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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 18 Dec 2016 14:47:10 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/18/t1482068845yxzvko0xlt2ni3d.htm/, Retrieved Wed, 08 May 2024 18:35:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301094, Retrieved Wed, 08 May 2024 18:35:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
-    D    [Exponential Smoothing] [] [2016-12-18 13:47:10] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataseries X:
7430.57
7434
7366.54
7428.69
7391.84
7336.24
7404.64
7513.03
7505.53
7472.11
7404.02
7401.52
7406.21
7403.4
7429.01
7491.47
7495.54
7413.39
7357.79
7416.83
7408.7
7407.77
7357.17
7281.89
7308.76
7300.95
7269.71
7372.79
7404.02
7440.56
7516.46
7543.01
7502.41
7456.49
7496.47
7370.29
7374.03
7385.9
7321.56
7277.83
7235.36
7265.65
7305.63
7197.88
7135.72
6934.57
6983.3
6988.61
7011.72
6977.05
6932.39
6977.68
6994.23
6940.51
6799.33
6735.92
6584.44
6574.13
6481.06
6516.66
6516.66
6640.66
6639.41
6726.55
6755.29
6767.16
6709.06
6722.18
6624.42
6630.67
6705.94
6697.51
6691.26
6643.78
6539.77
6541.34
6446.7
6452.32
6299.59
6326.45
6216.5
6244.3
6246.8
6275.22
6216.19
6343
6429.52
6518.54
6466.69
6696.26
6876.48
6665.65
6627.23
6566.01
6560.39




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301094&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301094&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301094&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.011836705896918
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.011836705896918 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301094&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.011836705896918[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301094&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301094&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
alpha1
beta0.011836705896918
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
37366.547437.43-70.8900000000003
47428.697369.1308959189759.5591040810323
57391.847431.98587951746-40.1458795174585
67336.247394.66068454864-58.4206845486378
77404.647338.3691760873466.2708239126614
87513.037407.55360433954105.47639566046
97505.537517.19209741404-11.6620974140396
107472.117509.55405659681-37.444056596808
117404.027475.69084231128-71.6708423112832
127401.527406.75249562946-5.23249562946057
137406.217404.190560117592.01943988241146
147403.47408.90446363355-5.50446363355331
157429.017406.029308916422.9806910835987
167491.477431.9113245980759.5586754019332
177495.547495.076303122410.463696877590337
187413.397499.15179176597-85.7617917659745
197357.797415.98665465965-58.1966546596486
207416.837359.6977979742657.132202025743
217408.77419.41405504688-10.7140550468794
227407.777411.15723592833-3.38723592832503
237357.177410.18714221284-53.0171422128396
247281.897358.95959389297-77.0695938929703
257308.767282.7673437764725.9926562235351
267300.957309.94501120366-8.99501120366222
277269.717302.0285399015-32.3185399015047
287372.797270.40599484967102.384005150327
297404.027374.6978842071929.3221157928147
307440.567406.274961468134.2850385318989
317516.467443.2207833858773.2392166141317
327543.017519.9876944530523.0223055469505
337502.417546.81020271288-44.4002027128781
347456.497505.6846505716-49.1946505716023
357496.477459.1823479610837.2876520389163
367370.297499.60371093186-129.313710931856
377374.037371.893062567122.13693743288331
