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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 20 Aug 2013 04:28:34 -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/2013/Aug/20/t1376987345hix1p0g081a09qv.htm/, Retrieved Sat, 27 Apr 2024 06:28:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211237, Retrieved Sat, 27 Apr 2024 06:28:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-08-20 08:28:34] [38a0db91cd47487c7649642dcb33e029] [Current]
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Dataseries X:
10320
11400
9360
10080
10080
10800
10320
9720
10440
11160
9480
11160
9840
11160
8760
10320
9600
10680
10200
10680
10200
12480
8880
11280
9480
11040
9240
9360
9240
10680
10680
10320
9960
12240
8880
11280
9360
10320
9840
9120
9360
10800
9840
11760
9960
11160
9240
11520
9000
10200
10200
9840
8760
11520
9120
11280
10560
10680
9960
10200
10200
10320
9600
10080
9120
10920
7800
11880
9360
10920
9840
9360
10680
9720
9960
10680
9120
10320
8040
11280
8880
11040
9600
9600
11040
9720
9480
10200
9360
10800
8520
11520
9120
11040
8880
9600
10440
8880
8520
10800
8880
10560
8400
12480
10560
10800
9840
8880




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211237&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]4 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=211237&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211237&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.277968810214052
beta0.356103913856205
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.277968810214052 \tabularnewline
beta & 0.356103913856205 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211237&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]0.277968810214052[/C][/ROW]
[ROW][C]beta[/C][C]0.356103913856205[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211237&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211237&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
alpha0.277968810214052
beta0.356103913856205
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3936012480-3120
41008012383.901674641-2303.90167464097
51008012286.5997226186-2206.59972261865
61080011997.9226809883-1197.92268098827
71032011871.0490840588-1551.04908405878
8972011492.4855556743-1772.48555567434
91044010876.9187272592-436.918727259161
101116010589.3490795406570.650920459364
11948010638.3386951873-1158.33869518731
121116010092.06406380831067.93593619172
13984010270.3348158893-430.334815889275
14111609989.536001687141170.46399831286
15876010269.5686225555-1509.56862255554
16103209655.20993501641664.790064983588
1796009711.05990877889-111.059908778885
18106809540.254436594281139.74556340572
19102009829.95247833878370.047521661221
20106809942.32791422569737.672085774311
211020010229.9105605192-29.910560519178
221248010301.1684516812178.83154831902
23888011202.0611019226-2322.06110192257
241128010621.9949449978658.005055002157
25948010935.4273765066-1455.42737650663
261104010517.3248936491522.675106350915
27924010700.8106081735-1460.81060817351
28936010188.3496792508-828.349679250799
2992409769.69832210112-529.698322101118
30106809381.630125128651298.36987487135
31106809630.22802627071049.7719737293
32103209913.63596356158406.364036438425
33996010058.420823659-98.4208236590403
341224010053.14897466032186.85102533973
35888010899.5785797578-2019.57857975779
361128010376.8423887698903.157611230199
37936010755.9354610972-1395.93546109725
381032010357.7746053511-37.77460535112
39984010333.4009579341-493.400957934055
40912010133.5377160981-1013.53771609814
4193609688.7668557953-328.766855795298
42108009401.797692731021398.20230726898
4398409733.2742409267106.725759073297
44117609716.324922242152043.67507775785
45996010440.0818753045-480.081875304502
