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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Jan 2011 08:17:23 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Jan/17/t129525209938td2rrhmmsvcq7.htm/, Retrieved Sat, 18 May 2024 23:22:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117506, Retrieved Sat, 18 May 2024 23:22:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-01-17 08:17:23] [391aa7ca16a929f44adfa61e9db4be9d] [Current]
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Dataseries X:
6715
7703
9856
8326
9269
7035
10342
11682
10304
11385
9777
8882
7897
6930
9545
9110
7459
7320
10017
12307
11072
10749
9589
9080
7384
8062
8511
8684
8306
7643
10577
13747
11783
11611
9946
8693
7303
7609
9423
8584
7586
6843
11811
13414
12103
11501
8213
7982
7687
7180
7862
8043
8340
6692
10065
12684
11587
9843
8110
7940
6475
6121
9669
7778
7826
7403
10741
14023
11519
10236
8075
8157




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117506&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117506&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117506&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.113673696771336
beta0
gamma0.687041745941993

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.113673696771336 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.687041745941993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117506&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]0.113673696771336[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.687041745941993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117506&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117506&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
alpha0.113673696771336
beta0
gamma0.687041745941993







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1378978033.04353241997-136.043532419971
1469307020.78799293574-90.7879929357387
1595459587.90823085265-42.9082308526486
1691109133.71624314024-23.7162431402376
1774597498.08212829965-39.0821282996476
1873207347.88711799718-27.887117997182
191001710286.1761146323-269.176114632271
201230711554.1148044881752.885195511892
211107210308.4913747681763.508625231909
221074911452.6349210914-703.634921091387
2395899803.733404871-214.733404871011
2490808938.38201277751141.617987222487
2573847874.41139417128-490.411394171285
2680626863.450022440181198.54997755982
2785119623.0059046685-1112.00590466849
2886849061.68444169751-377.684441697515
2983067394.00248774349911.99751225651
3076437358.23379465385284.766205346151
311057710208.6829044251368.317095574934
321374712198.43379690911548.56620309093
331178311015.6951503757767.304849624286
341161111267.6379926474343.362007352556
3599469993.27522487825-47.2752248782454
3686939342.10264062157-649.102640621568
3773037764.4653634404-461.4653634404
3876097772.73111870512-163.73111870512
3994238965.28179842135457.718201578655
4085849028.86834169099-444.86834169099
4175868113.08145946444-527.081459464444
4268437531.0107048825-688.010704882506
431181110278.55574570461532.44425429542
441341413100.3132055348313.686794465231
451210311322.7166137701780.283386229887
461150111318.4278467755182.572153224544
