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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 May 2011 12:41:13 +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/May/18/t1305722239z6svyk8dgz8ginu.htm/, Retrieved Tue, 14 May 2024 07:43:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121818, Retrieved Tue, 14 May 2024 07:43:23 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-05-18 12:41:13] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2851
2672
2755
2721
2946
3036
2282
2212
2922
4301
5764
7132
2541
2475
3031
3266
3776
3230
3028
1759
3595
4474
6838
8357
3113
3006
4047
3523
3937
3986
3260
1573
3528
5211
7614
9254
5375
3088
3718
4514
4520
4539
3663
1643
4734
5428
8314
10651
3633
4292
4154
4121
4647
4753
3965
1723
5048
6923
9858
11331
4016
3957
4510
4276
4968
4677
3523
1821




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121818&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121818&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121818&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 time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0409527574646179
beta0.213826354573099
gamma0.447049703127968

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0409527574646179 \tabularnewline
beta & 0.213826354573099 \tabularnewline
gamma & 0.447049703127968 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121818&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]0.0409527574646179[/C][/ROW]
[ROW][C]beta[/C][C]0.213826354573099[/C][/ROW]
[ROW][C]gamma[/C][C]0.447049703127968[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121818&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121818&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
alpha0.0409527574646179
beta0.213826354573099
gamma0.447049703127968







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325412393.50833868648147.491661313524
1424752352.71674743204122.283252567958
1530312909.94895616264121.051043837358
1632663143.69713027014122.302869729856
1737763628.34529602076147.654703979244
1832303064.23475525313165.765244746867
1930282423.0330404558604.966959544204
2017592419.06012184961-660.060121849606
2135953191.03786233196403.962137668041
2244744729.88256768319-255.882567683188
2368386291.64062789902546.359372100982
2483577810.17732415066546.822675849338
2531132867.70568146713245.294318532867
2630062817.92641705209188.073582947914
2740473481.96781679856565.032183201442
2835233789.84617732456-266.846177324564
2939374369.59721924909-432.597219249086
3039863695.31439670542290.685603294582
3132603166.9860069591593.0139930408532
3215732497.69029989874-924.690299898737
3335283918.88531217404-390.885312174042
3452115318.31789454648-107.317894546477
3576147503.12819436748110.871805632515
3692549194.5318414344159.4681585655926
3753753377.049325929011997.95067407099
3830883363.09759626089-275.097596260895
3937184291.02816634234-573.028166342339
4045144173.03737217756340.96262782244
4145204772.1122244441-252.112224444103
4245394360.09627193035178.903728069648
4336633649.6268581404513.3731418595548
4416432377.99734193208-734.997341932077
4547344262.99823563221471.001764367787
4654286048.21133711549-620.21133711549
4783148632.15450989888-318.154509898883
481065110513.2537071004137.74629289957
4936334803.64341602592-1170.64341602592
5042923549.8333992673742.166600732702
5141544456.01782046898-302.017820468982
5241214752.11165747155-631.111657471546
5346475057.35921811475-410.359218114747
5447534776.88814941631-23.888149416307
5539653903.7809814111861.2190185888244
5617232186.57995221726-463.579952217257
5750484735.44973133142312.550268668577