387385.97375.6583568670310.2416431329702
397321.567387.6495841847-66.089584184695
407277.837322.52730121385-44.6973012138524
417235.367278.268232405-42.9082324049978
427265.657235.2903402774630.3596597225369
437305.637265.9396986407339.6903013592719
447197.887306.38950106488-108.509501064878
457135.727197.35510601375-61.6351060137522
466934.577134.46554939094-199.895549390943
476983.36930.949444562752.3505554373014
486988.616980.299102690958.31089730904932
497011.726985.7074763381426.0125236618633
506977.057009.12537893036-32.075378930359
516932.396974.07571210343-41.6857121034282
526977.686928.9222905891648.7577094108437
536994.236974.7894212556619.4405787443393
546940.516991.56953366872-51.059533668722
556799.336937.24515698545-137.915156985452
566735.926794.43269583349-58.5126958334877
576584.446730.33009826167-145.890098261671
586574.136577.12324007528-2.99324007527503
596481.066566.77780997283-85.7178099728253
606516.666472.6931934660543.9668065339501
616516.666508.813615624227.84638437578178
626640.666508.90649096843131.753509031571
636639.416634.466018505724.94398149427798
646726.556633.2745389606393.2754610393704
656755.296721.5186131603533.7713868396477
666767.166750.658355134116.5016448658953
676709.066762.7236802512-53.6636802511966
686722.186703.9884790507218.1915209492827
696624.426717.32380673401-92.9038067340125
706630.676618.46413169712.2058683030027
716705.946624.8586089703281.0813910296829
726697.516701.08834554965-3.57834554964757
736691.266692.61598972578-1.35598972577918
746643.786686.3499392742-42.5699392741963
756539.776638.36605142296-98.5960514229564
766541.346533.188998959678.15100104033354
776446.76534.85547996175-88.155479961747
786452.326439.1720094722413.147990527762
796299.596444.94763836925-145.35763836925
806326.456290.49708275435.952917245997
816216.56317.78264686158-101.282646861579
826244.36206.6337939582237.6662060417821
836246.86234.8796377613911.9203622386131
846275.226237.5207355833937.6992644166094
856216.196266.38697068882-50.1969706888203
8663436206.76280390986136.23719609014
876429.526335.185403532294.3345964678001
886518.546422.8220144064995.7179855935055
896466.696512.97500005101-46.2850000510098
906696.266460.57713811797235.682861882034
916876.486692.93684683901183.543153160991
926665.656875.32939316237-209.679393162368
936627.236662.01747985286-34.787479852861
946566.016623.18571068495-57.1757106849473
956560.396561.28893861312-0.898938613122482

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 7366.54 & 7437.43 & -70.8900000000003 \tabularnewline
4 & 7428.69 & 7369.13089591897 & 59.5591040810323 \tabularnewline
5 & 7391.84 & 7431.98587951746 & -40.1458795174585 \tabularnewline
6 & 7336.24 & 7394.66068454864 & -58.4206845486378 \tabularnewline
7 & 7404.64 & 7338.36917608734 & 66.2708239126614 \tabularnewline
8 & 7513.03 & 7407.55360433954 & 105.47639566046 \tabularnewline
9 & 7505.53 & 7517.19209741404 & -11.6620974140396 \tabularnewline
10 & 7472.11 & 7509.55405659681 & -37.444056596808 \tabularnewline
11 & 7404.02 & 7475.69084231128 & -71.6708423112832 \tabularnewline
12 & 7401.52 & 7406.75249562946 & -5.23249562946057 \tabularnewline
13 & 7406.21 & 7404.19056011759 & 2.01943988241146 \tabularnewline
14 & 7403.4 & 7408.90446363355 & -5.50446363355331 \tabularnewline
15 & 7429.01 & 7406.0293089164 & 22.9806910835987 \tabularnewline
16 & 7491.47 & 7431.91132459807 & 59.5586754019332 \tabularnewline
