Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 12 May 2014 07:26:36 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/12/t1399894019yv0ftipdceklns4.htm/, Retrieved Wed, 15 May 2024 09:31:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234811, Retrieved Wed, 15 May 2024 09:31:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-05-12 11:26:36] [941d89646656d1688f5e273fb31a8e6b] [Current]
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Dataseries X:
8584
5522
6423
5173
5583
5716
4752
4977
4999
5285
5747
1713
9923
6737
7433
6388
6855
7658
6585
6847
6353
7361
6929
1714
11798
8378
8131
7676
7505
8168
6455
6141
6554
6888
5339
1624
9187
5047
5289
4169
3862
4253
3768
3066
4108
3890
3420
1221
5984
4064
5151
4027
3530
4819
3855
3584
4322
4154
4656
1464
7780
5060
6084
4778
4989
4903
4142
4101
4595
5034
5407
1782
8395
5291
6116
4210
4621
5299
4293
4542
3831
4360
4088
1508




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234811&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234811&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234811&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.233420479852583
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.233420479852583 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234811&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]0.233420479852583[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234811&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234811&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
alpha0.233420479852583
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
255228584-3062
364237869.26649069139-1446.26649069139
451737531.6782724395-2358.6782724395
555836981.11445826881-1398.11445826881
657166654.76591053087-938.765910530868
747526435.63872122551-1683.63872122551
849776042.64296301866-1065.64296301866
949995793.90007123932-794.900071239316
1052855608.35411517578-323.354115175783
1157475532.87664244914214.123357550856
1217135582.85741931631-3869.85741931631
1399234679.553443538425243.44655646158
1467375903.48125482905833.518745170945
1574336098.041600292981334.95839970702
1663886409.64823053583-21.6482305358286
1768556404.5950901762450.404909823804
1876586509.728820355231148.27117964477
1965856777.7588301088-192.758830108802
2068476732.76497148898114.235028511017
2163536759.42976666-406.429766659998
2273616664.56073549985696.439264500153
2369296827.12392280765101.876077192347
2417146850.90388563139-5136.90388563139
25117985651.845315690716146.15468430929
2683787086.483691350391291.51630864961
2781317387.95004785282743.049952147185
2876767561.39312423745114.60687576255
2975057588.14471617235-83.1447161723499
3081687568.73703662619599.262963373807
3164557708.61728509479-1253.61728509479
3261417415.99733685647-1274.99733685647
3365547118.38684667667-564.386846676668
3468886986.64739810291-98.6473981029139
3553396963.62107510152-1624.62107510152
3616246584.40124417271-4960.40124417271
3791875426.542005496563760.45799450344
3850476304.30991503904-1257.30991503904
3952896010.82803134722-721.828031347215
4041695842.3385858991-1673.3385858991
4138625451.74709022269-1589.74709022269
4242535080.66756157866-827.667561578664
4337684887.47300219656-1119.47300219656
4430664626.16507684182-1560.16507684182
4541084261.99059595616-153.990595956164
4638904226.04603715529-336.046037155291
4734204147.60600990994-727.606009909944
4812213977.76786593314-2756.76786593314
