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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 computationThu, 18 Aug 2011 19:53:45 -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/2011/Aug/18/t1313711646y1dc15zim5xo9og.htm/, Retrieved Thu, 16 May 2024 00:39:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124185, Retrieved Thu, 16 May 2024 00:39:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Jens Vanpachtenbe...] [2011-08-18 23:53:45] [d41d8cd98f00b204e9800998ecf8427e] [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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124185&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124185&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124185&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00399960078372102
beta0.645937398396141
gamma0.832270390608186

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00399960078372102 \tabularnewline
beta & 0.645937398396141 \tabularnewline
gamma & 0.832270390608186 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124185&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]0.00399960078372102[/C][/ROW]
[ROW][C]beta[/C][C]0.645937398396141[/C][/ROW]
[ROW][C]gamma[/C][C]0.832270390608186[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124185&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124185&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
alpha0.00399960078372102
beta0.645937398396141
gamma0.832270390608186







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310001001.78685897436-1.78685897435844
14960960.73051549685-0.73051549685033
1510601060.09317635747-0.0931763574678826
1610601060.29147893319-0.291478933192138
1711101110.48823534437-0.488235344366785
1810301034.01627678981-4.01627678980662
19960945.85316479339814.1468352066015
2011301117.7992462256612.2007537743445
2111501152.2690646555-2.2690646555036
2210301042.50848081179-12.5084808117922
2310401041.00796116786-1.00796116786273
2410301119.55083495198-89.550834951978
251070997.27701693668272.7229830633183
261000957.36362420971842.6363757902824
2710201057.50938431167-37.5093843116651
2811001057.378323303242.6216766968039
2910801107.67914897836-27.679148978362
309901028.19918301311-38.1991830131108
311000954.89248750742345.1075124925773
3211101125.36617260561-15.3661726056127
3311701147.6768416237122.3231583762936
3410301029.536014551820.463985448184758
3511001037.6634296146762.3365703853265
3610201043.26922158085-23.2692215808547
3710901056.1537070680733.8462929319282
38990991.422022343282-1.4220223432817
3910601025.1188248688634.8811751311398
4011201092.0517071911627.9482928088353
4110301084.33109156364-54.3310915636393
421050996.26770731054253.7322926894582
431030992.86626723967537.1337327603254
4411301113.6394817560416.3605182439571
4511401167.86184353339-27.8618435333894
469801031.81320804482-51.8132080448245
4711501091.2981298570258.7018701429831
489901026.19562110192-36.1956211019187
4910201086.60888157533-66.6088815753312
501060992.21556307345567.7844369265454
5110801056.4367121893223.5632878106799
5211801117.702449243862.2975507562014
539801042.12822664631-62.1282266463068
549601043.80556987707-83.8055698770659
5510201025.93314162666-5.93314162666297
5611701129.0414062628540.9585937371476
5711501146.495025253443.50497474656345
58950990.589228906951-40.589228906951