17 & 7495.54 & 7495.07630312241 & 0.463696877590337 \tabularnewline
18 & 7413.39 & 7499.15179176597 & -85.7617917659745 \tabularnewline
19 & 7357.79 & 7415.98665465965 & -58.1966546596486 \tabularnewline
20 & 7416.83 & 7359.69779797426 & 57.132202025743 \tabularnewline
21 & 7408.7 & 7419.41405504688 & -10.7140550468794 \tabularnewline
22 & 7407.77 & 7411.15723592833 & -3.38723592832503 \tabularnewline
23 & 7357.17 & 7410.18714221284 & -53.0171422128396 \tabularnewline
24 & 7281.89 & 7358.95959389297 & -77.0695938929703 \tabularnewline
25 & 7308.76 & 7282.76734377647 & 25.9926562235351 \tabularnewline
26 & 7300.95 & 7309.94501120366 & -8.99501120366222 \tabularnewline
27 & 7269.71 & 7302.0285399015 & -32.3185399015047 \tabularnewline
28 & 7372.79 & 7270.40599484967 & 102.384005150327 \tabularnewline
29 & 7404.02 & 7374.69788420719 & 29.3221157928147 \tabularnewline
30 & 7440.56 & 7406.2749614681 & 34.2850385318989 \tabularnewline
31 & 7516.46 & 7443.22078338587 & 73.2392166141317 \tabularnewline
32 & 7543.01 & 7519.98769445305 & 23.0223055469505 \tabularnewline
33 & 7502.41 & 7546.81020271288 & -44.4002027128781 \tabularnewline
34 & 7456.49 & 7505.6846505716 & -49.1946505716023 \tabularnewline
35 & 7496.47 & 7459.18234796108 & 37.2876520389163 \tabularnewline
36 & 7370.29 & 7499.60371093186 & -129.313710931856 \tabularnewline
37 & 7374.03 & 7371.89306256712 & 2.13693743288331 \tabularnewline
38 & 7385.9 & 7375.65835686703 & 10.2416431329702 \tabularnewline
39 & 7321.56 & 7387.6495841847 & -66.089584184695 \tabularnewline
40 & 7277.83 & 7322.52730121385 & -44.6973012138524 \tabularnewline
41 & 7235.36 & 7278.268232405 & -42.9082324049978 \tabularnewline
42 & 7265.65 & 7235.29034027746 & 30.3596597225369 \tabularnewline
43 & 7305.63 & 7265.93969864073 & 39.6903013592719 \tabularnewline
44 & 7197.88 & 7306.38950106488 & -108.509501064878 \tabularnewline
45 & 7135.72 & 7197.35510601375 & -61.6351060137522 \tabularnewline
46 & 6934.57 & 7134.46554939094 & -199.895549390943 \tabularnewline
47 & 6983.3 & 6930.9494445627 & 52.3505554373014 \tabularnewline
48 & 6988.61 & 6980.29910269095 & 8.31089730904932 \tabularnewline
49 & 7011.72 & 6985.70747633814 & 26.0125236618633 \tabularnewline
50 & 6977.05 & 7009.12537893036 & -32.075378930359 \tabularnewline
51 & 6932.39 & 6974.07571210343 & -41.6857121034282 \tabularnewline
52 & 6977.68 & 6928.92229058916 & 48.7577094108437 \tabularnewline
53 & 6994.23 & 6974.78942125566 & 19.4405787443393 \tabularnewline
54 & 6940.51 & 6991.56953366872 & -51.059533668722 \tabularnewline
55 & 6799.33 & 6937.24515698545 & -137.915156985452 \tabularnewline
56 & 6735.92 & 6794.43269583349 & -58.5126958334877 \tabularnewline
57 & 6584.44 & 6730.33009826167 & -145.890098261671 \tabularnewline
58 & 6574.13 & 6577.12324007528 & -2.99324007527503 \tabularnewline
59 & 6481.06 & 6566.77780997283 & -85.7178099728253 \tabularnewline
60 & 6516.66 & 6472.69319346605 & 43.9668065339501 \tabularnewline
61 & 6516.66 & 6508.81361562422 & 7.84638437578178 \tabularnewline
62 & 6640.66 & 6508.90649096843 & 131.753509031571 \tabularnewline
63 & 6639.41 & 6634.46601850572 & 4.94398149427798 \tabularnewline
64 & 6726.55 & 6633.27453896063 & 93.2754610393704 \tabularnewline
65 & 6755.29 & 6721.51861316035 & 33.7713868396477 \tabularnewline
66 & 6767.16 & 6750.6583551341 & 16.5016448658953 \tabularnewline
67 & 6709.06 & 6762.7236802512 & -53.6636802511966 \tabularnewline