4782139811.5665351329-1598.5665351329
4879828647.77384857799-665.773848577992
4976877227.59298198486459.407018015137
5071807516.56167840749-336.561678407485
5178629029.58391838196-1167.58391838196
5280438380.14685960922-337.146859609222
5383407462.42794031059877.572059689413
5466926951.24651036826-259.246510368259
551006511017.6530699823-952.653069982258
561268412734.0841470802-50.0841470801988
571158711264.0102411256322.989758874404
58984310865.6600082615-1022.6600082615
5981108279.43300262341-169.433002623409
6079407861.3541052566278.6458947433803
6164757232.74301618565-757.743016185649
6261216910.89276064295-789.89276064295
6396697790.988440824861878.01155917514
6477787992.62037207107-214.62037207107
6578267824.376192282771.62380771722565
6674036564.31497236196838.685027638036
671074110270.8576665589470.142333441121
681402312697.4800551631325.51994483697
691151911595.7800622879-76.780062287924
701023610316.0588405195-80.0588405195376
7180758321.69830060509-246.698300605085
7281578041.80556232065115.194437679349

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7897 & 8033.04353241997 & -136.043532419971 \tabularnewline
14 & 6930 & 7020.78799293574 & -90.7879929357387 \tabularnewline
15 & 9545 & 9587.90823085265 & -42.9082308526486 \tabularnewline
16 & 9110 & 9133.71624314024 & -23.7162431402376 \tabularnewline
17 & 7459 & 7498.08212829965 & -39.0821282996476 \tabularnewline
18 & 7320 & 7347.88711799718 & -27.887117997182 \tabularnewline
19 & 10017 & 10286.1761146323 & -269.176114632271 \tabularnewline
20 & 12307 & 11554.1148044881 & 752.885195511892 \tabularnewline
21 & 11072 & 10308.4913747681 & 763.508625231909 \tabularnewline
22 & 10749 & 11452.6349210914 & -703.634921091387 \tabularnewline
23 & 9589 & 9803.733404871 & -214.733404871011 \tabularnewline
24 & 9080 & 8938.38201277751 & 141.617987222487 \tabularnewline
25 & 7384 & 7874.41139417128 & -490.411394171285 \tabularnewline
26 & 8062 & 6863.45002244018 & 1198.54997755982 \tabularnewline
27 & 8511 & 9623.0059046685 & -1112.00590466849 \tabularnewline
28 & 8684 & 9061.68444169751 & -377.684441697515 \tabularnewline
29 & 8306 & 7394.00248774349 & 911.99751225651 \tabularnewline
30 & 7643 & 7358.23379465385 & 284.766205346151 \tabularnewline
31 & 10577 & 10208.6829044251 & 368.317095574934 \tabularnewline
32 & 13747 & 12198.4337969091 & 1548.56620309093 \tabularnewline
33 & 11783 & 11015.6951503757 & 767.304849624286 \tabularnewline
34 & 11611 & 11267.6379926474 & 343.362007352556 \tabularnewline
35 & 9946 & 9993.27522487825 & -47.2752248782454 \tabularnewline
36 & 8693 & 9342.10264062157 & -649.102640621568 \tabularnewline
37 & 7303 & 7764.4653634404 & -461.4653634404 \tabularnewline
38 & 7609 & 7772.73111870512 & -163.73111870512 \tabularnewline
39 & 9423 & 8965.28179842135 & 457.718201578655 \tabularnewline
40 & 8584 & 9028.86834169099 & -444.86834169099 \tabularnewline
41 & 7586 & 8113.08145946444 & -527.081459464444 \tabularnewline
42 & 6843 & 7531.0107048825 & -688.010704882506 \tabularnewline
43 & 11811 & 10278.5557457046 & 1532.44425429542 \tabularnewline
44 & 13414 & 13100.3132055348 & 313.686794465231 \tabularnewline
45 & 12103 & 11322.7166137701 & 780.283386229887 \tabularnewline