4959843334.281787824852649.71821217515
5040643952.7802843849111.219715615101
5151513978.741243772841172.25875622716
5240274252.37044516278-225.370445162778
5335304199.76436770829-669.764367708292
5448194043.42764760966775.572352390339
5538554224.46211826501-369.462118265011
5635844138.22209333224-554.222093332241
5743224008.85530636173313.144693638274
5841544081.9496910140672.050308985938
5946564098.76770871109557.232291288913
6014644228.8371375331-2764.8371375331
6177803583.467526175884196.53247382412
6250604563.02414993285496.975850067146
6360844679.028491330671404.97150866933
6447785006.97761506347-228.977615063474
6549894953.5295502798635.4704497201419
6649034961.80907967412-58.8090796741208
6741424948.0818360769-806.081836076899
6841014759.92582709938-658.925827099378
6945954606.11904435058-11.1190443505811
7050344603.52363168277430.476368317233
7154074704.00563214057702.994367859427
7217824868.09891481998-3086.09891481998
7383954147.740225250174247.25977474983
7452915139.13763993085151.862360069154
7561165174.58542488973941.414575110266
7642105394.33086675219-1184.33086675219
7746215117.88378753067-496.883787530667
7852995001.90093541429297.09906458571
7942935071.24994163364-778.24994163364
8045424889.59046681227-347.590466812271
8138314808.45573325677-977.455733256767
8243604580.29754696531-220.297546965315
8340884528.87558784232-440.875587842324
8415084425.96619657288-2917.96619657288

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 5522 & 8584 & -3062 \tabularnewline
3 & 6423 & 7869.26649069139 & -1446.26649069139 \tabularnewline
4 & 5173 & 7531.6782724395 & -2358.6782724395 \tabularnewline
5 & 5583 & 6981.11445826881 & -1398.11445826881 \tabularnewline
6 & 5716 & 6654.76591053087 & -938.765910530868 \tabularnewline
7 & 4752 & 6435.63872122551 & -1683.63872122551 \tabularnewline
8 & 4977 & 6042.64296301866 & -1065.64296301866 \tabularnewline
9 & 4999 & 5793.90007123932 & -794.900071239316 \tabularnewline
10 & 5285 & 5608.35411517578 & -323.354115175783 \tabularnewline
11 & 5747 & 5532.87664244914 & 214.123357550856 \tabularnewline
12 & 1713 & 5582.85741931631 & -3869.85741931631 \tabularnewline
13 & 9923 & 4679.55344353842 & 5243.44655646158 \tabularnewline
14 & 6737 & 5903.48125482905 & 833.518745170945 \tabularnewline
15 & 7433 & 6098.04160029298 & 1334.95839970702 \tabularnewline
16 & 6388 & 6409.64823053583 & -21.6482305358286 \tabularnewline
17 & 6855 & 6404.5950901762 & 450.404909823804 \tabularnewline
18 & 7658 & 6509.72882035523 & 1148.27117964477 \tabularnewline
19 & 6585 & 6777.7588301088 & -192.758830108802 \tabularnewline
20 & 6847 & 6732.76497148898 & 114.235028511017 \tabularnewline
21 & 6353 & 6759.42976666 & -406.429766659998 \tabularnewline
22 & 7361 & 6664.56073549985 & 696.439264500153 \tabularnewline
23 & 6929 & 6827.12392280765 & 101.876077192347 \tabularnewline
24 & 1714 & 6850.90388563139 & -5136.90388563139 \tabularnewline
25 & 11798 & 5651.84531569071 & 6146.15468430929 \tabularnewline
26 & 8378 & 7086.48369135039 & 1291.51630864961 \tabularnewline
27 & 8131 & 7387.95004785282 & 743.049952147185 \tabularnewline
28 & 7676 & 7561.39312423745 & 114.60687576255 \tabularnewline
29 & 7505 & 7588.14471617235 & -83.1447161723499 \tabularnewline
30 & 8168 & 7568.73703662619 & 599.262963373807 \tabularnewline
31 & 6455 & 7708.61728509479 & -1253.61728509479 \tabularnewline
