Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 13 Aug 2013 13:52:07 -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/13/t1376416342eyk73qgyn1aht08.htm/, Retrieved Thu, 02 May 2024 17:24:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211078, Retrieved Thu, 02 May 2024 17:24:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Bezoekers musée J...] [2013-08-13 17:52:07] [a5e81fc5b84eaf53b9dc73271fe36a59] [Current]
Feedback Forum

Post a new message
Dataseries X:
1200
1400
1210
1260
1320
1320
1310
1260
1340
1180
1330
1390
1130
1340
1140
1290
1260
1280
1330
1270
1300
1150
1410
1250
1030
1320
1160
1300
1190
1310
1290
1320
1300
1230
1330
1220
1010
1290
1170
1240
1260
1260
1310
1360
1250
1170
1360
1140
1030
1260
1210
1190
1230
1350
1300
1340
1270
1220
1400
1120
1000
1260
1260
1150
1240
1360
1350
1280
1320
1210
1370
1060
1040
1260
1210
1200
1200
1290
1400
1280
1280
1220
1350
1000
980
1240
1190
1200
1150
1270
1410
1420
1260
1300
1410
1000
950
1280
1330
1190
1170
1270
1340
1470
1270
1280
1430
980




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211078&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211078&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211078&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0240970395380311
beta0.141764472865109
gamma0.959889360448135

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0240970395380311 \tabularnewline
beta & 0.141764472865109 \tabularnewline
gamma & 0.959889360448135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211078&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]0.0240970395380311[/C][/ROW]
[ROW][C]beta[/C][C]0.141764472865109[/C][/ROW]
[ROW][C]gamma[/C][C]0.959889360448135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211078&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211078&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
alpha0.0240970395380311
beta0.141764472865109
gamma0.959889360448135







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311301147.95673076923-17.9567307692312
1413401354.50085481934-14.5008548193391
1511401153.57871881914-13.5787188191368
1612901304.29908391612-14.2990839161218
1712601269.95324318758-9.95324318758026
1812801290.2614563733-10.2614563732952
1913301295.9438549970934.0561450029129
2012701250.3105159503119.68948404969
2113001334.39824423385-34.3982442338538
2211501173.315110407-23.3151104070014
2314101322.0027337830887.99726621692
2412501386.589930389-136.589930388996
2510301105.14417488422-75.1441748842233
2613201312.897495764967.1025042350368
2711601112.7834776496647.2165223503362
2813001263.925424368136.0745756319004
2911901234.66793089903-44.6679308990308
3013101253.5357988097856.4642011902247
3112901302.2538335207-12.2538335206987
3213201241.8011034781878.1988965218179
3313001276.5860899284223.413910071584
3412301127.43028780318102.569712196818
3513301384.00626040086-54.0062604008613
3612201234.88448708044-14.8844870804435
3710101014.44403018403-4.44403018403136
3812901301.70054170111-11.7005417011135
3911701139.4005752839330.5994247160679
4012401280.33800322217-40.338003222171
4112601173.9751219109586.0248780890472
4212601291.5473696373-31.5473696373008
4313101274.2903493082435.7096506917583
4413601300.4076342596859.5923657403209
4512501284.04221459778-34.04221459778
4611701208.07379161927-38.0737916192681
4713601314.5282903710445.4717096289551
4811401204.73268600533-64.7326860053272
491030992.98231530648337.0176846935174
5012601274.69305705048-14.6930570504771
5112101152.188352973257.8116470268042
5211901227.66571437636-37.6657143763591
5312301240.08337006247-10.0833700624726
5413501245.21912501576104.78087498424
5513001294.732810770075.26718922992609
5613401342.86686174908-2.86686174907572
5712701237.4479629496332.5520370503698
5812201159.6997685274760.3002314725277
5914001347.5149549022152.4850450977945
6011201135.40554015106-15.4055401510554
6110001021.080010394-21.080010393998
6212601253.672446602846.32755339716391
6312601200.3876830081259.612316991881
6411501187.26930290345-37.2693029034476
6512401226.3360034871413.6639965128632
6613601340.5267102806219.4732897193835
6713501295.3555988912654.6444011087397
6812801337.81971858799-57.8197185879878
6913201264.8277299930655.1722700069449
7012101214.26740030436-4.26740030436054
7113701393.63459987862-23.6345998786205
7210601116.26263369766-56.2626336976564
731040995.66620102191544.3337989780853
7412601255.761897616364.2381023836374
7512101252.58732430053-42.5873243005337
7612001146.1479591505453.8520408494633
7712001235.33035467898-35.3303546789773
7812901353.82270016911-63.8227001691068
7914001339.3470553396260.6529446603815
8012801276.380530245413.61946975459068
8112801310.70150287949-30.7015028794901
8212201202.084088716417.9159112836046
8313501363.61208250377-13.6120825037683
8410001055.7199052762-55.7199052761966
859801029.17588122188-49.1758812218754
8612401248.94356319303-8.94356319303211
8711901201.0274783117-11.0274783116984
8812001185.2371155944414.7628844055619
8911501189.34971860632-39.34971860632
9012701280.45556179892-10.4555617989174
9114101383.4526887276626.5473112723409
9214201265.70431451813154.295685481871
9312601271.48699713102-11.4869971310191
9413001208.922363053491.0776369466009
9514101342.9761116157167.0238883842858
961000998.1545085873891.84549141261095
97950979.896824569382-29.8968245693818
9812801238.6519265397341.3480734602731
9913301191.00226780488138.997732195121
10011901204.50559381239-14.5055938123871
10111701158.6416425018511.3583574981503
10212701279.6286720433-9.6286720433045
10313401418.90373301569-78.9037330156857
10414701419.5187305003450.4812694996642
10512701268.381761170261.61823882974113
10612801303.13639024446-23.1363902444646
10714301412.4403247701717.5596752298345
1089801005.73633251781-25.7363325178142