46 & 11501 & 11318.4278467755 & 182.572153224544 \tabularnewline
47 & 8213 & 9811.5665351329 & -1598.5665351329 \tabularnewline
48 & 7982 & 8647.77384857799 & -665.773848577992 \tabularnewline
49 & 7687 & 7227.59298198486 & 459.407018015137 \tabularnewline
50 & 7180 & 7516.56167840749 & -336.561678407485 \tabularnewline
51 & 7862 & 9029.58391838196 & -1167.58391838196 \tabularnewline
52 & 8043 & 8380.14685960922 & -337.146859609222 \tabularnewline
53 & 8340 & 7462.42794031059 & 877.572059689413 \tabularnewline
54 & 6692 & 6951.24651036826 & -259.246510368259 \tabularnewline
55 & 10065 & 11017.6530699823 & -952.653069982258 \tabularnewline
56 & 12684 & 12734.0841470802 & -50.0841470801988 \tabularnewline
57 & 11587 & 11264.0102411256 & 322.989758874404 \tabularnewline
58 & 9843 & 10865.6600082615 & -1022.6600082615 \tabularnewline
59 & 8110 & 8279.43300262341 & -169.433002623409 \tabularnewline
60 & 7940 & 7861.35410525662 & 78.6458947433803 \tabularnewline
61 & 6475 & 7232.74301618565 & -757.743016185649 \tabularnewline
62 & 6121 & 6910.89276064295 & -789.89276064295 \tabularnewline
63 & 9669 & 7790.98844082486 & 1878.01155917514 \tabularnewline
64 & 7778 & 7992.62037207107 & -214.62037207107 \tabularnewline
65 & 7826 & 7824.37619228277 & 1.62380771722565 \tabularnewline
66 & 7403 & 6564.31497236196 & 838.685027638036 \tabularnewline
67 & 10741 & 10270.8576665589 & 470.142333441121 \tabularnewline
68 & 14023 & 12697.480055163 & 1325.51994483697 \tabularnewline
69 & 11519 & 11595.7800622879 & -76.780062287924 \tabularnewline
70 & 10236 & 10316.0588405195 & -80.0588405195376 \tabularnewline
71 & 8075 & 8321.69830060509 & -246.698300605085 \tabularnewline
72 & 8157 & 8041.80556232065 & 115.194437679349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117506&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]7897[/C][C]8033.04353241997[/C][C]-136.043532419971[/C][/ROW]
[ROW][C]14[/C][C]6930[/C][C]7020.78799293574[/C][C]-90.7879929357387[/C][/ROW]
[ROW][C]15[/C][C]9545[/C][C]9587.90823085265[/C][C]-42.9082308526486[/C][/ROW]
[ROW][C]16[/C][C]9110[/C][C]9133.71624314024[/C][C]-23.7162431402376[/C][/ROW]
[ROW][C]17[/C][C]7459[/C][C]7498.08212829965[/C][C]-39.0821282996476[/C][/ROW]
[ROW][C]18[/C][C]7320[/C][C]7347.88711799718[/C][C]-27.887117997182[/C][/ROW]
[ROW][C]19[/C][C]10017[/C][C]10286.1761146323[/C][C]-269.176114632271[/C][/ROW]
[ROW][C]20[/C][C]12307[/C][C]11554.1148044881[/C][C]752.885195511892[/C][/ROW]
[ROW][C]21[/C][C]11072[/C][C]10308.4913747681[/C][C]763.508625231909[/C][/ROW]
[ROW][C]22[/C][C]10749[/C][C]11452.6349210914[/C][C]-703.634921091387[/C][/ROW]
[ROW][C]23[/C][C]9589[/C][C]9803.733404871[/C][C]-214.733404871011[/C][/ROW]
[ROW][C]24[/C][C]9080[/C][C]8938.38201277751[/C][C]141.617987222487[/C][/ROW]
[ROW][C]25[/C][C]7384[/C][C]7874.41139417128[/C][C]-490.411394171285[/C][/ROW]
[ROW][C]26[/C][C]8062[/C][C]6863.45002244018[/C][C]1198.54997755982[/C][/ROW]
[ROW][C]27[/C][C]8511[/C][C]9623.0059046685[/C][C]-1112.00590466849[/C][/ROW]
[ROW][C]28[/C][C]8684[/C][C]9061.68444169751[/C][C]-377.684441697515[/C][/ROW]
[ROW][C]29[/C][C]8306[/C][C]7394.00248774349[/C][C]911.99751225651[/C][/ROW]
