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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 03 Aug 2012 09:48:38 -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/2012/Aug/03/t13440017484fgjjvvz957le4m.htm/, Retrieved Mon, 29 Apr 2024 17:37:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169003, Retrieved Mon, 29 Apr 2024 17:37:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSelleslaghs Tessa
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B stap 27] [2012-08-03 13:48:38] [5f178b5bce8a01d64692a8a5c649399b] [Current]
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Dataseries X:
1020
970
1030
970
1070
1650
1010
980
1050
1010
1040
1120
1090
1060
990
950
1540
870
1070
1050
1020
960
1100
1190
1040
1090
1050
850
1100
850
1040
990
1040
1100
1030
1290
1040
1170
1040
860
1090
870
1080
1000
980
1080
1040
1280
1140
1220
1080
790
1020
830
1150
1030
900
1140
1010
1270
1090
1090
980
850
1010
810
1070
1040
880
1110
1010
1230
490
1040
1010
860
1010
800
1130
1040
940
1070
1030
1320
1040
1070
1070
770
1010
810
1150
1030
890
1010
1120
1250
990
1020
1110
830
1030
870
1260
980
940
970
1100
1320




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169003&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169003&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169003&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00161353096763727
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00161353096763727 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169003&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]0.00161353096763727[/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=169003&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169003&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
alpha0.00161353096763727
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
29701020-50
310301019.9193234516210.0806765483819
49701019.9355889354-49.9355889354036
510701019.8550163162750.1449836837309
616501019.93592680031630.064073199685
710101020.95255469402-10.9525546940179
89801020.93488240784-40.9348824078443
910501020.8688327074229.1311672925774
1010101020.91583674797-10.9158367479725
1110401020.8982237073419.101776292658
1211201020.9290450149399.0709549850729
1310901021.0888990687968.9111009312111
1410601021.2000892641638.7999107358446
159901021.26269412167-31.2626941216693
169501021.21225079657-71.2122507965722
1715401021.09734762464518.902652375363
188701021.93461312343-151.934613123434
1910701021.689461920148.3105380798971
2010501021.7674124693628.232587530642
2110201021.81296662364-1.81296662363513
229601021.81004134584-61.8100413458446
2311001021.7103089300278.2896910699778
2411901021.83663177101168.16336822899
2510401022.1079685732717.8920314267301
2610901022.1368379200567.8631620799491
2710501022.2463372336327.7536627663713
288501022.29111862797-172.291118627968
2911001022.0131215726177.9868784273875
308501022.13895581602-172.138955816024
3110401021.8612042800818.1387957199214
329901021.89047178869-31.8904717886884
3310401021.8390155248818.1609844751152
3411001021.8683188357478.1316811642619
3510301021.994386722858.00561327714979
3612901022.00730402779267.992695972212
3710401022.4397185418417.5602814581605
3811701022.46805259977147.531947400227
3910401022.7060999656217.2939000343812
408601022.73400420888-162.734004208875
4110901022.471427853667.5285721464031
428701022.58038729596-152.580387295955
4310801022.33419411657.6658058840006
4410001022.42723967957-22.4272396795669
459801022.39105263383-42.3910526338253
4610801022.3226533576557.6773466423501
4710401022.4157175425917.5842824574115
4812801022.44409032688257.555909673123