5869236088.11011265394834.88988734606
5998589004.22351387919853.77648612081
601133111240.729659400890.2703405991979
6140164557.17612771076-541.176127710756
6239574116.08279119259-159.082791192587
6345104545.77811521034-35.7781152103371
6442764706.3851694402-430.3851694402
6549685124.26571975536-156.265719755356
6646775005.43847633557-328.438476335567
6735234106.88558389211-583.88558389211
6818212054.40221049811-233.402210498113

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2541 & 2393.50833868648 & 147.491661313524 \tabularnewline
14 & 2475 & 2352.71674743204 & 122.283252567958 \tabularnewline
15 & 3031 & 2909.94895616264 & 121.051043837358 \tabularnewline
16 & 3266 & 3143.69713027014 & 122.302869729856 \tabularnewline
17 & 3776 & 3628.34529602076 & 147.654703979244 \tabularnewline
18 & 3230 & 3064.23475525313 & 165.765244746867 \tabularnewline
19 & 3028 & 2423.0330404558 & 604.966959544204 \tabularnewline
20 & 1759 & 2419.06012184961 & -660.060121849606 \tabularnewline
21 & 3595 & 3191.03786233196 & 403.962137668041 \tabularnewline
22 & 4474 & 4729.88256768319 & -255.882567683188 \tabularnewline
23 & 6838 & 6291.64062789902 & 546.359372100982 \tabularnewline
24 & 8357 & 7810.17732415066 & 546.822675849338 \tabularnewline
25 & 3113 & 2867.70568146713 & 245.294318532867 \tabularnewline
26 & 3006 & 2817.92641705209 & 188.073582947914 \tabularnewline
27 & 4047 & 3481.96781679856 & 565.032183201442 \tabularnewline
28 & 3523 & 3789.84617732456 & -266.846177324564 \tabularnewline
29 & 3937 & 4369.59721924909 & -432.597219249086 \tabularnewline
30 & 3986 & 3695.31439670542 & 290.685603294582 \tabularnewline
31 & 3260 & 3166.98600695915 & 93.0139930408532 \tabularnewline
32 & 1573 & 2497.69029989874 & -924.690299898737 \tabularnewline
33 & 3528 & 3918.88531217404 & -390.885312174042 \tabularnewline
34 & 5211 & 5318.31789454648 & -107.317894546477 \tabularnewline
35 & 7614 & 7503.12819436748 & 110.871805632515 \tabularnewline
36 & 9254 & 9194.53184143441 & 59.4681585655926 \tabularnewline
37 & 5375 & 3377.04932592901 & 1997.95067407099 \tabularnewline
38 & 3088 & 3363.09759626089 & -275.097596260895 \tabularnewline
39 & 3718 & 4291.02816634234 & -573.028166342339 \tabularnewline
40 & 4514 & 4173.03737217756 & 340.96262782244 \tabularnewline
41 & 4520 & 4772.1122244441 & -252.112224444103 \tabularnewline
42 & 4539 & 4360.09627193035 & 178.903728069648 \tabularnewline
43 & 3663 & 3649.62685814045 & 13.3731418595548 \tabularnewline
44 & 1643 & 2377.99734193208 & -734.997341932077 \tabularnewline
45 & 4734 & 4262.99823563221 & 471.001764367787 \tabularnewline
46 & 5428 & 6048.21133711549 & -620.21133711549 \tabularnewline
47 & 8314 & 8632.15450989888 & -318.154509898883 \tabularnewline
48 & 10651 & 10513.2537071004 & 137.74629289957 \tabularnewline
49 & 3633 & 4803.64341602592 & -1170.64341602592 \tabularnewline
50 & 4292 & 3549.8333992673 & 742.166600732702 \tabularnewline
51 & 4154 & 4456.01782046898 & -302.017820468982 \tabularnewline
52 & 4121 & 4752.11165747155 & -631.111657471546 \tabularnewline
53 & 4647 & 5057.35921811475 & -410.359218114747 \tabularnewline
54 & 4753 & 4776.88814941631 & -23.888149416307 \tabularnewline
55 & 3965 & 3903.78098141118 & 61.2190185888244 \tabularnewline
56 & 1723 & 2186.57995221726 & -463.579952217257 \tabularnewline
57 & 5048 & 4735.44973133142 & 312.550268668577 \tabularnewline
58 & 6923 & 6088.11011265394 & 834.88988734606 \tabularnewline
59 & 9858 & 9004.22351387919 & 853.77648612081 \tabularnewline
60 & 11331 & 11240.7296594008 & 90.2703405991979 \tabularnewline
61 & 4016 & 4557.17612771076 & -541.176127710756 \tabularnewline