[ROW][C]30[/C][C]7643[/C][C]7358.23379465385[/C][C]284.766205346151[/C][/ROW]
[ROW][C]31[/C][C]10577[/C][C]10208.6829044251[/C][C]368.317095574934[/C][/ROW]
[ROW][C]32[/C][C]13747[/C][C]12198.4337969091[/C][C]1548.56620309093[/C][/ROW]
[ROW][C]33[/C][C]11783[/C][C]11015.6951503757[/C][C]767.304849624286[/C][/ROW]
[ROW][C]34[/C][C]11611[/C][C]11267.6379926474[/C][C]343.362007352556[/C][/ROW]
[ROW][C]35[/C][C]9946[/C][C]9993.27522487825[/C][C]-47.2752248782454[/C][/ROW]
[ROW][C]36[/C][C]8693[/C][C]9342.10264062157[/C][C]-649.102640621568[/C][/ROW]
[ROW][C]37[/C][C]7303[/C][C]7764.4653634404[/C][C]-461.4653634404[/C][/ROW]
[ROW][C]38[/C][C]7609[/C][C]7772.73111870512[/C][C]-163.73111870512[/C][/ROW]
[ROW][C]39[/C][C]9423[/C][C]8965.28179842135[/C][C]457.718201578655[/C][/ROW]
[ROW][C]40[/C][C]8584[/C][C]9028.86834169099[/C][C]-444.86834169099[/C][/ROW]
[ROW][C]41[/C][C]7586[/C][C]8113.08145946444[/C][C]-527.081459464444[/C][/ROW]
[ROW][C]42[/C][C]6843[/C][C]7531.0107048825[/C][C]-688.010704882506[/C][/ROW]
[ROW][C]43[/C][C]11811[/C][C]10278.5557457046[/C][C]1532.44425429542[/C][/ROW]
[ROW][C]44[/C][C]13414[/C][C]13100.3132055348[/C][C]313.686794465231[/C][/ROW]
[ROW][C]45[/C][C]12103[/C][C]11322.7166137701[/C][C]780.283386229887[/C][/ROW]
[ROW][C]46[/C][C]11501[/C][C]11318.4278467755[/C][C]182.572153224544[/C][/ROW]
[ROW][C]47[/C][C]8213[/C][C]9811.5665351329[/C][C]-1598.5665351329[/C][/ROW]
[ROW][C]48[/C][C]7982[/C][C]8647.77384857799[/C][C]-665.773848577992[/C][/ROW]
[ROW][C]49[/C][C]7687[/C][C]7227.59298198486[/C][C]459.407018015137[/C][/ROW]
[ROW][C]50[/C][C]7180[/C][C]7516.56167840749[/C][C]-336.561678407485[/C][/ROW]
[ROW][C]51[/C][C]7862[/C][C]9029.58391838196[/C][C]-1167.58391838196[/C][/ROW]
[ROW][C]52[/C][C]8043[/C][C]8380.14685960922[/C][C]-337.146859609222[/C][/ROW]
[ROW][C]53[/C][C]8340[/C][C]7462.42794031059[/C][C]877.572059689413[/C][/ROW]
[ROW][C]54[/C][C]6692[/C][C]6951.24651036826[/C][C]-259.246510368259[/C][/ROW]
[ROW][C]55[/C][C]10065[/C][C]11017.6530699823[/C][C]-952.653069982258[/C][/ROW]
[ROW][C]56[/C][C]12684[/C][C]12734.0841470802[/C][C]-50.0841470801988[/C][/ROW]
[ROW][C]57[/C][C]11587[/C][C]11264.0102411256[/C][C]322.989758874404[/C][/ROW]
[ROW][C]58[/C][C]9843[/C][C]10865.6600082615[/C][C]-1022.6600082615[/C][/ROW]
[ROW][C]59[/C][C]8110[/C][C]8279.43300262341[/C][C]-169.433002623409[/C][/ROW]
[ROW][C]60[/C][C]7940[/C][C]7861.35410525662[/C][C]78.6458947433803[/C][/ROW]
[ROW][C]61[/C][C]6475[/C][C]7232.74301618565[/C][C]-757.743016185649[/C][/ROW]
[ROW][C]62[/C][C]6121[/C][C]6910.89276064295[/C][C]-789.89276064295[/C][/ROW]
[ROW][C]63[/C][C]9669[/C][C]7790.98844082486[/C][C]1878.01155917514[/C][/ROW]
[ROW][C]64[/C][C]7778[/C][C]7992.62037207107[/C][C]-214.62037207107[/C][/ROW]
[ROW][C]65[/C][C]7826[/C][C]7824.37619228277[/C][C]1.62380771722565[/C][/ROW]
[ROW][C]66[/C][C]7403[/C][C]6564.31497236196[/C][C]838.685027638036[/C][/ROW]
[ROW][C]67[/C][C]10741[/C][C]10270.8576665589[/C][C]470.142333441121[/C][/ROW]
[ROW][C]68[/C][C]14023[/C][C]12697.480055163[/C][C]1325.51994483697[/C][/ROW]
[ROW][C]69[/C][C]11519[/C][C]11595.7800622879[/C][C]-76.780062287924[/C][/ROW]