4911401022.85966476303117.140335236967
5012201023.0486743215196.951325678503
5110801023.366461384656.6335386154035
527901023.45784135296-233.457841352959
5310201023.0811498963-3.0811498962986
548301023.07617836553-193.076178365525
5511501022.76464397262127.235356027381
5610301022.969942159757.03005784025231
579001022.98128537578-122.981285375777
5811401022.78285126338117.217148736616
5910101022.97198476281-12.9719847628082
6012701022.95105406368247.048945936318
6110901023.3496751884766.650324811528
6210901023.4572175515666.5427824484415
639801023.56458639171-43.5645863917118
648501023.49429358248-173.494293582477
6510101023.21435516707-13.2143551670729
668101023.19303339579-213.193033395793
6710701022.8490398343247.1509601656752
6810401022.9251193687117.074880631294
698801022.95267021737-142.952670217373
7011101022.7220116570787.2779883429289
7110101022.86283739406-12.8628373940555
7212301022.84208280759207.157917192411
734901023.17633852217-533.17633852217
7410401022.3160419887517.6839580112472
7510101022.34457560263-12.3445756026343
768601022.32465724762-162.324657247617
7710101022.06274138634-12.0627413863369
788001022.04327777956-222.043277779556
7911301021.6850040747108.314995925297
8010401021.8597736748918.1402263251125
819401021.88904349182-81.889043491823
8210701021.7569129842448.2430870157613
8310301021.834754699118.16524530088691
8413201021.84792957526298.152070424736
8510401022.3290071739617.6709928260401
8610701022.3575198681147.6424801318864
8710701022.4343924851847.5656075148186
887701022.5111410659-252.511141065901
8910101022.10370652012-12.1037065201177
908101022.08417681482-212.084176814824
9111501021.74197242779128.258027572212
9210301021.948920727128.05107927287634
938901021.96191139285-131.961911392853
9410101021.74898676227-11.7489867622724
9511201021.7300294082998.269970591707
9612501021.88859104903228.111408950968
979901022.25665587145-32.2566558714453
9810201022.20460875828-2.20460875828428
9911101022.2010515537887.7989484462188
1008301022.34271787603-192.342717876025
10110301022.032366944337.96763305566731
1028701022.04522296701-152.045222967007
10312601021.79989329127238.200106708732
1049801022.18423653994-42.1842365399373
1059401022.11617096793-82.116170967934
1069701021.98367398313-51.9836739831334
10711001021.8997967153578.10020328465
10813201022.02581381193297.974186188071

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 970 & 1020 & -50 \tabularnewline
3 & 1030 & 1019.91932345162 & 10.0806765483819 \tabularnewline
4 & 970 & 1019.9355889354 & -49.9355889354036 \tabularnewline
5 & 1070 & 1019.85501631627 & 50.1449836837309 \tabularnewline
6 & 1650 & 1019.93592680031 & 630.064073199685 \tabularnewline
7 & 1010 & 1020.95255469402 & -10.9525546940179 \tabularnewline
8 & 980 & 1020.93488240784 & -40.9348824078443 \tabularnewline
9 & 1050 & 1020.86883270742 & 29.1311672925774 \tabularnewline
10 & 1010 & 1020.91583674797 & -10.9158367479725 \tabularnewline
11 & 1040 & 1020.89822370734 & 19.101776292658 \tabularnewline
12 & 1120 & 1020.92904501493 & 99.0709549850729 \tabularnewline
13 & 1090 & 1021.08889906879 & 68.9111009312111 \tabularnewline
14 & 1060 & 1021.20008926416 & 38.7999107358446 \tabularnewline
15 & 990 & 1021.26269412167 & -31.2626941216693 \tabularnewline
16 & 950 & 1021.21225079657 & -71.2122507965722 \tabularnewline
17 & 1540 & 1021.09734762464 & 518.902652375363 \tabularnewline
18 & 870 & 1021.93461312343 & -151.934613123434 \tabularnewline
19 & 1070 & 1021.6894619201 & 48.3105380798971 \tabularnewline
20 & 1050 & 1021.76741246936 & 28.232587530642 \tabularnewline
21 & 1020 & 1021.81296662364 & -1.81296662363513 \tabularnewline