5911601141.6302573143318.3697426856702
601120997.498421143005122.501578856995
6110101033.54204905075-23.5420490507524
6210101051.04292155353-41.0429215535266
6310601078.20862102132-18.2086210213163
6411301171.34438150491-41.3443815049052
651000991.8748172270458.12518277295487
661000975.70628548768824.2937145123125
6710701022.9395752278447.0604247721603
6811501165.38887901191-15.3888790119101
6910801151.68326694024-71.6832669402418
70980958.84397862739821.1560213726017
7112101159.0837809432350.9162190567706
7210201101.56368729989-81.5636872998941
739801015.36464449123-35.364644491225
7410301017.9156392793912.0843607206081
7510501063.96399304631-13.9639930463093
7611901137.6913648586652.3086351413438
77970999.598538639463-29.5985386394627
78950996.579218962664-46.5792189626644
7910701062.115542446067.88445755394218
8011701152.2543418505817.7456581494191
8110501091.71510740345-41.7151074034457
82960975.730069317586-15.7300693175864
8313001200.1725517211999.8274482788102
8410801032.8370768209847.1629231790212
851030985.58886793696944.4111320630313
8610301028.137158800681.86284119931861
8710701052.8714267929517.1285732070519
8812601182.0589863761177.9410136238914
89990976.63832214265213.361677857348
90950960.291730300617-10.2917303006175
9110801071.79104421858.20895578149725
9211901170.776985195119.223014804902
9310501061.62945563494-11.6294556349378
94950968.057854938611-18.0578549386113
9512501289.02847828819-39.0284782881945
9611401077.8700969615162.1299030384887
9710801028.8276225671251.172377432878
9810201036.57732006089-16.5773200608853
9911401074.2890101227865.7109898772196
10013201254.6031308267665.3968691732407
1011100996.089673423791103.910326576209
1021040961.22175571691178.7782442830892
10310901089.367225272950.63277472705272
10412801198.3872259249481.612774075061
10510301065.00986564786-35.0098656478563
106930967.051114317412-37.051114317412
10712801271.548409886778.45159011323335
10810201145.54304950443-125.543049504432

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1000 & 1001.78685897436 & -1.78685897435844 \tabularnewline
14 & 960 & 960.73051549685 & -0.73051549685033 \tabularnewline
15 & 1060 & 1060.09317635747 & -0.0931763574678826 \tabularnewline
16 & 1060 & 1060.29147893319 & -0.291478933192138 \tabularnewline
17 & 1110 & 1110.48823534437 & -0.488235344366785 \tabularnewline
18 & 1030 & 1034.01627678981 & -4.01627678980662 \tabularnewline
19 & 960 & 945.853164793398 & 14.1468352066015 \tabularnewline
20 & 1130 & 1117.79924622566 & 12.2007537743445 \tabularnewline
21 & 1150 & 1152.2690646555 & -2.2690646555036 \tabularnewline
22 & 1030 & 1042.50848081179 & -12.5084808117922 \tabularnewline
23 & 1040 & 1041.00796116786 & -1.00796116786273 \tabularnewline
24 & 1030 & 1119.55083495198 & -89.550834951978 \tabularnewline
25 & 1070 & 997.277016936682 & 72.7229830633183 \tabularnewline
26 & 1000 & 957.363624209718 & 42.6363757902824 \tabularnewline
27 & 1020 & 1057.50938431167 & -37.5093843116651 \tabularnewline
28 & 1100 & 1057.3783233032 & 42.6216766968039 \tabularnewline
29 & 1080 & 1107.67914897836 & -27.679148978362 \tabularnewline
30 & 990 & 1028.19918301311 & -38.1991830131108 \tabularnewline
31 & 1000 & 954.892487507423 & 45.1075124925773 \tabularnewline
32 & 1110 & 1125.36617260561 & -15.3661726056127 \tabularnewline