[ROW][C]70[/C][C]10236[/C][C]10316.0588405195[/C][C]-80.0588405195376[/C][/ROW]
[ROW][C]71[/C][C]8075[/C][C]8321.69830060509[/C][C]-246.698300605085[/C][/ROW]
[ROW][C]72[/C][C]8157[/C][C]8041.80556232065[/C][C]115.194437679349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117506&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117506&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
1378978033.04353241997-136.043532419971
1469307020.78799293574-90.7879929357387
1595459587.90823085265-42.9082308526486
1691109133.71624314024-23.7162431402376
1774597498.08212829965-39.0821282996476
1873207347.88711799718-27.887117997182
191001710286.1761146323-269.176114632271
201230711554.1148044881752.885195511892
211107210308.4913747681763.508625231909
221074911452.6349210914-703.634921091387
2395899803.733404871-214.733404871011
2490808938.38201277751141.617987222487
2573847874.41139417128-490.411394171285
2680626863.450022440181198.54997755982
2785119623.0059046685-1112.00590466849
2886849061.68444169751-377.684441697515
2983067394.00248774349911.99751225651
3076437358.23379465385284.766205346151
311057710208.6829044251368.317095574934
321374712198.43379690911548.56620309093
331178311015.6951503757767.304849624286
341161111267.6379926474343.362007352556
3599469993.27522487825-47.2752248782454
3686939342.10264062157-649.102640621568
3773037764.4653634404-461.4653634404
3876097772.73111870512-163.73111870512
3994238965.28179842135457.718201578655
4085849028.86834169099-444.86834169099
4175868113.08145946444-527.081459464444
4268437531.0107048825-688.010704882506
431181110278.55574570461532.44425429542
441341413100.3132055348313.686794465231
451210311322.7166137701780.283386229887
461150111318.4278467755182.572153224544
4782139811.5665351329-1598.5665351329
4879828647.77384857799-665.773848577992
4976877227.59298198486459.407018015137
5071807516.56167840749-336.561678407485
5178629029.58391838196-1167.58391838196
5280438380.14685960922-337.146859609222
5383407462.42794031059877.572059689413
5466926951.24651036826-259.246510368259
551006511017.6530699823-952.653069982258
561268412734.0841470802-50.0841470801988
571158711264.0102411256322.989758874404
58984310865.6600082615-1022.6600082615
5981108279.43300262341-169.433002623409
6079407861.3541052566278.6458947433803
6164757232.74301618565-757.743016185649
6261216910.89276064295-789.89276064295
6396697790.988440824861878.01155917514
6477787992.62037207107-214.62037207107
6578267824.376192282771.62380771722565
6674036564.31497236196838.685027638036
671074110270.8576665589470.142333441121
681402312697.4800551631325.51994483697
691151911595.7800622879-76.780062287924
701023610316.0588405195-80.0588405195376
7180758321.69830060509-246.698300605085
7281578041.80556232065115.194437679349







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
736882.672942120085886.811448683387878.53443555678
746613.478862879425606.286616073647620.67110968521
759288.347045424318246.6812462422810330.0128446063
767982.176066392056943.460066229899020.89206655422
777969.903987558616919.518188246599020.28978687064
787198.19838765876147.984124286378248.41265103103
7910596.67643806039462.4741083610911730.8787677595