461116010414.791831365745.208168634952
47924010803.8592158707-1563.85921587067
481152010396.27806055761123.72193944236
49900010846.993135421-1846.99313542098
501020010289.1160169718-89.1160169717841
511020010211.0526910788-11.0526910788303
52984010153.5944757444-313.59447574437
5387609980.99768631004-1220.99768631004
54115209435.309696169962084.69030383004
55912010014.854561971-894.854561971037
56112809677.60100852671602.3989914733
571056010193.1207701768366.879229823237
581068010401.5204008724278.479599127571
59996010612.9132120813-652.913212081303
601020010500.7787473321-300.778747332051
611020010456.7538614973-256.753861497302
621032010399.5515392293-79.5515392293073
63960010383.7314643893-783.731464389288
641008010094.5930622854-14.5930622853593
65912010017.8066410331-897.806641033092
66109209606.644300359861313.35569964014
6778009940.119664698-2140.119664698
68118809101.795173934942778.20482606506
6993609905.61426528865-545.614265288654
70109209731.507264142821188.49273585718
71984010157.0718048548-317.071804854771
72936010132.7507611696-772.750761169553
73106809905.27384235422774.726157645784
74972010184.6341154629-464.634115462877
75996010073.4987171158-113.498717115775
761068010048.733248487631.266751513002
77912010293.4757836354-1173.47578363535
78103209920.39876632804399.601233671958
79804010024.1429361991-1984.14293619907
80112809268.878636670632011.12136332937
8188809823.24562030483-943.245620304833
82110409463.022823928711576.97717607129
8396009959.44167751797-359.441677517969
8496009882.01687103705-282.016871037053
85110409798.19808559021241.8019144098
86972010260.8741275679-540.874127567931
87948010174.4829830863-694.482983086316
88102009976.64942715424223.350572845757
89936010056.0535036843-696.053503684285
90108009810.9925231033989.007476896702
91852010132.2236161925-1612.22361619245
92115209570.806383049851949.19361695015
93912010192.2945138555-1072.29451385555
94110409867.761273684251172.23872631575
95888010283.1732339018-1403.17323390182
9696009843.80679694377-243.806796943771
97104409702.57466280021737.425337199795
9888809907.08908064251-1027.08908064251
9985209519.4563100938-999.456310093801
100108009040.572624220381759.42737577962
10188809502.73084736737-622.730847367369
102105609241.081884051191318.91811594881
10384009649.70491302961-1249.70491302961
104124809220.627837609813259.37216239019
1051056010367.5650518774192.434948122598
1061080010681.037701373118.962298626993
107984010985.8628219736-1145.8628219736
108888010825.6818820368-1945.68188203685

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 9360 & 12480 & -3120 \tabularnewline
4 & 10080 & 12383.901674641 & -2303.90167464097 \tabularnewline
5 & 10080 & 12286.5997226186 & -2206.59972261865 \tabularnewline
6 & 10800 & 11997.9226809883 & -1197.92268098827 \tabularnewline
7 & 10320 & 11871.0490840588 & -1551.04908405878 \tabularnewline
8 & 9720 & 11492.4855556743 & -1772.48555567434 \tabularnewline
9 & 10440 & 10876.9187272592 & -436.918727259161 \tabularnewline
10 & 11160 & 10589.3490795406 & 570.650920459364 \tabularnewline
11 & 9480 & 10638.3386951873 & -1158.33869518731 \tabularnewline
12 & 11160 & 10092.0640638083 & 1067.93593619172 \tabularnewline
13 & 9840 & 10270.3348158893 & -430.334815889275 \tabularnewline
14 & 11160 & 9989.53600168714 & 1170.46399831286 \tabularnewline
15 & 8760 & 10269.5686225555 & -1509.56862255554 \tabularnewline
16 & 10320 & 9655.20993501641 & 664.790064983588 \tabularnewline
17 & 9600 & 9711.05990877889 & -111.059908778885 \tabularnewline
18 & 10680 & 9540.25443659428 & 1139.74556340572 \tabularnewline
19 & 10200 & 9829.95247833878 & 370.047521661221 \tabularnewline
20 & 10680 & 9942.32791422569 & 737.672085774311 \tabularnewline
