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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 computationWed, 07 Aug 2013 06:37:09 -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/07/t1375871873txvc8onv5zw4trt.htm/, Retrieved Tue, 30 Apr 2024 01:42:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210970, Retrieved Tue, 30 Apr 2024 01:42:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Camp Stef
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-08-07 10:37:09] [941d89646656d1688f5e273fb31a8e6b] [Current]
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Dataseries X:
940
1070
1060
1070
1070
1040
950
1120
1150
1040
1040
1120
1000
960
1060
1060
1110
1030
960
1130
1150
1030
1040
1030
1070
1000
1020
1100
1080
990
1000
1110
1170
1030
1100
1020
1090
990
1060
1120
1030
1050
1030
1130
1140
980
1150
990
1020
1060
1080
1180
980
960
1020
1170
1150
950
1160
1120
1010
1010
1060
1130
1000
1000
1070
1150
1080
980
1210
1020
980
1030
1050
1190
970
950
1070
1170
1050
960
1300
1080
1030
1030
1070
1260
990
950
1080
1190
1050
950
1250
1140
1080
1020
1140
1320
1100
1040
1090
1280
1030
930
1280
1020





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=210970&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=210970&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210970&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00399960079540507
beta0.645937396928935
gamma0.832270390579904

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00399960079540507 \tabularnewline
beta & 0.645937396928935 \tabularnewline
gamma & 0.832270390579904 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210970&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]0.00399960079540507[/C][/ROW]
[ROW][C]beta[/C][C]0.645937396928935[/C][/ROW]
[ROW][C]gamma[/C][C]0.832270390579904[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210970&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210970&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
alpha0.00399960079540507
beta0.645937396928935
gamma0.832270390579904







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310001001.78685897436-1.78685897435912
14960960.730515496827-0.730515496826911
1510601060.09317635743-0.0931763574321849
1610601060.29147893315-0.291478933150984
1711101110.48823534432-0.488235344317673
1810301034.01627678975-4.01627678974683
19960945.8531647932814.14683520672
2011301117.7992462257112.2007537742854
2111501152.26906465574-2.26906465573757
2210301042.50848081203-12.5084808120264
2310401041.00796116796-1.00796116795641
2410301119.55083495206-89.5508349520637
251070997.27701693564272.7229830643585
261000957.3636242094942.63637579051
2710201057.50938431197-37.5093843119737
2811001057.3783233030642.621676696936
2910801107.6791489788-27.6791489788018
309901028.19918301338-38.1991830133793
311000954.89248750655145.1075124934492
3211101125.36617260522-15.3661726052221
3311701147.6768416235422.3231583764587
3410301029.536014552340.463985447663163
3511001037.6634296149262.3365703850834
3610201043.26922158533-23.2692215853278
3710901056.153707067233.8462929328032
38990991.422022343402-1.42202234340175
3910601025.1188248716934.8811751283113
4011201092.0517071919327.9482928080718
4110301084.33109156717-54.3310915671739
421050996.26770731425353.7322926857466
431030992.86626724137137.1337327586288
4411301113.6394817602716.3605182397334
4511401167.86184353687-27.8618435368739