68 & 6722.18 & 6703.98847905072 & 18.1915209492827 \tabularnewline
69 & 6624.42 & 6717.32380673401 & -92.9038067340125 \tabularnewline
70 & 6630.67 & 6618.464131697 & 12.2058683030027 \tabularnewline
71 & 6705.94 & 6624.85860897032 & 81.0813910296829 \tabularnewline
72 & 6697.51 & 6701.08834554965 & -3.57834554964757 \tabularnewline
73 & 6691.26 & 6692.61598972578 & -1.35598972577918 \tabularnewline
74 & 6643.78 & 6686.3499392742 & -42.5699392741963 \tabularnewline
75 & 6539.77 & 6638.36605142296 & -98.5960514229564 \tabularnewline
76 & 6541.34 & 6533.18899895967 & 8.15100104033354 \tabularnewline
77 & 6446.7 & 6534.85547996175 & -88.155479961747 \tabularnewline
78 & 6452.32 & 6439.17200947224 & 13.147990527762 \tabularnewline
79 & 6299.59 & 6444.94763836925 & -145.35763836925 \tabularnewline
80 & 6326.45 & 6290.497082754 & 35.952917245997 \tabularnewline
81 & 6216.5 & 6317.78264686158 & -101.282646861579 \tabularnewline
82 & 6244.3 & 6206.63379395822 & 37.6662060417821 \tabularnewline
83 & 6246.8 & 6234.87963776139 & 11.9203622386131 \tabularnewline
84 & 6275.22 & 6237.52073558339 & 37.6992644166094 \tabularnewline
85 & 6216.19 & 6266.38697068882 & -50.1969706888203 \tabularnewline
86 & 6343 & 6206.76280390986 & 136.23719609014 \tabularnewline
87 & 6429.52 & 6335.1854035322 & 94.3345964678001 \tabularnewline
88 & 6518.54 & 6422.82201440649 & 95.7179855935055 \tabularnewline
89 & 6466.69 & 6512.97500005101 & -46.2850000510098 \tabularnewline
90 & 6696.26 & 6460.57713811797 & 235.682861882034 \tabularnewline
91 & 6876.48 & 6692.93684683901 & 183.543153160991 \tabularnewline
92 & 6665.65 & 6875.32939316237 & -209.679393162368 \tabularnewline
93 & 6627.23 & 6662.01747985286 & -34.787479852861 \tabularnewline
94 & 6566.01 & 6623.18571068495 & -57.1757106849473 \tabularnewline
95 & 6560.39 & 6561.28893861312 & -0.898938613122482 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301094&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]7366.54[/C][C]7437.43[/C][C]-70.8900000000003[/C][/ROW]
[ROW][C]4[/C][C]7428.69[/C][C]7369.13089591897[/C][C]59.5591040810323[/C][/ROW]
[ROW][C]5[/C][C]7391.84[/C][C]7431.98587951746[/C][C]-40.1458795174585[/C][/ROW]
[ROW][C]6[/C][C]7336.24[/C][C]7394.66068454864[/C][C]-58.4206845486378[/C][/ROW]
[ROW][C]7[/C][C]7404.64[/C][C]7338.36917608734[/C][C]66.2708239126614[/C][/ROW]
[ROW][C]8[/C][C]7513.03[/C][C]7407.55360433954[/C][C]105.47639566046[/C][/ROW]
[ROW][C]9[/C][C]7505.53[/C][C]7517.19209741404[/C][C]-11.6620974140396[/C][/ROW]
[ROW][C]10[/C][C]7472.11[/C][C]7509.55405659681[/C][C]-37.444056596808[/C][/ROW]
[ROW][C]11[/C][C]7404.02[/C][C]7475.69084231128[/C][C]-71.6708423112832[/C][/ROW]
[ROW][C]12[/C][C]7401.52[/C][C]7406.75249562946[/C][C]-5.23249562946057[/C][/ROW]
[ROW][C]13[/C][C]7406.21[/C][C]7404.19056011759[/C][C]2.01943988241146[/C][/ROW]
[ROW][C]14[/C][C]7403.4[/C][C]7408.90446363355[/C][C]-5.50446363355331[/C][/ROW]
[ROW][C]15[/C][C]7429.01[/C][C]7406.0293089164[/C][C]22.9806910835987[/C][/ROW]
[ROW][C]16[/C][C]7491.47[/C][C]7431.91132459807[/C][C]59.5586754019332[/C][/ROW]
[ROW][C]17[/C][C]7495.54[/C][C]7495.07630312241[/C][C]0.463696877590337[/C][/ROW]
[ROW][C]18[/C][C]7413.39[/C][C]7499.15179176597[/C][C]-85.7617917659745[/C][/ROW]
[ROW][C]19[/C][C]7357.79[/C][C]7415.98665465965[/C][C]-58.1966546596486[/C][/ROW]
[ROW][C]20[/C][C]7416.83[/C][C]7359.69779797426[/C][C]57.132202025743[/C][/ROW]
[ROW][C]21[/C][C]7408.7[/C][C]7419.41405504688[/C][C]-10.7140550468794[/C][/ROW]