21 & 10200 & 10229.9105605192 & -29.910560519178 \tabularnewline
22 & 12480 & 10301.168451681 & 2178.83154831902 \tabularnewline
23 & 8880 & 11202.0611019226 & -2322.06110192257 \tabularnewline
24 & 11280 & 10621.9949449978 & 658.005055002157 \tabularnewline
25 & 9480 & 10935.4273765066 & -1455.42737650663 \tabularnewline
26 & 11040 & 10517.3248936491 & 522.675106350915 \tabularnewline
27 & 9240 & 10700.8106081735 & -1460.81060817351 \tabularnewline
28 & 9360 & 10188.3496792508 & -828.349679250799 \tabularnewline
29 & 9240 & 9769.69832210112 & -529.698322101118 \tabularnewline
30 & 10680 & 9381.63012512865 & 1298.36987487135 \tabularnewline
31 & 10680 & 9630.2280262707 & 1049.7719737293 \tabularnewline
32 & 10320 & 9913.63596356158 & 406.364036438425 \tabularnewline
33 & 9960 & 10058.420823659 & -98.4208236590403 \tabularnewline
34 & 12240 & 10053.1489746603 & 2186.85102533973 \tabularnewline
35 & 8880 & 10899.5785797578 & -2019.57857975779 \tabularnewline
36 & 11280 & 10376.8423887698 & 903.157611230199 \tabularnewline
37 & 9360 & 10755.9354610972 & -1395.93546109725 \tabularnewline
38 & 10320 & 10357.7746053511 & -37.77460535112 \tabularnewline
39 & 9840 & 10333.4009579341 & -493.400957934055 \tabularnewline
40 & 9120 & 10133.5377160981 & -1013.53771609814 \tabularnewline
41 & 9360 & 9688.7668557953 & -328.766855795298 \tabularnewline
42 & 10800 & 9401.79769273102 & 1398.20230726898 \tabularnewline
43 & 9840 & 9733.2742409267 & 106.725759073297 \tabularnewline
44 & 11760 & 9716.32492224215 & 2043.67507775785 \tabularnewline
45 & 9960 & 10440.0818753045 & -480.081875304502 \tabularnewline
46 & 11160 & 10414.791831365 & 745.208168634952 \tabularnewline
47 & 9240 & 10803.8592158707 & -1563.85921587067 \tabularnewline
48 & 11520 & 10396.2780605576 & 1123.72193944236 \tabularnewline
49 & 9000 & 10846.993135421 & -1846.99313542098 \tabularnewline
50 & 10200 & 10289.1160169718 & -89.1160169717841 \tabularnewline
51 & 10200 & 10211.0526910788 & -11.0526910788303 \tabularnewline
52 & 9840 & 10153.5944757444 & -313.59447574437 \tabularnewline
53 & 8760 & 9980.99768631004 & -1220.99768631004 \tabularnewline
54 & 11520 & 9435.30969616996 & 2084.69030383004 \tabularnewline
55 & 9120 & 10014.854561971 & -894.854561971037 \tabularnewline
56 & 11280 & 9677.6010085267 & 1602.3989914733 \tabularnewline
57 & 10560 & 10193.1207701768 & 366.879229823237 \tabularnewline
58 & 10680 & 10401.5204008724 & 278.479599127571 \tabularnewline
59 & 9960 & 10612.9132120813 & -652.913212081303 \tabularnewline
60 & 10200 & 10500.7787473321 & -300.778747332051 \tabularnewline
61 & 10200 & 10456.7538614973 & -256.753861497302 \tabularnewline
62 & 10320 & 10399.5515392293 & -79.5515392293073 \tabularnewline
63 & 9600 & 10383.7314643893 & -783.731464389288 \tabularnewline
64 & 10080 & 10094.5930622854 & -14.5930622853593 \tabularnewline
65 & 9120 & 10017.8066410331 & -897.806641033092 \tabularnewline
66 & 10920 & 9606.64430035986 & 1313.35569964014 \tabularnewline
67 & 7800 & 9940.119664698 & -2140.119664698 \tabularnewline
68 & 11880 & 9101.79517393494 & 2778.20482606506 \tabularnewline
69 & 9360 & 9905.61426528865 & -545.614265288654 \tabularnewline
70 & 10920 & 9731.50726414282 & 1188.49273585718 \tabularnewline
71 & 9840 & 10157.0718048548 & -317.071804854771 \tabularnewline
72 & 9360 & 10132.7507611696 & -772.750761169553 \tabularnewline
73 & 10680 & 9905.27384235422 & 774.726157645784 \tabularnewline
74 & 9720 & 10184.6341154629 & -464.634115462877 \tabularnewline
75 & 9960 & 10073.4987171158 & -113.498717115775 \tabularnewline
76 & 10680 & 10048.733248487 & 631.266751513002 \tabularnewline
77 & 9120 & 10293.4757836354 & -1173.47578363535 \tabularnewline
