418
13251
13156
13045
12980
12910
12851
12907
12586
12384
12297
12312
12301
12218
11897
11877
11802
11582
11493
11390
11162
10962
10805
10602
10552
10373
10279
10131
10164
10090
10107
10042
10029
9950
9781
9559
9275
9275
9219
9192
9105
9100
9083
9092
9098
9195
9087




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300668&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300668&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300668&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 Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.967121417904212
beta0.430427237971139
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.967121417904212 \tabularnewline
beta & 0.430427237971139 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300668&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]0.967121417904212[/C][/ROW]
[ROW][C]beta[/C][C]0.430427237971139[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300668&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300668&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
alpha0.967121417904212
beta0.430427237971139
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31466414113551
41466014290.2516470461369.748352953906
51460514446.1280879843158.871912015689
61448014464.195875192715.8041248073223
71441214350.478609566461.5213904335851
81445414306.5853321492147.41466785085
91391514407.1263829035-492.126382903491
101385813684.2934786105173.70652138954
111376813677.711588598790.2884114013013
121373813628.0391024101109.960897589928
131364713643.16631566253.83368433749092
141359113557.251496439733.7485035602622
151358913514.316611442374.6833885576798
161329413542.0595879622-248.059587962178
171341813154.4098150373263.590184962732
181325113371.3136058375-120.313605837504
191315613166.8522236616-10.8522236615954
201304513063.7357748683-18.735774868288
211298012945.195732663334.8042673367163
221291012892.923572321617.0764276784084
231285112830.614935327420.3850646726169
241290712779.9919529991127.008047000945
251258612885.3566661776-299.356666177608
261238412453.7601172399-69.7601172399154
271229712215.171887500481.8281124995556
281231212157.2509117628154.749088237239
291230112234.27161218866.7283878119742
301221812253.942994387-35.9429943869982
311189712159.356499465-262.356499465022
321187711736.5880975406140.411902459427
331180211761.795664530440.2043354695707
341158211706.8264231054-124.826423105442
351149311440.290231154552.7097688454905
361139011367.39487303922.6051269610234
371116211274.794629262-112.794629262016
381096211004.2927517709-42.2927517708777
391080510784.369317814120.630682185878
401060210633.8885300185-31.8885300184866
411055210419.3408766377132.659123362348
421037310419.1535128403-46.1535128403139
431027910226.820046728652.1799532714431
441013110151.3082127464-20.3082127463567
45101649997.23771146544166.762288534565
461009010093.5061371113-3.50613711128426
471010710023.644802891383.3551971086763
481004210072.4876434593-30.4876434593352
49100299998.539378641830.4606213581974
5099509996.21549347459-46.2154934745886
5197819900.49812234663-119.498122346627
5295599684.1634225145-125.163422514499
5392759410.24723569206-135.247235692055
5492759070.27867994136204.721320058643
5592199144.3214454085774.6785545914263
5691929123.6839123845468.3160876154616
5791059125.33140802312-20.331408023123
5891009032.7825469646267.2174530353805
5990839052.8850367446630.114963255337
6090929049.6410323967742.3589676032261
6190989075.8714631065422.1285368934605
6291959091.7481765455103.2518234545
6390879229.06215208905-142.062152089047

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 14664 & 14113 & 551 \tabularnewline
4 & 14660 & 14290.2516470461 & 369.748352953906 \tabularnewline
