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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 19 Jan 2010 05:11:12 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/19/t12639031402vf4nh6oeqzc363.htm/, Retrieved Thu, 02 May 2024 05:57:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72287, Retrieved Thu, 02 May 2024 05:57:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact229

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Nieuwe personenwa...] [2009-01-13 17:37:29] [74be16979710d4c4e7c6647856088456]
-       [Classical Decomposition] [roger dirkx oefen...] [2009-01-14 16:39:03] [74be16979710d4c4e7c6647856088456]
- RMP     [Exponential Smoothing] [roger dirkx oef 10] [2009-01-24 20:53:30] [74be16979710d4c4e7c6647856088456]
-           [Exponential Smoothing] [Dennis Collin oef 10] [2009-01-25 12:25:31] [2097edf1f094fab6879a8cb46df74ec2]
-             [Exponential Smoothing] [Dennis Collin oef 2] [2009-01-25 12:34:26] [2097edf1f094fab6879a8cb46df74ec2]
-               [Exponential Smoothing] [Dennis Collin oef 10] [2009-01-25 12:39:06] [2097edf1f094fab6879a8cb46df74ec2]
- RM D            [Exponential Smoothing] [exponential smoot...] [2010-01-19 12:03:37] [74be16979710d4c4e7c6647856088456]
-    D                [Exponential Smoothing] [Exponential smoot...] [2010-01-19 12:11:12] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
 2357402 
 2199181 
 2603060 
 2629720 
 2638792 
 2717481 
 3810804 
 3871664 
 2998364 
 2923432 
 2712359 
 2996099 
 2395029 
 2483862 
 3120231 
 3360606 
 3177203 
 3062783 
 4242509 
 4026394 
 3192481 
 3118695 
 2782482 
 3209833 
 2630190 
 2592882 
 3785309 
 3231539 
 3421369 
 3312134 
 4647303 
 4289177 
 3463853 
 3304422 
 3006121 
 3464238 
 2921118 
 2624018 
 3500718 
 3939351 
 3467672 
 3343628 
 4852445 
 4597807 
 3653145 
 3572079 
 3334861 
 3695369 
 3075704 
 2852998 
 3942704 
 4004560 
 3822145 
 3760085 
 5267816 
 5271333 
 4144142 
 4109749 
 3896808 
 4211074 
 3402318 
 3279817 
 4706628 
 4079499 
 4344530 
 4048625 
 5394915 
 5611967 
 4145481 
 4025610 
 3552218 
 3910443

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72287&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72287&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72287&T=0

As an alternative you can also use a QR Code:  
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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.322318927826622
beta0
gamma0.338239344476265

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.322318927826622 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.338239344476265 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72287&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]0.322318927826622[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.338239344476265[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72287&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72287&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.322318927826622
beta0
gamma0.338239344476265






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1323950292203500.6160181191528.383981902
1424838622354144.51729817129717.482701827
1531202313024971.3267128595259.6732871505
1633606063305337.886340355268.1136596985
1731772033160208.7330710816994.2669289159
1830627833068546.80818926-5763.80818926031
1942425094251562.93097811-9053.9309781082
2040263944335650.44624688-309256.446246878
2131924813272999.23247284-80518.2324728402
2231186953139278.4121909-20583.4121909016
2327824822881878.36115006-99396.3611500566
2432098333138729.5466627971103.4533372121
2526301902572471.7965466857718.2034533215
2625928822671481.48897259-78599.488972587
2737853093320809.75094113464499.249058865
2832315393737656.90952928-506117.909529283
2934213693388407.3873309232961.6126690833
3033121343287221.187959824912.8120402023
3146473034565262.4793934682040.5206065373
3242891774606439.06063027-317262.060630268
3334638533516916.71738083-53063.7173808296
3433044223395459.5595987-91037.5595986987
3530061213074556.92854807-68435.9285480664
3634642383404200.5515514960037.4484485136
3729211182783641.23042907137476.769570934
3826240182879134.50493975-255116.504939751
3935007183640546.3209408-139828.320940798
4039393513634876.18096818304474.819031818
4134676723663130.60759224-195458.607592242
4233436283478396.57140973-134768.571409733
4348524454768456.2660886683988.7339113439
4445978074712411.15555613-114604.155556130
4536531453696038.55611583-42893.5561158336
4635720793561063.1040994211015.8959005778
4733348613257637.313101677223.6868984029
4836953693692096.490547813272.50945219304
4930757043022407.6046456653296.3953543375
5028529982995061.36786489-142063.367864885
5139427043883588.3753776959115.6246223105
5240045604052379.9997273-47819.9997273041
5338221453838502.99915632-16357.9991563158
5437600853714367.8875101845717.1124898195
5552678165241009.3896573626806.6103426442
5652713335105758.50216002165574.497839981
5741441424087212.263482356929.736517698
5841097493980562.71638617129186.283613828
5938968083689704.6973044207103.302695602
6042110744199356.8994078111717.1005921895
6134023183449644.37776311-47326.3777631079
6232798173330476.98177587-50659.9817758738
6347066284424002.23306473282625.766935269
6440794994654716.02486776-575217.024867761
6543445304253790.1263649590739.873635048
6640486254162635.76029505-114010.760295053
6753949155785139.51096908-390224.510969085
6856119675535331.2369605576635.7630394455
6941454814384473.44600513-238992.446005126
7040256104192393.20272735-166783.202727349
7135522183815830.19195126-263612.191951261
7239104434121881.72220775-211438.722207753