78 & 10320 & 9920.39876632804 & 399.601233671958 \tabularnewline
79 & 8040 & 10024.1429361991 & -1984.14293619907 \tabularnewline
80 & 11280 & 9268.87863667063 & 2011.12136332937 \tabularnewline
81 & 8880 & 9823.24562030483 & -943.245620304833 \tabularnewline
82 & 11040 & 9463.02282392871 & 1576.97717607129 \tabularnewline
83 & 9600 & 9959.44167751797 & -359.441677517969 \tabularnewline
84 & 9600 & 9882.01687103705 & -282.016871037053 \tabularnewline
85 & 11040 & 9798.1980855902 & 1241.8019144098 \tabularnewline
86 & 9720 & 10260.8741275679 & -540.874127567931 \tabularnewline
87 & 9480 & 10174.4829830863 & -694.482983086316 \tabularnewline
88 & 10200 & 9976.64942715424 & 223.350572845757 \tabularnewline
89 & 9360 & 10056.0535036843 & -696.053503684285 \tabularnewline
90 & 10800 & 9810.9925231033 & 989.007476896702 \tabularnewline
91 & 8520 & 10132.2236161925 & -1612.22361619245 \tabularnewline
92 & 11520 & 9570.80638304985 & 1949.19361695015 \tabularnewline
93 & 9120 & 10192.2945138555 & -1072.29451385555 \tabularnewline
94 & 11040 & 9867.76127368425 & 1172.23872631575 \tabularnewline
95 & 8880 & 10283.1732339018 & -1403.17323390182 \tabularnewline
96 & 9600 & 9843.80679694377 & -243.806796943771 \tabularnewline
97 & 10440 & 9702.57466280021 & 737.425337199795 \tabularnewline
98 & 8880 & 9907.08908064251 & -1027.08908064251 \tabularnewline
99 & 8520 & 9519.4563100938 & -999.456310093801 \tabularnewline
100 & 10800 & 9040.57262422038 & 1759.42737577962 \tabularnewline
101 & 8880 & 9502.73084736737 & -622.730847367369 \tabularnewline
102 & 10560 & 9241.08188405119 & 1318.91811594881 \tabularnewline
103 & 8400 & 9649.70491302961 & -1249.70491302961 \tabularnewline
104 & 12480 & 9220.62783760981 & 3259.37216239019 \tabularnewline
105 & 10560 & 10367.5650518774 & 192.434948122598 \tabularnewline
106 & 10800 & 10681.037701373 & 118.962298626993 \tabularnewline
107 & 9840 & 10985.8628219736 & -1145.8628219736 \tabularnewline
108 & 8880 & 10825.6818820368 & -1945.68188203685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211237&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]3[/C][C]9360[/C][C]12480[/C][C]-3120[/C][/ROW]
[ROW][C]4[/C][C]10080[/C][C]12383.901674641[/C][C]-2303.90167464097[/C][/ROW]
[ROW][C]5[/C][C]10080[/C][C]12286.5997226186[/C][C]-2206.59972261865[/C][/ROW]
[ROW][C]6[/C][C]10800[/C][C]11997.9226809883[/C][C]-1197.92268098827[/C][/ROW]
[ROW][C]7[/C][C]10320[/C][C]11871.0490840588[/C][C]-1551.04908405878[/C][/ROW]
[ROW][C]8[/C][C]9720[/C][C]11492.4855556743[/C][C]-1772.48555567434[/C][/ROW]
[ROW][C]9[/C][C]10440[/C][C]10876.9187272592[/C][C]-436.918727259161[/C][/ROW]
[ROW][C]10[/C][C]11160[/C][C]10589.3490795406[/C][C]570.650920459364[/C][/ROW]
[ROW][C]11[/C][C]9480[/C][C]10638.3386951873[/C][C]-1158.33869518731[/C][/ROW]
[ROW][C]12[/C][C]11160[/C][C]10092.0640638083[/C][C]1067.93593619172[/C][/ROW]
[ROW][C]13[/C][C]9840[/C][C]10270.3348158893[/C][C]-430.334815889275[/C][/ROW]
[ROW][C]14[/C][C]11160[/C][C]9989.53600168714[/C][C]1170.46399831286[/C][/ROW]
[ROW][C]15[/C][C]8760[/C][C]10269.5686225555[/C][C]-1509.56862255554[/C][/ROW]
[ROW][C]16[/C][C]10320[/C][C]9655.20993501641[/C][C]664.790064983588[/C][/ROW]
[ROW][C]17[/C][C]9600[/C][C]9711.05990877889[/C][C]-111.059908778885[/C][/ROW]
[ROW][C]18[/C][C]10680[/C][C]9540.25443659428[/C][C]1139.74556340572[/C][/ROW]
[ROW][C]19[/C][C]10200[/C][C]9829.95247833878[/C][C]370.047521661221[/C][/ROW]
[ROW][C]20[/C][C]10680[/C][C]9942.32791422569[/C][C]737.672085774311[/C][/ROW]
[ROW][C]21[/C][C]10200[/C][C]10229.9105605192[/C][C]-29.910560519178[/C][/ROW]
[ROW][C]22[/C][C]12480[/C][C]10301.168451681[/C][C]2178.83154831902[/C][/ROW]
[ROW][C]23[/C][C]8880[/C][C]11202.0611019226[/C][C]-2322.06110192257[/C][/ROW]
