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of Irreproducible Research!

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, 11 Dec 2016 13:41:21 +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/11/t148146021529eiy55negw6sos.htm/, Retrieved Thu, 02 May 2024 00:04:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298773, Retrieved Thu, 02 May 2024 00:04:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [N2474 exp smoothing] [2016-12-11 12:41:21] [fe6e63930acb843607fc81833855c27b] [Current]
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Dataseries X:
6788
6783
6795
6835
6889
6926
6957
6984
7159
7121
7165
7208
7217
7250
7281
7298
7310
7362
7387
7414
7449
7473
7513
7522
7588
7602
7643
7651
7661
7688
7728
7750
7759
7760
7806
7864
7859
7926
7978
7999
8056
8104
8146
8171
8199
8212
8242
8269
8279
8323
8350
8372
8403
8412
8460
8484
8498
8527
8519
8537
8526
8549
8594
8767
8690
8657
8680
8714
8746
8671
8654
8677
8765
8760
8812
8822
8837
8997
8875
8905
8927
8950
9010
9086
9161
9248
9285
9335
9354
9267
9403
9469
9464
9630
9724
9764
9806
9869
9907
9914
9922
9950
9982
9981
10045
10067
10080
10051
9962
9896
9849
9854
9847
9845




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=298773&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=298773&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298773&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
alpha0.876781542793911
beta0.167070413692615
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.876781542793911 \tabularnewline
beta & 0.167070413692615 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298773&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]0.876781542793911[/C][/ROW]
[ROW][C]beta[/C][C]0.167070413692615[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298773&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298773&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
alpha0.876781542793911
beta0.167070413692615
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
36795677817
468356790.3955185637344.6044814362695
568896833.5279911852755.4720088147278
669266894.3146871166631.6853128833391
769576938.8870465458218.1129534541833
869846974.212674229229.78732577077517
971597003.67223435233155.327765647668
1071217183.4920379326-62.4920379325995
1171657163.177358454171.8226415458339
1272087199.519591162248.48040883776412
1372177242.9414777194-25.9414777193979
1472507252.38287143589-2.38287143588514
1572817282.13096316849-1.13096316848623
1672987312.81103666596-14.811036665963
1773107329.32709054392-19.3270905439213
1873627339.0524372743722.9475627256252
1973877389.20487635117-2.20487635117479
2074147416.98114141936-2.98114141935912
2174497443.640101323365.35989867663739
2274737478.39747199615-5.39747199615249
2375137502.9323339494210.0676660505842
2475227542.50149806056-20.5014980605574
2575887552.2650366291435.7349633708609
2676027616.57027610226-14.5702761022585
2776437634.634494058488.36550594152413
2876517674.03379728638-23.0337972863754
2976617682.52868235048-21.5286823504757
3076887689.18961141335-1.18961141335149
3177287713.5092031297614.4907968702364
3277507753.69976099764-3.69976099764335
3377597777.39921674015-18.3992167401548
3477607785.51526544041-25.5152654404137
3578067783.6545093316422.3454906683555
3678647827.0304433579936.9695566420078
3778597888.64394647571-29.6439464757077
3879267887.5095881420638.4904118579407
3979787951.7524169339126.2475830660915
4079998009.10581706237-10.1058170623719
4180568033.1048838561122.8951161438854
4281048089.3923338132214.6076661867828
4381468140.553293710825.44670628917538
4481718184.4799497693-13.4799497693039
4581998209.83746272853-10.8374627285266
4682128235.92434189751-23.9243418975093
4782428247.0323475574-5.03234755739504
4882698273.96734547805-4.96734547804772
4982798300.23169812007-21.2316981200747