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2395029 & 2203500.6160181 & 191528.383981902 \tabularnewline
14 & 2483862 & 2354144.51729817 & 129717.482701827 \tabularnewline
15 & 3120231 & 3024971.32671285 & 95259.6732871505 \tabularnewline
16 & 3360606 & 3305337.8863403 & 55268.1136596985 \tabularnewline
17 & 3177203 & 3160208.73307108 & 16994.2669289159 \tabularnewline
18 & 3062783 & 3068546.80818926 & -5763.80818926031 \tabularnewline
19 & 4242509 & 4251562.93097811 & -9053.9309781082 \tabularnewline
20 & 4026394 & 4335650.44624688 & -309256.446246878 \tabularnewline
21 & 3192481 & 3272999.23247284 & -80518.2324728402 \tabularnewline
22 & 3118695 & 3139278.4121909 & -20583.4121909016 \tabularnewline
23 & 2782482 & 2881878.36115006 & -99396.3611500566 \tabularnewline
24 & 3209833 & 3138729.54666279 & 71103.4533372121 \tabularnewline
25 & 2630190 & 2572471.79654668 & 57718.2034533215 \tabularnewline
26 & 2592882 & 2671481.48897259 & -78599.488972587 \tabularnewline
27 & 3785309 & 3320809.75094113 & 464499.249058865 \tabularnewline
28 & 3231539 & 3737656.90952928 & -506117.909529283 \tabularnewline
29 & 3421369 & 3388407.38733092 & 32961.6126690833 \tabularnewline
30 & 3312134 & 3287221.1879598 & 24912.8120402023 \tabularnewline
31 & 4647303 & 4565262.47939346 & 82040.5206065373 \tabularnewline
32 & 4289177 & 4606439.06063027 & -317262.060630268 \tabularnewline
33 & 3463853 & 3516916.71738083 & -53063.7173808296 \tabularnewline
34 & 3304422 & 3395459.5595987 & -91037.5595986987 \tabularnewline
35 & 3006121 & 3074556.92854807 & -68435.9285480664 \tabularnewline
36 & 3464238 & 3404200.55155149 & 60037.4484485136 \tabularnewline
37 & 2921118 & 2783641.23042907 & 137476.769570934 \tabularnewline
38 & 2624018 & 2879134.50493975 & -255116.504939751 \tabularnewline
39 & 3500718 & 3640546.3209408 & -139828.320940798 \tabularnewline
40 & 3939351 & 3634876.18096818 & 304474.819031818 \tabularnewline
41 & 3467672 & 3663130.60759224 & -195458.607592242 \tabularnewline
42 & 3343628 & 3478396.57140973 & -134768.571409733 \tabularnewline
43 & 4852445 & 4768456.26608866 & 83988.7339113439 \tabularnewline
44 & 4597807 & 4712411.15555613 & -114604.155556130 \tabularnewline
45 & 3653145 & 3696038.55611583 & -42893.5561158336 \tabularnewline
46 & 3572079 & 3561063.10409942 & 11015.8959005778 \tabularnewline
47 & 3334861 & 3257637.3131016 & 77223.6868984029 \tabularnewline
48 & 3695369 & 3692096.49054781 & 3272.50945219304 \tabularnewline
49 & 3075704 & 3022407.60464566 & 53296.3953543375 \tabularnewline
50 & 2852998 & 2995061.36786489 & -142063.367864885 \tabularnewline
51 & 3942704 & 3883588.37537769 & 59115.6246223105 \tabularnewline
52 & 4004560 & 4052379.9997273 & -47819.9997273041 \tabularnewline
53 & 3822145 & 3838502.99915632 & -16357.9991563158 \tabularnewline
54 & 3760085 & 3714367.88751018 & 45717.1124898195 \tabularnewline
55 & 5267816 & 5241009.38965736 & 26806.6103426442 \tabularnewline