[ROW][C]24[/C][C]11280[/C][C]10621.9949449978[/C][C]658.005055002157[/C][/ROW]
[ROW][C]25[/C][C]9480[/C][C]10935.4273765066[/C][C]-1455.42737650663[/C][/ROW]
[ROW][C]26[/C][C]11040[/C][C]10517.3248936491[/C][C]522.675106350915[/C][/ROW]
[ROW][C]27[/C][C]9240[/C][C]10700.8106081735[/C][C]-1460.81060817351[/C][/ROW]
[ROW][C]28[/C][C]9360[/C][C]10188.3496792508[/C][C]-828.349679250799[/C][/ROW]
[ROW][C]29[/C][C]9240[/C][C]9769.69832210112[/C][C]-529.698322101118[/C][/ROW]
[ROW][C]30[/C][C]10680[/C][C]9381.63012512865[/C][C]1298.36987487135[/C][/ROW]
[ROW][C]31[/C][C]10680[/C][C]9630.2280262707[/C][C]1049.7719737293[/C][/ROW]
[ROW][C]32[/C][C]10320[/C][C]9913.63596356158[/C][C]406.364036438425[/C][/ROW]
[ROW][C]33[/C][C]9960[/C][C]10058.420823659[/C][C]-98.4208236590403[/C][/ROW]
[ROW][C]34[/C][C]12240[/C][C]10053.1489746603[/C][C]2186.85102533973[/C][/ROW]
[ROW][C]35[/C][C]8880[/C][C]10899.5785797578[/C][C]-2019.57857975779[/C][/ROW]
[ROW][C]36[/C][C]11280[/C][C]10376.8423887698[/C][C]903.157611230199[/C][/ROW]
[ROW][C]37[/C][C]9360[/C][C]10755.9354610972[/C][C]-1395.93546109725[/C][/ROW]
[ROW][C]38[/C][C]10320[/C][C]10357.7746053511[/C][C]-37.77460535112[/C][/ROW]
[ROW][C]39[/C][C]9840[/C][C]10333.4009579341[/C][C]-493.400957934055[/C][/ROW]
[ROW][C]40[/C][C]9120[/C][C]10133.5377160981[/C][C]-1013.53771609814[/C][/ROW]
[ROW][C]41[/C][C]9360[/C][C]9688.7668557953[/C][C]-328.766855795298[/C][/ROW]
[ROW][C]42[/C][C]10800[/C][C]9401.79769273102[/C][C]1398.20230726898[/C][/ROW]
[ROW][C]43[/C][C]9840[/C][C]9733.2742409267[/C][C]106.725759073297[/C][/ROW]
[ROW][C]44[/C][C]11760[/C][C]9716.32492224215[/C][C]2043.67507775785[/C][/ROW]
[ROW][C]45[/C][C]9960[/C][C]10440.0818753045[/C][C]-480.081875304502[/C][/ROW]
[ROW][C]46[/C][C]11160[/C][C]10414.791831365[/C][C]745.208168634952[/C][/ROW]
[ROW][C]47[/C][C]9240[/C][C]10803.8592158707[/C][C]-1563.85921587067[/C][/ROW]
[ROW][C]48[/C][C]11520[/C][C]10396.2780605576[/C][C]1123.72193944236[/C][/ROW]
[ROW][C]49[/C][C]9000[/C][C]10846.993135421[/C][C]-1846.99313542098[/C][/ROW]
[ROW][C]50[/C][C]10200[/C][C]10289.1160169718[/C][C]-89.1160169717841[/C][/ROW]
[ROW][C]51[/C][C]10200[/C][C]10211.0526910788[/C][C]-11.0526910788303[/C][/ROW]
[ROW][C]52[/C][C]9840[/C][C]10153.5944757444[/C][C]-313.59447574437[/C][/ROW]
[ROW][C]53[/C][C]8760[/C][C]9980.99768631004[/C][C]-1220.99768631004[/C][/ROW]
[ROW][C]54[/C][C]11520[/C][C]9435.30969616996[/C][C]2084.69030383004[/C][/ROW]
[ROW][C]55[/C][C]9120[/C][C]10014.854561971[/C][C]-894.854561971037[/C][/ROW]
[ROW][C]56[/C][C]11280[/C][C]9677.6010085267[/C][C]1602.3989914733[/C][/ROW]
[ROW][C]57[/C][C]10560[/C][C]10193.1207701768[/C][C]366.879229823237[/C][/ROW]
[ROW][C]58[/C][C]10680[/C][C]10401.5204008724[/C][C]278.479599127571[/C][/ROW]
[ROW][C]59[/C][C]9960[/C][C]10612.9132120813[/C][C]-652.913212081303[/C][/ROW]
[ROW][C]60[/C][C]10200[/C][C]10500.7787473321[/C][C]-300.778747332051[/C][/ROW]
[ROW][C]61[/C][C]10200[/C][C]10456.7538614973[/C][C]-256.753861497302[/C][/ROW]
[ROW][C]62[/C][C]10320[/C][C]10399.5515392293[/C][C]-79.5515392293073[/C][/ROW]
[ROW][C]63[/C][C]9600[/C][C]10383.7314643893[/C][C]-783.731464389288[/C][/ROW]
[ROW][C]64[/C][C]10080[/C][C]10094.5930622854[/C][C]-14.5930622853593[/C][/ROW]
[ROW][C]65[/C][C]9120[/C][C]10017.8066410331[/C][C]-897.806641033092[/C][/ROW]
[ROW][C]66[/C][C]10920[/C][C]9606.64430035986[/C][C]1313.35569964014[/C][/ROW]
[ROW][C]67[/C][C]7800[/C][C]9940.119664698[/C][C]-2140.119664698[/C][/ROW]
[ROW][C]68[/C][C]11880[/C][C]9101.79517393494[/C][C]2778.20482606506[/C][/ROW]
[ROW][C]69[/C][C]9360[/C][C]9905.61426528865[/C][C]-545.614265288654[/C][/ROW]
[ROW][C]70[/C][C]10920[/C][C]9731.50726414282[/C][C]1188.49273585718[/C][/ROW]
