Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 15 Jul 2012 06:12:05 -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/2012/Jul/15/t13423473360n2bvf2l002o1sh.htm/, Retrieved Tue, 30 Apr 2024 02:02:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168802, Retrieved Tue, 30 Apr 2024 02:02:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMargot Avonts
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2- stap 27] [2012-07-15 10:12:05] [f26bc165187ae19198203e315c1ca52f] [Current]
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Dataseries X:
1120
1120
1190
1190
1190
1190
1070
1200
1090
1130
1140
1240
1180
1080
1190
1140
1160
1200
980
1260
1100
1210
1150
1140
1110
1120
1100
1170
1120
1250
910
1260
1090
1240
1130
1200
1120
1120
1120
1070
1100
1230
930
1240
980
1270
1140
1160
1160
1220
1160
1090
1060
1230
1070
1240
1050
1350
1100
1130
1170
1360
1150
1180
1010
1190
1000
1270
990
1470
1130
1150
1150
1410
1190
1180
990
1170
1080
1350
960
1490
1120
1090
1220
1370
1180
1190
1000
1250
1090
1370
980
1530
1150
1120
1290
1370
1130
1200
910
1220
1040
1340
950
1500
1120
1150




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168802&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168802&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168802&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00622700651239415
beta0.442874882632437
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00622700651239415 \tabularnewline
beta & 0.442874882632437 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168802&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]0.00622700651239415[/C][/ROW]
[ROW][C]beta[/C][C]0.442874882632437[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168802&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168802&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
alpha0.00622700651239415
beta0.442874882632437
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311801190.52993743234-10.5299374323372
1410801090.238478984-10.238478983998
1511901197.55332090533-7.5533209053342
1611401142.85844726727-2.85844726726987
1711601158.502665084631.49733491536904
1812001201.71926806351-1.71926806350575
199801066.32742591428-86.3274259142795
2012601193.5126077191166.4873922808863
2111001085.3871272947214.6128727052846
2212101126.6999642135183.3000357864917
2311501140.067926005159.93207399484868
2411401240.61540694708-100.615406947084
2511101172.35042402815-62.3504240281511
2611201072.4597954167247.5402045832839
2711001181.96814526387-81.9681452638736
2811701131.5447486020538.4552513979525
2911201151.45194174817-31.4519417481729
3012501190.6858193066959.3141806933127
31910973.094885483988-63.094885483988
3212601250.12208199849.87791800159971
3310901091.14106819361-1.14106819361473
3412401199.4294817730140.5705182269908
3511301139.75304671188-9.75304671187587
3612001129.9228908703370.0771091296735
3711201100.9936592923719.0063407076261
3811201110.957847286579.04215271342946
3911201091.7656215537728.2343784462255
4010701161.6158593563-91.6158593562996
4111001111.68535720249-11.6853572024881
4212301240.3881952519-10.3881952519025
43930903.27259929616626.7274007038341
4412401251.11452645241-11.1145264524062
459801082.43601271054-102.436012710538
4612701230.2916148361439.7083851638563
4711401121.3248140246318.6751859753665
4811601190.41387175642-30.4138717564192
4911601110.4531731983549.546826801648