[ROW][C]22[/C][C]7407.77[/C][C]7411.15723592833[/C][C]-3.38723592832503[/C][/ROW]
[ROW][C]23[/C][C]7357.17[/C][C]7410.18714221284[/C][C]-53.0171422128396[/C][/ROW]
[ROW][C]24[/C][C]7281.89[/C][C]7358.95959389297[/C][C]-77.0695938929703[/C][/ROW]
[ROW][C]25[/C][C]7308.76[/C][C]7282.76734377647[/C][C]25.9926562235351[/C][/ROW]
[ROW][C]26[/C][C]7300.95[/C][C]7309.94501120366[/C][C]-8.99501120366222[/C][/ROW]
[ROW][C]27[/C][C]7269.71[/C][C]7302.0285399015[/C][C]-32.3185399015047[/C][/ROW]
[ROW][C]28[/C][C]7372.79[/C][C]7270.40599484967[/C][C]102.384005150327[/C][/ROW]
[ROW][C]29[/C][C]7404.02[/C][C]7374.69788420719[/C][C]29.3221157928147[/C][/ROW]
[ROW][C]30[/C][C]7440.56[/C][C]7406.2749614681[/C][C]34.2850385318989[/C][/ROW]
[ROW][C]31[/C][C]7516.46[/C][C]7443.22078338587[/C][C]73.2392166141317[/C][/ROW]
[ROW][C]32[/C][C]7543.01[/C][C]7519.98769445305[/C][C]23.0223055469505[/C][/ROW]
[ROW][C]33[/C][C]7502.41[/C][C]7546.81020271288[/C][C]-44.4002027128781[/C][/ROW]
[ROW][C]34[/C][C]7456.49[/C][C]7505.6846505716[/C][C]-49.1946505716023[/C][/ROW]
[ROW][C]35[/C][C]7496.47[/C][C]7459.18234796108[/C][C]37.2876520389163[/C][/ROW]
[ROW][C]36[/C][C]7370.29[/C][C]7499.60371093186[/C][C]-129.313710931856[/C][/ROW]
[ROW][C]37[/C][C]7374.03[/C][C]7371.89306256712[/C][C]2.13693743288331[/C][/ROW]
[ROW][C]38[/C][C]7385.9[/C][C]7375.65835686703[/C][C]10.2416431329702[/C][/ROW]
[ROW][C]39[/C][C]7321.56[/C][C]7387.6495841847[/C][C]-66.089584184695[/C][/ROW]
[ROW][C]40[/C][C]7277.83[/C][C]7322.52730121385[/C][C]-44.6973012138524[/C][/ROW]
[ROW][C]41[/C][C]7235.36[/C][C]7278.268232405[/C][C]-42.9082324049978[/C][/ROW]
[ROW][C]42[/C][C]7265.65[/C][C]7235.29034027746[/C][C]30.3596597225369[/C][/ROW]
[ROW][C]43[/C][C]7305.63[/C][C]7265.93969864073[/C][C]39.6903013592719[/C][/ROW]
[ROW][C]44[/C][C]7197.88[/C][C]7306.38950106488[/C][C]-108.509501064878[/C][/ROW]
[ROW][C]45[/C][C]7135.72[/C][C]7197.35510601375[/C][C]-61.6351060137522[/C][/ROW]
[ROW][C]46[/C][C]6934.57[/C][C]7134.46554939094[/C][C]-199.895549390943[/C][/ROW]
[ROW][C]47[/C][C]6983.3[/C][C]6930.9494445627[/C][C]52.3505554373014[/C][/ROW]
[ROW][C]48[/C][C]6988.61[/C][C]6980.29910269095[/C][C]8.31089730904932[/C][/ROW]
[ROW][C]49[/C][C]7011.72[/C][C]6985.70747633814[/C][C]26.0125236618633[/C][/ROW]
[ROW][C]50[/C][C]6977.05[/C][C]7009.12537893036[/C][C]-32.075378930359[/C][/ROW]
[ROW][C]51[/C][C]6932.39[/C][C]6974.07571210343[/C][C]-41.6857121034282[/C][/ROW]
[ROW][C]52[/C][C]6977.68[/C][C]6928.92229058916[/C][C]48.7577094108437[/C][/ROW]
[ROW][C]53[/C][C]6994.23[/C][C]6974.78942125566[/C][C]19.4405787443393[/C][/ROW]
[ROW][C]54[/C][C]6940.51[/C][C]6991.56953366872[/C][C]-51.059533668722[/C][/ROW]
[ROW][C]55[/C][C]6799.33[/C][C]6937.24515698545[/C][C]-137.915156985452[/C][/ROW]
[ROW][C]56[/C][C]6735.92[/C][C]6794.43269583349[/C][C]-58.5126958334877[/C][/ROW]
[ROW][C]57[/C][C]6584.44[/C][C]6730.33009826167[/C][C]-145.890098261671[/C][/ROW]
[ROW][C]58[/C][C]6574.13[/C][C]6577.12324007528[/C][C]-2.99324007527503[/C][/ROW]
[ROW][C]59[/C][C]6481.06[/C][C]6566.77780997283[/C][C]-85.7178099728253[/C][/ROW]
[ROW][C]60[/C][C]6516.66[/C][C]6472.69319346605[/C][C]43.9668065339501[/C][/ROW]
[ROW][C]61[/C][C]6516.66[/C][C]6508.81361562422[/C][C]7.84638437578178[/C][/ROW]
[ROW][C]62[/C][C]6640.66[/C][C]6508.90649096843[/C][C]131.753509031571[/C][/ROW]
[ROW][C]63[/C][C]6639.41[/C][C]6634.46601850572[/C][C]4.94398149427798[/C][/ROW]