469801031.81320804886-51.8132080488581
4711501091.2981298581458.7018701418588
489901026.19562110706-36.1956211070637
4910201086.60888157732-66.6088815773189
501060992.21556307566367.7844369243367
5110801056.4367121914323.5632878085726
5211801117.7024492456862.297550754321
539801042.12822665222-62.1282266522244
549601043.80556987885-83.8055698788471
5510201025.93314162693-5.93314162693264
5611701129.0414062635840.9585937364216
5711501146.49502525583.50497474420195
58950990.589228910525-40.5892289105254
5911601141.6302573132118.369742686788
601120997.498421145507122.501578854493
6110101033.5420490558-23.5420490558038
6210101051.04292155415-41.0429215541499
6310601078.20862102229-18.2086210222901
6411301171.34438150378-41.344381503779
651000991.8748172298498.12518277015056
661000975.70628549128924.2937145087113
6710701022.9395752295147.0604247704858
6811501165.38887901261-15.3888790126114
6910801151.683266942-71.6832669420014
70980958.84397863005321.1560213699471
7112101159.0837809435750.9162190564289
7210201101.56368729733-81.5636872973337
739801015.36464449199-35.364644491991
7410301017.9156392796512.0843607203459
7510501063.96399304619-13.9639930461904
7611901137.6913648589252.3086351410798
77970999.598538639579-29.5985386395786
78950996.579218961782-46.5792189617823
7910701062.115542442977.88445755702514
8011701152.2543418490117.7456581509932
8110501091.71510740439-41.7151074043911
82960975.730069315382-15.7300693153823
8313001200.1725517168699.8274482831368
8410801032.8370768216747.1629231783272
851030985.58886793808644.4111320619138
8610301028.137158801091.86284119890684
8710701052.8714267943917.1285732056085
8812601182.0589863757477.9410136242589
89990976.63832214598813.3616778540123
90950960.291730305302-10.2917303053019
9110801071.791044221588.20895577841839
9211901170.7769851984619.2230148015417
9310501061.62945564139-11.6294556413873
94950968.057854944311-18.0578549443105
9512501289.02847828951-39.0284782895126
9611401077.8700969642162.1299030357898
9710801028.8276225703651.1723774296436
9810201036.57732006588-16.5773200658791
9911401074.2890101272965.7109898727067
10013201254.6031308294465.3968691705584
1011100996.089673429595103.910326570405
1021040961.22175572523478.7782442747657
10310901089.367225281810.632774718194014
10412801198.3872259337781.6127740662255
10510301065.00986565964-35.0098656596447
106930967.051114329517-37.0511143295165
10712801271.548409899128.45159010088491
10810201145.54304951419-125.543049514192

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1000 & 1001.78685897436 & -1.78685897435912 \tabularnewline
14 & 960 & 960.730515496827 & -0.730515496826911 \tabularnewline
15 & 1060 & 1060.09317635743 & -0.0931763574321849 \tabularnewline
16 & 1060 & 1060.29147893315 & -0.291478933150984 \tabularnewline
17 & 1110 & 1110.48823534432 & -0.488235344317673 \tabularnewline
18 & 1030 & 1034.01627678975 & -4.01627678974683 \tabularnewline
19 & 960 & 945.85316479328 & 14.14683520672 \tabularnewline
20 & 1130 & 1117.79924622571 & 12.2007537742854 \tabularnewline
21 & 1150 & 1152.26906465574 & -2.26906465573757 \tabularnewline
22 & 1030 & 1042.50848081203 & -12.5084808120264 \tabularnewline
23 & 1040 & 1041.00796116796 & -1.00796116795641 \tabularnewline
24 & 1030 & 1119.55083495206 & -89.5508349520637 \tabularnewline
25 & 1070 & 997.277016935642 & 72.7229830643585 \tabularnewline
26 & 1000 & 957.36362420949 & 42.63637579051 \tabularnewline