22 & 960 & 1021.81004134584 & -61.8100413458446 \tabularnewline
23 & 1100 & 1021.71030893002 & 78.2896910699778 \tabularnewline
24 & 1190 & 1021.83663177101 & 168.16336822899 \tabularnewline
25 & 1040 & 1022.10796857327 & 17.8920314267301 \tabularnewline
26 & 1090 & 1022.13683792005 & 67.8631620799491 \tabularnewline
27 & 1050 & 1022.24633723363 & 27.7536627663713 \tabularnewline
28 & 850 & 1022.29111862797 & -172.291118627968 \tabularnewline
29 & 1100 & 1022.01312157261 & 77.9868784273875 \tabularnewline
30 & 850 & 1022.13895581602 & -172.138955816024 \tabularnewline
31 & 1040 & 1021.86120428008 & 18.1387957199214 \tabularnewline
32 & 990 & 1021.89047178869 & -31.8904717886884 \tabularnewline
33 & 1040 & 1021.83901552488 & 18.1609844751152 \tabularnewline
34 & 1100 & 1021.86831883574 & 78.1316811642619 \tabularnewline
35 & 1030 & 1021.99438672285 & 8.00561327714979 \tabularnewline
36 & 1290 & 1022.00730402779 & 267.992695972212 \tabularnewline
37 & 1040 & 1022.43971854184 & 17.5602814581605 \tabularnewline
38 & 1170 & 1022.46805259977 & 147.531947400227 \tabularnewline
39 & 1040 & 1022.70609996562 & 17.2939000343812 \tabularnewline
40 & 860 & 1022.73400420888 & -162.734004208875 \tabularnewline
41 & 1090 & 1022.4714278536 & 67.5285721464031 \tabularnewline
42 & 870 & 1022.58038729596 & -152.580387295955 \tabularnewline
43 & 1080 & 1022.334194116 & 57.6658058840006 \tabularnewline
44 & 1000 & 1022.42723967957 & -22.4272396795669 \tabularnewline
45 & 980 & 1022.39105263383 & -42.3910526338253 \tabularnewline
46 & 1080 & 1022.32265335765 & 57.6773466423501 \tabularnewline
47 & 1040 & 1022.41571754259 & 17.5842824574115 \tabularnewline
48 & 1280 & 1022.44409032688 & 257.555909673123 \tabularnewline
49 & 1140 & 1022.85966476303 & 117.140335236967 \tabularnewline
50 & 1220 & 1023.0486743215 & 196.951325678503 \tabularnewline
51 & 1080 & 1023.3664613846 & 56.6335386154035 \tabularnewline
52 & 790 & 1023.45784135296 & -233.457841352959 \tabularnewline
53 & 1020 & 1023.0811498963 & -3.0811498962986 \tabularnewline
54 & 830 & 1023.07617836553 & -193.076178365525 \tabularnewline
55 & 1150 & 1022.76464397262 & 127.235356027381 \tabularnewline
56 & 1030 & 1022.96994215975 & 7.03005784025231 \tabularnewline
57 & 900 & 1022.98128537578 & -122.981285375777 \tabularnewline
58 & 1140 & 1022.78285126338 & 117.217148736616 \tabularnewline
59 & 1010 & 1022.97198476281 & -12.9719847628082 \tabularnewline
60 & 1270 & 1022.95105406368 & 247.048945936318 \tabularnewline
61 & 1090 & 1023.34967518847 & 66.650324811528 \tabularnewline
62 & 1090 & 1023.45721755156 & 66.5427824484415 \tabularnewline
63 & 980 & 1023.56458639171 & -43.5645863917118 \tabularnewline
64 & 850 & 1023.49429358248 & -173.494293582477 \tabularnewline
65 & 1010 & 1023.21435516707 & -13.2143551670729 \tabularnewline
66 & 810 & 1023.19303339579 & -213.193033395793 \tabularnewline
67 & 1070 & 1022.84903983432 & 47.1509601656752 \tabularnewline
68 & 1040 & 1022.92511936871 & 17.074880631294 \tabularnewline
69 & 880 & 1022.95267021737 & -142.952670217373 \tabularnewline
70 & 1110 & 1022.72201165707 & 87.2779883429289 \tabularnewline
71 & 1010 & 1022.86283739406 & -12.8628373940555 \tabularnewline
72 & 1230 & 1022.84208280759 & 207.157917192411 \tabularnewline
73 & 490 & 1023.17633852217 & -533.17633852217 \tabularnewline
74 & 1040 & 1022.31604198875 & 17.6839580112472 \tabularnewline
75 & 1010 & 1022.34457560263 & -12.3445756026343 \tabularnewline
76 & 860 & 1022.32465724762 & -162.324657247617 \tabularnewline
77 & 1010 & 1022.06274138634 & -12.0627413863369 \tabularnewline
78 & 800 & 1022.04327777956 & -222.043277779556 \tabularnewline