5083238309.1256570770413.8743429229635
5183508350.83231764879-0.832317648790195
5283728379.52252824433-7.52252824432981
5384038401.244953726161.75504627383816
5484128431.35887195346-19.35887195346
5584608440.1247264458519.8752735541457
5684848486.20177020755-2.20177020755182
5784988512.59954481085-14.5995448108461
5885278525.988576024241.01142397576405
5985198553.21317422251-34.2131742225101
6085378544.54180352855-7.54180352854928
6185268558.15064290829-32.1506429082856
6285498545.473343153763.52665684623753
6385948564.5938410217529.4061589782505
6487678610.71254798826156.287452011742
6586908790.9720817975-100.972081797496
6686578730.88038446979-73.8803844697886
6786808683.71987423844-3.71987423843893
6887148697.5299014041616.4700985958407
6987468731.4547342242714.5452657757305
7086718765.82256157673-94.8225615767333
7186548690.40868423444-36.4086842344404
7286778660.8777174006416.1222825993591
7387658679.7665932684785.233406731526
7487608771.7361792695-11.7361792694992
7588128776.9654565747735.0345434252322
7688228828.33444927736-6.33444927736309
7788378842.50397565066-5.50397565065759
7889978856.5954001985140.404599801501
7988759019.18383384884-144.183833848841
8089058911.12972008707-6.12972008706856
8189278923.220997697633.7790023023681
8289508944.55362454915.4463754508979
8390108968.1459816529241.8540183470759
8490869029.7908427641156.2091572358859
8591619112.2557812232248.7442187767847
8692489195.315859999952.6841400001031
8792859289.5477859873-4.54778598730445
8893359332.933636567832.0663634321736
8993549382.4213409887-28.4213409886997
9092679401.0147099283-134.014709928297
9194039307.3947169876195.6052830123917
9294699429.1059643768639.894035623136
9394649507.81446641929-43.8144664192878
9496309506.71076942116123.289230578845
9597249670.1804407834353.8195592165685
9697649780.62410455148-16.6241045514798
9798069826.86889454945-20.8688945494523
9898699866.33496655192.66503344810008
9999079926.82553769143-19.8255376914294
10099149964.69266204878-50.6926620487848
10199229968.07038465262-46.0703846526212
10299509968.75224878634-18.7522487863371
10399829990.63924103674-8.63924103674435
104998110020.1276190365-39.1276190364679
1051004510017.15276980927.8472301910151
1061006710076.9794129859-9.97941298593287
1071008010102.1785267222-22.178526722173
1081005110113.4328777305-62.4328777305309
109996210080.2475231712-118.247523171214
11098969980.803517326-84.8035173260014
11198499898.26021845993-49.2602184599255
11298549839.6647816038114.335218396187
11398479838.928533777138.07146622287291
11498459833.8826863732411.1173136267553

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 6795 & 6778 & 17 \tabularnewline
4 & 6835 & 6790.39551856373 & 44.6044814362695 \tabularnewline
5 & 6889 & 6833.52799118527 & 55.4720088147278 \tabularnewline
6 & 6926 & 6894.31468711666 & 31.6853128833391 \tabularnewline
7 & 6957 & 6938.88704654582 & 18.1129534541833 \tabularnewline
8 & 6984 & 6974.21267422922 & 9.78732577077517 \tabularnewline
9 & 7159 & 7003.67223435233 & 155.327765647668 \tabularnewline
10 & 7121 & 7183.4920379326 & -62.4920379325995 \tabularnewline
11 & 7165 & 7163.17735845417 & 1.8226415458339 \tabularnewline
12 & 7208 & 7199.51959116224 & 8.48040883776412 \tabularnewline
13 & 7217 & 7242.9414777194 & -25.9414777193979 \tabularnewline
14 & 7250 & 7252.38287143589 & -2.38287143588514 \tabularnewline
15 & 7281 & 7282.13096316849 & -1.13096316848623 \tabularnewline
16 & 7298 & 7312.81103666596 & -14.811036665963 \tabularnewline
17 & 7310 & 7329.32709054392 & -19.3270905439213 \tabularnewline
18 & 7362 & 7339.05243727437 & 22.9475627256252 \tabularnewline
19 & 7387 & 7389.20487635117 & -2.20487635117479 \tabularnewline
20 & 7414 & 7416.98114141936 & -2.98114141935912 \tabularnewline
21 & 7449 & 7443.64010132336 & 5.35989867663739 \tabularnewline
22 & 7473 & 7478.39747199615 & -5.39747199615249 \tabularnewline