27 & 1020 & 1057.50938431197 & -37.5093843119737 \tabularnewline
28 & 1100 & 1057.37832330306 & 42.621676696936 \tabularnewline
29 & 1080 & 1107.6791489788 & -27.6791489788018 \tabularnewline
30 & 990 & 1028.19918301338 & -38.1991830133793 \tabularnewline
31 & 1000 & 954.892487506551 & 45.1075124934492 \tabularnewline
32 & 1110 & 1125.36617260522 & -15.3661726052221 \tabularnewline
33 & 1170 & 1147.67684162354 & 22.3231583764587 \tabularnewline
34 & 1030 & 1029.53601455234 & 0.463985447663163 \tabularnewline
35 & 1100 & 1037.66342961492 & 62.3365703850834 \tabularnewline
36 & 1020 & 1043.26922158533 & -23.2692215853278 \tabularnewline
37 & 1090 & 1056.1537070672 & 33.8462929328032 \tabularnewline
38 & 990 & 991.422022343402 & -1.42202234340175 \tabularnewline
39 & 1060 & 1025.11882487169 & 34.8811751283113 \tabularnewline
40 & 1120 & 1092.05170719193 & 27.9482928080718 \tabularnewline
41 & 1030 & 1084.33109156717 & -54.3310915671739 \tabularnewline
42 & 1050 & 996.267707314253 & 53.7322926857466 \tabularnewline
43 & 1030 & 992.866267241371 & 37.1337327586288 \tabularnewline
44 & 1130 & 1113.63948176027 & 16.3605182397334 \tabularnewline
45 & 1140 & 1167.86184353687 & -27.8618435368739 \tabularnewline
46 & 980 & 1031.81320804886 & -51.8132080488581 \tabularnewline
47 & 1150 & 1091.29812985814 & 58.7018701418588 \tabularnewline
48 & 990 & 1026.19562110706 & -36.1956211070637 \tabularnewline
49 & 1020 & 1086.60888157732 & -66.6088815773189 \tabularnewline
50 & 1060 & 992.215563075663 & 67.7844369243367 \tabularnewline
51 & 1080 & 1056.43671219143 & 23.5632878085726 \tabularnewline
52 & 1180 & 1117.70244924568 & 62.297550754321 \tabularnewline
53 & 980 & 1042.12822665222 & -62.1282266522244 \tabularnewline
54 & 960 & 1043.80556987885 & -83.8055698788471 \tabularnewline
55 & 1020 & 1025.93314162693 & -5.93314162693264 \tabularnewline
56 & 1170 & 1129.04140626358 & 40.9585937364216 \tabularnewline
57 & 1150 & 1146.4950252558 & 3.50497474420195 \tabularnewline
58 & 950 & 990.589228910525 & -40.5892289105254 \tabularnewline
59 & 1160 & 1141.63025731321 & 18.369742686788 \tabularnewline
60 & 1120 & 997.498421145507 & 122.501578854493 \tabularnewline
61 & 1010 & 1033.5420490558 & -23.5420490558038 \tabularnewline
62 & 1010 & 1051.04292155415 & -41.0429215541499 \tabularnewline
63 & 1060 & 1078.20862102229 & -18.2086210222901 \tabularnewline
64 & 1130 & 1171.34438150378 & -41.344381503779 \tabularnewline
65 & 1000 & 991.874817229849 & 8.12518277015056 \tabularnewline
66 & 1000 & 975.706285491289 & 24.2937145087113 \tabularnewline
67 & 1070 & 1022.93957522951 & 47.0604247704858 \tabularnewline
68 & 1150 & 1165.38887901261 & -15.3888790126114 \tabularnewline
69 & 1080 & 1151.683266942 & -71.6832669420014 \tabularnewline
70 & 980 & 958.843978630053 & 21.1560213699471 \tabularnewline
71 & 1210 & 1159.08378094357 & 50.9162190564289 \tabularnewline
72 & 1020 & 1101.56368729733 & -81.5636872973337 \tabularnewline
73 & 980 & 1015.36464449199 & -35.364644491991 \tabularnewline
74 & 1030 & 1017.91563927965 & 12.0843607203459 \tabularnewline
75 & 1050 & 1063.96399304619 & -13.9639930461904 \tabularnewline
76 & 1190 & 1137.69136485892 & 52.3086351410798 \tabularnewline
77 & 970 & 999.598538639579 & -29.5985386395786 \tabularnewline
78 & 950 & 996.579218961782 & -46.5792189617823 \tabularnewline
79 & 1070 & 1062.11554244297 & 7.88445755702514 \tabularnewline