62 & 3957 & 4116.08279119259 & -159.082791192587 \tabularnewline
63 & 4510 & 4545.77811521034 & -35.7781152103371 \tabularnewline
64 & 4276 & 4706.3851694402 & -430.3851694402 \tabularnewline
65 & 4968 & 5124.26571975536 & -156.265719755356 \tabularnewline
66 & 4677 & 5005.43847633557 & -328.438476335567 \tabularnewline
67 & 3523 & 4106.88558389211 & -583.88558389211 \tabularnewline
68 & 1821 & 2054.40221049811 & -233.402210498113 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121818&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]2541[/C][C]2393.50833868648[/C][C]147.491661313524[/C][/ROW]
[ROW][C]14[/C][C]2475[/C][C]2352.71674743204[/C][C]122.283252567958[/C][/ROW]
[ROW][C]15[/C][C]3031[/C][C]2909.94895616264[/C][C]121.051043837358[/C][/ROW]
[ROW][C]16[/C][C]3266[/C][C]3143.69713027014[/C][C]122.302869729856[/C][/ROW]
[ROW][C]17[/C][C]3776[/C][C]3628.34529602076[/C][C]147.654703979244[/C][/ROW]
[ROW][C]18[/C][C]3230[/C][C]3064.23475525313[/C][C]165.765244746867[/C][/ROW]
[ROW][C]19[/C][C]3028[/C][C]2423.0330404558[/C][C]604.966959544204[/C][/ROW]
[ROW][C]20[/C][C]1759[/C][C]2419.06012184961[/C][C]-660.060121849606[/C][/ROW]
[ROW][C]21[/C][C]3595[/C][C]3191.03786233196[/C][C]403.962137668041[/C][/ROW]
[ROW][C]22[/C][C]4474[/C][C]4729.88256768319[/C][C]-255.882567683188[/C][/ROW]
[ROW][C]23[/C][C]6838[/C][C]6291.64062789902[/C][C]546.359372100982[/C][/ROW]
[ROW][C]24[/C][C]8357[/C][C]7810.17732415066[/C][C]546.822675849338[/C][/ROW]
[ROW][C]25[/C][C]3113[/C][C]2867.70568146713[/C][C]245.294318532867[/C][/ROW]
[ROW][C]26[/C][C]3006[/C][C]2817.92641705209[/C][C]188.073582947914[/C][/ROW]
[ROW][C]27[/C][C]4047[/C][C]3481.96781679856[/C][C]565.032183201442[/C][/ROW]
[ROW][C]28[/C][C]3523[/C][C]3789.84617732456[/C][C]-266.846177324564[/C][/ROW]
[ROW][C]29[/C][C]3937[/C][C]4369.59721924909[/C][C]-432.597219249086[/C][/ROW]
[ROW][C]30[/C][C]3986[/C][C]3695.31439670542[/C][C]290.685603294582[/C][/ROW]
[ROW][C]31[/C][C]3260[/C][C]3166.98600695915[/C][C]93.0139930408532[/C][/ROW]
[ROW][C]32[/C][C]1573[/C][C]2497.69029989874[/C][C]-924.690299898737[/C][/ROW]
[ROW][C]33[/C][C]3528[/C][C]3918.88531217404[/C][C]-390.885312174042[/C][/ROW]
[ROW][C]34[/C][C]5211[/C][C]5318.31789454648[/C][C]-107.317894546477[/C][/ROW]
[ROW][C]35[/C][C]7614[/C][C]7503.12819436748[/C][C]110.871805632515[/C][/ROW]
[ROW][C]36[/C][C]9254[/C][C]9194.53184143441[/C][C]59.4681585655926[/C][/ROW]
[ROW][C]37[/C][C]5375[/C][C]3377.04932592901[/C][C]1997.95067407099[/C][/ROW]
[ROW][C]38[/C][C]3088[/C][C]3363.09759626089[/C][C]-275.097596260895[/C][/ROW]
[ROW][C]39[/C][C]3718[/C][C]4291.02816634234[/C][C]-573.028166342339[/C][/ROW]
[ROW][C]40[/C][C]4514[/C][C]4173.03737217756[/C][C]340.96262782244[/C][/ROW]
[ROW][C]41[/C][C]4520[/C][C]4772.1122244441[/C][C]-252.112224444103[/C][/ROW]
[ROW][C]42[/C][C]4539[/C][C]4360.09627193035[/C][C]178.903728069648[/C][/ROW]
[ROW][C]43[/C][C]3663[/C][C]3649.62685814045[/C][C]13.3731418595548[/C][/ROW]
[ROW][C]44[/C][C]1643[/C][C]2377.99734193208[/C][C]-734.997341932077[/C][/ROW]
[ROW][C]45[/C][C]4734[/C][C]4262.99823563221[/C][C]471.001764367787[/C][/ROW]
[ROW][C]46[/C][C]5428[/C][C]6048.21133711549[/C][C]-620.21133711549[/C][/ROW]
[ROW][C]47[/C][C]8314[/C][C]8632.15450989888[/C][C]-318.154509898883[/C][/ROW]
[ROW][C]48[/C][C]10651[/C][C]10513.2537071004[/C][C]137.74629289957[/C][/ROW]
[ROW][C]49[/C][C]3633[/C][C]4803.64341602592[/C][C]-1170.64341602592[/C][/ROW]
[ROW][C]50[/C][C]4292[/C][C]3549.8333992673[/C][C]742.166600732702[/C][/ROW]
[ROW][C]51[/C][C]4154[/C][C]4456.01782046898[/C][C]-302.017820468982[/C][/ROW]
[ROW][C]52[/C][C]4121[/C][C]4752.11165747155[/C][C]-631.111657471546[/C][/ROW]