5 & 14605 & 14446.1280879843 & 158.871912015689 \tabularnewline
6 & 14480 & 14464.1958751927 & 15.8041248073223 \tabularnewline
7 & 14412 & 14350.4786095664 & 61.5213904335851 \tabularnewline
8 & 14454 & 14306.5853321492 & 147.41466785085 \tabularnewline
9 & 13915 & 14407.1263829035 & -492.126382903491 \tabularnewline
10 & 13858 & 13684.2934786105 & 173.70652138954 \tabularnewline
11 & 13768 & 13677.7115885987 & 90.2884114013013 \tabularnewline
12 & 13738 & 13628.0391024101 & 109.960897589928 \tabularnewline
13 & 13647 & 13643.1663156625 & 3.83368433749092 \tabularnewline
14 & 13591 & 13557.2514964397 & 33.7485035602622 \tabularnewline
15 & 13589 & 13514.3166114423 & 74.6833885576798 \tabularnewline
16 & 13294 & 13542.0595879622 & -248.059587962178 \tabularnewline
17 & 13418 & 13154.4098150373 & 263.590184962732 \tabularnewline
18 & 13251 & 13371.3136058375 & -120.313605837504 \tabularnewline
19 & 13156 & 13166.8522236616 & -10.8522236615954 \tabularnewline
20 & 13045 & 13063.7357748683 & -18.735774868288 \tabularnewline
21 & 12980 & 12945.1957326633 & 34.8042673367163 \tabularnewline
22 & 12910 & 12892.9235723216 & 17.0764276784084 \tabularnewline
23 & 12851 & 12830.6149353274 & 20.3850646726169 \tabularnewline
24 & 12907 & 12779.9919529991 & 127.008047000945 \tabularnewline
25 & 12586 & 12885.3566661776 & -299.356666177608 \tabularnewline
26 & 12384 & 12453.7601172399 & -69.7601172399154 \tabularnewline
27 & 12297 & 12215.1718875004 & 81.8281124995556 \tabularnewline
28 & 12312 & 12157.2509117628 & 154.749088237239 \tabularnewline
29 & 12301 & 12234.271612188 & 66.7283878119742 \tabularnewline
30 & 12218 & 12253.942994387 & -35.9429943869982 \tabularnewline
31 & 11897 & 12159.356499465 & -262.356499465022 \tabularnewline
32 & 11877 & 11736.5880975406 & 140.411902459427 \tabularnewline
33 & 11802 & 11761.7956645304 & 40.2043354695707 \tabularnewline
34 & 11582 & 11706.8264231054 & -124.826423105442 \tabularnewline
35 & 11493 & 11440.2902311545 & 52.7097688454905 \tabularnewline
36 & 11390 & 11367.394873039 & 22.6051269610234 \tabularnewline
37 & 11162 & 11274.794629262 & -112.794629262016 \tabularnewline
38 & 10962 & 11004.2927517709 & -42.2927517708777 \tabularnewline
39 & 10805 & 10784.3693178141 & 20.630682185878 \tabularnewline
40 & 10602 & 10633.8885300185 & -31.8885300184866 \tabularnewline
41 & 10552 & 10419.3408766377 & 132.659123362348 \tabularnewline
42 & 10373 & 10419.1535128403 & -46.1535128403139 \tabularnewline
43 & 10279 & 10226.8200467286 & 52.1799532714431 \tabularnewline
44 & 10131 & 10151.3082127464 & -20.3082127463567 \tabularnewline
45 & 10164 & 9997.23771146544 & 166.762288534565 \tabularnewline
46 & 10090 & 10093.5061371113 & -3.50613711128426 \tabularnewline
47 & 10107 & 10023.6448028913 & 83.3551971086763 \tabularnewline
48 & 10042 & 10072.4876434593 & -30.4876434593352 \tabularnewline
49 & 10029 & 9998.5393786418 & 30.4606213581974 \tabularnewline
50 & 9950 & 9996.21549347459 & -46.2154934745886 \tabularnewline
51 & 9781 & 9900.49812234663 & -119.498122346627 \tabularnewline
52 & 9559 & 9684.1634225145 & -125.163422514499 \tabularnewline
53 & 9275 & 9410.24723569206 & -135.247235692055 \tabularnewline
54 & 9275 & 9070.27867994136 & 204.721320058643 \tabularnewline
55 & 9219 & 9144.32144540857 & 74.6785545914263 \tabularnewline
56 & 9192 & 9123.68391238454 & 68.3160876154616 \tabularnewline
57 & 9105 & 9125.33140802312 & -20.331408023123 \tabularnewline
58 & 9100 & 9032.78254696462 & 67.2174530353805 \tabularnewline
59 & 9083 & 9052.88503674466 & 30.114963255337 \tabularnewline
60 & 9092 & 9049.64103239677 & 42.3589676032261 \tabularnewline
61 & 9098 & 9075.87146310654 & 22.1285368934605 \tabularnewline