56 & 5271333 & 5105758.50216002 & 165574.497839981 \tabularnewline
57 & 4144142 & 4087212.2634823 & 56929.736517698 \tabularnewline
58 & 4109749 & 3980562.71638617 & 129186.283613828 \tabularnewline
59 & 3896808 & 3689704.6973044 & 207103.302695602 \tabularnewline
60 & 4211074 & 4199356.89940781 & 11717.1005921895 \tabularnewline
61 & 3402318 & 3449644.37776311 & -47326.3777631079 \tabularnewline
62 & 3279817 & 3330476.98177587 & -50659.9817758738 \tabularnewline
63 & 4706628 & 4424002.23306473 & 282625.766935269 \tabularnewline
64 & 4079499 & 4654716.02486776 & -575217.024867761 \tabularnewline
65 & 4344530 & 4253790.12636495 & 90739.873635048 \tabularnewline
66 & 4048625 & 4162635.76029505 & -114010.760295053 \tabularnewline
67 & 5394915 & 5785139.51096908 & -390224.510969085 \tabularnewline
68 & 5611967 & 5535331.23696055 & 76635.7630394455 \tabularnewline
69 & 4145481 & 4384473.44600513 & -238992.446005126 \tabularnewline
70 & 4025610 & 4192393.20272735 & -166783.202727349 \tabularnewline
71 & 3552218 & 3815830.19195126 & -263612.191951261 \tabularnewline
72 & 3910443 & 4121881.72220775 & -211438.722207753 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72287&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]2395029[/C][C]2203500.6160181[/C][C]191528.383981902[/C][/ROW]
[ROW][C]14[/C][C]2483862[/C][C]2354144.51729817[/C][C]129717.482701827[/C][/ROW]
[ROW][C]15[/C][C]3120231[/C][C]3024971.32671285[/C][C]95259.6732871505[/C][/ROW]
[ROW][C]16[/C][C]3360606[/C][C]3305337.8863403[/C][C]55268.1136596985[/C][/ROW]
[ROW][C]17[/C][C]3177203[/C][C]3160208.73307108[/C][C]16994.2669289159[/C][/ROW]
[ROW][C]18[/C][C]3062783[/C][C]3068546.80818926[/C][C]-5763.80818926031[/C][/ROW]
[ROW][C]19[/C][C]4242509[/C][C]4251562.93097811[/C][C]-9053.9309781082[/C][/ROW]
[ROW][C]20[/C][C]4026394[/C][C]4335650.44624688[/C][C]-309256.446246878[/C][/ROW]
[ROW][C]21[/C][C]3192481[/C][C]3272999.23247284[/C][C]-80518.2324728402[/C][/ROW]
[ROW][C]22[/C][C]3118695[/C][C]3139278.4121909[/C][C]-20583.4121909016[/C][/ROW]
[ROW][C]23[/C][C]2782482[/C][C]2881878.36115006[/C][C]-99396.3611500566[/C][/ROW]
[ROW][C]24[/C][C]3209833[/C][C]3138729.54666279[/C][C]71103.4533372121[/C][/ROW]
[ROW][C]25[/C][C]2630190[/C][C]2572471.79654668[/C][C]57718.2034533215[/C][/ROW]
[ROW][C]26[/C][C]2592882[/C][C]2671481.48897259[/C][C]-78599.488972587[/C][/ROW]
[ROW][C]27[/C][C]3785309[/C][C]3320809.75094113[/C][C]464499.249058865[/C][/ROW]
[ROW][C]28[/C][C]3231539[/C][C]3737656.90952928[/C][C]-506117.909529283[/C][/ROW]
[ROW][C]29[/C][C]3421369[/C][C]3388407.38733092[/C][C]32961.6126690833[/C][/ROW]
[ROW][C]30[/C][C]3312134[/C][C]3287221.1879598[/C][C]24912.8120402023[/C][/ROW]
[ROW][C]31[/C][C]4647303[/C][C]4565262.47939346[/C][C]82040.5206065373[/C][/ROW]
[ROW][C]32[/C][C]4289177[/C][C]4606439.06063027[/C][C]-317262.060630268[/C][/ROW]
[ROW][C]33[/C][C]3463853[/C][C]3516916.71738083[/C][C]-53063.7173808296[/C][/ROW]