23 & 7513 & 7502.93233394942 & 10.0676660505842 \tabularnewline
24 & 7522 & 7542.50149806056 & -20.5014980605574 \tabularnewline
25 & 7588 & 7552.26503662914 & 35.7349633708609 \tabularnewline
26 & 7602 & 7616.57027610226 & -14.5702761022585 \tabularnewline
27 & 7643 & 7634.63449405848 & 8.36550594152413 \tabularnewline
28 & 7651 & 7674.03379728638 & -23.0337972863754 \tabularnewline
29 & 7661 & 7682.52868235048 & -21.5286823504757 \tabularnewline
30 & 7688 & 7689.18961141335 & -1.18961141335149 \tabularnewline
31 & 7728 & 7713.50920312976 & 14.4907968702364 \tabularnewline
32 & 7750 & 7753.69976099764 & -3.69976099764335 \tabularnewline
33 & 7759 & 7777.39921674015 & -18.3992167401548 \tabularnewline
34 & 7760 & 7785.51526544041 & -25.5152654404137 \tabularnewline
35 & 7806 & 7783.65450933164 & 22.3454906683555 \tabularnewline
36 & 7864 & 7827.03044335799 & 36.9695566420078 \tabularnewline
37 & 7859 & 7888.64394647571 & -29.6439464757077 \tabularnewline
38 & 7926 & 7887.50958814206 & 38.4904118579407 \tabularnewline
39 & 7978 & 7951.75241693391 & 26.2475830660915 \tabularnewline
40 & 7999 & 8009.10581706237 & -10.1058170623719 \tabularnewline
41 & 8056 & 8033.10488385611 & 22.8951161438854 \tabularnewline
42 & 8104 & 8089.39233381322 & 14.6076661867828 \tabularnewline
43 & 8146 & 8140.55329371082 & 5.44670628917538 \tabularnewline
44 & 8171 & 8184.4799497693 & -13.4799497693039 \tabularnewline
45 & 8199 & 8209.83746272853 & -10.8374627285266 \tabularnewline
46 & 8212 & 8235.92434189751 & -23.9243418975093 \tabularnewline
47 & 8242 & 8247.0323475574 & -5.03234755739504 \tabularnewline
48 & 8269 & 8273.96734547805 & -4.96734547804772 \tabularnewline
49 & 8279 & 8300.23169812007 & -21.2316981200747 \tabularnewline
50 & 8323 & 8309.12565707704 & 13.8743429229635 \tabularnewline
51 & 8350 & 8350.83231764879 & -0.832317648790195 \tabularnewline
52 & 8372 & 8379.52252824433 & -7.52252824432981 \tabularnewline
53 & 8403 & 8401.24495372616 & 1.75504627383816 \tabularnewline
54 & 8412 & 8431.35887195346 & -19.35887195346 \tabularnewline
55 & 8460 & 8440.12472644585 & 19.8752735541457 \tabularnewline
56 & 8484 & 8486.20177020755 & -2.20177020755182 \tabularnewline
57 & 8498 & 8512.59954481085 & -14.5995448108461 \tabularnewline
58 & 8527 & 8525.98857602424 & 1.01142397576405 \tabularnewline
59 & 8519 & 8553.21317422251 & -34.2131742225101 \tabularnewline
60 & 8537 & 8544.54180352855 & -7.54180352854928 \tabularnewline
61 & 8526 & 8558.15064290829 & -32.1506429082856 \tabularnewline
62 & 8549 & 8545.47334315376 & 3.52665684623753 \tabularnewline
63 & 8594 & 8564.59384102175 & 29.4061589782505 \tabularnewline
64 & 8767 & 8610.71254798826 & 156.287452011742 \tabularnewline
65 & 8690 & 8790.9720817975 & -100.972081797496 \tabularnewline
66 & 8657 & 8730.88038446979 & -73.8803844697886 \tabularnewline
67 & 8680 & 8683.71987423844 & -3.71987423843893 \tabularnewline
68 & 8714 & 8697.52990140416 & 16.4700985958407 \tabularnewline
69 & 8746 & 8731.45473422427 & 14.5452657757305 \tabularnewline
70 & 8671 & 8765.82256157673 & -94.8225615767333 \tabularnewline
71 & 8654 & 8690.40868423444 & -36.4086842344404 \tabularnewline
72 & 8677 & 8660.87771740064 & 16.1222825993591 \tabularnewline
73 & 8765 & 8679.76659326847 & 85.233406731526 \tabularnewline
74 & 8760 & 8771.7361792695 & -11.7361792694992 \tabularnewline
75 & 8812 & 8776.96545657477 & 35.0345434252322 \tabularnewline
76 & 8822 & 8828.33444927736 & -6.33444927736309 \tabularnewline
77 & 8837 & 8842.50397565066 & -5.50397565065759 \tabularnewline
78 & 8997 & 8856.5954001985 & 140.404599801501 \tabularnewline
79 & 8875 & 9019.18383384884 & -144.183833848841 \tabularnewline
80 & 8905 & 8911.12972008707 & -6.12972008706856 \tabularnewline
81 & 8927 & 8923.22099769763 & 3.7790023023681 \tabularnewline