5012201110.48540083225109.514599167751
5111601111.0457302042148.9542697957875
5210901062.3665845444527.6334154555536
5310601092.82886361836-32.8288636183568
5412301222.229653615257.7703463847497
551070924.341563670789145.658436329211
5612401234.636701096745.36329890325578
571050977.11420383749472.8857961625065
5813501268.1611428741281.8388571258793
5911001140.19933685539-40.1993368553919
6011301161.50590567516-31.5059056751556
6111701162.357089287887.64291071211755
6213601223.09241098215136.907589017846
6311501164.72457550672-14.7245755067236
6411801095.2203478150384.779652184965
6510101066.95680272819-56.9568027281859
6611901238.8874850098-48.8874850098027
6710001077.38334840078-77.3833484007769
6812701248.3024495104321.6975504895729
699901056.97806343372-66.9780634337164
7014701357.79005096003112.209949039972
7111301107.1337230608622.8662769391387
7211501137.8150351891412.1849648108582
7311501178.39821739124-28.3982173912368
7414101368.8074970280841.1925029719243
7511901157.6680254467732.3319745532322
7611801187.5451487768-7.54514877680299
779901016.5583670242-26.5583670242024
7811701197.68407630512-27.6840763051196
7910801006.6882057389173.3117942610903
8013501279.3502445853370.6497554146711
81960998.452750897238-38.4527508972384
8214901482.168207966027.83179203398163
8311201139.56665667814-19.566656678137
8410901159.74113297906-69.7411329790575
8512201159.4609416067360.5390583932694
8613701422.06994218686-52.0699421868649
8711801199.71521750289-19.7152175028875
8811901189.42439830920.575601690801705
891000997.9783529505952.02164704940458
9012501179.5941384978970.4058615021104
9110901088.99722294351.0027770564991
9213701360.804407244289.19559275571601
93980967.8397777979112.1602222020903
9415301502.2670802488227.732919751179
9511501129.5356617810820.4643382189192
9611201099.9852655838220.0147344161796
9712901231.3698634638758.6301365361307
9813701383.98545465016-13.9854546501572
9911301192.60327635658-62.6032763565827
10012001202.70809317559-2.70809317558769
1019101010.97589529108-100.975895291077
10212201262.51439680222-42.5143968022248
10310401100.43592103965-60.4359210396524
10413401382.07252135911-42.0725213591086
105950987.903535848675-37.9035358486751
10615001540.84868424923-40.8486842492257
10711201156.98031087966-36.9803108796621
10811501125.4628096394924.5371903605101

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1180 & 1190.52993743234 & -10.5299374323372 \tabularnewline
14 & 1080 & 1090.238478984 & -10.238478983998 \tabularnewline
15 & 1190 & 1197.55332090533 & -7.5533209053342 \tabularnewline
16 & 1140 & 1142.85844726727 & -2.85844726726987 \tabularnewline
17 & 1160 & 1158.50266508463 & 1.49733491536904 \tabularnewline
18 & 1200 & 1201.71926806351 & -1.71926806350575 \tabularnewline
19 & 980 & 1066.32742591428 & -86.3274259142795 \tabularnewline
20 & 1260 & 1193.51260771911 & 66.4873922808863 \tabularnewline
21 & 1100 & 1085.38712729472 & 14.6128727052846 \tabularnewline
22 & 1210 & 1126.69996421351 & 83.3000357864917 \tabularnewline
23 & 1150 & 1140.06792600515 & 9.93207399484868 \tabularnewline
24 & 1140 & 1240.61540694708 & -100.615406947084 \tabularnewline
25 & 1110 & 1172.35042402815 & -62.3504240281511 \tabularnewline
26 & 1120 & 1072.45979541672 & 47.5402045832839 \tabularnewline
27 & 1100 & 1181.96814526387 & -81.9681452638736 \tabularnewline
28 & 1170 & 1131.54474860205 & 38.4552513979525 \tabularnewline