80 & 1170 & 1152.25434184901 & 17.7456581509932 \tabularnewline
81 & 1050 & 1091.71510740439 & -41.7151074043911 \tabularnewline
82 & 960 & 975.730069315382 & -15.7300693153823 \tabularnewline
83 & 1300 & 1200.17255171686 & 99.8274482831368 \tabularnewline
84 & 1080 & 1032.83707682167 & 47.1629231783272 \tabularnewline
85 & 1030 & 985.588867938086 & 44.4111320619138 \tabularnewline
86 & 1030 & 1028.13715880109 & 1.86284119890684 \tabularnewline
87 & 1070 & 1052.87142679439 & 17.1285732056085 \tabularnewline
88 & 1260 & 1182.05898637574 & 77.9410136242589 \tabularnewline
89 & 990 & 976.638322145988 & 13.3616778540123 \tabularnewline
90 & 950 & 960.291730305302 & -10.2917303053019 \tabularnewline
91 & 1080 & 1071.79104422158 & 8.20895577841839 \tabularnewline
92 & 1190 & 1170.77698519846 & 19.2230148015417 \tabularnewline
93 & 1050 & 1061.62945564139 & -11.6294556413873 \tabularnewline
94 & 950 & 968.057854944311 & -18.0578549443105 \tabularnewline
95 & 1250 & 1289.02847828951 & -39.0284782895126 \tabularnewline
96 & 1140 & 1077.87009696421 & 62.1299030357898 \tabularnewline
97 & 1080 & 1028.82762257036 & 51.1723774296436 \tabularnewline
98 & 1020 & 1036.57732006588 & -16.5773200658791 \tabularnewline
99 & 1140 & 1074.28901012729 & 65.7109898727067 \tabularnewline
100 & 1320 & 1254.60313082944 & 65.3968691705584 \tabularnewline
101 & 1100 & 996.089673429595 & 103.910326570405 \tabularnewline
102 & 1040 & 961.221755725234 & 78.7782442747657 \tabularnewline
103 & 1090 & 1089.36722528181 & 0.632774718194014 \tabularnewline
104 & 1280 & 1198.38722593377 & 81.6127740662255 \tabularnewline
105 & 1030 & 1065.00986565964 & -35.0098656596447 \tabularnewline
106 & 930 & 967.051114329517 & -37.0511143295165 \tabularnewline
107 & 1280 & 1271.54840989912 & 8.45159010088491 \tabularnewline
108 & 1020 & 1145.54304951419 & -125.543049514192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210970&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]13[/C][C]1000[/C][C]1001.78685897436[/C][C]-1.78685897435912[/C][/ROW]
[ROW][C]14[/C][C]960[/C][C]960.730515496827[/C][C]-0.730515496826911[/C][/ROW]
[ROW][C]15[/C][C]1060[/C][C]1060.09317635743[/C][C]-0.0931763574321849[/C][/ROW]
[ROW][C]16[/C][C]1060[/C][C]1060.29147893315[/C][C]-0.291478933150984[/C][/ROW]
[ROW][C]17[/C][C]1110[/C][C]1110.48823534432[/C][C]-0.488235344317673[/C][/ROW]
[ROW][C]18[/C][C]1030[/C][C]1034.01627678975[/C][C]-4.01627678974683[/C][/ROW]
[ROW][C]19[/C][C]960[/C][C]945.85316479328[/C][C]14.14683520672[/C][/ROW]
[ROW][C]20[/C][C]1130[/C][C]1117.79924622571[/C][C]12.2007537742854[/C][/ROW]
[ROW][C]21[/C][C]1150[/C][C]1152.26906465574[/C][C]-2.26906465573757[/C][/ROW]
[ROW][C]22[/C][C]1030[/C][C]1042.50848081203[/C][C]-12.5084808120264[/C][/ROW]
[ROW][C]23[/C][C]1040[/C][C]1041.00796116796[/C][C]-1.00796116795641[/C][/ROW]
[ROW][C]24[/C][C]1030[/C][C]1119.55083495206[/C][C]-89.5508349520637[/C][/ROW]
[ROW][C]25[/C][C]1070[/C][C]997.277016935642[/C][C]72.7229830643585[/C][/ROW]
[ROW][C]26[/C][C]1000[/C][C]957.36362420949[/C][C]42.63637579051[/C][/ROW]
[ROW][C]27[/C][C]1020[/C][C]1057.50938431197[/C][C]-37.5093843119737[/C][/ROW]
[ROW][C]28[/C][C]1100[/C][C]1057.37832330306[/C][C]42.621676696936[/C][/ROW]
[ROW][C]29[/C][C]1080[/C][C]1107.6791489788[/C][C]-27.6791489788018[/C][/ROW]
[ROW][C]30[/C][C]990[/C][C]1028.19918301338[/C][C]-38.1991830133793[/C][/ROW]