82 & 8950 & 8944.5536245491 & 5.4463754508979 \tabularnewline
83 & 9010 & 8968.14598165292 & 41.8540183470759 \tabularnewline
84 & 9086 & 9029.79084276411 & 56.2091572358859 \tabularnewline
85 & 9161 & 9112.25578122322 & 48.7442187767847 \tabularnewline
86 & 9248 & 9195.3158599999 & 52.6841400001031 \tabularnewline
87 & 9285 & 9289.5477859873 & -4.54778598730445 \tabularnewline
88 & 9335 & 9332.93363656783 & 2.0663634321736 \tabularnewline
89 & 9354 & 9382.4213409887 & -28.4213409886997 \tabularnewline
90 & 9267 & 9401.0147099283 & -134.014709928297 \tabularnewline
91 & 9403 & 9307.39471698761 & 95.6052830123917 \tabularnewline
92 & 9469 & 9429.10596437686 & 39.894035623136 \tabularnewline
93 & 9464 & 9507.81446641929 & -43.8144664192878 \tabularnewline
94 & 9630 & 9506.71076942116 & 123.289230578845 \tabularnewline
95 & 9724 & 9670.18044078343 & 53.8195592165685 \tabularnewline
96 & 9764 & 9780.62410455148 & -16.6241045514798 \tabularnewline
97 & 9806 & 9826.86889454945 & -20.8688945494523 \tabularnewline
98 & 9869 & 9866.3349665519 & 2.66503344810008 \tabularnewline
99 & 9907 & 9926.82553769143 & -19.8255376914294 \tabularnewline
100 & 9914 & 9964.69266204878 & -50.6926620487848 \tabularnewline
101 & 9922 & 9968.07038465262 & -46.0703846526212 \tabularnewline
102 & 9950 & 9968.75224878634 & -18.7522487863371 \tabularnewline
103 & 9982 & 9990.63924103674 & -8.63924103674435 \tabularnewline
104 & 9981 & 10020.1276190365 & -39.1276190364679 \tabularnewline
105 & 10045 & 10017.152769809 & 27.8472301910151 \tabularnewline
106 & 10067 & 10076.9794129859 & -9.97941298593287 \tabularnewline
107 & 10080 & 10102.1785267222 & -22.178526722173 \tabularnewline
108 & 10051 & 10113.4328777305 & -62.4328777305309 \tabularnewline
109 & 9962 & 10080.2475231712 & -118.247523171214 \tabularnewline
110 & 9896 & 9980.803517326 & -84.8035173260014 \tabularnewline
111 & 9849 & 9898.26021845993 & -49.2602184599255 \tabularnewline
112 & 9854 & 9839.66478160381 & 14.335218396187 \tabularnewline
113 & 9847 & 9838.92853377713 & 8.07146622287291 \tabularnewline
114 & 9845 & 9833.88268637324 & 11.1173136267553 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298773&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]6795[/C][C]6778[/C][C]17[/C][/ROW]
[ROW][C]4[/C][C]6835[/C][C]6790.39551856373[/C][C]44.6044814362695[/C][/ROW]
[ROW][C]5[/C][C]6889[/C][C]6833.52799118527[/C][C]55.4720088147278[/C][/ROW]
[ROW][C]6[/C][C]6926[/C][C]6894.31468711666[/C][C]31.6853128833391[/C][/ROW]
[ROW][C]7[/C][C]6957[/C][C]6938.88704654582[/C][C]18.1129534541833[/C][/ROW]
[ROW][C]8[/C][C]6984[/C][C]6974.21267422922[/C][C]9.78732577077517[/C][/ROW]
[ROW][C]9[/C][C]7159[/C][C]7003.67223435233[/C][C]155.327765647668[/C][/ROW]
[ROW][C]10[/C][C]7121[/C][C]7183.4920379326[/C][C]-62.4920379325995[/C][/ROW]
[ROW][C]11[/C][C]7165[/C][C]7163.17735845417[/C][C]1.8226415458339[/C][/ROW]
[ROW][C]12[/C][C]7208[/C][C]7199.51959116224[/C][C]8.48040883776412[/C][/ROW]
[ROW][C]13[/C][C]7217[/C][C]7242.9414777194[/C][C]-25.9414777193979[/C][/ROW]
[ROW][C]14[/C][C]7250[/C][C]7252.38287143589[/C][C]-2.38287143588514[/C][/ROW]
[ROW][C]15[/C][C]7281[/C][C]7282.13096316849[/C][C]-1.13096316848623[/C][/ROW]
[ROW][C]16[/C][C]7298[/C][C]7312.81103666596[/C][C]-14.811036665963[/C][/ROW]
[ROW][C]17[/C][C]7310[/C][C]7329.32709054392[/C][C]-19.3270905439213[/C][/ROW]
[ROW][C]18[/C][C]7362[/C][C]7339.05243727437[/C][C]22.9475627256252[/C][/ROW]
[ROW][C]19[/C][C]7387[/C][C]7389.20487635117[/C][C]-2.20487635117479[/C][/ROW]
[ROW][C]20[/C][C]7414[/C][C]7416.98114141936[/C][C]-2.98114141935912[/C][/ROW]
[ROW][C]21[/C][C]7449[/C][C]7443.64010132336[/C][C]5.35989867663739[/C][/ROW]
[ROW][C]22[/C][C]7473[/C][C]7478.39747199615[/C][C]-5.39747199615249[/C][/ROW]
[ROW][C]23[/C][C]7513[/C][C]7502.93233394942[/C][C]10.0676660505842[/C][/ROW]