79 & 1130 & 1021.6850040747 & 108.314995925297 \tabularnewline
80 & 1040 & 1021.85977367489 & 18.1402263251125 \tabularnewline
81 & 940 & 1021.88904349182 & -81.889043491823 \tabularnewline
82 & 1070 & 1021.75691298424 & 48.2430870157613 \tabularnewline
83 & 1030 & 1021.83475469911 & 8.16524530088691 \tabularnewline
84 & 1320 & 1021.84792957526 & 298.152070424736 \tabularnewline
85 & 1040 & 1022.32900717396 & 17.6709928260401 \tabularnewline
86 & 1070 & 1022.35751986811 & 47.6424801318864 \tabularnewline
87 & 1070 & 1022.43439248518 & 47.5656075148186 \tabularnewline
88 & 770 & 1022.5111410659 & -252.511141065901 \tabularnewline
89 & 1010 & 1022.10370652012 & -12.1037065201177 \tabularnewline
90 & 810 & 1022.08417681482 & -212.084176814824 \tabularnewline
91 & 1150 & 1021.74197242779 & 128.258027572212 \tabularnewline
92 & 1030 & 1021.94892072712 & 8.05107927287634 \tabularnewline
93 & 890 & 1021.96191139285 & -131.961911392853 \tabularnewline
94 & 1010 & 1021.74898676227 & -11.7489867622724 \tabularnewline
95 & 1120 & 1021.73002940829 & 98.269970591707 \tabularnewline
96 & 1250 & 1021.88859104903 & 228.111408950968 \tabularnewline
97 & 990 & 1022.25665587145 & -32.2566558714453 \tabularnewline
98 & 1020 & 1022.20460875828 & -2.20460875828428 \tabularnewline
99 & 1110 & 1022.20105155378 & 87.7989484462188 \tabularnewline
100 & 830 & 1022.34271787603 & -192.342717876025 \tabularnewline
101 & 1030 & 1022.03236694433 & 7.96763305566731 \tabularnewline
102 & 870 & 1022.04522296701 & -152.045222967007 \tabularnewline
103 & 1260 & 1021.79989329127 & 238.200106708732 \tabularnewline
104 & 980 & 1022.18423653994 & -42.1842365399373 \tabularnewline
105 & 940 & 1022.11617096793 & -82.116170967934 \tabularnewline
106 & 970 & 1021.98367398313 & -51.9836739831334 \tabularnewline
107 & 1100 & 1021.89979671535 & 78.10020328465 \tabularnewline
108 & 1320 & 1022.02581381193 & 297.974186188071 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169003&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]970[/C][C]1020[/C][C]-50[/C][/ROW]
[ROW][C]3[/C][C]1030[/C][C]1019.91932345162[/C][C]10.0806765483819[/C][/ROW]
[ROW][C]4[/C][C]970[/C][C]1019.9355889354[/C][C]-49.9355889354036[/C][/ROW]
[ROW][C]5[/C][C]1070[/C][C]1019.85501631627[/C][C]50.1449836837309[/C][/ROW]
[ROW][C]6[/C][C]1650[/C][C]1019.93592680031[/C][C]630.064073199685[/C][/ROW]
[ROW][C]7[/C][C]1010[/C][C]1020.95255469402[/C][C]-10.9525546940179[/C][/ROW]
[ROW][C]8[/C][C]980[/C][C]1020.93488240784[/C][C]-40.9348824078443[/C][/ROW]
[ROW][C]9[/C][C]1050[/C][C]1020.86883270742[/C][C]29.1311672925774[/C][/ROW]
[ROW][C]10[/C][C]1010[/C][C]1020.91583674797[/C][C]-10.9158367479725[/C][/ROW]
[ROW][C]11[/C][C]1040[/C][C]1020.89822370734[/C][C]19.101776292658[/C][/ROW]
[ROW][C]12[/C][C]1120[/C][C]1020.92904501493[/C][C]99.0709549850729[/C][/ROW]
[ROW][C]13[/C][C]1090[/C][C]1021.08889906879[/C][C]68.9111009312111[/C][/ROW]
[ROW][C]14[/C][C]1060[/C][C]1021.20008926416[/C][C]38.7999107358446[/C][/ROW]
[ROW][C]15[/C][C]990[/C][C]1021.26269412167[/C][C]-31.2626941216693[/C][/ROW]
[ROW][C]16[/C][C]950[/C][C]1021.21225079657[/C][C]-71.2122507965722[/C][/ROW]
[ROW][C]17[/C][C]1540[/C][C]1021.09734762464[/C][C]518.902652375363[/C][/ROW]
[ROW][C]18[/C][C]870[/C][C]1021.93461312343[/C][C]-151.934613123434[/C][/ROW]
[ROW][C]19[/C][C]1070[/C][C]1021.6894619201[/C][C]48.3105380798971[/C][/ROW]
[ROW][C]20[/C][C]1050[/C][C]1021.76741246936[/C][C]28.232587530642[/C][/ROW]
[ROW][C]21[/C][C]1020[/C][C]1021.81296662364[/C][C]-1.81296662363513[/C][/ROW]
[ROW][C]22[/C][C]960[/C][C]1021.81004134584[/C][C]-61.8100413458446[/C][/ROW]
[ROW][C]23[/C][C]1100[/C][C]1021.71030893002[/C][C]78.2896910699778[/C][/ROW]