[ROW][C]64[/C][C]6726.55[/C][C]6633.27453896063[/C][C]93.2754610393704[/C][/ROW]
[ROW][C]65[/C][C]6755.29[/C][C]6721.51861316035[/C][C]33.7713868396477[/C][/ROW]
[ROW][C]66[/C][C]6767.16[/C][C]6750.6583551341[/C][C]16.5016448658953[/C][/ROW]
[ROW][C]67[/C][C]6709.06[/C][C]6762.7236802512[/C][C]-53.6636802511966[/C][/ROW]
[ROW][C]68[/C][C]6722.18[/C][C]6703.98847905072[/C][C]18.1915209492827[/C][/ROW]
[ROW][C]69[/C][C]6624.42[/C][C]6717.32380673401[/C][C]-92.9038067340125[/C][/ROW]
[ROW][C]70[/C][C]6630.67[/C][C]6618.464131697[/C][C]12.2058683030027[/C][/ROW]
[ROW][C]71[/C][C]6705.94[/C][C]6624.85860897032[/C][C]81.0813910296829[/C][/ROW]
[ROW][C]72[/C][C]6697.51[/C][C]6701.08834554965[/C][C]-3.57834554964757[/C][/ROW]
[ROW][C]73[/C][C]6691.26[/C][C]6692.61598972578[/C][C]-1.35598972577918[/C][/ROW]
[ROW][C]74[/C][C]6643.78[/C][C]6686.3499392742[/C][C]-42.5699392741963[/C][/ROW]
[ROW][C]75[/C][C]6539.77[/C][C]6638.36605142296[/C][C]-98.5960514229564[/C][/ROW]
[ROW][C]76[/C][C]6541.34[/C][C]6533.18899895967[/C][C]8.15100104033354[/C][/ROW]
[ROW][C]77[/C][C]6446.7[/C][C]6534.85547996175[/C][C]-88.155479961747[/C][/ROW]
[ROW][C]78[/C][C]6452.32[/C][C]6439.17200947224[/C][C]13.147990527762[/C][/ROW]
[ROW][C]79[/C][C]6299.59[/C][C]6444.94763836925[/C][C]-145.35763836925[/C][/ROW]
[ROW][C]80[/C][C]6326.45[/C][C]6290.497082754[/C][C]35.952917245997[/C][/ROW]
[ROW][C]81[/C][C]6216.5[/C][C]6317.78264686158[/C][C]-101.282646861579[/C][/ROW]
[ROW][C]82[/C][C]6244.3[/C][C]6206.63379395822[/C][C]37.6662060417821[/C][/ROW]
[ROW][C]83[/C][C]6246.8[/C][C]6234.87963776139[/C][C]11.9203622386131[/C][/ROW]
[ROW][C]84[/C][C]6275.22[/C][C]6237.52073558339[/C][C]37.6992644166094[/C][/ROW]
[ROW][C]85[/C][C]6216.19[/C][C]6266.38697068882[/C][C]-50.1969706888203[/C][/ROW]
[ROW][C]86[/C][C]6343[/C][C]6206.76280390986[/C][C]136.23719609014[/C][/ROW]
[ROW][C]87[/C][C]6429.52[/C][C]6335.1854035322[/C][C]94.3345964678001[/C][/ROW]
[ROW][C]88[/C][C]6518.54[/C][C]6422.82201440649[/C][C]95.7179855935055[/C][/ROW]
[ROW][C]89[/C][C]6466.69[/C][C]6512.97500005101[/C][C]-46.2850000510098[/C][/ROW]
[ROW][C]90[/C][C]6696.26[/C][C]6460.57713811797[/C][C]235.682861882034[/C][/ROW]
[ROW][C]91[/C][C]6876.48[/C][C]6692.93684683901[/C][C]183.543153160991[/C][/ROW]
[ROW][C]92[/C][C]6665.65[/C][C]6875.32939316237[/C][C]-209.679393162368[/C][/ROW]
[ROW][C]93[/C][C]6627.23[/C][C]6662.01747985286[/C][C]-34.787479852861[/C][/ROW]
[ROW][C]94[/C][C]6566.01[/C][C]6623.18571068495[/C][C]-57.1757106849473[/C][/ROW]
[ROW][C]95[/C][C]6560.39[/C][C]6561.28893861312[/C][C]-0.898938613122482[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301094&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301094&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
37366.547437.43-70.8900000000003
47428.697369.1308959189759.5591040810323
57391.847431.98587951746-40.1458795174585
67336.247394.66068454864-58.4206845486378
77404.647338.3691760873466.2708239126614
87513.037407.55360433954105.47639566046
97505.537517.19209741404-11.6620974140396
107472.117509.55405659681-37.444056596808
117404.027475.69084231128-71.6708423112832
127401.527406.75249562946-5.23249562946057
137406.217404.190560117592.01943988241146
147403.47408.90446363355-5.50446363355331
157429.017406.029308916422.9806910835987
167491.477431.9113245980759.5586754019332
177495.547495.076303122410.463696877590337
187413.397499.15179176597-85.7617917659745
197357.797415.98665465965-58.1966546596486