33 & 1170 & 1147.67684162371 & 22.3231583762936 \tabularnewline
34 & 1030 & 1029.53601455182 & 0.463985448184758 \tabularnewline
35 & 1100 & 1037.66342961467 & 62.3365703853265 \tabularnewline
36 & 1020 & 1043.26922158085 & -23.2692215808547 \tabularnewline
37 & 1090 & 1056.15370706807 & 33.8462929319282 \tabularnewline
38 & 990 & 991.422022343282 & -1.4220223432817 \tabularnewline
39 & 1060 & 1025.11882486886 & 34.8811751311398 \tabularnewline
40 & 1120 & 1092.05170719116 & 27.9482928088353 \tabularnewline
41 & 1030 & 1084.33109156364 & -54.3310915636393 \tabularnewline
42 & 1050 & 996.267707310542 & 53.7322926894582 \tabularnewline
43 & 1030 & 992.866267239675 & 37.1337327603254 \tabularnewline
44 & 1130 & 1113.63948175604 & 16.3605182439571 \tabularnewline
45 & 1140 & 1167.86184353339 & -27.8618435333894 \tabularnewline
46 & 980 & 1031.81320804482 & -51.8132080448245 \tabularnewline
47 & 1150 & 1091.29812985702 & 58.7018701429831 \tabularnewline
48 & 990 & 1026.19562110192 & -36.1956211019187 \tabularnewline
49 & 1020 & 1086.60888157533 & -66.6088815753312 \tabularnewline
50 & 1060 & 992.215563073455 & 67.7844369265454 \tabularnewline
51 & 1080 & 1056.43671218932 & 23.5632878106799 \tabularnewline
52 & 1180 & 1117.7024492438 & 62.2975507562014 \tabularnewline
53 & 980 & 1042.12822664631 & -62.1282266463068 \tabularnewline
54 & 960 & 1043.80556987707 & -83.8055698770659 \tabularnewline
55 & 1020 & 1025.93314162666 & -5.93314162666297 \tabularnewline
56 & 1170 & 1129.04140626285 & 40.9585937371476 \tabularnewline
57 & 1150 & 1146.49502525344 & 3.50497474656345 \tabularnewline
58 & 950 & 990.589228906951 & -40.589228906951 \tabularnewline
59 & 1160 & 1141.63025731433 & 18.3697426856702 \tabularnewline
60 & 1120 & 997.498421143005 & 122.501578856995 \tabularnewline
61 & 1010 & 1033.54204905075 & -23.5420490507524 \tabularnewline
62 & 1010 & 1051.04292155353 & -41.0429215535266 \tabularnewline
63 & 1060 & 1078.20862102132 & -18.2086210213163 \tabularnewline
64 & 1130 & 1171.34438150491 & -41.3443815049052 \tabularnewline
65 & 1000 & 991.874817227045 & 8.12518277295487 \tabularnewline
66 & 1000 & 975.706285487688 & 24.2937145123125 \tabularnewline
67 & 1070 & 1022.93957522784 & 47.0604247721603 \tabularnewline
68 & 1150 & 1165.38887901191 & -15.3888790119101 \tabularnewline
69 & 1080 & 1151.68326694024 & -71.6832669402418 \tabularnewline
70 & 980 & 958.843978627398 & 21.1560213726017 \tabularnewline
71 & 1210 & 1159.08378094323 & 50.9162190567706 \tabularnewline
72 & 1020 & 1101.56368729989 & -81.5636872998941 \tabularnewline
73 & 980 & 1015.36464449123 & -35.364644491225 \tabularnewline
74 & 1030 & 1017.91563927939 & 12.0843607206081 \tabularnewline
75 & 1050 & 1063.96399304631 & -13.9639930463093 \tabularnewline
76 & 1190 & 1137.69136485866 & 52.3086351413438 \tabularnewline
77 & 970 & 999.598538639463 & -29.5985386394627 \tabularnewline
78 & 950 & 996.579218962664 & -46.5792189626644 \tabularnewline
79 & 1070 & 1062.11554244606 & 7.88445755394218 \tabularnewline
80 & 1170 & 1152.25434185058 & 17.7456581494191 \tabularnewline
81 & 1050 & 1091.71510740345 & -41.7151074034457 \tabularnewline
82 & 960 & 975.730069317586 & -15.7300693175864 \tabularnewline
83 & 1300 & 1200.17255172119 & 99.8274482788102 \tabularnewline
84 & 1080 & 1032.83707682098 & 47.1629231790212 \tabularnewline