[ROW][C]24[/C][C]1190[/C][C]1021.83663177101[/C][C]168.16336822899[/C][/ROW]
[ROW][C]25[/C][C]1040[/C][C]1022.10796857327[/C][C]17.8920314267301[/C][/ROW]
[ROW][C]26[/C][C]1090[/C][C]1022.13683792005[/C][C]67.8631620799491[/C][/ROW]
[ROW][C]27[/C][C]1050[/C][C]1022.24633723363[/C][C]27.7536627663713[/C][/ROW]
[ROW][C]28[/C][C]850[/C][C]1022.29111862797[/C][C]-172.291118627968[/C][/ROW]
[ROW][C]29[/C][C]1100[/C][C]1022.01312157261[/C][C]77.9868784273875[/C][/ROW]
[ROW][C]30[/C][C]850[/C][C]1022.13895581602[/C][C]-172.138955816024[/C][/ROW]
[ROW][C]31[/C][C]1040[/C][C]1021.86120428008[/C][C]18.1387957199214[/C][/ROW]
[ROW][C]32[/C][C]990[/C][C]1021.89047178869[/C][C]-31.8904717886884[/C][/ROW]
[ROW][C]33[/C][C]1040[/C][C]1021.83901552488[/C][C]18.1609844751152[/C][/ROW]
[ROW][C]34[/C][C]1100[/C][C]1021.86831883574[/C][C]78.1316811642619[/C][/ROW]
[ROW][C]35[/C][C]1030[/C][C]1021.99438672285[/C][C]8.00561327714979[/C][/ROW]
[ROW][C]36[/C][C]1290[/C][C]1022.00730402779[/C][C]267.992695972212[/C][/ROW]
[ROW][C]37[/C][C]1040[/C][C]1022.43971854184[/C][C]17.5602814581605[/C][/ROW]
[ROW][C]38[/C][C]1170[/C][C]1022.46805259977[/C][C]147.531947400227[/C][/ROW]
[ROW][C]39[/C][C]1040[/C][C]1022.70609996562[/C][C]17.2939000343812[/C][/ROW]
[ROW][C]40[/C][C]860[/C][C]1022.73400420888[/C][C]-162.734004208875[/C][/ROW]
[ROW][C]41[/C][C]1090[/C][C]1022.4714278536[/C][C]67.5285721464031[/C][/ROW]
[ROW][C]42[/C][C]870[/C][C]1022.58038729596[/C][C]-152.580387295955[/C][/ROW]
[ROW][C]43[/C][C]1080[/C][C]1022.334194116[/C][C]57.6658058840006[/C][/ROW]
[ROW][C]44[/C][C]1000[/C][C]1022.42723967957[/C][C]-22.4272396795669[/C][/ROW]
[ROW][C]45[/C][C]980[/C][C]1022.39105263383[/C][C]-42.3910526338253[/C][/ROW]
[ROW][C]46[/C][C]1080[/C][C]1022.32265335765[/C][C]57.6773466423501[/C][/ROW]
[ROW][C]47[/C][C]1040[/C][C]1022.41571754259[/C][C]17.5842824574115[/C][/ROW]
[ROW][C]48[/C][C]1280[/C][C]1022.44409032688[/C][C]257.555909673123[/C][/ROW]
[ROW][C]49[/C][C]1140[/C][C]1022.85966476303[/C][C]117.140335236967[/C][/ROW]
[ROW][C]50[/C][C]1220[/C][C]1023.0486743215[/C][C]196.951325678503[/C][/ROW]
[ROW][C]51[/C][C]1080[/C][C]1023.3664613846[/C][C]56.6335386154035[/C][/ROW]
[ROW][C]52[/C][C]790[/C][C]1023.45784135296[/C][C]-233.457841352959[/C][/ROW]
[ROW][C]53[/C][C]1020[/C][C]1023.0811498963[/C][C]-3.0811498962986[/C][/ROW]
[ROW][C]54[/C][C]830[/C][C]1023.07617836553[/C][C]-193.076178365525[/C][/ROW]
[ROW][C]55[/C][C]1150[/C][C]1022.76464397262[/C][C]127.235356027381[/C][/ROW]
[ROW][C]56[/C][C]1030[/C][C]1022.96994215975[/C][C]7.03005784025231[/C][/ROW]
[ROW][C]57[/C][C]900[/C][C]1022.98128537578[/C][C]-122.981285375777[/C][/ROW]
[ROW][C]58[/C][C]1140[/C][C]1022.78285126338[/C][C]117.217148736616[/C][/ROW]
[ROW][C]59[/C][C]1010[/C][C]1022.97198476281[/C][C]-12.9719847628082[/C][/ROW]
[ROW][C]60[/C][C]1270[/C][C]1022.95105406368[/C][C]247.048945936318[/C][/ROW]
[ROW][C]61[/C][C]1090[/C][C]1023.34967518847[/C][C]66.650324811528[/C][/ROW]
[ROW][C]62[/C][C]1090[/C][C]1023.45721755156[/C][C]66.5427824484415[/C][/ROW]
[ROW][C]63[/C][C]980[/C][C]1023.56458639171[/C][C]-43.5645863917118[/C][/ROW]
[ROW][C]64[/C][C]850[/C][C]1023.49429358248[/C][C]-173.494293582477[/C][/ROW]
[ROW][C]65[/C][C]1010[/C][C]1023.21435516707[/C][C]-13.2143551670729[/C][/ROW]
[ROW][C]66[/C][C]810[/C][C]1023.19303339579[/C][C]-213.193033395793[/C][/ROW]
[ROW][C]67[/C][C]1070[/C][C]1022.84903983432[/C][C]47.1509601656752[/C][/ROW]
[ROW][C]68[/C][C]1040[/C][C]1022.92511936871[/C][C]17.074880631294[/C][/ROW]
[ROW][C]69[/C][C]880[/C][C]1022.95267021737[/C][C]-142.952670217373[/C][/ROW]