29 & 1120 & 1151.45194174817 & -31.4519417481729 \tabularnewline
30 & 1250 & 1190.68581930669 & 59.3141806933127 \tabularnewline
31 & 910 & 973.094885483988 & -63.094885483988 \tabularnewline
32 & 1260 & 1250.1220819984 & 9.87791800159971 \tabularnewline
33 & 1090 & 1091.14106819361 & -1.14106819361473 \tabularnewline
34 & 1240 & 1199.42948177301 & 40.5705182269908 \tabularnewline
35 & 1130 & 1139.75304671188 & -9.75304671187587 \tabularnewline
36 & 1200 & 1129.92289087033 & 70.0771091296735 \tabularnewline
37 & 1120 & 1100.99365929237 & 19.0063407076261 \tabularnewline
38 & 1120 & 1110.95784728657 & 9.04215271342946 \tabularnewline
39 & 1120 & 1091.76562155377 & 28.2343784462255 \tabularnewline
40 & 1070 & 1161.6158593563 & -91.6158593562996 \tabularnewline
41 & 1100 & 1111.68535720249 & -11.6853572024881 \tabularnewline
42 & 1230 & 1240.3881952519 & -10.3881952519025 \tabularnewline
43 & 930 & 903.272599296166 & 26.7274007038341 \tabularnewline
44 & 1240 & 1251.11452645241 & -11.1145264524062 \tabularnewline
45 & 980 & 1082.43601271054 & -102.436012710538 \tabularnewline
46 & 1270 & 1230.29161483614 & 39.7083851638563 \tabularnewline
47 & 1140 & 1121.32481402463 & 18.6751859753665 \tabularnewline
48 & 1160 & 1190.41387175642 & -30.4138717564192 \tabularnewline
49 & 1160 & 1110.45317319835 & 49.546826801648 \tabularnewline
50 & 1220 & 1110.48540083225 & 109.514599167751 \tabularnewline
51 & 1160 & 1111.04573020421 & 48.9542697957875 \tabularnewline
52 & 1090 & 1062.36658454445 & 27.6334154555536 \tabularnewline
53 & 1060 & 1092.82886361836 & -32.8288636183568 \tabularnewline
54 & 1230 & 1222.22965361525 & 7.7703463847497 \tabularnewline
55 & 1070 & 924.341563670789 & 145.658436329211 \tabularnewline
56 & 1240 & 1234.63670109674 & 5.36329890325578 \tabularnewline
57 & 1050 & 977.114203837494 & 72.8857961625065 \tabularnewline
58 & 1350 & 1268.16114287412 & 81.8388571258793 \tabularnewline
59 & 1100 & 1140.19933685539 & -40.1993368553919 \tabularnewline
60 & 1130 & 1161.50590567516 & -31.5059056751556 \tabularnewline
61 & 1170 & 1162.35708928788 & 7.64291071211755 \tabularnewline
62 & 1360 & 1223.09241098215 & 136.907589017846 \tabularnewline
63 & 1150 & 1164.72457550672 & -14.7245755067236 \tabularnewline
64 & 1180 & 1095.22034781503 & 84.779652184965 \tabularnewline
65 & 1010 & 1066.95680272819 & -56.9568027281859 \tabularnewline
66 & 1190 & 1238.8874850098 & -48.8874850098027 \tabularnewline
67 & 1000 & 1077.38334840078 & -77.3833484007769 \tabularnewline
68 & 1270 & 1248.30244951043 & 21.6975504895729 \tabularnewline
69 & 990 & 1056.97806343372 & -66.9780634337164 \tabularnewline
70 & 1470 & 1357.79005096003 & 112.209949039972 \tabularnewline
71 & 1130 & 1107.13372306086 & 22.8662769391387 \tabularnewline
72 & 1150 & 1137.81503518914 & 12.1849648108582 \tabularnewline
73 & 1150 & 1178.39821739124 & -28.3982173912368 \tabularnewline
74 & 1410 & 1368.80749702808 & 41.1925029719243 \tabularnewline
75 & 1190 & 1157.66802544677 & 32.3319745532322 \tabularnewline
76 & 1180 & 1187.5451487768 & -7.54514877680299 \tabularnewline
77 & 990 & 1016.5583670242 & -26.5583670242024 \tabularnewline
78 & 1170 & 1197.68407630512 & -27.6840763051196 \tabularnewline
79 & 1080 & 1006.68820573891 & 73.3117942610903 \tabularnewline
80 & 1350 & 1279.35024458533 & 70.6497554146711 \tabularnewline
81 & 960 & 998.452750897238 & -38.4527508972384 \tabularnewline