62 & 9195 & 9091.7481765455 & 103.2518234545 \tabularnewline
63 & 9087 & 9229.06215208905 & -142.062152089047 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300668&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]14664[/C][C]14113[/C][C]551[/C][/ROW]
[ROW][C]4[/C][C]14660[/C][C]14290.2516470461[/C][C]369.748352953906[/C][/ROW]
[ROW][C]5[/C][C]14605[/C][C]14446.1280879843[/C][C]158.871912015689[/C][/ROW]
[ROW][C]6[/C][C]14480[/C][C]14464.1958751927[/C][C]15.8041248073223[/C][/ROW]
[ROW][C]7[/C][C]14412[/C][C]14350.4786095664[/C][C]61.5213904335851[/C][/ROW]
[ROW][C]8[/C][C]14454[/C][C]14306.5853321492[/C][C]147.41466785085[/C][/ROW]
[ROW][C]9[/C][C]13915[/C][C]14407.1263829035[/C][C]-492.126382903491[/C][/ROW]
[ROW][C]10[/C][C]13858[/C][C]13684.2934786105[/C][C]173.70652138954[/C][/ROW]
[ROW][C]11[/C][C]13768[/C][C]13677.7115885987[/C][C]90.2884114013013[/C][/ROW]
[ROW][C]12[/C][C]13738[/C][C]13628.0391024101[/C][C]109.960897589928[/C][/ROW]
[ROW][C]13[/C][C]13647[/C][C]13643.1663156625[/C][C]3.83368433749092[/C][/ROW]
[ROW][C]14[/C][C]13591[/C][C]13557.2514964397[/C][C]33.7485035602622[/C][/ROW]
[ROW][C]15[/C][C]13589[/C][C]13514.3166114423[/C][C]74.6833885576798[/C][/ROW]
[ROW][C]16[/C][C]13294[/C][C]13542.0595879622[/C][C]-248.059587962178[/C][/ROW]
[ROW][C]17[/C][C]13418[/C][C]13154.4098150373[/C][C]263.590184962732[/C][/ROW]
[ROW][C]18[/C][C]13251[/C][C]13371.3136058375[/C][C]-120.313605837504[/C][/ROW]
[ROW][C]19[/C][C]13156[/C][C]13166.8522236616[/C][C]-10.8522236615954[/C][/ROW]
[ROW][C]20[/C][C]13045[/C][C]13063.7357748683[/C][C]-18.735774868288[/C][/ROW]
[ROW][C]21[/C][C]12980[/C][C]12945.1957326633[/C][C]34.8042673367163[/C][/ROW]
[ROW][C]22[/C][C]12910[/C][C]12892.9235723216[/C][C]17.0764276784084[/C][/ROW]
[ROW][C]23[/C][C]12851[/C][C]12830.6149353274[/C][C]20.3850646726169[/C][/ROW]
[ROW][C]24[/C][C]12907[/C][C]12779.9919529991[/C][C]127.008047000945[/C][/ROW]
[ROW][C]25[/C][C]12586[/C][C]12885.3566661776[/C][C]-299.356666177608[/C][/ROW]
[ROW][C]26[/C][C]12384[/C][C]12453.7601172399[/C][C]-69.7601172399154[/C][/ROW]
[ROW][C]27[/C][C]12297[/C][C]12215.1718875004[/C][C]81.8281124995556[/C][/ROW]
[ROW][C]28[/C][C]12312[/C][C]12157.2509117628[/C][C]154.749088237239[/C][/ROW]
[ROW][C]29[/C][C]12301[/C][C]12234.271612188[/C][C]66.7283878119742[/C][/ROW]
[ROW][C]30[/C][C]12218[/C][C]12253.942994387[/C][C]-35.9429943869982[/C][/ROW]
[ROW][C]31[/C][C]11897[/C][C]12159.356499465[/C][C]-262.356499465022[/C][/ROW]
[ROW][C]32[/C][C]11877[/C][C]11736.5880975406[/C][C]140.411902459427[/C][/ROW]
[ROW][C]33[/C][C]11802[/C][C]11761.7956645304[/C][C]40.2043354695707[/C][/ROW]
[ROW][C]34[/C][C]11582[/C][C]11706.8264231054[/C][C]-124.826423105442[/C][/ROW]
[ROW][C]35[/C][C]11493[/C][C]11440.2902311545[/C][C]52.7097688454905[/C][/ROW]
[ROW][C]36[/C][C]11390[/C][C]11367.394873039[/C][C]22.6051269610234[/C][/ROW]
[ROW][C]37[/C][C]11162[/C][C]11274.794629262[/C][C]-112.794629262016[/C][/ROW]
[ROW][C]38[/C][C]10962[/C][C]11004.2927517709[/C][C]-42.2927517708777[/C][/ROW]
[ROW][C]39[/C][C]10805[/C][C]10784.3693178141[/C][C]20.630682185878[/C][/ROW]
[ROW][C]40[/C][C]10602[/C][C]10633.8885300185[/C][C]-31.8885300184866[/C][/ROW]
[ROW][C]41[/C][C]10552[/C][C]10419.3408766377[/C][C]132.659123362348[/C][/ROW]
[ROW][C]42[/C][C]10373[/C][C]10419.1535128403[/C][C]-46.1535128403139[/C][/ROW]
[ROW][C]43[/C][C]10279[/C][C]10226.8200467286[/C][C]52.1799532714431[/C][/ROW]
[ROW][C]44[/C][C]10131[/C][C]10151.3082127464[/C][C]-20.3082127463567[/C][/ROW]
[ROW][C]45[/C][C]10164[/C][C]9997.23771146544[/C][C]166.762288534565[/C][/ROW]
[ROW][C]46[/C][C]10090[/C][C]10093.5061371113[/C][C]-3.50613711128426[/C][/ROW]
[ROW][C]47[/C][C]10107[/C][C]10023.6448028913[/C][C]83.3551971086763[/C][/ROW]