207416.837359.6977979742657.132202025743
217408.77419.41405504688-10.7140550468794
227407.777411.15723592833-3.38723592832503
237357.177410.18714221284-53.0171422128396
247281.897358.95959389297-77.0695938929703
257308.767282.7673437764725.9926562235351
267300.957309.94501120366-8.99501120366222
277269.717302.0285399015-32.3185399015047
287372.797270.40599484967102.384005150327
297404.027374.6978842071929.3221157928147
307440.567406.274961468134.2850385318989
317516.467443.2207833858773.2392166141317
327543.017519.9876944530523.0223055469505
337502.417546.81020271288-44.4002027128781
347456.497505.6846505716-49.1946505716023
357496.477459.1823479610837.2876520389163
367370.297499.60371093186-129.313710931856
377374.037371.893062567122.13693743288331
387385.97375.6583568670310.2416431329702
397321.567387.6495841847-66.089584184695
407277.837322.52730121385-44.6973012138524
417235.367278.268232405-42.9082324049978
427265.657235.2903402774630.3596597225369
437305.637265.9396986407339.6903013592719
447197.887306.38950106488-108.509501064878
457135.727197.35510601375-61.6351060137522
466934.577134.46554939094-199.895549390943
476983.36930.949444562752.3505554373014
486988.616980.299102690958.31089730904932
497011.726985.7074763381426.0125236618633
506977.057009.12537893036-32.075378930359
516932.396974.07571210343-41.6857121034282
526977.686928.9222905891648.7577094108437
536994.236974.7894212556619.4405787443393
546940.516991.56953366872-51.059533668722
556799.336937.24515698545-137.915156985452
566735.926794.43269583349-58.5126958334877
576584.446730.33009826167-145.890098261671
586574.136577.12324007528-2.99324007527503
596481.066566.77780997283-85.7178099728253
606516.666472.6931934660543.9668065339501
616516.666508.813615624227.84638437578178
626640.666508.90649096843131.753509031571
636639.416634.466018505724.94398149427798
646726.556633.2745389606393.2754610393704
656755.296721.5186131603533.7713868396477
666767.166750.658355134116.5016448658953
676709.066762.7236802512-53.6636802511966
686722.186703.9884790507218.1915209492827
696624.426717.32380673401-92.9038067340125
706630.676618.46413169712.2058683030027
716705.946624.8586089703281.0813910296829
726697.516701.08834554965-3.57834554964757
736691.266692.61598972578-1.35598972577918
746643.786686.3499392742-42.5699392741963
756539.776638.36605142296-98.5960514229564
766541.346533.188998959678.15100104033354
776446.76534.85547996175-88.155479961747
786452.326439.1720094722413.147990527762
796299.596444.94763836925-145.35763836925
806326.456290.49708275435.952917245997
816216.56317.78264686158-101.282646861579
826244.36206.6337939582237.6662060417821
836246.86234.8796377613911.9203622386131
846275.226237.5207355833937.6992644166094
856216.196266.38697068882-50.1969706888203
8663436206.76280390986136.23719609014
876429.526335.185403532294.3345964678001
886518.546422.8220144064995.7179855935055
896466.696512.97500005101-46.2850000510098
906696.266460.57713811797235.682861882034
916876.486692.93684683901183.543153160991
926665.656875.32939316237-209.679393162368
936627.236662.01747985286-34.787479852861
946566.016623.18571068495-57.1757106849473
956560.396561.28893861312-0.898938613122482







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
966555.658298141146409.487285610496701.82931067179
976550.926596282286342.982544604386758.87064796018
986546.194894423426290.010823411256802.37896543559