32 & 6141 & 7415.99733685647 & -1274.99733685647 \tabularnewline
33 & 6554 & 7118.38684667667 & -564.386846676668 \tabularnewline
34 & 6888 & 6986.64739810291 & -98.6473981029139 \tabularnewline
35 & 5339 & 6963.62107510152 & -1624.62107510152 \tabularnewline
36 & 1624 & 6584.40124417271 & -4960.40124417271 \tabularnewline
37 & 9187 & 5426.54200549656 & 3760.45799450344 \tabularnewline
38 & 5047 & 6304.30991503904 & -1257.30991503904 \tabularnewline
39 & 5289 & 6010.82803134722 & -721.828031347215 \tabularnewline
40 & 4169 & 5842.3385858991 & -1673.3385858991 \tabularnewline
41 & 3862 & 5451.74709022269 & -1589.74709022269 \tabularnewline
42 & 4253 & 5080.66756157866 & -827.667561578664 \tabularnewline
43 & 3768 & 4887.47300219656 & -1119.47300219656 \tabularnewline
44 & 3066 & 4626.16507684182 & -1560.16507684182 \tabularnewline
45 & 4108 & 4261.99059595616 & -153.990595956164 \tabularnewline
46 & 3890 & 4226.04603715529 & -336.046037155291 \tabularnewline
47 & 3420 & 4147.60600990994 & -727.606009909944 \tabularnewline
48 & 1221 & 3977.76786593314 & -2756.76786593314 \tabularnewline
49 & 5984 & 3334.28178782485 & 2649.71821217515 \tabularnewline
50 & 4064 & 3952.7802843849 & 111.219715615101 \tabularnewline
51 & 5151 & 3978.74124377284 & 1172.25875622716 \tabularnewline
52 & 4027 & 4252.37044516278 & -225.370445162778 \tabularnewline
53 & 3530 & 4199.76436770829 & -669.764367708292 \tabularnewline
54 & 4819 & 4043.42764760966 & 775.572352390339 \tabularnewline
55 & 3855 & 4224.46211826501 & -369.462118265011 \tabularnewline
56 & 3584 & 4138.22209333224 & -554.222093332241 \tabularnewline
57 & 4322 & 4008.85530636173 & 313.144693638274 \tabularnewline
58 & 4154 & 4081.94969101406 & 72.050308985938 \tabularnewline
59 & 4656 & 4098.76770871109 & 557.232291288913 \tabularnewline
60 & 1464 & 4228.8371375331 & -2764.8371375331 \tabularnewline
61 & 7780 & 3583.46752617588 & 4196.53247382412 \tabularnewline
62 & 5060 & 4563.02414993285 & 496.975850067146 \tabularnewline
63 & 6084 & 4679.02849133067 & 1404.97150866933 \tabularnewline
64 & 4778 & 5006.97761506347 & -228.977615063474 \tabularnewline
65 & 4989 & 4953.52955027986 & 35.4704497201419 \tabularnewline
66 & 4903 & 4961.80907967412 & -58.8090796741208 \tabularnewline
67 & 4142 & 4948.0818360769 & -806.081836076899 \tabularnewline
68 & 4101 & 4759.92582709938 & -658.925827099378 \tabularnewline
69 & 4595 & 4606.11904435058 & -11.1190443505811 \tabularnewline
70 & 5034 & 4603.52363168277 & 430.476368317233 \tabularnewline
71 & 5407 & 4704.00563214057 & 702.994367859427 \tabularnewline
72 & 1782 & 4868.09891481998 & -3086.09891481998 \tabularnewline
73 & 8395 & 4147.74022525017 & 4247.25977474983 \tabularnewline
74 & 5291 & 5139.13763993085 & 151.862360069154 \tabularnewline
75 & 6116 & 5174.58542488973 & 941.414575110266 \tabularnewline
76 & 4210 & 5394.33086675219 & -1184.33086675219 \tabularnewline
77 & 4621 & 5117.88378753067 & -496.883787530667 \tabularnewline
78 & 5299 & 5001.90093541429 & 297.09906458571 \tabularnewline
79 & 4293 & 5071.24994163364 & -778.24994163364 \tabularnewline
80 & 4542 & 4889.59046681227 & -347.590466812271 \tabularnewline
81 & 3831 & 4808.45573325677 & -977.455733256767 \tabularnewline
82 & 4360 & 4580.29754696531 & -220.297546965315 \tabularnewline
83 & 4088 & 4528.87558784232 & -440.875587842324 \tabularnewline