[ROW][C]24[/C][C]7522[/C][C]7542.50149806056[/C][C]-20.5014980605574[/C][/ROW]
[ROW][C]25[/C][C]7588[/C][C]7552.26503662914[/C][C]35.7349633708609[/C][/ROW]
[ROW][C]26[/C][C]7602[/C][C]7616.57027610226[/C][C]-14.5702761022585[/C][/ROW]
[ROW][C]27[/C][C]7643[/C][C]7634.63449405848[/C][C]8.36550594152413[/C][/ROW]
[ROW][C]28[/C][C]7651[/C][C]7674.03379728638[/C][C]-23.0337972863754[/C][/ROW]
[ROW][C]29[/C][C]7661[/C][C]7682.52868235048[/C][C]-21.5286823504757[/C][/ROW]
[ROW][C]30[/C][C]7688[/C][C]7689.18961141335[/C][C]-1.18961141335149[/C][/ROW]
[ROW][C]31[/C][C]7728[/C][C]7713.50920312976[/C][C]14.4907968702364[/C][/ROW]
[ROW][C]32[/C][C]7750[/C][C]7753.69976099764[/C][C]-3.69976099764335[/C][/ROW]
[ROW][C]33[/C][C]7759[/C][C]7777.39921674015[/C][C]-18.3992167401548[/C][/ROW]
[ROW][C]34[/C][C]7760[/C][C]7785.51526544041[/C][C]-25.5152654404137[/C][/ROW]
[ROW][C]35[/C][C]7806[/C][C]7783.65450933164[/C][C]22.3454906683555[/C][/ROW]
[ROW][C]36[/C][C]7864[/C][C]7827.03044335799[/C][C]36.9695566420078[/C][/ROW]
[ROW][C]37[/C][C]7859[/C][C]7888.64394647571[/C][C]-29.6439464757077[/C][/ROW]
[ROW][C]38[/C][C]7926[/C][C]7887.50958814206[/C][C]38.4904118579407[/C][/ROW]
[ROW][C]39[/C][C]7978[/C][C]7951.75241693391[/C][C]26.2475830660915[/C][/ROW]
[ROW][C]40[/C][C]7999[/C][C]8009.10581706237[/C][C]-10.1058170623719[/C][/ROW]
[ROW][C]41[/C][C]8056[/C][C]8033.10488385611[/C][C]22.8951161438854[/C][/ROW]
[ROW][C]42[/C][C]8104[/C][C]8089.39233381322[/C][C]14.6076661867828[/C][/ROW]
[ROW][C]43[/C][C]8146[/C][C]8140.55329371082[/C][C]5.44670628917538[/C][/ROW]
[ROW][C]44[/C][C]8171[/C][C]8184.4799497693[/C][C]-13.4799497693039[/C][/ROW]
[ROW][C]45[/C][C]8199[/C][C]8209.83746272853[/C][C]-10.8374627285266[/C][/ROW]
[ROW][C]46[/C][C]8212[/C][C]8235.92434189751[/C][C]-23.9243418975093[/C][/ROW]
[ROW][C]47[/C][C]8242[/C][C]8247.0323475574[/C][C]-5.03234755739504[/C][/ROW]
[ROW][C]48[/C][C]8269[/C][C]8273.96734547805[/C][C]-4.96734547804772[/C][/ROW]
[ROW][C]49[/C][C]8279[/C][C]8300.23169812007[/C][C]-21.2316981200747[/C][/ROW]
[ROW][C]50[/C][C]8323[/C][C]8309.12565707704[/C][C]13.8743429229635[/C][/ROW]
[ROW][C]51[/C][C]8350[/C][C]8350.83231764879[/C][C]-0.832317648790195[/C][/ROW]
[ROW][C]52[/C][C]8372[/C][C]8379.52252824433[/C][C]-7.52252824432981[/C][/ROW]
[ROW][C]53[/C][C]8403[/C][C]8401.24495372616[/C][C]1.75504627383816[/C][/ROW]
[ROW][C]54[/C][C]8412[/C][C]8431.35887195346[/C][C]-19.35887195346[/C][/ROW]
[ROW][C]55[/C][C]8460[/C][C]8440.12472644585[/C][C]19.8752735541457[/C][/ROW]
[ROW][C]56[/C][C]8484[/C][C]8486.20177020755[/C][C]-2.20177020755182[/C][/ROW]
[ROW][C]57[/C][C]8498[/C][C]8512.59954481085[/C][C]-14.5995448108461[/C][/ROW]
[ROW][C]58[/C][C]8527[/C][C]8525.98857602424[/C][C]1.01142397576405[/C][/ROW]
[ROW][C]59[/C][C]8519[/C][C]8553.21317422251[/C][C]-34.2131742225101[/C][/ROW]
[ROW][C]60[/C][C]8537[/C][C]8544.54180352855[/C][C]-7.54180352854928[/C][/ROW]
[ROW][C]61[/C][C]8526[/C][C]8558.15064290829[/C][C]-32.1506429082856[/C][/ROW]
[ROW][C]62[/C][C]8549[/C][C]8545.47334315376[/C][C]3.52665684623753[/C][/ROW]
[ROW][C]63[/C][C]8594[/C][C]8564.59384102175[/C][C]29.4061589782505[/C][/ROW]
[ROW][C]64[/C][C]8767[/C][C]8610.71254798826[/C][C]156.287452011742[/C][/ROW]
[ROW][C]65[/C][C]8690[/C][C]8790.9720817975[/C][C]-100.972081797496[/C][/ROW]
[ROW][C]66[/C][C]8657[/C][C]8730.88038446979[/C][C]-73.8803844697886[/C][/ROW]
[ROW][C]67[/C][C]8680[/C][C]8683.71987423844[/C][C]-3.71987423843893[/C][/ROW]
[ROW][C]68[/C][C]8714[/C][C]8697.52990140416[/C][C]16.4700985958407[/C][/ROW]
[ROW][C]69[/C][C]8746[/C][C]8731.45473422427[/C][C]14.5452657757305[/C][/ROW]
[ROW][C]70[/C][C]8671[/C][C]8765.82256157673[/C][C]-94.8225615767333[/C][/ROW]
[ROW][C]71[/C][C]8654[/C][C]8690.40868423444[/C][C]-36.4086842344404[/C][/ROW]
[ROW][C]72[/C][C]8677[/C][C]8660.87771740064[/C][C]16.1222825993591[/C][/ROW]