82 & 1490 & 1482.16820796602 & 7.83179203398163 \tabularnewline
83 & 1120 & 1139.56665667814 & -19.566656678137 \tabularnewline
84 & 1090 & 1159.74113297906 & -69.7411329790575 \tabularnewline
85 & 1220 & 1159.46094160673 & 60.5390583932694 \tabularnewline
86 & 1370 & 1422.06994218686 & -52.0699421868649 \tabularnewline
87 & 1180 & 1199.71521750289 & -19.7152175028875 \tabularnewline
88 & 1190 & 1189.4243983092 & 0.575601690801705 \tabularnewline
89 & 1000 & 997.978352950595 & 2.02164704940458 \tabularnewline
90 & 1250 & 1179.59413849789 & 70.4058615021104 \tabularnewline
91 & 1090 & 1088.9972229435 & 1.0027770564991 \tabularnewline
92 & 1370 & 1360.80440724428 & 9.19559275571601 \tabularnewline
93 & 980 & 967.83977779791 & 12.1602222020903 \tabularnewline
94 & 1530 & 1502.26708024882 & 27.732919751179 \tabularnewline
95 & 1150 & 1129.53566178108 & 20.4643382189192 \tabularnewline
96 & 1120 & 1099.98526558382 & 20.0147344161796 \tabularnewline
97 & 1290 & 1231.36986346387 & 58.6301365361307 \tabularnewline
98 & 1370 & 1383.98545465016 & -13.9854546501572 \tabularnewline
99 & 1130 & 1192.60327635658 & -62.6032763565827 \tabularnewline
100 & 1200 & 1202.70809317559 & -2.70809317558769 \tabularnewline
101 & 910 & 1010.97589529108 & -100.975895291077 \tabularnewline
102 & 1220 & 1262.51439680222 & -42.5143968022248 \tabularnewline
103 & 1040 & 1100.43592103965 & -60.4359210396524 \tabularnewline
104 & 1340 & 1382.07252135911 & -42.0725213591086 \tabularnewline
105 & 950 & 987.903535848675 & -37.9035358486751 \tabularnewline
106 & 1500 & 1540.84868424923 & -40.8486842492257 \tabularnewline
107 & 1120 & 1156.98031087966 & -36.9803108796621 \tabularnewline
108 & 1150 & 1125.46280963949 & 24.5371903605101 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168802&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]1180[/C][C]1190.52993743234[/C][C]-10.5299374323372[/C][/ROW]
[ROW][C]14[/C][C]1080[/C][C]1090.238478984[/C][C]-10.238478983998[/C][/ROW]
[ROW][C]15[/C][C]1190[/C][C]1197.55332090533[/C][C]-7.5533209053342[/C][/ROW]
[ROW][C]16[/C][C]1140[/C][C]1142.85844726727[/C][C]-2.85844726726987[/C][/ROW]
[ROW][C]17[/C][C]1160[/C][C]1158.50266508463[/C][C]1.49733491536904[/C][/ROW]
[ROW][C]18[/C][C]1200[/C][C]1201.71926806351[/C][C]-1.71926806350575[/C][/ROW]
[ROW][C]19[/C][C]980[/C][C]1066.32742591428[/C][C]-86.3274259142795[/C][/ROW]
[ROW][C]20[/C][C]1260[/C][C]1193.51260771911[/C][C]66.4873922808863[/C][/ROW]
[ROW][C]21[/C][C]1100[/C][C]1085.38712729472[/C][C]14.6128727052846[/C][/ROW]
[ROW][C]22[/C][C]1210[/C][C]1126.69996421351[/C][C]83.3000357864917[/C][/ROW]
[ROW][C]23[/C][C]1150[/C][C]1140.06792600515[/C][C]9.93207399484868[/C][/ROW]
[ROW][C]24[/C][C]1140[/C][C]1240.61540694708[/C][C]-100.615406947084[/C][/ROW]
[ROW][C]25[/C][C]1110[/C][C]1172.35042402815[/C][C]-62.3504240281511[/C][/ROW]
[ROW][C]26[/C][C]1120[/C][C]1072.45979541672[/C][C]47.5402045832839[/C][/ROW]
[ROW][C]27[/C][C]1100[/C][C]1181.96814526387[/C][C]-81.9681452638736[/C][/ROW]
[ROW][C]28[/C][C]1170[/C][C]1131.54474860205[/C][C]38.4552513979525[/C][/ROW]
[ROW][C]29[/C][C]1120[/C][C]1151.45194174817[/C][C]-31.4519417481729[/C][/ROW]
[ROW][C]30[/C][C]1250[/C][C]1190.68581930669[/C][C]59.3141806933127[/C][/ROW]
[ROW][C]31[/C][C]910[/C][C]973.094885483988[/C][C]-63.094885483988[/C][/ROW]
[ROW][C]32[/C][C]1260[/C][C]1250.1220819984[/C][C]9.87791800159971[/C][/ROW]