[ROW][C]31[/C][C]1000[/C][C]954.892487506551[/C][C]45.1075124934492[/C][/ROW]
[ROW][C]32[/C][C]1110[/C][C]1125.36617260522[/C][C]-15.3661726052221[/C][/ROW]
[ROW][C]33[/C][C]1170[/C][C]1147.67684162354[/C][C]22.3231583764587[/C][/ROW]
[ROW][C]34[/C][C]1030[/C][C]1029.53601455234[/C][C]0.463985447663163[/C][/ROW]
[ROW][C]35[/C][C]1100[/C][C]1037.66342961492[/C][C]62.3365703850834[/C][/ROW]
[ROW][C]36[/C][C]1020[/C][C]1043.26922158533[/C][C]-23.2692215853278[/C][/ROW]
[ROW][C]37[/C][C]1090[/C][C]1056.1537070672[/C][C]33.8462929328032[/C][/ROW]
[ROW][C]38[/C][C]990[/C][C]991.422022343402[/C][C]-1.42202234340175[/C][/ROW]
[ROW][C]39[/C][C]1060[/C][C]1025.11882487169[/C][C]34.8811751283113[/C][/ROW]
[ROW][C]40[/C][C]1120[/C][C]1092.05170719193[/C][C]27.9482928080718[/C][/ROW]
[ROW][C]41[/C][C]1030[/C][C]1084.33109156717[/C][C]-54.3310915671739[/C][/ROW]
[ROW][C]42[/C][C]1050[/C][C]996.267707314253[/C][C]53.7322926857466[/C][/ROW]
[ROW][C]43[/C][C]1030[/C][C]992.866267241371[/C][C]37.1337327586288[/C][/ROW]
[ROW][C]44[/C][C]1130[/C][C]1113.63948176027[/C][C]16.3605182397334[/C][/ROW]
[ROW][C]45[/C][C]1140[/C][C]1167.86184353687[/C][C]-27.8618435368739[/C][/ROW]
[ROW][C]46[/C][C]980[/C][C]1031.81320804886[/C][C]-51.8132080488581[/C][/ROW]
[ROW][C]47[/C][C]1150[/C][C]1091.29812985814[/C][C]58.7018701418588[/C][/ROW]
[ROW][C]48[/C][C]990[/C][C]1026.19562110706[/C][C]-36.1956211070637[/C][/ROW]
[ROW][C]49[/C][C]1020[/C][C]1086.60888157732[/C][C]-66.6088815773189[/C][/ROW]
[ROW][C]50[/C][C]1060[/C][C]992.215563075663[/C][C]67.7844369243367[/C][/ROW]
[ROW][C]51[/C][C]1080[/C][C]1056.43671219143[/C][C]23.5632878085726[/C][/ROW]
[ROW][C]52[/C][C]1180[/C][C]1117.70244924568[/C][C]62.297550754321[/C][/ROW]
[ROW][C]53[/C][C]980[/C][C]1042.12822665222[/C][C]-62.1282266522244[/C][/ROW]
[ROW][C]54[/C][C]960[/C][C]1043.80556987885[/C][C]-83.8055698788471[/C][/ROW]
[ROW][C]55[/C][C]1020[/C][C]1025.93314162693[/C][C]-5.93314162693264[/C][/ROW]
[ROW][C]56[/C][C]1170[/C][C]1129.04140626358[/C][C]40.9585937364216[/C][/ROW]
[ROW][C]57[/C][C]1150[/C][C]1146.4950252558[/C][C]3.50497474420195[/C][/ROW]
[ROW][C]58[/C][C]950[/C][C]990.589228910525[/C][C]-40.5892289105254[/C][/ROW]
[ROW][C]59[/C][C]1160[/C][C]1141.63025731321[/C][C]18.369742686788[/C][/ROW]
[ROW][C]60[/C][C]1120[/C][C]997.498421145507[/C][C]122.501578854493[/C][/ROW]
[ROW][C]61[/C][C]1010[/C][C]1033.5420490558[/C][C]-23.5420490558038[/C][/ROW]
[ROW][C]62[/C][C]1010[/C][C]1051.04292155415[/C][C]-41.0429215541499[/C][/ROW]
[ROW][C]63[/C][C]1060[/C][C]1078.20862102229[/C][C]-18.2086210222901[/C][/ROW]
[ROW][C]64[/C][C]1130[/C][C]1171.34438150378[/C][C]-41.344381503779[/C][/ROW]
[ROW][C]65[/C][C]1000[/C][C]991.874817229849[/C][C]8.12518277015056[/C][/ROW]
[ROW][C]66[/C][C]1000[/C][C]975.706285491289[/C][C]24.2937145087113[/C][/ROW]
[ROW][C]67[/C][C]1070[/C][C]1022.93957522951[/C][C]47.0604247704858[/C][/ROW]
[ROW][C]68[/C][C]1150[/C][C]1165.38887901261[/C][C]-15.3888790126114[/C][/ROW]
[ROW][C]69[/C][C]1080[/C][C]1151.683266942[/C][C]-71.6832669420014[/C][/ROW]
[ROW][C]70[/C][C]980[/C][C]958.843978630053[/C][C]21.1560213699471[/C][/ROW]
[ROW][C]71[/C][C]1210[/C][C]1159.08378094357[/C][C]50.9162190564289[/C][/ROW]
[ROW][C]72[/C][C]1020[/C][C]1101.56368729733[/C][C]-81.5636872973337[/C][/ROW]
[ROW][C]73[/C][C]980[/C][C]1015.36464449199[/C][C]-35.364644491991[/C][/ROW]
[ROW][C]74[/C][C]1030[/C][C]1017.91563927965[/C][C]12.0843607203459[/C][/ROW]