[ROW][C]34[/C][C]3304422[/C][C]3395459.5595987[/C][C]-91037.5595986987[/C][/ROW]
[ROW][C]35[/C][C]3006121[/C][C]3074556.92854807[/C][C]-68435.9285480664[/C][/ROW]
[ROW][C]36[/C][C]3464238[/C][C]3404200.55155149[/C][C]60037.4484485136[/C][/ROW]
[ROW][C]37[/C][C]2921118[/C][C]2783641.23042907[/C][C]137476.769570934[/C][/ROW]
[ROW][C]38[/C][C]2624018[/C][C]2879134.50493975[/C][C]-255116.504939751[/C][/ROW]
[ROW][C]39[/C][C]3500718[/C][C]3640546.3209408[/C][C]-139828.320940798[/C][/ROW]
[ROW][C]40[/C][C]3939351[/C][C]3634876.18096818[/C][C]304474.819031818[/C][/ROW]
[ROW][C]41[/C][C]3467672[/C][C]3663130.60759224[/C][C]-195458.607592242[/C][/ROW]
[ROW][C]42[/C][C]3343628[/C][C]3478396.57140973[/C][C]-134768.571409733[/C][/ROW]
[ROW][C]43[/C][C]4852445[/C][C]4768456.26608866[/C][C]83988.7339113439[/C][/ROW]
[ROW][C]44[/C][C]4597807[/C][C]4712411.15555613[/C][C]-114604.155556130[/C][/ROW]
[ROW][C]45[/C][C]3653145[/C][C]3696038.55611583[/C][C]-42893.5561158336[/C][/ROW]
[ROW][C]46[/C][C]3572079[/C][C]3561063.10409942[/C][C]11015.8959005778[/C][/ROW]
[ROW][C]47[/C][C]3334861[/C][C]3257637.3131016[/C][C]77223.6868984029[/C][/ROW]
[ROW][C]48[/C][C]3695369[/C][C]3692096.49054781[/C][C]3272.50945219304[/C][/ROW]
[ROW][C]49[/C][C]3075704[/C][C]3022407.60464566[/C][C]53296.3953543375[/C][/ROW]
[ROW][C]50[/C][C]2852998[/C][C]2995061.36786489[/C][C]-142063.367864885[/C][/ROW]
[ROW][C]51[/C][C]3942704[/C][C]3883588.37537769[/C][C]59115.6246223105[/C][/ROW]
[ROW][C]52[/C][C]4004560[/C][C]4052379.9997273[/C][C]-47819.9997273041[/C][/ROW]
[ROW][C]53[/C][C]3822145[/C][C]3838502.99915632[/C][C]-16357.9991563158[/C][/ROW]
[ROW][C]54[/C][C]3760085[/C][C]3714367.88751018[/C][C]45717.1124898195[/C][/ROW]
[ROW][C]55[/C][C]5267816[/C][C]5241009.38965736[/C][C]26806.6103426442[/C][/ROW]
[ROW][C]56[/C][C]5271333[/C][C]5105758.50216002[/C][C]165574.497839981[/C][/ROW]
[ROW][C]57[/C][C]4144142[/C][C]4087212.2634823[/C][C]56929.736517698[/C][/ROW]
[ROW][C]58[/C][C]4109749[/C][C]3980562.71638617[/C][C]129186.283613828[/C][/ROW]
[ROW][C]59[/C][C]3896808[/C][C]3689704.6973044[/C][C]207103.302695602[/C][/ROW]
[ROW][C]60[/C][C]4211074[/C][C]4199356.89940781[/C][C]11717.1005921895[/C][/ROW]
[ROW][C]61[/C][C]3402318[/C][C]3449644.37776311[/C][C]-47326.3777631079[/C][/ROW]
[ROW][C]62[/C][C]3279817[/C][C]3330476.98177587[/C][C]-50659.9817758738[/C][/ROW]
[ROW][C]63[/C][C]4706628[/C][C]4424002.23306473[/C][C]282625.766935269[/C][/ROW]
[ROW][C]64[/C][C]4079499[/C][C]4654716.02486776[/C][C]-575217.024867761[/C][/ROW]
[ROW][C]65[/C][C]4344530[/C][C]4253790.12636495[/C][C]90739.873635048[/C][/ROW]
[ROW][C]66[/C][C]4048625[/C][C]4162635.76029505[/C][C]-114010.760295053[/C][/ROW]
[ROW][C]67[/C][C]5394915[/C][C]5785139.51096908[/C][C]-390224.510969085[/C][/ROW]
[ROW][C]68[/C][C]5611967[/C][C]5535331.23696055[/C][C]76635.7630394455[/C][/ROW]
[ROW][C]69[/C][C]4145481[/C][C]4384473.44600513[/C][C]-238992.446005126[/C][/ROW]