85 & 1030 & 985.588867936969 & 44.4111320630313 \tabularnewline
86 & 1030 & 1028.13715880068 & 1.86284119931861 \tabularnewline
87 & 1070 & 1052.87142679295 & 17.1285732070519 \tabularnewline
88 & 1260 & 1182.05898637611 & 77.9410136238914 \tabularnewline
89 & 990 & 976.638322142652 & 13.361677857348 \tabularnewline
90 & 950 & 960.291730300617 & -10.2917303006175 \tabularnewline
91 & 1080 & 1071.7910442185 & 8.20895578149725 \tabularnewline
92 & 1190 & 1170.7769851951 & 19.223014804902 \tabularnewline
93 & 1050 & 1061.62945563494 & -11.6294556349378 \tabularnewline
94 & 950 & 968.057854938611 & -18.0578549386113 \tabularnewline
95 & 1250 & 1289.02847828819 & -39.0284782881945 \tabularnewline
96 & 1140 & 1077.87009696151 & 62.1299030384887 \tabularnewline
97 & 1080 & 1028.82762256712 & 51.172377432878 \tabularnewline
98 & 1020 & 1036.57732006089 & -16.5773200608853 \tabularnewline
99 & 1140 & 1074.28901012278 & 65.7109898772196 \tabularnewline
100 & 1320 & 1254.60313082676 & 65.3968691732407 \tabularnewline
101 & 1100 & 996.089673423791 & 103.910326576209 \tabularnewline
102 & 1040 & 961.221755716911 & 78.7782442830892 \tabularnewline
103 & 1090 & 1089.36722527295 & 0.63277472705272 \tabularnewline
104 & 1280 & 1198.38722592494 & 81.612774075061 \tabularnewline
105 & 1030 & 1065.00986564786 & -35.0098656478563 \tabularnewline
106 & 930 & 967.051114317412 & -37.051114317412 \tabularnewline
107 & 1280 & 1271.54840988677 & 8.45159011323335 \tabularnewline
108 & 1020 & 1145.54304950443 & -125.543049504432 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124185&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]-1.78685897435844[/C][/ROW]
[ROW][C]14[/C][C]960[/C][C]960.73051549685[/C][C]-0.73051549685033[/C][/ROW]
[ROW][C]15[/C][C]1060[/C][C]1060.09317635747[/C][C]-0.0931763574678826[/C][/ROW]
[ROW][C]16[/C][C]1060[/C][C]1060.29147893319[/C][C]-0.291478933192138[/C][/ROW]
[ROW][C]17[/C][C]1110[/C][C]1110.48823534437[/C][C]-0.488235344366785[/C][/ROW]
[ROW][C]18[/C][C]1030[/C][C]1034.01627678981[/C][C]-4.01627678980662[/C][/ROW]
[ROW][C]19[/C][C]960[/C][C]945.853164793398[/C][C]14.1468352066015[/C][/ROW]
[ROW][C]20[/C][C]1130[/C][C]1117.79924622566[/C][C]12.2007537743445[/C][/ROW]
[ROW][C]21[/C][C]1150[/C][C]1152.2690646555[/C][C]-2.2690646555036[/C][/ROW]
[ROW][C]22[/C][C]1030[/C][C]1042.50848081179[/C][C]-12.5084808117922[/C][/ROW]
[ROW][C]23[/C][C]1040[/C][C]1041.00796116786[/C][C]-1.00796116786273[/C][/ROW]
[ROW][C]24[/C][C]1030[/C][C]1119.55083495198[/C][C]-89.550834951978[/C][/ROW]
[ROW][C]25[/C][C]1070[/C][C]997.277016936682[/C][C]72.7229830633183[/C][/ROW]
[ROW][C]26[/C][C]1000[/C][C]957.363624209718[/C][C]42.6363757902824[/C][/ROW]
[ROW][C]27[/C][C]1020[/C][C]1057.50938431167[/C][C]-37.5093843116651[/C][/ROW]
[ROW][C]28[/C][C]1100[/C][C]1057.3783233032[/C][C]42.6216766968039[/C][/ROW]
[ROW][C]29[/C][C]1080[/C][C]1107.67914897836[/C][C]-27.679148978362[/C][/ROW]
[ROW][C]30[/C][C]990[/C][C]1028.19918301311[/C][C]-38.1991830131108[/C][/ROW]
[ROW][C]31[/C][C]1000[/C][C]954.892487507423[/C][C]45.1075124925773[/C][/ROW]
[ROW][C]32[/C][C]1110[/C][C]1125.36617260561[/C][C]-15.3661726056127[/C][/ROW]
[ROW][C]33[/C][C]1170[/C][C]1147.67684162371[/C][C]22.3231583762936[/C][/ROW]
[ROW][C]34[/C][C]1030[/C][C]1029.53601455182[/C][C]0.463985448184758[/C][/ROW]