84 & 1508 & 4425.96619657288 & -2917.96619657288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234811&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]2[/C][C]5522[/C][C]8584[/C][C]-3062[/C][/ROW]
[ROW][C]3[/C][C]6423[/C][C]7869.26649069139[/C][C]-1446.26649069139[/C][/ROW]
[ROW][C]4[/C][C]5173[/C][C]7531.6782724395[/C][C]-2358.6782724395[/C][/ROW]
[ROW][C]5[/C][C]5583[/C][C]6981.11445826881[/C][C]-1398.11445826881[/C][/ROW]
[ROW][C]6[/C][C]5716[/C][C]6654.76591053087[/C][C]-938.765910530868[/C][/ROW]
[ROW][C]7[/C][C]4752[/C][C]6435.63872122551[/C][C]-1683.63872122551[/C][/ROW]
[ROW][C]8[/C][C]4977[/C][C]6042.64296301866[/C][C]-1065.64296301866[/C][/ROW]
[ROW][C]9[/C][C]4999[/C][C]5793.90007123932[/C][C]-794.900071239316[/C][/ROW]
[ROW][C]10[/C][C]5285[/C][C]5608.35411517578[/C][C]-323.354115175783[/C][/ROW]
[ROW][C]11[/C][C]5747[/C][C]5532.87664244914[/C][C]214.123357550856[/C][/ROW]
[ROW][C]12[/C][C]1713[/C][C]5582.85741931631[/C][C]-3869.85741931631[/C][/ROW]
[ROW][C]13[/C][C]9923[/C][C]4679.55344353842[/C][C]5243.44655646158[/C][/ROW]
[ROW][C]14[/C][C]6737[/C][C]5903.48125482905[/C][C]833.518745170945[/C][/ROW]
[ROW][C]15[/C][C]7433[/C][C]6098.04160029298[/C][C]1334.95839970702[/C][/ROW]
[ROW][C]16[/C][C]6388[/C][C]6409.64823053583[/C][C]-21.6482305358286[/C][/ROW]
[ROW][C]17[/C][C]6855[/C][C]6404.5950901762[/C][C]450.404909823804[/C][/ROW]
[ROW][C]18[/C][C]7658[/C][C]6509.72882035523[/C][C]1148.27117964477[/C][/ROW]
[ROW][C]19[/C][C]6585[/C][C]6777.7588301088[/C][C]-192.758830108802[/C][/ROW]
[ROW][C]20[/C][C]6847[/C][C]6732.76497148898[/C][C]114.235028511017[/C][/ROW]
[ROW][C]21[/C][C]6353[/C][C]6759.42976666[/C][C]-406.429766659998[/C][/ROW]
[ROW][C]22[/C][C]7361[/C][C]6664.56073549985[/C][C]696.439264500153[/C][/ROW]
[ROW][C]23[/C][C]6929[/C][C]6827.12392280765[/C][C]101.876077192347[/C][/ROW]
[ROW][C]24[/C][C]1714[/C][C]6850.90388563139[/C][C]-5136.90388563139[/C][/ROW]
[ROW][C]25[/C][C]11798[/C][C]5651.84531569071[/C][C]6146.15468430929[/C][/ROW]
[ROW][C]26[/C][C]8378[/C][C]7086.48369135039[/C][C]1291.51630864961[/C][/ROW]
[ROW][C]27[/C][C]8131[/C][C]7387.95004785282[/C][C]743.049952147185[/C][/ROW]
[ROW][C]28[/C][C]7676[/C][C]7561.39312423745[/C][C]114.60687576255[/C][/ROW]
[ROW][C]29[/C][C]7505[/C][C]7588.14471617235[/C][C]-83.1447161723499[/C][/ROW]
[ROW][C]30[/C][C]8168[/C][C]7568.73703662619[/C][C]599.262963373807[/C][/ROW]
[ROW][C]31[/C][C]6455[/C][C]7708.61728509479[/C][C]-1253.61728509479[/C][/ROW]
[ROW][C]32[/C][C]6141[/C][C]7415.99733685647[/C][C]-1274.99733685647[/C][/ROW]
[ROW][C]33[/C][C]6554[/C][C]7118.38684667667[/C][C]-564.386846676668[/C][/ROW]
[ROW][C]34[/C][C]6888[/C][C]6986.64739810291[/C][C]-98.6473981029139[/C][/ROW]
[ROW][C]35[/C][C]5339[/C][C]6963.62107510152[/C][C]-1624.62107510152[/C][/ROW]
[ROW][C]36[/C][C]1624[/C][C]6584.40124417271[/C][C]-4960.40124417271[/C][/ROW]
[ROW][C]37[/C][C]9187[/C][C]5426.54200549656[/C][C]3760.45799450344[/C][/ROW]
[ROW][C]38[/C][C]5047[/C][C]6304.30991503904[/C][C]-1257.30991503904[/C][/ROW]
[ROW][C]39[/C][C]5289[/C][C]6010.82803134722[/C][C]-721.828031347215[/C][/ROW]
[ROW][C]40[/C][C]4169[/C][C]5842.3385858991[/C][C]-1673.3385858991[/C][/ROW]
[ROW][C]41[/C][C]3862[/C][C]5451.74709022269[/C][C]-1589.74709022269[/C][/ROW]
[ROW][C]42[/C][C]4253[/C][C]5080.66756157866[/C][C]-827.667561578664[/C][/ROW]
[ROW][C]43[/C][C]3768[/C][C]4887.47300219656[/C][C]-1119.47300219656[/C][/ROW]
[ROW][C]44[/C][C]3066[/C][C]4626.16507684182[/C][C]-1560.16507684182[/C][/ROW]