[ROW][C]70[/C][C]4025610[/C][C]4192393.20272735[/C][C]-166783.202727349[/C][/ROW]
[ROW][C]71[/C][C]3552218[/C][C]3815830.19195126[/C][C]-263612.191951261[/C][/ROW]
[ROW][C]72[/C][C]3910443[/C][C]4121881.72220775[/C][C]-211438.722207753[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72287&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72287&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1323950292203500.6160181191528.383981902
1424838622354144.51729817129717.482701827
1531202313024971.3267128595259.6732871505
1633606063305337.886340355268.1136596985
1731772033160208.7330710816994.2669289159
1830627833068546.80818926-5763.80818926031
1942425094251562.93097811-9053.9309781082
2040263944335650.44624688-309256.446246878
2131924813272999.23247284-80518.2324728402
2231186953139278.4121909-20583.4121909016
2327824822881878.36115006-99396.3611500566
2432098333138729.5466627971103.4533372121
2526301902572471.7965466857718.2034533215
2625928822671481.48897259-78599.488972587
2737853093320809.75094113464499.249058865
2832315393737656.90952928-506117.909529283
2934213693388407.3873309232961.6126690833
3033121343287221.187959824912.8120402023
3146473034565262.4793934682040.5206065373
3242891774606439.06063027-317262.060630268
3334638533516916.71738083-53063.7173808296
3433044223395459.5595987-91037.5595986987
3530061213074556.92854807-68435.9285480664
3634642383404200.5515514960037.4484485136
3729211182783641.23042907137476.769570934
3826240182879134.50493975-255116.504939751
3935007183640546.3209408-139828.320940798
4039393513634876.18096818304474.819031818
4134676723663130.60759224-195458.607592242
4233436283478396.57140973-134768.571409733
4348524454768456.2660886683988.7339113439
4445978074712411.15555613-114604.155556130
4536531453696038.55611583-42893.5561158336
4635720793561063.1040994211015.8959005778
4733348613257637.313101677223.6868984029
4836953693692096.490547813272.50945219304
4930757043022407.6046456653296.3953543375
5028529982995061.36786489-142063.367864885
5139427043883588.3753776959115.6246223105
5240045604052379.9997273-47819.9997273041
5338221453838502.99915632-16357.9991563158
5437600853714367.8875101845717.1124898195
5552678165241009.3896573626806.6103426442
5652713335105758.50216002165574.497839981
5741441424087212.263482356929.736517698
5841097493980562.71638617129186.283613828
5938968083689704.6973044207103.302695602
6042110744199356.8994078111717.1005921895
6134023183449644.37776311-47326.3777631079
6232798173330476.98177587-50659.9817758738
6347066284424002.23306473282625.766935269
6440794994654716.02486776-575217.024867761
6543445304253790.1263649590739.873635048
6640486254162635.76029505-114010.760295053
6753949155785139.51096908-390224.510969085
6856119675535331.2369605576635.7630394455
6941454814384473.44600513-238992.446005126
7040256104192393.20272735-166783.202727349
7135522183815830.19195126-263612.191951261
7239104434121881.72220775-211438.722207753