[ROW][C]33[/C][C]1090[/C][C]1091.14106819361[/C][C]-1.14106819361473[/C][/ROW]
[ROW][C]34[/C][C]1240[/C][C]1199.42948177301[/C][C]40.5705182269908[/C][/ROW]
[ROW][C]35[/C][C]1130[/C][C]1139.75304671188[/C][C]-9.75304671187587[/C][/ROW]
[ROW][C]36[/C][C]1200[/C][C]1129.92289087033[/C][C]70.0771091296735[/C][/ROW]
[ROW][C]37[/C][C]1120[/C][C]1100.99365929237[/C][C]19.0063407076261[/C][/ROW]
[ROW][C]38[/C][C]1120[/C][C]1110.95784728657[/C][C]9.04215271342946[/C][/ROW]
[ROW][C]39[/C][C]1120[/C][C]1091.76562155377[/C][C]28.2343784462255[/C][/ROW]
[ROW][C]40[/C][C]1070[/C][C]1161.6158593563[/C][C]-91.6158593562996[/C][/ROW]
[ROW][C]41[/C][C]1100[/C][C]1111.68535720249[/C][C]-11.6853572024881[/C][/ROW]
[ROW][C]42[/C][C]1230[/C][C]1240.3881952519[/C][C]-10.3881952519025[/C][/ROW]
[ROW][C]43[/C][C]930[/C][C]903.272599296166[/C][C]26.7274007038341[/C][/ROW]
[ROW][C]44[/C][C]1240[/C][C]1251.11452645241[/C][C]-11.1145264524062[/C][/ROW]
[ROW][C]45[/C][C]980[/C][C]1082.43601271054[/C][C]-102.436012710538[/C][/ROW]
[ROW][C]46[/C][C]1270[/C][C]1230.29161483614[/C][C]39.7083851638563[/C][/ROW]
[ROW][C]47[/C][C]1140[/C][C]1121.32481402463[/C][C]18.6751859753665[/C][/ROW]
[ROW][C]48[/C][C]1160[/C][C]1190.41387175642[/C][C]-30.4138717564192[/C][/ROW]
[ROW][C]49[/C][C]1160[/C][C]1110.45317319835[/C][C]49.546826801648[/C][/ROW]
[ROW][C]50[/C][C]1220[/C][C]1110.48540083225[/C][C]109.514599167751[/C][/ROW]
[ROW][C]51[/C][C]1160[/C][C]1111.04573020421[/C][C]48.9542697957875[/C][/ROW]
[ROW][C]52[/C][C]1090[/C][C]1062.36658454445[/C][C]27.6334154555536[/C][/ROW]
[ROW][C]53[/C][C]1060[/C][C]1092.82886361836[/C][C]-32.8288636183568[/C][/ROW]
[ROW][C]54[/C][C]1230[/C][C]1222.22965361525[/C][C]7.7703463847497[/C][/ROW]
[ROW][C]55[/C][C]1070[/C][C]924.341563670789[/C][C]145.658436329211[/C][/ROW]
[ROW][C]56[/C][C]1240[/C][C]1234.63670109674[/C][C]5.36329890325578[/C][/ROW]
[ROW][C]57[/C][C]1050[/C][C]977.114203837494[/C][C]72.8857961625065[/C][/ROW]
[ROW][C]58[/C][C]1350[/C][C]1268.16114287412[/C][C]81.8388571258793[/C][/ROW]
[ROW][C]59[/C][C]1100[/C][C]1140.19933685539[/C][C]-40.1993368553919[/C][/ROW]
[ROW][C]60[/C][C]1130[/C][C]1161.50590567516[/C][C]-31.5059056751556[/C][/ROW]
[ROW][C]61[/C][C]1170[/C][C]1162.35708928788[/C][C]7.64291071211755[/C][/ROW]
[ROW][C]62[/C][C]1360[/C][C]1223.09241098215[/C][C]136.907589017846[/C][/ROW]
[ROW][C]63[/C][C]1150[/C][C]1164.72457550672[/C][C]-14.7245755067236[/C][/ROW]
[ROW][C]64[/C][C]1180[/C][C]1095.22034781503[/C][C]84.779652184965[/C][/ROW]
[ROW][C]65[/C][C]1010[/C][C]1066.95680272819[/C][C]-56.9568027281859[/C][/ROW]
[ROW][C]66[/C][C]1190[/C][C]1238.8874850098[/C][C]-48.8874850098027[/C][/ROW]
[ROW][C]67[/C][C]1000[/C][C]1077.38334840078[/C][C]-77.3833484007769[/C][/ROW]
[ROW][C]68[/C][C]1270[/C][C]1248.30244951043[/C][C]21.6975504895729[/C][/ROW]
[ROW][C]69[/C][C]990[/C][C]1056.97806343372[/C][C]-66.9780634337164[/C][/ROW]
[ROW][C]70[/C][C]1470[/C][C]1357.79005096003[/C][C]112.209949039972[/C][/ROW]
[ROW][C]71[/C][C]1130[/C][C]1107.13372306086[/C][C]22.8662769391387[/C][/ROW]
[ROW][C]72[/C][C]1150[/C][C]1137.81503518914[/C][C]12.1849648108582[/C][/ROW]
[ROW][C]73[/C][C]1150[/C][C]1178.39821739124[/C][C]-28.3982173912368[/C][/ROW]
[ROW][C]74[/C][C]1410[/C][C]1368.80749702808[/C][C]41.1925029719243[/C][/ROW]
[ROW][C]75[/C][C]1190[/C][C]1157.66802544677[/C][C]32.3319745532322[/C][/ROW]