[ROW][C]71[/C][C]9840[/C][C]10157.0718048548[/C][C]-317.071804854771[/C][/ROW]
[ROW][C]72[/C][C]9360[/C][C]10132.7507611696[/C][C]-772.750761169553[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]9905.27384235422[/C][C]774.726157645784[/C][/ROW]
[ROW][C]74[/C][C]9720[/C][C]10184.6341154629[/C][C]-464.634115462877[/C][/ROW]
[ROW][C]75[/C][C]9960[/C][C]10073.4987171158[/C][C]-113.498717115775[/C][/ROW]
[ROW][C]76[/C][C]10680[/C][C]10048.733248487[/C][C]631.266751513002[/C][/ROW]
[ROW][C]77[/C][C]9120[/C][C]10293.4757836354[/C][C]-1173.47578363535[/C][/ROW]
[ROW][C]78[/C][C]10320[/C][C]9920.39876632804[/C][C]399.601233671958[/C][/ROW]
[ROW][C]79[/C][C]8040[/C][C]10024.1429361991[/C][C]-1984.14293619907[/C][/ROW]
[ROW][C]80[/C][C]11280[/C][C]9268.87863667063[/C][C]2011.12136332937[/C][/ROW]
[ROW][C]81[/C][C]8880[/C][C]9823.24562030483[/C][C]-943.245620304833[/C][/ROW]
[ROW][C]82[/C][C]11040[/C][C]9463.02282392871[/C][C]1576.97717607129[/C][/ROW]
[ROW][C]83[/C][C]9600[/C][C]9959.44167751797[/C][C]-359.441677517969[/C][/ROW]
[ROW][C]84[/C][C]9600[/C][C]9882.01687103705[/C][C]-282.016871037053[/C][/ROW]
[ROW][C]85[/C][C]11040[/C][C]9798.1980855902[/C][C]1241.8019144098[/C][/ROW]
[ROW][C]86[/C][C]9720[/C][C]10260.8741275679[/C][C]-540.874127567931[/C][/ROW]
[ROW][C]87[/C][C]9480[/C][C]10174.4829830863[/C][C]-694.482983086316[/C][/ROW]
[ROW][C]88[/C][C]10200[/C][C]9976.64942715424[/C][C]223.350572845757[/C][/ROW]
[ROW][C]89[/C][C]9360[/C][C]10056.0535036843[/C][C]-696.053503684285[/C][/ROW]
[ROW][C]90[/C][C]10800[/C][C]9810.9925231033[/C][C]989.007476896702[/C][/ROW]
[ROW][C]91[/C][C]8520[/C][C]10132.2236161925[/C][C]-1612.22361619245[/C][/ROW]
[ROW][C]92[/C][C]11520[/C][C]9570.80638304985[/C][C]1949.19361695015[/C][/ROW]
[ROW][C]93[/C][C]9120[/C][C]10192.2945138555[/C][C]-1072.29451385555[/C][/ROW]
[ROW][C]94[/C][C]11040[/C][C]9867.76127368425[/C][C]1172.23872631575[/C][/ROW]
[ROW][C]95[/C][C]8880[/C][C]10283.1732339018[/C][C]-1403.17323390182[/C][/ROW]
[ROW][C]96[/C][C]9600[/C][C]9843.80679694377[/C][C]-243.806796943771[/C][/ROW]
[ROW][C]97[/C][C]10440[/C][C]9702.57466280021[/C][C]737.425337199795[/C][/ROW]
[ROW][C]98[/C][C]8880[/C][C]9907.08908064251[/C][C]-1027.08908064251[/C][/ROW]
[ROW][C]99[/C][C]8520[/C][C]9519.4563100938[/C][C]-999.456310093801[/C][/ROW]
[ROW][C]100[/C][C]10800[/C][C]9040.57262422038[/C][C]1759.42737577962[/C][/ROW]
[ROW][C]101[/C][C]8880[/C][C]9502.73084736737[/C][C]-622.730847367369[/C][/ROW]
[ROW][C]102[/C][C]10560[/C][C]9241.08188405119[/C][C]1318.91811594881[/C][/ROW]
[ROW][C]103[/C][C]8400[/C][C]9649.70491302961[/C][C]-1249.70491302961[/C][/ROW]
[ROW][C]104[/C][C]12480[/C][C]9220.62783760981[/C][C]3259.37216239019[/C][/ROW]
[ROW][C]105[/C][C]10560[/C][C]10367.5650518774[/C][C]192.434948122598[/C][/ROW]
[ROW][C]106[/C][C]10800[/C][C]10681.037701373[/C][C]118.962298626993[/C][/ROW]
[ROW][C]107[/C][C]9840[/C][C]10985.8628219736[/C][C]-1145.8628219736[/C][/ROW]
[ROW][C]108[/C][C]8880[/C][C]10825.6818820368[/C][C]-1945.68188203685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211237&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211237&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
3936012480-3120
41008012383.901674641-2303.90167464097
51008012286.5997226186-2206.59972261865
61080011997.9226809883-1197.92268098827
71032011871.0490840588-1551.04908405878
8972011492.4855556743-1772.48555567434
91044010876.9187272592-436.918727259161
101116010589.3490795406570.650920459364
11948010638.3386951873-1158.33869518731
121116010092.06406380831067.93593619172
13984010270.3348158893-430.334815889275
14111609989.536001687141170.46399831286
15876010269.5686225555-1509.56862255554