[ROW][C]70[/C][C]1110[/C][C]1022.72201165707[/C][C]87.2779883429289[/C][/ROW]
[ROW][C]71[/C][C]1010[/C][C]1022.86283739406[/C][C]-12.8628373940555[/C][/ROW]
[ROW][C]72[/C][C]1230[/C][C]1022.84208280759[/C][C]207.157917192411[/C][/ROW]
[ROW][C]73[/C][C]490[/C][C]1023.17633852217[/C][C]-533.17633852217[/C][/ROW]
[ROW][C]74[/C][C]1040[/C][C]1022.31604198875[/C][C]17.6839580112472[/C][/ROW]
[ROW][C]75[/C][C]1010[/C][C]1022.34457560263[/C][C]-12.3445756026343[/C][/ROW]
[ROW][C]76[/C][C]860[/C][C]1022.32465724762[/C][C]-162.324657247617[/C][/ROW]
[ROW][C]77[/C][C]1010[/C][C]1022.06274138634[/C][C]-12.0627413863369[/C][/ROW]
[ROW][C]78[/C][C]800[/C][C]1022.04327777956[/C][C]-222.043277779556[/C][/ROW]
[ROW][C]79[/C][C]1130[/C][C]1021.6850040747[/C][C]108.314995925297[/C][/ROW]
[ROW][C]80[/C][C]1040[/C][C]1021.85977367489[/C][C]18.1402263251125[/C][/ROW]
[ROW][C]81[/C][C]940[/C][C]1021.88904349182[/C][C]-81.889043491823[/C][/ROW]
[ROW][C]82[/C][C]1070[/C][C]1021.75691298424[/C][C]48.2430870157613[/C][/ROW]
[ROW][C]83[/C][C]1030[/C][C]1021.83475469911[/C][C]8.16524530088691[/C][/ROW]
[ROW][C]84[/C][C]1320[/C][C]1021.84792957526[/C][C]298.152070424736[/C][/ROW]
[ROW][C]85[/C][C]1040[/C][C]1022.32900717396[/C][C]17.6709928260401[/C][/ROW]
[ROW][C]86[/C][C]1070[/C][C]1022.35751986811[/C][C]47.6424801318864[/C][/ROW]
[ROW][C]87[/C][C]1070[/C][C]1022.43439248518[/C][C]47.5656075148186[/C][/ROW]
[ROW][C]88[/C][C]770[/C][C]1022.5111410659[/C][C]-252.511141065901[/C][/ROW]
[ROW][C]89[/C][C]1010[/C][C]1022.10370652012[/C][C]-12.1037065201177[/C][/ROW]
[ROW][C]90[/C][C]810[/C][C]1022.08417681482[/C][C]-212.084176814824[/C][/ROW]
[ROW][C]91[/C][C]1150[/C][C]1021.74197242779[/C][C]128.258027572212[/C][/ROW]
[ROW][C]92[/C][C]1030[/C][C]1021.94892072712[/C][C]8.05107927287634[/C][/ROW]
[ROW][C]93[/C][C]890[/C][C]1021.96191139285[/C][C]-131.961911392853[/C][/ROW]
[ROW][C]94[/C][C]1010[/C][C]1021.74898676227[/C][C]-11.7489867622724[/C][/ROW]
[ROW][C]95[/C][C]1120[/C][C]1021.73002940829[/C][C]98.269970591707[/C][/ROW]
[ROW][C]96[/C][C]1250[/C][C]1021.88859104903[/C][C]228.111408950968[/C][/ROW]
[ROW][C]97[/C][C]990[/C][C]1022.25665587145[/C][C]-32.2566558714453[/C][/ROW]
[ROW][C]98[/C][C]1020[/C][C]1022.20460875828[/C][C]-2.20460875828428[/C][/ROW]
[ROW][C]99[/C][C]1110[/C][C]1022.20105155378[/C][C]87.7989484462188[/C][/ROW]
[ROW][C]100[/C][C]830[/C][C]1022.34271787603[/C][C]-192.342717876025[/C][/ROW]
[ROW][C]101[/C][C]1030[/C][C]1022.03236694433[/C][C]7.96763305566731[/C][/ROW]
[ROW][C]102[/C][C]870[/C][C]1022.04522296701[/C][C]-152.045222967007[/C][/ROW]
[ROW][C]103[/C][C]1260[/C][C]1021.79989329127[/C][C]238.200106708732[/C][/ROW]
[ROW][C]104[/C][C]980[/C][C]1022.18423653994[/C][C]-42.1842365399373[/C][/ROW]
[ROW][C]105[/C][C]940[/C][C]1022.11617096793[/C][C]-82.116170967934[/C][/ROW]
[ROW][C]106[/C][C]970[/C][C]1021.98367398313[/C][C]-51.9836739831334[/C][/ROW]
[ROW][C]107[/C][C]1100[/C][C]1021.89979671535[/C][C]78.10020328465[/C][/ROW]
[ROW][C]108[/C][C]1320[/C][C]1022.02581381193[/C][C]297.974186188071[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169003&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169003&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
29701020-50
310301019.9193234516210.0806765483819
49701019.9355889354-49.9355889354036
510701019.8550163162750.1449836837309
616501019.93592680031630.064073199685
710101020.95255469402-10.9525546940179
89801020.93488240784-40.9348824078443
910501020.8688327074229.1311672925774
1010101020.91583674797-10.9158367479725
1110401020.8982237073419.101776292658
1211201020.9290450149399.0709549850729
1310901021.0888990687968.9111009312111
1410601021.2000892641638.7999107358446