[ROW][C]76[/C][C]1180[/C][C]1187.5451487768[/C][C]-7.54514877680299[/C][/ROW]
[ROW][C]77[/C][C]990[/C][C]1016.5583670242[/C][C]-26.5583670242024[/C][/ROW]
[ROW][C]78[/C][C]1170[/C][C]1197.68407630512[/C][C]-27.6840763051196[/C][/ROW]
[ROW][C]79[/C][C]1080[/C][C]1006.68820573891[/C][C]73.3117942610903[/C][/ROW]
[ROW][C]80[/C][C]1350[/C][C]1279.35024458533[/C][C]70.6497554146711[/C][/ROW]
[ROW][C]81[/C][C]960[/C][C]998.452750897238[/C][C]-38.4527508972384[/C][/ROW]
[ROW][C]82[/C][C]1490[/C][C]1482.16820796602[/C][C]7.83179203398163[/C][/ROW]
[ROW][C]83[/C][C]1120[/C][C]1139.56665667814[/C][C]-19.566656678137[/C][/ROW]
[ROW][C]84[/C][C]1090[/C][C]1159.74113297906[/C][C]-69.7411329790575[/C][/ROW]
[ROW][C]85[/C][C]1220[/C][C]1159.46094160673[/C][C]60.5390583932694[/C][/ROW]
[ROW][C]86[/C][C]1370[/C][C]1422.06994218686[/C][C]-52.0699421868649[/C][/ROW]
[ROW][C]87[/C][C]1180[/C][C]1199.71521750289[/C][C]-19.7152175028875[/C][/ROW]
[ROW][C]88[/C][C]1190[/C][C]1189.4243983092[/C][C]0.575601690801705[/C][/ROW]
[ROW][C]89[/C][C]1000[/C][C]997.978352950595[/C][C]2.02164704940458[/C][/ROW]
[ROW][C]90[/C][C]1250[/C][C]1179.59413849789[/C][C]70.4058615021104[/C][/ROW]
[ROW][C]91[/C][C]1090[/C][C]1088.9972229435[/C][C]1.0027770564991[/C][/ROW]
[ROW][C]92[/C][C]1370[/C][C]1360.80440724428[/C][C]9.19559275571601[/C][/ROW]
[ROW][C]93[/C][C]980[/C][C]967.83977779791[/C][C]12.1602222020903[/C][/ROW]
[ROW][C]94[/C][C]1530[/C][C]1502.26708024882[/C][C]27.732919751179[/C][/ROW]
[ROW][C]95[/C][C]1150[/C][C]1129.53566178108[/C][C]20.4643382189192[/C][/ROW]
[ROW][C]96[/C][C]1120[/C][C]1099.98526558382[/C][C]20.0147344161796[/C][/ROW]
[ROW][C]97[/C][C]1290[/C][C]1231.36986346387[/C][C]58.6301365361307[/C][/ROW]
[ROW][C]98[/C][C]1370[/C][C]1383.98545465016[/C][C]-13.9854546501572[/C][/ROW]
[ROW][C]99[/C][C]1130[/C][C]1192.60327635658[/C][C]-62.6032763565827[/C][/ROW]
[ROW][C]100[/C][C]1200[/C][C]1202.70809317559[/C][C]-2.70809317558769[/C][/ROW]
[ROW][C]101[/C][C]910[/C][C]1010.97589529108[/C][C]-100.975895291077[/C][/ROW]
[ROW][C]102[/C][C]1220[/C][C]1262.51439680222[/C][C]-42.5143968022248[/C][/ROW]
[ROW][C]103[/C][C]1040[/C][C]1100.43592103965[/C][C]-60.4359210396524[/C][/ROW]
[ROW][C]104[/C][C]1340[/C][C]1382.07252135911[/C][C]-42.0725213591086[/C][/ROW]
[ROW][C]105[/C][C]950[/C][C]987.903535848675[/C][C]-37.9035358486751[/C][/ROW]
[ROW][C]106[/C][C]1500[/C][C]1540.84868424923[/C][C]-40.8486842492257[/C][/ROW]
[ROW][C]107[/C][C]1120[/C][C]1156.98031087966[/C][C]-36.9803108796621[/C][/ROW]
[ROW][C]108[/C][C]1150[/C][C]1125.46280963949[/C][C]24.5371903605101[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168802&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168802&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
1311801190.52993743234-10.5299374323372
1410801090.238478984-10.238478983998
1511901197.55332090533-7.5533209053342
1611401142.85844726727-2.85844726726987
1711601158.502665084631.49733491536904
1812001201.71926806351-1.71926806350575
199801066.32742591428-86.3274259142795
2012601193.5126077191166.4873922808863
2111001085.3871272947214.6128727052846
2212101126.6999642135183.3000357864917
2311501140.067926005159.93207399484868
2411401240.61540694708-100.615406947084
2511101172.35042402815-62.3504240281511
2611201072.4597954167247.5402045832839
2711001181.96814526387-81.9681452638736
2811701131.5447486020538.4552513979525
2911201151.45194174817-31.4519417481729