[ROW][C]75[/C][C]1050[/C][C]1063.96399304619[/C][C]-13.9639930461904[/C][/ROW]
[ROW][C]76[/C][C]1190[/C][C]1137.69136485892[/C][C]52.3086351410798[/C][/ROW]
[ROW][C]77[/C][C]970[/C][C]999.598538639579[/C][C]-29.5985386395786[/C][/ROW]
[ROW][C]78[/C][C]950[/C][C]996.579218961782[/C][C]-46.5792189617823[/C][/ROW]
[ROW][C]79[/C][C]1070[/C][C]1062.11554244297[/C][C]7.88445755702514[/C][/ROW]
[ROW][C]80[/C][C]1170[/C][C]1152.25434184901[/C][C]17.7456581509932[/C][/ROW]
[ROW][C]81[/C][C]1050[/C][C]1091.71510740439[/C][C]-41.7151074043911[/C][/ROW]
[ROW][C]82[/C][C]960[/C][C]975.730069315382[/C][C]-15.7300693153823[/C][/ROW]
[ROW][C]83[/C][C]1300[/C][C]1200.17255171686[/C][C]99.8274482831368[/C][/ROW]
[ROW][C]84[/C][C]1080[/C][C]1032.83707682167[/C][C]47.1629231783272[/C][/ROW]
[ROW][C]85[/C][C]1030[/C][C]985.588867938086[/C][C]44.4111320619138[/C][/ROW]
[ROW][C]86[/C][C]1030[/C][C]1028.13715880109[/C][C]1.86284119890684[/C][/ROW]
[ROW][C]87[/C][C]1070[/C][C]1052.87142679439[/C][C]17.1285732056085[/C][/ROW]
[ROW][C]88[/C][C]1260[/C][C]1182.05898637574[/C][C]77.9410136242589[/C][/ROW]
[ROW][C]89[/C][C]990[/C][C]976.638322145988[/C][C]13.3616778540123[/C][/ROW]
[ROW][C]90[/C][C]950[/C][C]960.291730305302[/C][C]-10.2917303053019[/C][/ROW]
[ROW][C]91[/C][C]1080[/C][C]1071.79104422158[/C][C]8.20895577841839[/C][/ROW]
[ROW][C]92[/C][C]1190[/C][C]1170.77698519846[/C][C]19.2230148015417[/C][/ROW]
[ROW][C]93[/C][C]1050[/C][C]1061.62945564139[/C][C]-11.6294556413873[/C][/ROW]
[ROW][C]94[/C][C]950[/C][C]968.057854944311[/C][C]-18.0578549443105[/C][/ROW]
[ROW][C]95[/C][C]1250[/C][C]1289.02847828951[/C][C]-39.0284782895126[/C][/ROW]
[ROW][C]96[/C][C]1140[/C][C]1077.87009696421[/C][C]62.1299030357898[/C][/ROW]
[ROW][C]97[/C][C]1080[/C][C]1028.82762257036[/C][C]51.1723774296436[/C][/ROW]
[ROW][C]98[/C][C]1020[/C][C]1036.57732006588[/C][C]-16.5773200658791[/C][/ROW]
[ROW][C]99[/C][C]1140[/C][C]1074.28901012729[/C][C]65.7109898727067[/C][/ROW]
[ROW][C]100[/C][C]1320[/C][C]1254.60313082944[/C][C]65.3968691705584[/C][/ROW]
[ROW][C]101[/C][C]1100[/C][C]996.089673429595[/C][C]103.910326570405[/C][/ROW]
[ROW][C]102[/C][C]1040[/C][C]961.221755725234[/C][C]78.7782442747657[/C][/ROW]
[ROW][C]103[/C][C]1090[/C][C]1089.36722528181[/C][C]0.632774718194014[/C][/ROW]
[ROW][C]104[/C][C]1280[/C][C]1198.38722593377[/C][C]81.6127740662255[/C][/ROW]
[ROW][C]105[/C][C]1030[/C][C]1065.00986565964[/C][C]-35.0098656596447[/C][/ROW]
[ROW][C]106[/C][C]930[/C][C]967.051114329517[/C][C]-37.0511143295165[/C][/ROW]
[ROW][C]107[/C][C]1280[/C][C]1271.54840989912[/C][C]8.45159010088491[/C][/ROW]
[ROW][C]108[/C][C]1020[/C][C]1145.54304951419[/C][C]-125.543049514192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210970&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210970&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
1310001001.78685897436-1.78685897435912
14960960.730515496827-0.730515496826911
1510601060.09317635743-0.0931763574321849
1610601060.29147893315-0.291478933150984
1711101110.48823534432-0.488235344317673
1810301034.01627678975-4.01627678974683
19960945.8531647932814.14683520672
2011301117.7992462257112.2007537742854
2111501152.26906465574-2.26906465573757
2210301042.50848081203-12.5084808120264
2310401041.00796116796-1.00796116795641
2410301119.55083495206-89.5508349520637
251070997.27701693564272.7229830643585
261000957.3636242094942.63637579051
2710201057.50938431197-37.5093843119737