[ROW][C]35[/C][C]1100[/C][C]1037.66342961467[/C][C]62.3365703853265[/C][/ROW]
[ROW][C]36[/C][C]1020[/C][C]1043.26922158085[/C][C]-23.2692215808547[/C][/ROW]
[ROW][C]37[/C][C]1090[/C][C]1056.15370706807[/C][C]33.8462929319282[/C][/ROW]
[ROW][C]38[/C][C]990[/C][C]991.422022343282[/C][C]-1.4220223432817[/C][/ROW]
[ROW][C]39[/C][C]1060[/C][C]1025.11882486886[/C][C]34.8811751311398[/C][/ROW]
[ROW][C]40[/C][C]1120[/C][C]1092.05170719116[/C][C]27.9482928088353[/C][/ROW]
[ROW][C]41[/C][C]1030[/C][C]1084.33109156364[/C][C]-54.3310915636393[/C][/ROW]
[ROW][C]42[/C][C]1050[/C][C]996.267707310542[/C][C]53.7322926894582[/C][/ROW]
[ROW][C]43[/C][C]1030[/C][C]992.866267239675[/C][C]37.1337327603254[/C][/ROW]
[ROW][C]44[/C][C]1130[/C][C]1113.63948175604[/C][C]16.3605182439571[/C][/ROW]
[ROW][C]45[/C][C]1140[/C][C]1167.86184353339[/C][C]-27.8618435333894[/C][/ROW]
[ROW][C]46[/C][C]980[/C][C]1031.81320804482[/C][C]-51.8132080448245[/C][/ROW]
[ROW][C]47[/C][C]1150[/C][C]1091.29812985702[/C][C]58.7018701429831[/C][/ROW]
[ROW][C]48[/C][C]990[/C][C]1026.19562110192[/C][C]-36.1956211019187[/C][/ROW]
[ROW][C]49[/C][C]1020[/C][C]1086.60888157533[/C][C]-66.6088815753312[/C][/ROW]
[ROW][C]50[/C][C]1060[/C][C]992.215563073455[/C][C]67.7844369265454[/C][/ROW]
[ROW][C]51[/C][C]1080[/C][C]1056.43671218932[/C][C]23.5632878106799[/C][/ROW]
[ROW][C]52[/C][C]1180[/C][C]1117.7024492438[/C][C]62.2975507562014[/C][/ROW]
[ROW][C]53[/C][C]980[/C][C]1042.12822664631[/C][C]-62.1282266463068[/C][/ROW]
[ROW][C]54[/C][C]960[/C][C]1043.80556987707[/C][C]-83.8055698770659[/C][/ROW]
[ROW][C]55[/C][C]1020[/C][C]1025.93314162666[/C][C]-5.93314162666297[/C][/ROW]
[ROW][C]56[/C][C]1170[/C][C]1129.04140626285[/C][C]40.9585937371476[/C][/ROW]
[ROW][C]57[/C][C]1150[/C][C]1146.49502525344[/C][C]3.50497474656345[/C][/ROW]
[ROW][C]58[/C][C]950[/C][C]990.589228906951[/C][C]-40.589228906951[/C][/ROW]
[ROW][C]59[/C][C]1160[/C][C]1141.63025731433[/C][C]18.3697426856702[/C][/ROW]
[ROW][C]60[/C][C]1120[/C][C]997.498421143005[/C][C]122.501578856995[/C][/ROW]
[ROW][C]61[/C][C]1010[/C][C]1033.54204905075[/C][C]-23.5420490507524[/C][/ROW]
[ROW][C]62[/C][C]1010[/C][C]1051.04292155353[/C][C]-41.0429215535266[/C][/ROW]
[ROW][C]63[/C][C]1060[/C][C]1078.20862102132[/C][C]-18.2086210213163[/C][/ROW]
[ROW][C]64[/C][C]1130[/C][C]1171.34438150491[/C][C]-41.3443815049052[/C][/ROW]
[ROW][C]65[/C][C]1000[/C][C]991.874817227045[/C][C]8.12518277295487[/C][/ROW]
[ROW][C]66[/C][C]1000[/C][C]975.706285487688[/C][C]24.2937145123125[/C][/ROW]
[ROW][C]67[/C][C]1070[/C][C]1022.93957522784[/C][C]47.0604247721603[/C][/ROW]
[ROW][C]68[/C][C]1150[/C][C]1165.38887901191[/C][C]-15.3888790119101[/C][/ROW]
[ROW][C]69[/C][C]1080[/C][C]1151.68326694024[/C][C]-71.6832669402418[/C][/ROW]
[ROW][C]70[/C][C]980[/C][C]958.843978627398[/C][C]21.1560213726017[/C][/ROW]
[ROW][C]71[/C][C]1210[/C][C]1159.08378094323[/C][C]50.9162190567706[/C][/ROW]
[ROW][C]72[/C][C]1020[/C][C]1101.56368729989[/C][C]-81.5636872998941[/C][/ROW]
[ROW][C]73[/C][C]980[/C][C]1015.36464449123[/C][C]-35.364644491225[/C][/ROW]
[ROW][C]74[/C][C]1030[/C][C]1017.91563927939[/C][C]12.0843607206081[/C][/ROW]
[ROW][C]75[/C][C]1050[/C][C]1063.96399304631[/C][C]-13.9639930463093[/C][/ROW]
[ROW][C]76[/C][C]1190[/C][C]1137.69136485866[/C][C]52.3086351413438[/C][/ROW]
[ROW][C]77[/C][C]970[/C][C]999.598538639463[/C][C]-29.5985386394627[/C][/ROW]