[ROW][C]73[/C][C]8765[/C][C]8679.76659326847[/C][C]85.233406731526[/C][/ROW]
[ROW][C]74[/C][C]8760[/C][C]8771.7361792695[/C][C]-11.7361792694992[/C][/ROW]
[ROW][C]75[/C][C]8812[/C][C]8776.96545657477[/C][C]35.0345434252322[/C][/ROW]
[ROW][C]76[/C][C]8822[/C][C]8828.33444927736[/C][C]-6.33444927736309[/C][/ROW]
[ROW][C]77[/C][C]8837[/C][C]8842.50397565066[/C][C]-5.50397565065759[/C][/ROW]
[ROW][C]78[/C][C]8997[/C][C]8856.5954001985[/C][C]140.404599801501[/C][/ROW]
[ROW][C]79[/C][C]8875[/C][C]9019.18383384884[/C][C]-144.183833848841[/C][/ROW]
[ROW][C]80[/C][C]8905[/C][C]8911.12972008707[/C][C]-6.12972008706856[/C][/ROW]
[ROW][C]81[/C][C]8927[/C][C]8923.22099769763[/C][C]3.7790023023681[/C][/ROW]
[ROW][C]82[/C][C]8950[/C][C]8944.5536245491[/C][C]5.4463754508979[/C][/ROW]
[ROW][C]83[/C][C]9010[/C][C]8968.14598165292[/C][C]41.8540183470759[/C][/ROW]
[ROW][C]84[/C][C]9086[/C][C]9029.79084276411[/C][C]56.2091572358859[/C][/ROW]
[ROW][C]85[/C][C]9161[/C][C]9112.25578122322[/C][C]48.7442187767847[/C][/ROW]
[ROW][C]86[/C][C]9248[/C][C]9195.3158599999[/C][C]52.6841400001031[/C][/ROW]
[ROW][C]87[/C][C]9285[/C][C]9289.5477859873[/C][C]-4.54778598730445[/C][/ROW]
[ROW][C]88[/C][C]9335[/C][C]9332.93363656783[/C][C]2.0663634321736[/C][/ROW]
[ROW][C]89[/C][C]9354[/C][C]9382.4213409887[/C][C]-28.4213409886997[/C][/ROW]
[ROW][C]90[/C][C]9267[/C][C]9401.0147099283[/C][C]-134.014709928297[/C][/ROW]
[ROW][C]91[/C][C]9403[/C][C]9307.39471698761[/C][C]95.6052830123917[/C][/ROW]
[ROW][C]92[/C][C]9469[/C][C]9429.10596437686[/C][C]39.894035623136[/C][/ROW]
[ROW][C]93[/C][C]9464[/C][C]9507.81446641929[/C][C]-43.8144664192878[/C][/ROW]
[ROW][C]94[/C][C]9630[/C][C]9506.71076942116[/C][C]123.289230578845[/C][/ROW]
[ROW][C]95[/C][C]9724[/C][C]9670.18044078343[/C][C]53.8195592165685[/C][/ROW]
[ROW][C]96[/C][C]9764[/C][C]9780.62410455148[/C][C]-16.6241045514798[/C][/ROW]
[ROW][C]97[/C][C]9806[/C][C]9826.86889454945[/C][C]-20.8688945494523[/C][/ROW]
[ROW][C]98[/C][C]9869[/C][C]9866.3349665519[/C][C]2.66503344810008[/C][/ROW]
[ROW][C]99[/C][C]9907[/C][C]9926.82553769143[/C][C]-19.8255376914294[/C][/ROW]
[ROW][C]100[/C][C]9914[/C][C]9964.69266204878[/C][C]-50.6926620487848[/C][/ROW]
[ROW][C]101[/C][C]9922[/C][C]9968.07038465262[/C][C]-46.0703846526212[/C][/ROW]
[ROW][C]102[/C][C]9950[/C][C]9968.75224878634[/C][C]-18.7522487863371[/C][/ROW]
[ROW][C]103[/C][C]9982[/C][C]9990.63924103674[/C][C]-8.63924103674435[/C][/ROW]
[ROW][C]104[/C][C]9981[/C][C]10020.1276190365[/C][C]-39.1276190364679[/C][/ROW]
[ROW][C]105[/C][C]10045[/C][C]10017.152769809[/C][C]27.8472301910151[/C][/ROW]
[ROW][C]106[/C][C]10067[/C][C]10076.9794129859[/C][C]-9.97941298593287[/C][/ROW]
[ROW][C]107[/C][C]10080[/C][C]10102.1785267222[/C][C]-22.178526722173[/C][/ROW]
[ROW][C]108[/C][C]10051[/C][C]10113.4328777305[/C][C]-62.4328777305309[/C][/ROW]
[ROW][C]109[/C][C]9962[/C][C]10080.2475231712[/C][C]-118.247523171214[/C][/ROW]
[ROW][C]110[/C][C]9896[/C][C]9980.803517326[/C][C]-84.8035173260014[/C][/ROW]
[ROW][C]111[/C][C]9849[/C][C]9898.26021845993[/C][C]-49.2602184599255[/C][/ROW]
[ROW][C]112[/C][C]9854[/C][C]9839.66478160381[/C][C]14.335218396187[/C][/ROW]
[ROW][C]113[/C][C]9847[/C][C]9838.92853377713[/C][C]8.07146622287291[/C][/ROW]
[ROW][C]114[/C][C]9845[/C][C]9833.88268637324[/C][C]11.1173136267553[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298773&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298773&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
36795677817
468356790.3955185637344.6044814362695
568896833.5279911852755.4720088147278
669266894.3146871166631.6853128833391
769576938.8870465458218.1129534541833
869846974.212674229229.78732577077517
971597003.67223435233155.327765647668
1071217183.4920379326-62.4920379325995
1171657163.177358454171.8226415458339
1272087199.519591162248.48040883776412
1372177242.9414777194-25.9414777193979