159901021.26269412167-31.2626941216693
169501021.21225079657-71.2122507965722
1715401021.09734762464518.902652375363
188701021.93461312343-151.934613123434
1910701021.689461920148.3105380798971
2010501021.7674124693628.232587530642
2110201021.81296662364-1.81296662363513
229601021.81004134584-61.8100413458446
2311001021.7103089300278.2896910699778
2411901021.83663177101168.16336822899
2510401022.1079685732717.8920314267301
2610901022.1368379200567.8631620799491
2710501022.2463372336327.7536627663713
288501022.29111862797-172.291118627968
2911001022.0131215726177.9868784273875
308501022.13895581602-172.138955816024
3110401021.8612042800818.1387957199214
329901021.89047178869-31.8904717886884
3310401021.8390155248818.1609844751152
3411001021.8683188357478.1316811642619
3510301021.994386722858.00561327714979
3612901022.00730402779267.992695972212
3710401022.4397185418417.5602814581605
3811701022.46805259977147.531947400227
3910401022.7060999656217.2939000343812
408601022.73400420888-162.734004208875
4110901022.471427853667.5285721464031
428701022.58038729596-152.580387295955
4310801022.33419411657.6658058840006
4410001022.42723967957-22.4272396795669
459801022.39105263383-42.3910526338253
4610801022.3226533576557.6773466423501
4710401022.4157175425917.5842824574115
4812801022.44409032688257.555909673123
4911401022.85966476303117.140335236967
5012201023.0486743215196.951325678503
5110801023.366461384656.6335386154035
527901023.45784135296-233.457841352959
5310201023.0811498963-3.0811498962986
548301023.07617836553-193.076178365525
5511501022.76464397262127.235356027381
5610301022.969942159757.03005784025231
579001022.98128537578-122.981285375777
5811401022.78285126338117.217148736616
5910101022.97198476281-12.9719847628082
6012701022.95105406368247.048945936318
6110901023.3496751884766.650324811528
6210901023.4572175515666.5427824484415
639801023.56458639171-43.5645863917118
648501023.49429358248-173.494293582477
6510101023.21435516707-13.2143551670729
668101023.19303339579-213.193033395793
6710701022.8490398343247.1509601656752
6810401022.9251193687117.074880631294
698801022.95267021737-142.952670217373
7011101022.7220116570787.2779883429289
7110101022.86283739406-12.8628373940555
7212301022.84208280759207.157917192411
734901023.17633852217-533.17633852217
7410401022.3160419887517.6839580112472
7510101022.34457560263-12.3445756026343
768601022.32465724762-162.324657247617
7710101022.06274138634-12.0627413863369
788001022.04327777956-222.043277779556
7911301021.6850040747108.314995925297
8010401021.8597736748918.1402263251125
819401021.88904349182-81.889043491823
8210701021.7569129842448.2430870157613
8310301021.834754699118.16524530088691
8413201021.84792957526298.152070424736
8510401022.3290071739617.6709928260401
8610701022.3575198681147.6424801318864
8710701022.4343924851847.5656075148186
887701022.5111410659-252.511141065901
8910101022.10370652012-12.1037065201177
908101022.08417681482-212.084176814824
9111501021.74197242779128.258027572212
9210301021.948920727128.05107927287634
938901021.96191139285-131.961911392853
9410101021.74898676227-11.7489867622724
9511201021.7300294082998.269970591707
9612501021.88859104903228.111408950968
979901022.25665587145-32.2566558714453
9810201022.20460875828-2.20460875828428
9911101022.2010515537887.7989484462188
1008301022.34271787603-192.342717876025
10110301022.032366944337.96763305566731
1028701022.04522296701-152.045222967007
10312601021.79989329127238.200106708732
1049801022.18423653994-42.1842365399373
1059401022.11617096793-82.116170967934
1069701021.98367398313-51.9836739831334
10711001021.8997967153578.10020328465