[ROW][C]78[/C][C]950[/C][C]996.579218962664[/C][C]-46.5792189626644[/C][/ROW]
[ROW][C]79[/C][C]1070[/C][C]1062.11554244606[/C][C]7.88445755394218[/C][/ROW]
[ROW][C]80[/C][C]1170[/C][C]1152.25434185058[/C][C]17.7456581494191[/C][/ROW]
[ROW][C]81[/C][C]1050[/C][C]1091.71510740345[/C][C]-41.7151074034457[/C][/ROW]
[ROW][C]82[/C][C]960[/C][C]975.730069317586[/C][C]-15.7300693175864[/C][/ROW]
[ROW][C]83[/C][C]1300[/C][C]1200.17255172119[/C][C]99.8274482788102[/C][/ROW]
[ROW][C]84[/C][C]1080[/C][C]1032.83707682098[/C][C]47.1629231790212[/C][/ROW]
[ROW][C]85[/C][C]1030[/C][C]985.588867936969[/C][C]44.4111320630313[/C][/ROW]
[ROW][C]86[/C][C]1030[/C][C]1028.13715880068[/C][C]1.86284119931861[/C][/ROW]
[ROW][C]87[/C][C]1070[/C][C]1052.87142679295[/C][C]17.1285732070519[/C][/ROW]
[ROW][C]88[/C][C]1260[/C][C]1182.05898637611[/C][C]77.9410136238914[/C][/ROW]
[ROW][C]89[/C][C]990[/C][C]976.638322142652[/C][C]13.361677857348[/C][/ROW]
[ROW][C]90[/C][C]950[/C][C]960.291730300617[/C][C]-10.2917303006175[/C][/ROW]
[ROW][C]91[/C][C]1080[/C][C]1071.7910442185[/C][C]8.20895578149725[/C][/ROW]
[ROW][C]92[/C][C]1190[/C][C]1170.7769851951[/C][C]19.223014804902[/C][/ROW]
[ROW][C]93[/C][C]1050[/C][C]1061.62945563494[/C][C]-11.6294556349378[/C][/ROW]
[ROW][C]94[/C][C]950[/C][C]968.057854938611[/C][C]-18.0578549386113[/C][/ROW]
[ROW][C]95[/C][C]1250[/C][C]1289.02847828819[/C][C]-39.0284782881945[/C][/ROW]
[ROW][C]96[/C][C]1140[/C][C]1077.87009696151[/C][C]62.1299030384887[/C][/ROW]
[ROW][C]97[/C][C]1080[/C][C]1028.82762256712[/C][C]51.172377432878[/C][/ROW]
[ROW][C]98[/C][C]1020[/C][C]1036.57732006089[/C][C]-16.5773200608853[/C][/ROW]
[ROW][C]99[/C][C]1140[/C][C]1074.28901012278[/C][C]65.7109898772196[/C][/ROW]
[ROW][C]100[/C][C]1320[/C][C]1254.60313082676[/C][C]65.3968691732407[/C][/ROW]
[ROW][C]101[/C][C]1100[/C][C]996.089673423791[/C][C]103.910326576209[/C][/ROW]
[ROW][C]102[/C][C]1040[/C][C]961.221755716911[/C][C]78.7782442830892[/C][/ROW]
[ROW][C]103[/C][C]1090[/C][C]1089.36722527295[/C][C]0.63277472705272[/C][/ROW]
[ROW][C]104[/C][C]1280[/C][C]1198.38722592494[/C][C]81.612774075061[/C][/ROW]
[ROW][C]105[/C][C]1030[/C][C]1065.00986564786[/C][C]-35.0098656478563[/C][/ROW]
[ROW][C]106[/C][C]930[/C][C]967.051114317412[/C][C]-37.051114317412[/C][/ROW]
[ROW][C]107[/C][C]1280[/C][C]1271.54840988677[/C][C]8.45159011323335[/C][/ROW]
[ROW][C]108[/C][C]1020[/C][C]1145.54304950443[/C][C]-125.543049504432[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124185&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124185&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
1310001001.78685897436-1.78685897435844
14960960.73051549685-0.73051549685033
1510601060.09317635747-0.0931763574678826
1610601060.29147893319-0.291478933192138
1711101110.48823534437-0.488235344366785
1810301034.01627678981-4.01627678980662
19960945.85316479339814.1468352066015
2011301117.7992462256612.2007537743445
2111501152.2690646555-2.2690646555036
2210301042.50848081179-12.5084808117922
2310401041.00796116786-1.00796116786273
2410301119.55083495198-89.550834951978
251070997.27701693668272.7229830633183
261000957.36362420971842.6363757902824
2710201057.50938431167-37.5093843116651
2811001057.378323303242.6216766968039
2910801107.67914897836-27.679148978362
309901028.19918301311-38.1991830131108
311000954.89248750742345.1075124925773