1472507252.38287143589-2.38287143588514
1572817282.13096316849-1.13096316848623
1672987312.81103666596-14.811036665963
1773107329.32709054392-19.3270905439213
1873627339.0524372743722.9475627256252
1973877389.20487635117-2.20487635117479
2074147416.98114141936-2.98114141935912
2174497443.640101323365.35989867663739
2274737478.39747199615-5.39747199615249
2375137502.9323339494210.0676660505842
2475227542.50149806056-20.5014980605574
2575887552.2650366291435.7349633708609
2676027616.57027610226-14.5702761022585
2776437634.634494058488.36550594152413
2876517674.03379728638-23.0337972863754
2976617682.52868235048-21.5286823504757
3076887689.18961141335-1.18961141335149
3177287713.5092031297614.4907968702364
3277507753.69976099764-3.69976099764335
3377597777.39921674015-18.3992167401548
3477607785.51526544041-25.5152654404137
3578067783.6545093316422.3454906683555
3678647827.0304433579936.9695566420078
3778597888.64394647571-29.6439464757077
3879267887.5095881420638.4904118579407
3979787951.7524169339126.2475830660915
4079998009.10581706237-10.1058170623719
4180568033.1048838561122.8951161438854
4281048089.3923338132214.6076661867828
4381468140.553293710825.44670628917538
4481718184.4799497693-13.4799497693039
4581998209.83746272853-10.8374627285266
4682128235.92434189751-23.9243418975093
4782428247.0323475574-5.03234755739504
4882698273.96734547805-4.96734547804772
4982798300.23169812007-21.2316981200747
5083238309.1256570770413.8743429229635
5183508350.83231764879-0.832317648790195
5283728379.52252824433-7.52252824432981
5384038401.244953726161.75504627383816
5484128431.35887195346-19.35887195346
5584608440.1247264458519.8752735541457
5684848486.20177020755-2.20177020755182
5784988512.59954481085-14.5995448108461
5885278525.988576024241.01142397576405
5985198553.21317422251-34.2131742225101
6085378544.54180352855-7.54180352854928
6185268558.15064290829-32.1506429082856
6285498545.473343153763.52665684623753
6385948564.5938410217529.4061589782505
6487678610.71254798826156.287452011742
6586908790.9720817975-100.972081797496
6686578730.88038446979-73.8803844697886
6786808683.71987423844-3.71987423843893
6887148697.5299014041616.4700985958407
6987468731.4547342242714.5452657757305
7086718765.82256157673-94.8225615767333
7186548690.40868423444-36.4086842344404
7286778660.8777174006416.1222825993591
7387658679.7665932684785.233406731526
7487608771.7361792695-11.7361792694992
7588128776.9654565747735.0345434252322
7688228828.33444927736-6.33444927736309
7788378842.50397565066-5.50397565065759
7889978856.5954001985140.404599801501
7988759019.18383384884-144.183833848841
8089058911.12972008707-6.12972008706856
8189278923.220997697633.7790023023681
8289508944.55362454915.4463754508979
8390108968.1459816529241.8540183470759
8490869029.7908427641156.2091572358859
8591619112.2557812232248.7442187767847
8692489195.315859999952.6841400001031
8792859289.5477859873-4.54778598730445
8893359332.933636567832.0663634321736
8993549382.4213409887-28.4213409886997
9092679401.0147099283-134.014709928297
9194039307.3947169876195.6052830123917
9294699429.1059643768639.894035623136
9394649507.81446641929-43.8144664192878
9496309506.71076942116123.289230578845
9597249670.1804407834353.8195592165685
9697649780.62410455148-16.6241045514798
9798069826.86889454945-20.8688945494523
9898699866.33496655192.66503344810008
9999079926.82553769143-19.8255376914294
10099149964.69266204878-50.6926620487848
10199229968.07038465262-46.0703846526212
10299509968.75224878634-18.7522487863371
10399829990.63924103674-8.63924103674435
104998110020.1276190365-39.1276190364679
1051004510017.15276980927.8472301910151
1061006710076.9794129859-9.97941298593287
1071008010102.1785267222-22.178526722173
1081005110113.4328777305-62.4328777305309
109996210080.2475231712-118.247523171214
11098969980.803517326-84.8035173260014