996541.463192564566243.905465712976839.02091941615
1006536.73149070576202.100823547466871.36215786394
1016531.999788846846163.289179981526900.71039771216
1026527.268086987986126.698396498696927.83777747727
1036522.536385129126091.828407471726953.24436278651
1046517.804683270266058.333949278036977.27541726249
1056513.07298141146025.965145157457000.18081766534
1066508.341279552545994.534491625367022.14806747972
1076503.609577693685963.897195026847043.32196036051

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
96 & 6555.65829814114 & 6409.48728561049 & 6701.82931067179 \tabularnewline
97 & 6550.92659628228 & 6342.98254460438 & 6758.87064796018 \tabularnewline
98 & 6546.19489442342 & 6290.01082341125 & 6802.37896543559 \tabularnewline
99 & 6541.46319256456 & 6243.90546571297 & 6839.02091941615 \tabularnewline
100 & 6536.7314907057 & 6202.10082354746 & 6871.36215786394 \tabularnewline
101 & 6531.99978884684 & 6163.28917998152 & 6900.71039771216 \tabularnewline
102 & 6527.26808698798 & 6126.69839649869 & 6927.83777747727 \tabularnewline
103 & 6522.53638512912 & 6091.82840747172 & 6953.24436278651 \tabularnewline
104 & 6517.80468327026 & 6058.33394927803 & 6977.27541726249 \tabularnewline
105 & 6513.0729814114 & 6025.96514515745 & 7000.18081766534 \tabularnewline
106 & 6508.34127955254 & 5994.53449162536 & 7022.14806747972 \tabularnewline
107 & 6503.60957769368 & 5963.89719502684 & 7043.32196036051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301094&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]96[/C][C]6555.65829814114[/C][C]6409.48728561049[/C][C]6701.82931067179[/C][/ROW]
[ROW][C]97[/C][C]6550.92659628228[/C][C]6342.98254460438[/C][C]6758.87064796018[/C][/ROW]
[ROW][C]98[/C][C]6546.19489442342[/C][C]6290.01082341125[/C][C]6802.37896543559[/C][/ROW]
[ROW][C]99[/C][C]6541.46319256456[/C][C]6243.90546571297[/C][C]6839.02091941615[/C][/ROW]
[ROW][C]100[/C][C]6536.7314907057[/C][C]6202.10082354746[/C][C]6871.36215786394[/C][/ROW]
[ROW][C]101[/C][C]6531.99978884684[/C][C]6163.28917998152[/C][C]6900.71039771216[/C][/ROW]
[ROW][C]102[/C][C]6527.26808698798[/C][C]6126.69839649869[/C][C]6927.83777747727[/C][/ROW]
[ROW][C]103[/C][C]6522.53638512912[/C][C]6091.82840747172[/C][C]6953.24436278651[/C][/ROW]
[ROW][C]104[/C][C]6517.80468327026[/C][C]6058.33394927803[/C][C]6977.27541726249[/C][/ROW]
[ROW][C]105[/C][C]6513.0729814114[/C][C]6025.96514515745[/C][C]7000.18081766534[/C][/ROW]
[ROW][C]106[/C][C]6508.34127955254[/C][C]5994.53449162536[/C][C]7022.14806747972[/C][/ROW]
[ROW][C]107[/C][C]6503.60957769368[/C][C]5963.89719502684[/C][C]7043.32196036051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301094&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301094&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
966555.658298141146409.487285610496701.82931067179
976550.926596282286342.982544604386758.87064796018
986546.194894423426290.010823411256802.37896543559
996541.463192564566243.905465712976839.02091941615
1006536.73149070576202.100823547466871.36215786394
1016531.999788846846163.289179981526900.71039771216
1026527.268086987986126.698396498696927.83777747727
1036522.536385129126091.828407471726953.24436278651
1046517.804683270266058.333949278036977.27541726249
1056513.07298141146025.965145157457000.18081766534
1066508.341279552545994.534491625367022.14806747972
1076503.609577693685963.897195026847043.32196036051



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')