3211101125.36617260561-15.3661726056127
3311701147.6768416237122.3231583762936
3410301029.536014551820.463985448184758
3511001037.6634296146762.3365703853265
3610201043.26922158085-23.2692215808547
3710901056.1537070680733.8462929319282
38990991.422022343282-1.4220223432817
3910601025.1188248688634.8811751311398
4011201092.0517071911627.9482928088353
4110301084.33109156364-54.3310915636393
421050996.26770731054253.7322926894582
431030992.86626723967537.1337327603254
4411301113.6394817560416.3605182439571
4511401167.86184353339-27.8618435333894
469801031.81320804482-51.8132080448245
4711501091.2981298570258.7018701429831
489901026.19562110192-36.1956211019187
4910201086.60888157533-66.6088815753312
501060992.21556307345567.7844369265454
5110801056.4367121893223.5632878106799
5211801117.702449243862.2975507562014
539801042.12822664631-62.1282266463068
549601043.80556987707-83.8055698770659
5510201025.93314162666-5.93314162666297
5611701129.0414062628540.9585937371476
5711501146.495025253443.50497474656345
58950990.589228906951-40.589228906951
5911601141.6302573143318.3697426856702
601120997.498421143005122.501578856995
6110101033.54204905075-23.5420490507524
6210101051.04292155353-41.0429215535266
6310601078.20862102132-18.2086210213163
6411301171.34438150491-41.3443815049052
651000991.8748172270458.12518277295487
661000975.70628548768824.2937145123125
6710701022.9395752278447.0604247721603
6811501165.38887901191-15.3888790119101
6910801151.68326694024-71.6832669402418
70980958.84397862739821.1560213726017
7112101159.0837809432350.9162190567706
7210201101.56368729989-81.5636872998941
739801015.36464449123-35.364644491225
7410301017.9156392793912.0843607206081
7510501063.96399304631-13.9639930463093
7611901137.6913648586652.3086351413438
77970999.598538639463-29.5985386394627
78950996.579218962664-46.5792189626644
7910701062.115542446067.88445755394218
8011701152.2543418505817.7456581494191
8110501091.71510740345-41.7151074034457
82960975.730069317586-15.7300693175864
8313001200.1725517211999.8274482788102
8410801032.8370768209847.1629231790212
851030985.58886793696944.4111320630313
8610301028.137158800681.86284119931861
8710701052.8714267929517.1285732070519
8812601182.0589863761177.9410136238914
89990976.63832214265213.361677857348
90950960.291730300617-10.2917303006175
9110801071.79104421858.20895578149725
9211901170.776985195119.223014804902
9310501061.62945563494-11.6294556349378
94950968.057854938611-18.0578549386113
9512501289.02847828819-39.0284782881945
9611401077.8700969615162.1299030384887
9710801028.8276225671251.172377432878
9810201036.57732006089-16.5773200608853
9911401074.2890101227865.7109898772196
10013201254.6031308267665.3968691732407
1011100996.089673423791103.910326576209
1021040961.22175571691178.7782442830892
10310901089.367225272950.63277472705272
10412801198.3872259249481.612774075061
10510301065.00986564786-35.0098656478563
106930967.051114317412-37.051114317412
10712801271.548409886778.45159011323335
10810201145.54304950443-125.543049504432







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091087.29068241918997.427776577651177.1535882607
1101039.16683543757949.301982417961129.03168845718
1111145.691532274691055.822903993951235.56016055543
1121325.847181134441235.972350033841415.72201223503
1131099.193352298051009.309291676991189.07741291911