11198499898.26021845993-49.2602184599255
11298549839.6647816038114.335218396187
11398479838.928533777138.07146622287291
11498459833.8826863732411.1173136267553







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1159833.135893160289740.187479274389926.08430704618
1169822.641644553929689.654813626449955.6284754814
1179812.147395947569640.371583097319983.92320879782
1189801.653147341219590.7634410239910012.5428536584
1199791.158898734859540.2428275144310042.0749699553
1209780.664650128499488.5500970423710072.7792032146
1219770.170401522139435.5641511911310104.7766518531
1229759.676152915789381.2307417264510138.1215641051
1239749.181904309429325.5305923325610172.8332162863
1249738.687655703069268.4636452836510208.9116661225
1259728.193407096719210.0406793205910246.3461348728
1269717.699158490359150.278604873910285.1197121068

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
115 & 9833.13589316028 & 9740.18747927438 & 9926.08430704618 \tabularnewline
116 & 9822.64164455392 & 9689.65481362644 & 9955.6284754814 \tabularnewline
117 & 9812.14739594756 & 9640.37158309731 & 9983.92320879782 \tabularnewline
118 & 9801.65314734121 & 9590.76344102399 & 10012.5428536584 \tabularnewline
119 & 9791.15889873485 & 9540.24282751443 & 10042.0749699553 \tabularnewline
120 & 9780.66465012849 & 9488.55009704237 & 10072.7792032146 \tabularnewline
121 & 9770.17040152213 & 9435.56415119113 & 10104.7766518531 \tabularnewline
122 & 9759.67615291578 & 9381.23074172645 & 10138.1215641051 \tabularnewline
123 & 9749.18190430942 & 9325.53059233256 & 10172.8332162863 \tabularnewline
124 & 9738.68765570306 & 9268.46364528365 & 10208.9116661225 \tabularnewline
125 & 9728.19340709671 & 9210.04067932059 & 10246.3461348728 \tabularnewline
126 & 9717.69915849035 & 9150.2786048739 & 10285.1197121068 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298773&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]115[/C][C]9833.13589316028[/C][C]9740.18747927438[/C][C]9926.08430704618[/C][/ROW]
[ROW][C]116[/C][C]9822.64164455392[/C][C]9689.65481362644[/C][C]9955.6284754814[/C][/ROW]
[ROW][C]117[/C][C]9812.14739594756[/C][C]9640.37158309731[/C][C]9983.92320879782[/C][/ROW]
[ROW][C]118[/C][C]9801.65314734121[/C][C]9590.76344102399[/C][C]10012.5428536584[/C][/ROW]
[ROW][C]119[/C][C]9791.15889873485[/C][C]9540.24282751443[/C][C]10042.0749699553[/C][/ROW]
[ROW][C]120[/C][C]9780.66465012849[/C][C]9488.55009704237[/C][C]10072.7792032146[/C][/ROW]
[ROW][C]121[/C][C]9770.17040152213[/C][C]9435.56415119113[/C][C]10104.7766518531[/C][/ROW]
[ROW][C]122[/C][C]9759.67615291578[/C][C]9381.23074172645[/C][C]10138.1215641051[/C][/ROW]
[ROW][C]123[/C][C]9749.18190430942[/C][C]9325.53059233256[/C][C]10172.8332162863[/C][/ROW]
[ROW][C]124[/C][C]9738.68765570306[/C][C]9268.46364528365[/C][C]10208.9116661225[/C][/ROW]
[ROW][C]125[/C][C]9728.19340709671[/C][C]9210.04067932059[/C][C]10246.3461348728[/C][/ROW]
[ROW][C]126[/C][C]9717.69915849035[/C][C]9150.2786048739[/C][C]10285.1197121068[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298773&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298773&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
1159833.135893160289740.187479274389926.08430704618
1169822.641644553929689.654813626449955.6284754814
1179812.147395947569640.371583097319983.92320879782
1189801.653147341219590.7634410239910012.5428536584
1199791.158898734859540.2428275144310042.0749699553
1209780.664650128499488.5500970423710072.7792032146
1219770.170401522139435.5641511911310104.7766518531
1229759.676152915789381.2307417264510138.1215641051
1239749.181904309429325.5305923325610172.8332162863
1249738.687655703069268.4636452836510208.9116661225
1259728.193407096719210.0406793205910246.3461348728
1269717.699158490359150.278604873910285.1197121068



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')