2811001057.3783233030642.621676696936
2910801107.6791489788-27.6791489788018
309901028.19918301338-38.1991830133793
311000954.89248750655145.1075124934492
3211101125.36617260522-15.3661726052221
3311701147.6768416235422.3231583764587
3410301029.536014552340.463985447663163
3511001037.6634296149262.3365703850834
3610201043.26922158533-23.2692215853278
3710901056.153707067233.8462929328032
38990991.422022343402-1.42202234340175
3910601025.1188248716934.8811751283113
4011201092.0517071919327.9482928080718
4110301084.33109156717-54.3310915671739
421050996.26770731425353.7322926857466
431030992.86626724137137.1337327586288
4411301113.6394817602716.3605182397334
4511401167.86184353687-27.8618435368739
469801031.81320804886-51.8132080488581
4711501091.2981298581458.7018701418588
489901026.19562110706-36.1956211070637
4910201086.60888157732-66.6088815773189
501060992.21556307566367.7844369243367
5110801056.4367121914323.5632878085726
5211801117.7024492456862.297550754321
539801042.12822665222-62.1282266522244
549601043.80556987885-83.8055698788471
5510201025.93314162693-5.93314162693264
5611701129.0414062635840.9585937364216
5711501146.49502525583.50497474420195
58950990.589228910525-40.5892289105254
5911601141.6302573132118.369742686788
601120997.498421145507122.501578854493
6110101033.5420490558-23.5420490558038
6210101051.04292155415-41.0429215541499
6310601078.20862102229-18.2086210222901
6411301171.34438150378-41.344381503779
651000991.8748172298498.12518277015056
661000975.70628549128924.2937145087113
6710701022.9395752295147.0604247704858
6811501165.38887901261-15.3888790126114
6910801151.683266942-71.6832669420014
70980958.84397863005321.1560213699471
7112101159.0837809435750.9162190564289
7210201101.56368729733-81.5636872973337
739801015.36464449199-35.364644491991
7410301017.9156392796512.0843607203459
7510501063.96399304619-13.9639930461904
7611901137.6913648589252.3086351410798
77970999.598538639579-29.5985386395786
78950996.579218961782-46.5792189617823
7910701062.115542442977.88445755702514
8011701152.2543418490117.7456581509932
8110501091.71510740439-41.7151074043911
82960975.730069315382-15.7300693153823
8313001200.1725517168699.8274482831368
8410801032.8370768216747.1629231783272
851030985.58886793808644.4111320619138
8610301028.137158801091.86284119890684
8710701052.8714267943917.1285732056085
8812601182.0589863757477.9410136242589
89990976.63832214598813.3616778540123
90950960.291730305302-10.2917303053019
9110801071.791044221588.20895577841839
9211901170.7769851984619.2230148015417
9310501061.62945564139-11.6294556413873
94950968.057854944311-18.0578549443105
9512501289.02847828951-39.0284782895126
9611401077.8700969642162.1299030357898
9710801028.8276225703651.1723774296436
9810201036.57732006588-16.5773200658791
9911401074.2890101272965.7109898727067
10013201254.6031308294465.3968691705584
1011100996.089673429595103.910326570405
1021040961.22175572523478.7782442747657
10310901089.367225281810.632774718194014
10412801198.3872259337781.6127740662255
10510301065.00986565964-35.0098656596447
106930967.051114329517-37.0511143295165
10712801271.548409899128.45159010088491
10810201145.54304951419-125.543049514192







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091087.29068242739997.4277765852791177.15358826949
1101039.16683544815949.3019824279511129.03168846835
1111145.691532282411055.822904001071235.56016056376