3012501190.6858193066959.3141806933127
31910973.094885483988-63.094885483988
3212601250.12208199849.87791800159971
3310901091.14106819361-1.14106819361473
3412401199.4294817730140.5705182269908
3511301139.75304671188-9.75304671187587
3612001129.9228908703370.0771091296735
3711201100.9936592923719.0063407076261
3811201110.957847286579.04215271342946
3911201091.7656215537728.2343784462255
4010701161.6158593563-91.6158593562996
4111001111.68535720249-11.6853572024881
4212301240.3881952519-10.3881952519025
43930903.27259929616626.7274007038341
4412401251.11452645241-11.1145264524062
459801082.43601271054-102.436012710538
4612701230.2916148361439.7083851638563
4711401121.3248140246318.6751859753665
4811601190.41387175642-30.4138717564192
4911601110.4531731983549.546826801648
5012201110.48540083225109.514599167751
5111601111.0457302042148.9542697957875
5210901062.3665845444527.6334154555536
5310601092.82886361836-32.8288636183568
5412301222.229653615257.7703463847497
551070924.341563670789145.658436329211
5612401234.636701096745.36329890325578
571050977.11420383749472.8857961625065
5813501268.1611428741281.8388571258793
5911001140.19933685539-40.1993368553919
6011301161.50590567516-31.5059056751556
6111701162.357089287887.64291071211755
6213601223.09241098215136.907589017846
6311501164.72457550672-14.7245755067236
6411801095.2203478150384.779652184965
6510101066.95680272819-56.9568027281859
6611901238.8874850098-48.8874850098027
6710001077.38334840078-77.3833484007769
6812701248.3024495104321.6975504895729
699901056.97806343372-66.9780634337164
7014701357.79005096003112.209949039972
7111301107.1337230608622.8662769391387
7211501137.8150351891412.1849648108582
7311501178.39821739124-28.3982173912368
7414101368.8074970280841.1925029719243
7511901157.6680254467732.3319745532322
7611801187.5451487768-7.54514877680299
779901016.5583670242-26.5583670242024
7811701197.68407630512-27.6840763051196
7910801006.6882057389173.3117942610903
8013501279.3502445853370.6497554146711
81960998.452750897238-38.4527508972384
8214901482.168207966027.83179203398163
8311201139.56665667814-19.566656678137
8410901159.74113297906-69.7411329790575
8512201159.4609416067360.5390583932694
8613701422.06994218686-52.0699421868649
8711801199.71521750289-19.7152175028875
8811901189.42439830920.575601690801705
891000997.9783529505952.02164704940458
9012501179.5941384978970.4058615021104
9110901088.99722294351.0027770564991
9213701360.804407244289.19559275571601
93980967.8397777979112.1602222020903
9415301502.2670802488227.732919751179
9511501129.5356617810820.4643382189192
9611201099.9852655838220.0147344161796
9712901231.3698634638758.6301365361307
9813701383.98545465016-13.9854546501572
9911301192.60327635658-62.6032763565827
10012001202.70809317559-2.70809317558769
1019101010.97589529108-100.975895291077
10212201262.51439680222-42.5143968022248
10310401100.43592103965-60.4359210396524
10413401382.07252135911-42.0725213591086
105950987.903535848675-37.9035358486751
10615001540.84868424923-40.8486842492257
10711201156.98031087966-36.9803108796621
10811501125.4628096394924.5371903605101







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091294.966164447091192.609272831731397.32305606246
1101373.996200446821271.634658553031476.35774234061
1111132.57474385631030.209649589561234.93983812303
1121201.767340783311099.391139864131304.14354170249