16103209655.20993501641664.790064983588
1796009711.05990877889-111.059908778885
18106809540.254436594281139.74556340572
19102009829.95247833878370.047521661221
20106809942.32791422569737.672085774311
211020010229.9105605192-29.910560519178
221248010301.1684516812178.83154831902
23888011202.0611019226-2322.06110192257
241128010621.9949449978658.005055002157
25948010935.4273765066-1455.42737650663
261104010517.3248936491522.675106350915
27924010700.8106081735-1460.81060817351
28936010188.3496792508-828.349679250799
2992409769.69832210112-529.698322101118
30106809381.630125128651298.36987487135
31106809630.22802627071049.7719737293
32103209913.63596356158406.364036438425
33996010058.420823659-98.4208236590403
341224010053.14897466032186.85102533973
35888010899.5785797578-2019.57857975779
361128010376.8423887698903.157611230199
37936010755.9354610972-1395.93546109725
381032010357.7746053511-37.77460535112
39984010333.4009579341-493.400957934055
40912010133.5377160981-1013.53771609814
4193609688.7668557953-328.766855795298
42108009401.797692731021398.20230726898
4398409733.2742409267106.725759073297
44117609716.324922242152043.67507775785
45996010440.0818753045-480.081875304502
461116010414.791831365745.208168634952
47924010803.8592158707-1563.85921587067
481152010396.27806055761123.72193944236
49900010846.993135421-1846.99313542098
501020010289.1160169718-89.1160169717841
511020010211.0526910788-11.0526910788303
52984010153.5944757444-313.59447574437
5387609980.99768631004-1220.99768631004
54115209435.309696169962084.69030383004
55912010014.854561971-894.854561971037
56112809677.60100852671602.3989914733
571056010193.1207701768366.879229823237
581068010401.5204008724278.479599127571
59996010612.9132120813-652.913212081303
601020010500.7787473321-300.778747332051
611020010456.7538614973-256.753861497302
621032010399.5515392293-79.5515392293073
63960010383.7314643893-783.731464389288
641008010094.5930622854-14.5930622853593
65912010017.8066410331-897.806641033092
66109209606.644300359861313.35569964014
6778009940.119664698-2140.119664698
68118809101.795173934942778.20482606506
6993609905.61426528865-545.614265288654
70109209731.507264142821188.49273585718
71984010157.0718048548-317.071804854771
72936010132.7507611696-772.750761169553
73106809905.27384235422774.726157645784
74972010184.6341154629-464.634115462877
75996010073.4987171158-113.498717115775
761068010048.733248487631.266751513002
77912010293.4757836354-1173.47578363535
78103209920.39876632804399.601233671958
79804010024.1429361991-1984.14293619907
80112809268.878636670632011.12136332937
8188809823.24562030483-943.245620304833
82110409463.022823928711576.97717607129
8396009959.44167751797-359.441677517969
8496009882.01687103705-282.016871037053
85110409798.19808559021241.8019144098
86972010260.8741275679-540.874127567931
87948010174.4829830863-694.482983086316
88102009976.64942715424223.350572845757
89936010056.0535036843-696.053503684285
90108009810.9925231033989.007476896702
91852010132.2236161925-1612.22361619245
92115209570.806383049851949.19361695015
93912010192.2945138555-1072.29451385555
94110409867.761273684251172.23872631575
95888010283.1732339018-1403.17323390182
9696009843.80679694377-243.806796943771
97104409702.57466280021737.425337199795
9888809907.08908064251-1027.08908064251
9985209519.4563100938-999.456310093801
100108009040.572624220381759.42737577962
10188809502.73084736737-622.730847367369
102105609241.081884051191318.91811594881
10384009649.70491302961-1249.70491302961
104124809220.627837609813259.37216239019
1051056010367.5650518774192.434948122598
1061080010681.037701373118.962298626993
107984010985.8628219736-1145.8628219736
108888010825.6818820368-1945.68188203685