[ROW][C]45[/C][C]4108[/C][C]4261.99059595616[/C][C]-153.990595956164[/C][/ROW]
[ROW][C]46[/C][C]3890[/C][C]4226.04603715529[/C][C]-336.046037155291[/C][/ROW]
[ROW][C]47[/C][C]3420[/C][C]4147.60600990994[/C][C]-727.606009909944[/C][/ROW]
[ROW][C]48[/C][C]1221[/C][C]3977.76786593314[/C][C]-2756.76786593314[/C][/ROW]
[ROW][C]49[/C][C]5984[/C][C]3334.28178782485[/C][C]2649.71821217515[/C][/ROW]
[ROW][C]50[/C][C]4064[/C][C]3952.7802843849[/C][C]111.219715615101[/C][/ROW]
[ROW][C]51[/C][C]5151[/C][C]3978.74124377284[/C][C]1172.25875622716[/C][/ROW]
[ROW][C]52[/C][C]4027[/C][C]4252.37044516278[/C][C]-225.370445162778[/C][/ROW]
[ROW][C]53[/C][C]3530[/C][C]4199.76436770829[/C][C]-669.764367708292[/C][/ROW]
[ROW][C]54[/C][C]4819[/C][C]4043.42764760966[/C][C]775.572352390339[/C][/ROW]
[ROW][C]55[/C][C]3855[/C][C]4224.46211826501[/C][C]-369.462118265011[/C][/ROW]
[ROW][C]56[/C][C]3584[/C][C]4138.22209333224[/C][C]-554.222093332241[/C][/ROW]
[ROW][C]57[/C][C]4322[/C][C]4008.85530636173[/C][C]313.144693638274[/C][/ROW]
[ROW][C]58[/C][C]4154[/C][C]4081.94969101406[/C][C]72.050308985938[/C][/ROW]
[ROW][C]59[/C][C]4656[/C][C]4098.76770871109[/C][C]557.232291288913[/C][/ROW]
[ROW][C]60[/C][C]1464[/C][C]4228.8371375331[/C][C]-2764.8371375331[/C][/ROW]
[ROW][C]61[/C][C]7780[/C][C]3583.46752617588[/C][C]4196.53247382412[/C][/ROW]
[ROW][C]62[/C][C]5060[/C][C]4563.02414993285[/C][C]496.975850067146[/C][/ROW]
[ROW][C]63[/C][C]6084[/C][C]4679.02849133067[/C][C]1404.97150866933[/C][/ROW]
[ROW][C]64[/C][C]4778[/C][C]5006.97761506347[/C][C]-228.977615063474[/C][/ROW]
[ROW][C]65[/C][C]4989[/C][C]4953.52955027986[/C][C]35.4704497201419[/C][/ROW]
[ROW][C]66[/C][C]4903[/C][C]4961.80907967412[/C][C]-58.8090796741208[/C][/ROW]
[ROW][C]67[/C][C]4142[/C][C]4948.0818360769[/C][C]-806.081836076899[/C][/ROW]
[ROW][C]68[/C][C]4101[/C][C]4759.92582709938[/C][C]-658.925827099378[/C][/ROW]
[ROW][C]69[/C][C]4595[/C][C]4606.11904435058[/C][C]-11.1190443505811[/C][/ROW]
[ROW][C]70[/C][C]5034[/C][C]4603.52363168277[/C][C]430.476368317233[/C][/ROW]
[ROW][C]71[/C][C]5407[/C][C]4704.00563214057[/C][C]702.994367859427[/C][/ROW]
[ROW][C]72[/C][C]1782[/C][C]4868.09891481998[/C][C]-3086.09891481998[/C][/ROW]
[ROW][C]73[/C][C]8395[/C][C]4147.74022525017[/C][C]4247.25977474983[/C][/ROW]
[ROW][C]74[/C][C]5291[/C][C]5139.13763993085[/C][C]151.862360069154[/C][/ROW]
[ROW][C]75[/C][C]6116[/C][C]5174.58542488973[/C][C]941.414575110266[/C][/ROW]
[ROW][C]76[/C][C]4210[/C][C]5394.33086675219[/C][C]-1184.33086675219[/C][/ROW]
[ROW][C]77[/C][C]4621[/C][C]5117.88378753067[/C][C]-496.883787530667[/C][/ROW]
[ROW][C]78[/C][C]5299[/C][C]5001.90093541429[/C][C]297.09906458571[/C][/ROW]
[ROW][C]79[/C][C]4293[/C][C]5071.24994163364[/C][C]-778.24994163364[/C][/ROW]
[ROW][C]80[/C][C]4542[/C][C]4889.59046681227[/C][C]-347.590466812271[/C][/ROW]
[ROW][C]81[/C][C]3831[/C][C]4808.45573325677[/C][C]-977.455733256767[/C][/ROW]
[ROW][C]82[/C][C]4360[/C][C]4580.29754696531[/C][C]-220.297546965315[/C][/ROW]
[ROW][C]83[/C][C]4088[/C][C]4528.87558784232[/C][C]-440.875587842324[/C][/ROW]
[ROW][C]84[/C][C]1508[/C][C]4425.96619657288[/C][C]-2917.96619657288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234811&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234811&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
255228584-3062
364237869.26649069139-1446.26649069139
451737531.6782724395-2358.6782724395