10813201022.02581381193297.974186188071







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091022.5066043889729.4462677147551315.56694106304
1101022.5066043889729.445886226321315.56732255148
1111022.5066043889729.4455047383831315.56770403942
1121022.5066043889729.4451232509421315.56808552686
1131022.5066043889729.4447417639971315.5684670138
1141022.5066043889729.4443602775491315.56884850025
1151022.5066043889729.4439787915981315.5692299862
1161022.5066043889729.4435973061431315.56961147166
1171022.5066043889729.4432158211851315.56999295661
1181022.5066043889729.4428343367231315.57037444108
1191022.5066043889729.4424528527581315.57075592504
1201022.5066043889729.442071369291315.57113740851

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1022.5066043889 & 729.446267714755 & 1315.56694106304 \tabularnewline
110 & 1022.5066043889 & 729.44588622632 & 1315.56732255148 \tabularnewline
111 & 1022.5066043889 & 729.445504738383 & 1315.56770403942 \tabularnewline
112 & 1022.5066043889 & 729.445123250942 & 1315.56808552686 \tabularnewline
113 & 1022.5066043889 & 729.444741763997 & 1315.5684670138 \tabularnewline
114 & 1022.5066043889 & 729.444360277549 & 1315.56884850025 \tabularnewline
115 & 1022.5066043889 & 729.443978791598 & 1315.5692299862 \tabularnewline
116 & 1022.5066043889 & 729.443597306143 & 1315.56961147166 \tabularnewline
117 & 1022.5066043889 & 729.443215821185 & 1315.56999295661 \tabularnewline
118 & 1022.5066043889 & 729.442834336723 & 1315.57037444108 \tabularnewline
119 & 1022.5066043889 & 729.442452852758 & 1315.57075592504 \tabularnewline
120 & 1022.5066043889 & 729.44207136929 & 1315.57113740851 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169003&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]109[/C][C]1022.5066043889[/C][C]729.446267714755[/C][C]1315.56694106304[/C][/ROW]
[ROW][C]110[/C][C]1022.5066043889[/C][C]729.44588622632[/C][C]1315.56732255148[/C][/ROW]
[ROW][C]111[/C][C]1022.5066043889[/C][C]729.445504738383[/C][C]1315.56770403942[/C][/ROW]
[ROW][C]112[/C][C]1022.5066043889[/C][C]729.445123250942[/C][C]1315.56808552686[/C][/ROW]
[ROW][C]113[/C][C]1022.5066043889[/C][C]729.444741763997[/C][C]1315.5684670138[/C][/ROW]
[ROW][C]114[/C][C]1022.5066043889[/C][C]729.444360277549[/C][C]1315.56884850025[/C][/ROW]
[ROW][C]115[/C][C]1022.5066043889[/C][C]729.443978791598[/C][C]1315.5692299862[/C][/ROW]
[ROW][C]116[/C][C]1022.5066043889[/C][C]729.443597306143[/C][C]1315.56961147166[/C][/ROW]
[ROW][C]117[/C][C]1022.5066043889[/C][C]729.443215821185[/C][C]1315.56999295661[/C][/ROW]
[ROW][C]118[/C][C]1022.5066043889[/C][C]729.442834336723[/C][C]1315.57037444108[/C][/ROW]
[ROW][C]119[/C][C]1022.5066043889[/C][C]729.442452852758[/C][C]1315.57075592504[/C][/ROW]
[ROW][C]120[/C][C]1022.5066043889[/C][C]729.44207136929[/C][C]1315.57113740851[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169003&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169003&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
1091022.5066043889729.4462677147551315.56694106304
1101022.5066043889729.445886226321315.56732255148
1111022.5066043889729.4455047383831315.56770403942
1121022.5066043889729.4451232509421315.56808552686
1131022.5066043889729.4447417639971315.5684670138
1141022.5066043889729.4443602775491315.56884850025
1151022.5066043889729.4439787915981315.5692299862
1161022.5066043889729.4435973061431315.56961147166
1171022.5066043889729.4432158211851315.56999295661
1181022.5066043889729.4428343367231315.57037444108
1191022.5066043889729.4424528527581315.57075592504
1201022.5066043889729.442071369291315.57113740851



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')