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
733315247.210850823119057.917799253511436.50390239
743214540.737947672989427.679370133439653.79652520
754368723.172181814077817.834884734659628.50947889
764310497.429948964001622.091424964619372.76847296
774248056.039454333923094.055994994573018.02291366
784083022.852643733748926.586172684417119.11911478
795670625.309327995220459.544059196120791.07459679
805652529.96486495191774.794685886113285.13504393
814386470.64099733999729.449053114773211.83294148
824283465.140892233889287.067062444677643.21472202
833920467.149722063538392.917737484302541.38170663
844348079.372324933965400.054432534730758.69021734

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 3315247.21085082 & 3119057.91779925 & 3511436.50390239 \tabularnewline
74 & 3214540.73794767 & 2989427.67937013 & 3439653.79652520 \tabularnewline
75 & 4368723.17218181 & 4077817.83488473 & 4659628.50947889 \tabularnewline
76 & 4310497.42994896 & 4001622.09142496 & 4619372.76847296 \tabularnewline
77 & 4248056.03945433 & 3923094.05599499 & 4573018.02291366 \tabularnewline
78 & 4083022.85264373 & 3748926.58617268 & 4417119.11911478 \tabularnewline
79 & 5670625.30932799 & 5220459.54405919 & 6120791.07459679 \tabularnewline
80 & 5652529.9648649 & 5191774.79468588 & 6113285.13504393 \tabularnewline
81 & 4386470.6409973 & 3999729.44905311 & 4773211.83294148 \tabularnewline
82 & 4283465.14089223 & 3889287.06706244 & 4677643.21472202 \tabularnewline
83 & 3920467.14972206 & 3538392.91773748 & 4302541.38170663 \tabularnewline
84 & 4348079.37232493 & 3965400.05443253 & 4730758.69021734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72287&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]3315247.21085082[/C][C]3119057.91779925[/C][C]3511436.50390239[/C][/ROW]
[ROW][C]74[/C][C]3214540.73794767[/C][C]2989427.67937013[/C][C]3439653.79652520[/C][/ROW]
[ROW][C]75[/C][C]4368723.17218181[/C][C]4077817.83488473[/C][C]4659628.50947889[/C][/ROW]
[ROW][C]76[/C][C]4310497.42994896[/C][C]4001622.09142496[/C][C]4619372.76847296[/C][/ROW]
[ROW][C]77[/C][C]4248056.03945433[/C][C]3923094.05599499[/C][C]4573018.02291366[/C][/ROW]
[ROW][C]78[/C][C]4083022.85264373[/C][C]3748926.58617268[/C][C]4417119.11911478[/C][/ROW]
[ROW][C]79[/C][C]5670625.30932799[/C][C]5220459.54405919[/C][C]6120791.07459679[/C][/ROW]
[ROW][C]80[/C][C]5652529.9648649[/C][C]5191774.79468588[/C][C]6113285.13504393[/C][/ROW]
[ROW][C]81[/C][C]4386470.6409973[/C][C]3999729.44905311[/C][C]4773211.83294148[/C][/ROW]
[ROW][C]82[/C][C]4283465.14089223[/C][C]3889287.06706244[/C][C]4677643.21472202[/C][/ROW]
[ROW][C]83[/C][C]3920467.14972206[/C][C]3538392.91773748[/C][C]4302541.38170663[/C][/ROW]
[ROW][C]84[/C][C]4348079.37232493[/C][C]3965400.05443253[/C][C]4730758.69021734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72287&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72287&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
733315247.210850823119057.917799253511436.50390239
743214540.737947672989427.679370133439653.79652520
754368723.172181814077817.834884734659628.50947889
764310497.429948964001622.091424964619372.76847296
774248056.039454333923094.055994994573018.02291366
784083022.852643733748926.586172684417119.11911478
795670625.309327995220459.544059196120791.07459679
805652529.96486495191774.794685886113285.13504393
814386470.64099733999729.449053114773211.83294148
824283465.140892233889287.067062444677643.21472202
833920467.149722063538392.917737484302541.38170663
844348079.372324933965400.054432534730758.69021734


Figures (Output of Computation)

Input Parameters & R Code

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')