555836981.11445826881-1398.11445826881
657166654.76591053087-938.765910530868
747526435.63872122551-1683.63872122551
849776042.64296301866-1065.64296301866
949995793.90007123932-794.900071239316
1052855608.35411517578-323.354115175783
1157475532.87664244914214.123357550856
1217135582.85741931631-3869.85741931631
1399234679.553443538425243.44655646158
1467375903.48125482905833.518745170945
1574336098.041600292981334.95839970702
1663886409.64823053583-21.6482305358286
1768556404.5950901762450.404909823804
1876586509.728820355231148.27117964477
1965856777.7588301088-192.758830108802
2068476732.76497148898114.235028511017
2163536759.42976666-406.429766659998
2273616664.56073549985696.439264500153
2369296827.12392280765101.876077192347
2417146850.90388563139-5136.90388563139
25117985651.845315690716146.15468430929
2683787086.483691350391291.51630864961
2781317387.95004785282743.049952147185
2876767561.39312423745114.60687576255
2975057588.14471617235-83.1447161723499
3081687568.73703662619599.262963373807
3164557708.61728509479-1253.61728509479
3261417415.99733685647-1274.99733685647
3365547118.38684667667-564.386846676668
3468886986.64739810291-98.6473981029139
3553396963.62107510152-1624.62107510152
3616246584.40124417271-4960.40124417271
3791875426.542005496563760.45799450344
3850476304.30991503904-1257.30991503904
3952896010.82803134722-721.828031347215
4041695842.3385858991-1673.3385858991
4138625451.74709022269-1589.74709022269
4242535080.66756157866-827.667561578664
4337684887.47300219656-1119.47300219656
4430664626.16507684182-1560.16507684182
4541084261.99059595616-153.990595956164
4638904226.04603715529-336.046037155291
4734204147.60600990994-727.606009909944
4812213977.76786593314-2756.76786593314
4959843334.281787824852649.71821217515
5040643952.7802843849111.219715615101
5151513978.741243772841172.25875622716
5240274252.37044516278-225.370445162778
5335304199.76436770829-669.764367708292
5448194043.42764760966775.572352390339
5538554224.46211826501-369.462118265011
5635844138.22209333224-554.222093332241
5743224008.85530636173313.144693638274
5841544081.9496910140672.050308985938
5946564098.76770871109557.232291288913
6014644228.8371375331-2764.8371375331
6177803583.467526175884196.53247382412
6250604563.02414993285496.975850067146
6360844679.028491330671404.97150866933
6447785006.97761506347-228.977615063474
6549894953.5295502798635.4704497201419
6649034961.80907967412-58.8090796741208
6741424948.0818360769-806.081836076899
6841014759.92582709938-658.925827099378
6945954606.11904435058-11.1190443505811
7050344603.52363168277430.476368317233
7154074704.00563214057702.994367859427
7217824868.09891481998-3086.09891481998
7383954147.740225250174247.25977474983
7452915139.13763993085151.862360069154
7561165174.58542488973941.414575110266
7642105394.33086675219-1184.33086675219
7746215117.88378753067-496.883787530667
7852995001.90093541429297.09906458571
7942935071.24994163364-778.24994163364
8045424889.59046681227-347.590466812271
8138314808.45573325677-977.455733256767
8243604580.29754696531-220.297546965315
8340884528.87558784232-440.875587842324
8415084425.96619657288-2917.96619657288







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
853744.85312677522131.6759410106457358.0303125398
863744.8531267752234.54918868808237455.15706486236
873744.85312677522-60.09907400736447549.80532755781
883744.85312677522-152.4494259521847642.15567950263