113911.167888696736808.7917862860821013.54399110739
1141221.167675142361118.753338992581323.58201129215
1151040.89077052218938.4718630430921143.30967800127
1161341.011673817711238.50753954281443.51580809262
117950.747577270457848.2901524585451053.20500208237
1181501.276293419041398.584810395591603.96777644249
1191121.144611714611018.547623602611223.74159982661
1201151.0881203774551.78010588505282250.39613486986

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1294.96616444709 & 1192.60927283173 & 1397.32305606246 \tabularnewline
110 & 1373.99620044682 & 1271.63465855303 & 1476.35774234061 \tabularnewline
111 & 1132.5747438563 & 1030.20964958956 & 1234.93983812303 \tabularnewline
112 & 1201.76734078331 & 1099.39113986413 & 1304.14354170249 \tabularnewline
113 & 911.167888696736 & 808.791786286082 & 1013.54399110739 \tabularnewline
114 & 1221.16767514236 & 1118.75333899258 & 1323.58201129215 \tabularnewline
115 & 1040.89077052218 & 938.471863043092 & 1143.30967800127 \tabularnewline
116 & 1341.01167381771 & 1238.5075395428 & 1443.51580809262 \tabularnewline
117 & 950.747577270457 & 848.290152458545 & 1053.20500208237 \tabularnewline
118 & 1501.27629341904 & 1398.58481039559 & 1603.96777644249 \tabularnewline
119 & 1121.14461171461 & 1018.54762360261 & 1223.74159982661 \tabularnewline
120 & 1151.08812037745 & 51.7801058850528 & 2250.39613486986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168802&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]1294.96616444709[/C][C]1192.60927283173[/C][C]1397.32305606246[/C][/ROW]
[ROW][C]110[/C][C]1373.99620044682[/C][C]1271.63465855303[/C][C]1476.35774234061[/C][/ROW]
[ROW][C]111[/C][C]1132.5747438563[/C][C]1030.20964958956[/C][C]1234.93983812303[/C][/ROW]
[ROW][C]112[/C][C]1201.76734078331[/C][C]1099.39113986413[/C][C]1304.14354170249[/C][/ROW]
[ROW][C]113[/C][C]911.167888696736[/C][C]808.791786286082[/C][C]1013.54399110739[/C][/ROW]
[ROW][C]114[/C][C]1221.16767514236[/C][C]1118.75333899258[/C][C]1323.58201129215[/C][/ROW]
[ROW][C]115[/C][C]1040.89077052218[/C][C]938.471863043092[/C][C]1143.30967800127[/C][/ROW]
[ROW][C]116[/C][C]1341.01167381771[/C][C]1238.5075395428[/C][C]1443.51580809262[/C][/ROW]
[ROW][C]117[/C][C]950.747577270457[/C][C]848.290152458545[/C][C]1053.20500208237[/C][/ROW]
[ROW][C]118[/C][C]1501.27629341904[/C][C]1398.58481039559[/C][C]1603.96777644249[/C][/ROW]
[ROW][C]119[/C][C]1121.14461171461[/C][C]1018.54762360261[/C][C]1223.74159982661[/C][/ROW]
[ROW][C]120[/C][C]1151.08812037745[/C][C]51.7801058850528[/C][C]2250.39613486986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168802&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168802&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
1091294.966164447091192.609272831731397.32305606246
1101373.996200446821271.634658553031476.35774234061
1111132.57474385631030.209649589561234.93983812303
1121201.767340783311099.391139864131304.14354170249
113911.167888696736808.7917862860821013.54399110739
1141221.167675142361118.753338992581323.58201129215
1151040.89077052218938.4718630430921143.30967800127
1161341.011673817711238.50753954281443.51580809262
117950.747577270457848.2901524585451053.20500208237
1181501.276293419041398.584810395591603.96777644249
1191121.144611714611018.547623602611223.74159982661
1201151.0881203774551.78010588505282250.39613486986



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