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10910250.58134843597806.4814671175512694.6812297542
11010216.31969263987604.3386522857912828.3007329937
11110182.05803684367322.7599121200313041.3561615673
11210147.79638104756961.8729651721613333.7197969229
11310113.53472525146527.022067833613700.0473826692
11410079.27306945536025.6891976995914132.8569412109
11510045.01141365915465.4288069397714624.5940203785
11610010.7497578634852.9170414627315168.5824742633
1179976.488102066874193.7043441791715759.2718599546
1189942.226446270743492.2894557681816392.1634367733
1199907.964790474612752.2959012243617063.6336797249
1209873.703134678491976.6543471119217770.7519222451

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 10250.5813484359 & 7806.48146711755 & 12694.6812297542 \tabularnewline
110 & 10216.3196926398 & 7604.33865228579 & 12828.3007329937 \tabularnewline
111 & 10182.0580368436 & 7322.75991212003 & 13041.3561615673 \tabularnewline
112 & 10147.7963810475 & 6961.87296517216 & 13333.7197969229 \tabularnewline
113 & 10113.5347252514 & 6527.0220678336 & 13700.0473826692 \tabularnewline
114 & 10079.2730694553 & 6025.68919769959 & 14132.8569412109 \tabularnewline
115 & 10045.0114136591 & 5465.42880693977 & 14624.5940203785 \tabularnewline
116 & 10010.749757863 & 4852.91704146273 & 15168.5824742633 \tabularnewline
117 & 9976.48810206687 & 4193.70434417917 & 15759.2718599546 \tabularnewline
118 & 9942.22644627074 & 3492.28945576818 & 16392.1634367733 \tabularnewline
119 & 9907.96479047461 & 2752.29590122436 & 17063.6336797249 \tabularnewline
120 & 9873.70313467849 & 1976.65434711192 & 17770.7519222451 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211237&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]10250.5813484359[/C][C]7806.48146711755[/C][C]12694.6812297542[/C][/ROW]
[ROW][C]110[/C][C]10216.3196926398[/C][C]7604.33865228579[/C][C]12828.3007329937[/C][/ROW]
[ROW][C]111[/C][C]10182.0580368436[/C][C]7322.75991212003[/C][C]13041.3561615673[/C][/ROW]
[ROW][C]112[/C][C]10147.7963810475[/C][C]6961.87296517216[/C][C]13333.7197969229[/C][/ROW]
[ROW][C]113[/C][C]10113.5347252514[/C][C]6527.0220678336[/C][C]13700.0473826692[/C][/ROW]
[ROW][C]114[/C][C]10079.2730694553[/C][C]6025.68919769959[/C][C]14132.8569412109[/C][/ROW]
[ROW][C]115[/C][C]10045.0114136591[/C][C]5465.42880693977[/C][C]14624.5940203785[/C][/ROW]
[ROW][C]116[/C][C]10010.749757863[/C][C]4852.91704146273[/C][C]15168.5824742633[/C][/ROW]
[ROW][C]117[/C][C]9976.48810206687[/C][C]4193.70434417917[/C][C]15759.2718599546[/C][/ROW]
[ROW][C]118[/C][C]9942.22644627074[/C][C]3492.28945576818[/C][C]16392.1634367733[/C][/ROW]
[ROW][C]119[/C][C]9907.96479047461[/C][C]2752.29590122436[/C][C]17063.6336797249[/C][/ROW]
[ROW][C]120[/C][C]9873.70313467849[/C][C]1976.65434711192[/C][C]17770.7519222451[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211237&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211237&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
10910250.58134843597806.4814671175512694.6812297542
11010216.31969263987604.3386522857912828.3007329937
11110182.05803684367322.7599121200313041.3561615673
11210147.79638104756961.8729651721613333.7197969229
11310113.53472525146527.022067833613700.0473826692
11410079.27306945536025.6891976995914132.8569412109
11510045.01141365915465.4288069397714624.5940203785
11610010.7497578634852.9170414627315168.5824742633
1179976.488102066874193.7043441791715759.2718599546
1189942.226446270743492.2894557681816392.1634367733
1199907.964790474612752.2959012243617063.6336797249
1209873.703134678491976.6543471119217770.7519222451



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
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')