1121325.847181141141235.972350039921415.72201224235
1131099.1933523031009.309291681291189.0774129247
1141043.00413510221953.1072196329121132.9010505715
1151105.780296271341015.866302737451195.69428980524
1161281.647631810471191.711740101961371.58352351897
1171050.78181687515960.8186112849321140.74502246536
118950.872788944953860.8762598018741040.86931808803
1191292.934855856731202.89840153291382.97131018056
1201055.4976165725965.4140459012511145.58118724376

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1087.29068242739 & 997.427776585279 & 1177.15358826949 \tabularnewline
110 & 1039.16683544815 & 949.301982427951 & 1129.03168846835 \tabularnewline
111 & 1145.69153228241 & 1055.82290400107 & 1235.56016056376 \tabularnewline
112 & 1325.84718114114 & 1235.97235003992 & 1415.72201224235 \tabularnewline
113 & 1099.193352303 & 1009.30929168129 & 1189.0774129247 \tabularnewline
114 & 1043.00413510221 & 953.107219632912 & 1132.9010505715 \tabularnewline
115 & 1105.78029627134 & 1015.86630273745 & 1195.69428980524 \tabularnewline
116 & 1281.64763181047 & 1191.71174010196 & 1371.58352351897 \tabularnewline
117 & 1050.78181687515 & 960.818611284932 & 1140.74502246536 \tabularnewline
118 & 950.872788944953 & 860.876259801874 & 1040.86931808803 \tabularnewline
119 & 1292.93485585673 & 1202.8984015329 & 1382.97131018056 \tabularnewline
120 & 1055.4976165725 & 965.414045901251 & 1145.58118724376 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210970&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]1087.29068242739[/C][C]997.427776585279[/C][C]1177.15358826949[/C][/ROW]
[ROW][C]110[/C][C]1039.16683544815[/C][C]949.301982427951[/C][C]1129.03168846835[/C][/ROW]
[ROW][C]111[/C][C]1145.69153228241[/C][C]1055.82290400107[/C][C]1235.56016056376[/C][/ROW]
[ROW][C]112[/C][C]1325.84718114114[/C][C]1235.97235003992[/C][C]1415.72201224235[/C][/ROW]
[ROW][C]113[/C][C]1099.193352303[/C][C]1009.30929168129[/C][C]1189.0774129247[/C][/ROW]
[ROW][C]114[/C][C]1043.00413510221[/C][C]953.107219632912[/C][C]1132.9010505715[/C][/ROW]
[ROW][C]115[/C][C]1105.78029627134[/C][C]1015.86630273745[/C][C]1195.69428980524[/C][/ROW]
[ROW][C]116[/C][C]1281.64763181047[/C][C]1191.71174010196[/C][C]1371.58352351897[/C][/ROW]
[ROW][C]117[/C][C]1050.78181687515[/C][C]960.818611284932[/C][C]1140.74502246536[/C][/ROW]
[ROW][C]118[/C][C]950.872788944953[/C][C]860.876259801874[/C][C]1040.86931808803[/C][/ROW]
[ROW][C]119[/C][C]1292.93485585673[/C][C]1202.8984015329[/C][C]1382.97131018056[/C][/ROW]
[ROW][C]120[/C][C]1055.4976165725[/C][C]965.414045901251[/C][C]1145.58118724376[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210970&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210970&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
1091087.29068242739997.4277765852791177.15358826949
1101039.16683544815949.3019824279511129.03168846835
1111145.691532282411055.822904001071235.56016056376
1121325.847181141141235.972350039921415.72201224235
1131099.1933523031009.309291681291189.0774129247
1141043.00413510221953.1072196329121132.9010505715
1151105.780296271341015.866302737451195.69428980524
1161281.647631810471191.711740101961371.58352351897
1171050.78181687515960.8186112849321140.74502246536
118950.872788944953860.8762598018741040.86931808803
1191292.934855856731202.89840153291382.97131018056
1201055.4976165725965.4140459012511145.58118724376



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