[ROW][C]48[/C][C]10042[/C][C]10072.4876434593[/C][C]-30.4876434593352[/C][/ROW]
[ROW][C]49[/C][C]10029[/C][C]9998.5393786418[/C][C]30.4606213581974[/C][/ROW]
[ROW][C]50[/C][C]9950[/C][C]9996.21549347459[/C][C]-46.2154934745886[/C][/ROW]
[ROW][C]51[/C][C]9781[/C][C]9900.49812234663[/C][C]-119.498122346627[/C][/ROW]
[ROW][C]52[/C][C]9559[/C][C]9684.1634225145[/C][C]-125.163422514499[/C][/ROW]
[ROW][C]53[/C][C]9275[/C][C]9410.24723569206[/C][C]-135.247235692055[/C][/ROW]
[ROW][C]54[/C][C]9275[/C][C]9070.27867994136[/C][C]204.721320058643[/C][/ROW]
[ROW][C]55[/C][C]9219[/C][C]9144.32144540857[/C][C]74.6785545914263[/C][/ROW]
[ROW][C]56[/C][C]9192[/C][C]9123.68391238454[/C][C]68.3160876154616[/C][/ROW]
[ROW][C]57[/C][C]9105[/C][C]9125.33140802312[/C][C]-20.331408023123[/C][/ROW]
[ROW][C]58[/C][C]9100[/C][C]9032.78254696462[/C][C]67.2174530353805[/C][/ROW]
[ROW][C]59[/C][C]9083[/C][C]9052.88503674466[/C][C]30.114963255337[/C][/ROW]
[ROW][C]60[/C][C]9092[/C][C]9049.64103239677[/C][C]42.3589676032261[/C][/ROW]
[ROW][C]61[/C][C]9098[/C][C]9075.87146310654[/C][C]22.1285368934605[/C][/ROW]
[ROW][C]62[/C][C]9195[/C][C]9091.7481765455[/C][C]103.2518234545[/C][/ROW]
[ROW][C]63[/C][C]9087[/C][C]9229.06215208905[/C][C]-142.062152089047[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300668&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300668&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
31466414113551
41466014290.2516470461369.748352953906
51460514446.1280879843158.871912015689
61448014464.195875192715.8041248073223
71441214350.478609566461.5213904335851
81445414306.5853321492147.41466785085
91391514407.1263829035-492.126382903491
101385813684.2934786105173.70652138954
111376813677.711588598790.2884114013013
121373813628.0391024101109.960897589928
131364713643.16631566253.83368433749092
141359113557.251496439733.7485035602622
151358913514.316611442374.6833885576798
161329413542.0595879622-248.059587962178
171341813154.4098150373263.590184962732
181325113371.3136058375-120.313605837504
191315613166.8522236616-10.8522236615954
201304513063.7357748683-18.735774868288
211298012945.195732663334.8042673367163
221291012892.923572321617.0764276784084
231285112830.614935327420.3850646726169
241290712779.9919529991127.008047000945
251258612885.3566661776-299.356666177608
261238412453.7601172399-69.7601172399154
271229712215.171887500481.8281124995556
281231212157.2509117628154.749088237239
291230112234.27161218866.7283878119742
301221812253.942994387-35.9429943869982
311189712159.356499465-262.356499465022
321187711736.5880975406140.411902459427
331180211761.795664530440.2043354695707
341158211706.8264231054-124.826423105442
351149311440.290231154552.7097688454905
361139011367.39487303922.6051269610234
371116211274.794629262-112.794629262016
381096211004.2927517709-42.2927517708777
391080510784.369317814120.630682185878
401060210633.8885300185-31.8885300184866
411055210419.3408766377132.659123362348
421037310419.1535128403-46.1535128403139
431027910226.820046728652.1799532714431
441013110151.3082127464-20.3082127463567
45101649997.23771146544166.762288534565
461009010093.5061371113-3.50613711128426
471010710023.644802891383.3551971086763
481004210072.4876434593-30.4876434593352
49100299998.539378641830.4606213581974
5099509996.21549347459-46.2154934745886
5197819900.49812234663-119.498122346627
5295599684.1634225145-125.163422514499
5392759410.24723569206-135.247235692055
5492759070.27867994136204.721320058643
5592199144.3214454085774.6785545914263
5691929123.6839123845468.3160876154616
5791059125.33140802312-20.331408023123
5891009032.7825469646267.2174530353805
5990839052.8850367446630.114963255337
6090929049.6410323967742.3589676032261
6190989075.8714631065422.1285368934605