[ROW][C]53[/C][C]4647[/C][C]5057.35921811475[/C][C]-410.359218114747[/C][/ROW]
[ROW][C]54[/C][C]4753[/C][C]4776.88814941631[/C][C]-23.888149416307[/C][/ROW]
[ROW][C]55[/C][C]3965[/C][C]3903.78098141118[/C][C]61.2190185888244[/C][/ROW]
[ROW][C]56[/C][C]1723[/C][C]2186.57995221726[/C][C]-463.579952217257[/C][/ROW]
[ROW][C]57[/C][C]5048[/C][C]4735.44973133142[/C][C]312.550268668577[/C][/ROW]
[ROW][C]58[/C][C]6923[/C][C]6088.11011265394[/C][C]834.88988734606[/C][/ROW]
[ROW][C]59[/C][C]9858[/C][C]9004.22351387919[/C][C]853.77648612081[/C][/ROW]
[ROW][C]60[/C][C]11331[/C][C]11240.7296594008[/C][C]90.2703405991979[/C][/ROW]
[ROW][C]61[/C][C]4016[/C][C]4557.17612771076[/C][C]-541.176127710756[/C][/ROW]
[ROW][C]62[/C][C]3957[/C][C]4116.08279119259[/C][C]-159.082791192587[/C][/ROW]
[ROW][C]63[/C][C]4510[/C][C]4545.77811521034[/C][C]-35.7781152103371[/C][/ROW]
[ROW][C]64[/C][C]4276[/C][C]4706.3851694402[/C][C]-430.3851694402[/C][/ROW]
[ROW][C]65[/C][C]4968[/C][C]5124.26571975536[/C][C]-156.265719755356[/C][/ROW]
[ROW][C]66[/C][C]4677[/C][C]5005.43847633557[/C][C]-328.438476335567[/C][/ROW]
[ROW][C]67[/C][C]3523[/C][C]4106.88558389211[/C][C]-583.88558389211[/C][/ROW]
[ROW][C]68[/C][C]1821[/C][C]2054.40221049811[/C][C]-233.402210498113[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121818&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121818&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
1325412393.50833868648147.491661313524
1424752352.71674743204122.283252567958
1530312909.94895616264121.051043837358
1632663143.69713027014122.302869729856
1737763628.34529602076147.654703979244
1832303064.23475525313165.765244746867
1930282423.0330404558604.966959544204
2017592419.06012184961-660.060121849606
2135953191.03786233196403.962137668041
2244744729.88256768319-255.882567683188
2368386291.64062789902546.359372100982
2483577810.17732415066546.822675849338
2531132867.70568146713245.294318532867
2630062817.92641705209188.073582947914
2740473481.96781679856565.032183201442
2835233789.84617732456-266.846177324564
2939374369.59721924909-432.597219249086
3039863695.31439670542290.685603294582
3132603166.9860069591593.0139930408532
3215732497.69029989874-924.690299898737
3335283918.88531217404-390.885312174042
3452115318.31789454648-107.317894546477
3576147503.12819436748110.871805632515
3692549194.5318414344159.4681585655926
3753753377.049325929011997.95067407099
3830883363.09759626089-275.097596260895
3937184291.02816634234-573.028166342339
4045144173.03737217756340.96262782244
4145204772.1122244441-252.112224444103
4245394360.09627193035178.903728069648
4336633649.6268581404513.3731418595548
4416432377.99734193208-734.997341932077
4547344262.99823563221471.001764367787
4654286048.21133711549-620.21133711549
4783148632.15450989888-318.154509898883
481065110513.2537071004137.74629289957
4936334803.64341602592-1170.64341602592
5042923549.8333992673742.166600732702
5141544456.01782046898-302.017820468982
5241214752.11165747155-631.111657471546
5346475057.35921811475-410.359218114747
5447534776.88814941631-23.888149416307
5539653903.7809814111861.2190185888244
5617232186.57995221726-463.579952217257
5750484735.44973133142312.550268668577
5869236088.11011265394834.88988734606
5998589004.22351387919853.77648612081
601133111240.729659400890.2703405991979
6140164557.17612771076-541.176127710756
6239574116.08279119259-159.082791192587
6345104545.77811521034-35.7781152103371
6442764706.3851694402-430.3851694402
6549685124.26571975536-156.265719755356
6646775005.43847633557-328.438476335567
6735234106.88558389211-583.88558389211