893744.85312677522-242.6615283390227732.36778188946
903744.85312677522-330.8773675050577820.5836210555
913744.85312677522-417.2238786706747906.93013222112
923744.85312677522-501.8150891932437991.52134274369
933744.85312677522-584.7538846949998074.46013824544
943744.85312677522-666.1334761320478155.83972968249
953744.85312677522-746.0386274627628235.74488101321
963744.85312677522-824.5466899991898314.25294354963

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3744.85312677522 & 131.675941010645 & 7358.0303125398 \tabularnewline
86 & 3744.85312677522 & 34.5491886880823 & 7455.15706486236 \tabularnewline
87 & 3744.85312677522 & -60.0990740073644 & 7549.80532755781 \tabularnewline
88 & 3744.85312677522 & -152.449425952184 & 7642.15567950263 \tabularnewline
89 & 3744.85312677522 & -242.661528339022 & 7732.36778188946 \tabularnewline
90 & 3744.85312677522 & -330.877367505057 & 7820.5836210555 \tabularnewline
91 & 3744.85312677522 & -417.223878670674 & 7906.93013222112 \tabularnewline
92 & 3744.85312677522 & -501.815089193243 & 7991.52134274369 \tabularnewline
93 & 3744.85312677522 & -584.753884694999 & 8074.46013824544 \tabularnewline
94 & 3744.85312677522 & -666.133476132047 & 8155.83972968249 \tabularnewline
95 & 3744.85312677522 & -746.038627462762 & 8235.74488101321 \tabularnewline
96 & 3744.85312677522 & -824.546689999189 & 8314.25294354963 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234811&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]85[/C][C]3744.85312677522[/C][C]131.675941010645[/C][C]7358.0303125398[/C][/ROW]
[ROW][C]86[/C][C]3744.85312677522[/C][C]34.5491886880823[/C][C]7455.15706486236[/C][/ROW]
[ROW][C]87[/C][C]3744.85312677522[/C][C]-60.0990740073644[/C][C]7549.80532755781[/C][/ROW]
[ROW][C]88[/C][C]3744.85312677522[/C][C]-152.449425952184[/C][C]7642.15567950263[/C][/ROW]
[ROW][C]89[/C][C]3744.85312677522[/C][C]-242.661528339022[/C][C]7732.36778188946[/C][/ROW]
[ROW][C]90[/C][C]3744.85312677522[/C][C]-330.877367505057[/C][C]7820.5836210555[/C][/ROW]
[ROW][C]91[/C][C]3744.85312677522[/C][C]-417.223878670674[/C][C]7906.93013222112[/C][/ROW]
[ROW][C]92[/C][C]3744.85312677522[/C][C]-501.815089193243[/C][C]7991.52134274369[/C][/ROW]
[ROW][C]93[/C][C]3744.85312677522[/C][C]-584.753884694999[/C][C]8074.46013824544[/C][/ROW]
[ROW][C]94[/C][C]3744.85312677522[/C][C]-666.133476132047[/C][C]8155.83972968249[/C][/ROW]
[ROW][C]95[/C][C]3744.85312677522[/C][C]-746.038627462762[/C][C]8235.74488101321[/C][/ROW]
[ROW][C]96[/C][C]3744.85312677522[/C][C]-824.546689999189[/C][C]8314.25294354963[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234811&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234811&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
853744.85312677522131.6759410106457358.0303125398
863744.8531267752234.54918868808237455.15706486236
873744.85312677522-60.09907400736447549.80532755781
883744.85312677522-152.4494259521847642.15567950263
893744.85312677522-242.6615283390227732.36778188946
903744.85312677522-330.8773675050577820.5836210555
913744.85312677522-417.2238786706747906.93013222112
923744.85312677522-501.8150891932437991.52134274369
933744.85312677522-584.7538846949998074.46013824544
943744.85312677522-666.1334761320478155.83972968249
953744.85312677522-746.0386274627628235.74488101321
963744.85312677522-824.5466899991898314.25294354963



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')