1141043.0041350973953.107219628681132.90105056592
1151105.780296264621015.866302731441195.6942897978
1161281.647631807111191.711740099361371.58352351486
1171050.78181686821960.8186112788161140.74502245761
118950.872788937782860.8762597955821040.86931807998
1191292.934855851011202.898401528141382.97131017388
1201055.49761656244965.4140458922291145.58118723265

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1087.29068241918 & 997.42777657765 & 1177.1535882607 \tabularnewline
110 & 1039.16683543757 & 949.30198241796 & 1129.03168845718 \tabularnewline
111 & 1145.69153227469 & 1055.82290399395 & 1235.56016055543 \tabularnewline
112 & 1325.84718113444 & 1235.97235003384 & 1415.72201223503 \tabularnewline
113 & 1099.19335229805 & 1009.30929167699 & 1189.07741291911 \tabularnewline
114 & 1043.0041350973 & 953.10721962868 & 1132.90105056592 \tabularnewline
115 & 1105.78029626462 & 1015.86630273144 & 1195.6942897978 \tabularnewline
116 & 1281.64763180711 & 1191.71174009936 & 1371.58352351486 \tabularnewline
117 & 1050.78181686821 & 960.818611278816 & 1140.74502245761 \tabularnewline
118 & 950.872788937782 & 860.876259795582 & 1040.86931807998 \tabularnewline
119 & 1292.93485585101 & 1202.89840152814 & 1382.97131017388 \tabularnewline
120 & 1055.49761656244 & 965.414045892229 & 1145.58118723265 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124185&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]1087.29068241918[/C][C]997.42777657765[/C][C]1177.1535882607[/C][/ROW]
[ROW][C]110[/C][C]1039.16683543757[/C][C]949.30198241796[/C][C]1129.03168845718[/C][/ROW]
[ROW][C]111[/C][C]1145.69153227469[/C][C]1055.82290399395[/C][C]1235.56016055543[/C][/ROW]
[ROW][C]112[/C][C]1325.84718113444[/C][C]1235.97235003384[/C][C]1415.72201223503[/C][/ROW]
[ROW][C]113[/C][C]1099.19335229805[/C][C]1009.30929167699[/C][C]1189.07741291911[/C][/ROW]
[ROW][C]114[/C][C]1043.0041350973[/C][C]953.10721962868[/C][C]1132.90105056592[/C][/ROW]
[ROW][C]115[/C][C]1105.78029626462[/C][C]1015.86630273144[/C][C]1195.6942897978[/C][/ROW]
[ROW][C]116[/C][C]1281.64763180711[/C][C]1191.71174009936[/C][C]1371.58352351486[/C][/ROW]
[ROW][C]117[/C][C]1050.78181686821[/C][C]960.818611278816[/C][C]1140.74502245761[/C][/ROW]
[ROW][C]118[/C][C]950.872788937782[/C][C]860.876259795582[/C][C]1040.86931807998[/C][/ROW]
[ROW][C]119[/C][C]1292.93485585101[/C][C]1202.89840152814[/C][C]1382.97131017388[/C][/ROW]
[ROW][C]120[/C][C]1055.49761656244[/C][C]965.414045892229[/C][C]1145.58118723265[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124185&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124185&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
1091087.29068241918997.427776577651177.1535882607
1101039.16683543757949.301982417961129.03168845718
1111145.691532274691055.822903993951235.56016055543
1121325.847181134441235.972350033841415.72201223503
1131099.193352298051009.309291676991189.07741291911
1141043.0041350973953.107219628681132.90105056592
1151105.780296264621015.866302731441195.6942897978
1161281.647631807111191.711740099361371.58352351486
1171050.78181686821960.8186112788161140.74502245761
118950.872788937782860.8762597955821040.86931807998
1191292.934855851011202.898401528141382.97131017388
1201055.49761656244965.4140458922291145.58118723265



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')