8013477.469264909512249.074479214714705.8640506043
8111398.449166081310223.767107172112573.1312249904
8210140.96201429988992.519073393811289.4049552058
838077.50061440516975.114858369019179.88637044117
848046.111570614047534.215526077878558.0076151502

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 6882.67294212008 & 5886.81144868338 & 7878.53443555678 \tabularnewline
74 & 6613.47886287942 & 5606.28661607364 & 7620.67110968521 \tabularnewline
75 & 9288.34704542431 & 8246.68124624228 & 10330.0128446063 \tabularnewline
76 & 7982.17606639205 & 6943.46006622989 & 9020.89206655422 \tabularnewline
77 & 7969.90398755861 & 6919.51818824659 & 9020.28978687064 \tabularnewline
78 & 7198.1983876587 & 6147.98412428637 & 8248.41265103103 \tabularnewline
79 & 10596.6764380603 & 9462.47410836109 & 11730.8787677595 \tabularnewline
80 & 13477.4692649095 & 12249.0744792147 & 14705.8640506043 \tabularnewline
81 & 11398.4491660813 & 10223.7671071721 & 12573.1312249904 \tabularnewline
82 & 10140.9620142998 & 8992.5190733938 & 11289.4049552058 \tabularnewline
83 & 8077.5006144051 & 6975.11485836901 & 9179.88637044117 \tabularnewline
84 & 8046.11157061404 & 7534.21552607787 & 8558.0076151502 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117506&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]6882.67294212008[/C][C]5886.81144868338[/C][C]7878.53443555678[/C][/ROW]
[ROW][C]74[/C][C]6613.47886287942[/C][C]5606.28661607364[/C][C]7620.67110968521[/C][/ROW]
[ROW][C]75[/C][C]9288.34704542431[/C][C]8246.68124624228[/C][C]10330.0128446063[/C][/ROW]
[ROW][C]76[/C][C]7982.17606639205[/C][C]6943.46006622989[/C][C]9020.89206655422[/C][/ROW]
[ROW][C]77[/C][C]7969.90398755861[/C][C]6919.51818824659[/C][C]9020.28978687064[/C][/ROW]
[ROW][C]78[/C][C]7198.1983876587[/C][C]6147.98412428637[/C][C]8248.41265103103[/C][/ROW]
[ROW][C]79[/C][C]10596.6764380603[/C][C]9462.47410836109[/C][C]11730.8787677595[/C][/ROW]
[ROW][C]80[/C][C]13477.4692649095[/C][C]12249.0744792147[/C][C]14705.8640506043[/C][/ROW]
[ROW][C]81[/C][C]11398.4491660813[/C][C]10223.7671071721[/C][C]12573.1312249904[/C][/ROW]
[ROW][C]82[/C][C]10140.9620142998[/C][C]8992.5190733938[/C][C]11289.4049552058[/C][/ROW]
[ROW][C]83[/C][C]8077.5006144051[/C][C]6975.11485836901[/C][C]9179.88637044117[/C][/ROW]
[ROW][C]84[/C][C]8046.11157061404[/C][C]7534.21552607787[/C][C]8558.0076151502[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117506&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117506&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
736882.672942120085886.811448683387878.53443555678
746613.478862879425606.286616073647620.67110968521
759288.347045424318246.6812462422810330.0128446063
767982.176066392056943.460066229899020.89206655422
777969.903987558616919.518188246599020.28978687064
787198.19838765876147.984124286378248.41265103103
7910596.67643806039462.4741083610911730.8787677595
8013477.469264909512249.074479214714705.8640506043
8111398.449166081310223.767107172112573.1312249904
8210140.96201429988992.519073393811289.4049552058
838077.50061440516975.114858369019179.88637044117
848046.111570614047534.215526077878558.0076151502



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')