6818212054.40221049811-233.402210498113







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
695042.575959912664565.48783734875519.66408247662
706632.943381878836151.260104107677114.62665964998
719545.872861763039050.3989545550210041.346768971
7211387.024396867910871.959885587111902.0889081488
734340.416921586483855.55562440544825.27821876755
744065.31697605093577.311550435694553.32240166612
754539.179601978214041.771247482135036.5879564743
764513.748166477884008.988050984655018.5082819711
775052.229927039024529.579386771345574.8804673067
784851.87892162314321.173772015015382.58407123118
793847.024375292663326.932496422724367.1162541626
801959.243780722991830.566270013362087.92129143262

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
69 & 5042.57595991266 & 4565.4878373487 & 5519.66408247662 \tabularnewline
70 & 6632.94338187883 & 6151.26010410767 & 7114.62665964998 \tabularnewline
71 & 9545.87286176303 & 9050.39895455502 & 10041.346768971 \tabularnewline
72 & 11387.0243968679 & 10871.9598855871 & 11902.0889081488 \tabularnewline
73 & 4340.41692158648 & 3855.5556244054 & 4825.27821876755 \tabularnewline
74 & 4065.3169760509 & 3577.31155043569 & 4553.32240166612 \tabularnewline
75 & 4539.17960197821 & 4041.77124748213 & 5036.5879564743 \tabularnewline
76 & 4513.74816647788 & 4008.98805098465 & 5018.5082819711 \tabularnewline
77 & 5052.22992703902 & 4529.57938677134 & 5574.8804673067 \tabularnewline
78 & 4851.8789216231 & 4321.17377201501 & 5382.58407123118 \tabularnewline
79 & 3847.02437529266 & 3326.93249642272 & 4367.1162541626 \tabularnewline
80 & 1959.24378072299 & 1830.56627001336 & 2087.92129143262 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121818&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]69[/C][C]5042.57595991266[/C][C]4565.4878373487[/C][C]5519.66408247662[/C][/ROW]
[ROW][C]70[/C][C]6632.94338187883[/C][C]6151.26010410767[/C][C]7114.62665964998[/C][/ROW]
[ROW][C]71[/C][C]9545.87286176303[/C][C]9050.39895455502[/C][C]10041.346768971[/C][/ROW]
[ROW][C]72[/C][C]11387.0243968679[/C][C]10871.9598855871[/C][C]11902.0889081488[/C][/ROW]
[ROW][C]73[/C][C]4340.41692158648[/C][C]3855.5556244054[/C][C]4825.27821876755[/C][/ROW]
[ROW][C]74[/C][C]4065.3169760509[/C][C]3577.31155043569[/C][C]4553.32240166612[/C][/ROW]
[ROW][C]75[/C][C]4539.17960197821[/C][C]4041.77124748213[/C][C]5036.5879564743[/C][/ROW]
[ROW][C]76[/C][C]4513.74816647788[/C][C]4008.98805098465[/C][C]5018.5082819711[/C][/ROW]
[ROW][C]77[/C][C]5052.22992703902[/C][C]4529.57938677134[/C][C]5574.8804673067[/C][/ROW]
[ROW][C]78[/C][C]4851.8789216231[/C][C]4321.17377201501[/C][C]5382.58407123118[/C][/ROW]
[ROW][C]79[/C][C]3847.02437529266[/C][C]3326.93249642272[/C][C]4367.1162541626[/C][/ROW]
[ROW][C]80[/C][C]1959.24378072299[/C][C]1830.56627001336[/C][C]2087.92129143262[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121818&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121818&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
695042.575959912664565.48783734875519.66408247662
706632.943381878836151.260104107677114.62665964998
719545.872861763039050.3989545550210041.346768971
7211387.024396867910871.959885587111902.0889081488
734340.416921586483855.55562440544825.27821876755
744065.31697605093577.311550435694553.32240166612
754539.179601978214041.771247482135036.5879564743
764513.748166477884008.988050984655018.5082819711
775052.229927039024529.579386771345574.8804673067
784851.87892162314321.173772015015382.58407123118
793847.024375292663326.932496422724367.1162541626
801959.243780722991830.566270013362087.92129143262



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')