6291959091.7481765455103.2518234545
6390879229.06215208905-142.062152089047







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
649069.990748489278772.587625186389367.39387179216
659048.310694848388540.648985500779555.97240419598
669026.630641207488288.93858360629764.32269880877
679004.950587566598015.754057879269994.14711725392
688983.27053392577721.7893834147910244.7516844366
698961.59048028487408.1047215606110515.076239009
708939.910426643917075.7448285267610804.0760247611
718918.230373003026725.657799177411110.8029468286
728896.550319362126358.6860558740811434.4145828502
738874.870265721235975.5757589730911774.1647724694
748853.190212080345576.9898188096112129.3906053511
758831.510158439445163.5202682712612499.5000486076

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
64 & 9069.99074848927 & 8772.58762518638 & 9367.39387179216 \tabularnewline
65 & 9048.31069484838 & 8540.64898550077 & 9555.97240419598 \tabularnewline
66 & 9026.63064120748 & 8288.9385836062 & 9764.32269880877 \tabularnewline
67 & 9004.95058756659 & 8015.75405787926 & 9994.14711725392 \tabularnewline
68 & 8983.2705339257 & 7721.78938341479 & 10244.7516844366 \tabularnewline
69 & 8961.5904802848 & 7408.10472156061 & 10515.076239009 \tabularnewline
70 & 8939.91042664391 & 7075.74482852676 & 10804.0760247611 \tabularnewline
71 & 8918.23037300302 & 6725.6577991774 & 11110.8029468286 \tabularnewline
72 & 8896.55031936212 & 6358.68605587408 & 11434.4145828502 \tabularnewline
73 & 8874.87026572123 & 5975.57575897309 & 11774.1647724694 \tabularnewline
74 & 8853.19021208034 & 5576.98981880961 & 12129.3906053511 \tabularnewline
75 & 8831.51015843944 & 5163.52026827126 & 12499.5000486076 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300668&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]64[/C][C]9069.99074848927[/C][C]8772.58762518638[/C][C]9367.39387179216[/C][/ROW]
[ROW][C]65[/C][C]9048.31069484838[/C][C]8540.64898550077[/C][C]9555.97240419598[/C][/ROW]
[ROW][C]66[/C][C]9026.63064120748[/C][C]8288.9385836062[/C][C]9764.32269880877[/C][/ROW]
[ROW][C]67[/C][C]9004.95058756659[/C][C]8015.75405787926[/C][C]9994.14711725392[/C][/ROW]
[ROW][C]68[/C][C]8983.2705339257[/C][C]7721.78938341479[/C][C]10244.7516844366[/C][/ROW]
[ROW][C]69[/C][C]8961.5904802848[/C][C]7408.10472156061[/C][C]10515.076239009[/C][/ROW]
[ROW][C]70[/C][C]8939.91042664391[/C][C]7075.74482852676[/C][C]10804.0760247611[/C][/ROW]
[ROW][C]71[/C][C]8918.23037300302[/C][C]6725.6577991774[/C][C]11110.8029468286[/C][/ROW]
[ROW][C]72[/C][C]8896.55031936212[/C][C]6358.68605587408[/C][C]11434.4145828502[/C][/ROW]
[ROW][C]73[/C][C]8874.87026572123[/C][C]5975.57575897309[/C][C]11774.1647724694[/C][/ROW]
[ROW][C]74[/C][C]8853.19021208034[/C][C]5576.98981880961[/C][C]12129.3906053511[/C][/ROW]
[ROW][C]75[/C][C]8831.51015843944[/C][C]5163.52026827126[/C][C]12499.5000486076[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300668&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300668&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
649069.990748489278772.587625186389367.39387179216
659048.310694848388540.648985500779555.97240419598
669026.630641207488288.93858360629764.32269880877
679004.950587566598015.754057879269994.14711725392
688983.27053392577721.7893834147910244.7516844366
698961.59048028487408.1047215606110515.076239009
708939.910426643917075.7448285267610804.0760247611
718918.230373003026725.657799177411110.8029468286
728896.550319362126358.6860558740811434.4145828502
738874.870265721235975.5757589730911774.1647724694
748853.190212080345576.9898188096112129.3906053511
758831.510158439445163.5202682712612499.5000486076



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')