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1130 & 1147.95673076923 & -17.9567307692312 \tabularnewline
14 & 1340 & 1354.50085481934 & -14.5008548193391 \tabularnewline
15 & 1140 & 1153.57871881914 & -13.5787188191368 \tabularnewline
16 & 1290 & 1304.29908391612 & -14.2990839161218 \tabularnewline
17 & 1260 & 1269.95324318758 & -9.95324318758026 \tabularnewline
18 & 1280 & 1290.2614563733 & -10.2614563732952 \tabularnewline
19 & 1330 & 1295.94385499709 & 34.0561450029129 \tabularnewline
20 & 1270 & 1250.31051595031 & 19.68948404969 \tabularnewline
21 & 1300 & 1334.39824423385 & -34.3982442338538 \tabularnewline
22 & 1150 & 1173.315110407 & -23.3151104070014 \tabularnewline
23 & 1410 & 1322.00273378308 & 87.99726621692 \tabularnewline
24 & 1250 & 1386.589930389 & -136.589930388996 \tabularnewline
25 & 1030 & 1105.14417488422 & -75.1441748842233 \tabularnewline
26 & 1320 & 1312.89749576496 & 7.1025042350368 \tabularnewline
27 & 1160 & 1112.78347764966 & 47.2165223503362 \tabularnewline
28 & 1300 & 1263.9254243681 & 36.0745756319004 \tabularnewline
29 & 1190 & 1234.66793089903 & -44.6679308990308 \tabularnewline
30 & 1310 & 1253.53579880978 & 56.4642011902247 \tabularnewline
31 & 1290 & 1302.2538335207 & -12.2538335206987 \tabularnewline
32 & 1320 & 1241.80110347818 & 78.1988965218179 \tabularnewline
33 & 1300 & 1276.58608992842 & 23.413910071584 \tabularnewline
34 & 1230 & 1127.43028780318 & 102.569712196818 \tabularnewline
35 & 1330 & 1384.00626040086 & -54.0062604008613 \tabularnewline
36 & 1220 & 1234.88448708044 & -14.8844870804435 \tabularnewline
37 & 1010 & 1014.44403018403 & -4.44403018403136 \tabularnewline
38 & 1290 & 1301.70054170111 & -11.7005417011135 \tabularnewline
39 & 1170 & 1139.40057528393 & 30.5994247160679 \tabularnewline
40 & 1240 & 1280.33800322217 & -40.338003222171 \tabularnewline
41 & 1260 & 1173.97512191095 & 86.0248780890472 \tabularnewline
42 & 1260 & 1291.5473696373 & -31.5473696373008 \tabularnewline
43 & 1310 & 1274.29034930824 & 35.7096506917583 \tabularnewline
44 & 1360 & 1300.40763425968 & 59.5923657403209 \tabularnewline
45 & 1250 & 1284.04221459778 & -34.04221459778 \tabularnewline
46 & 1170 & 1208.07379161927 & -38.0737916192681 \tabularnewline
47 & 1360 & 1314.52829037104 & 45.4717096289551 \tabularnewline
48 & 1140 & 1204.73268600533 & -64.7326860053272 \tabularnewline
49 & 1030 & 992.982315306483 & 37.0176846935174 \tabularnewline
50 & 1260 & 1274.69305705048 & -14.6930570504771 \tabularnewline
51 & 1210 & 1152.1883529732 & 57.8116470268042 \tabularnewline
52 & 1190 & 1227.66571437636 & -37.6657143763591 \tabularnewline
53 & 1230 & 1240.08337006247 & -10.0833700624726 \tabularnewline
54 & 1350 & 1245.21912501576 & 104.78087498424 \tabularnewline
55 & 1300 & 1294.73281077007 & 5.26718922992609 \tabularnewline
56 & 1340 & 1342.86686174908 & -2.86686174907572 \tabularnewline
57 & 1270 & 1237.44796294963 & 32.5520370503698 \tabularnewline
58 & 1220 & 1159.69976852747 & 60.3002314725277 \tabularnewline
59 & 1400 & 1347.51495490221 & 52.4850450977945 \tabularnewline
60 & 1120 & 1135.40554015106 & -15.4055401510554 \tabularnewline
61 & 1000 & 1021.080010394 & -21.080010393998 \tabularnewline
62 & 1260 & 1253.67244660284 & 6.32755339716391 \tabularnewline
63 & 1260 & 1200.38768300812 & 59.612316991881 \tabularnewline
64 & 1150 & 1187.26930290345 & -37.2693029034476 \tabularnewline
65 & 1240 & 1226.33600348714 & 13.6639965128632 \tabularnewline
66 & 1360 & 1340.52671028062 & 19.4732897193835 \tabularnewline
67 & 1350 & 1295.35559889126 & 54.6444011087397 \tabularnewline
68 & 1280 & 1337.81971858799 & -57.8197185879878 \tabularnewline
69 & 1320 & 1264.82772999306 & 55.1722700069449 \tabularnewline
70 & 1210 & 1214.26740030436 & -4.26740030436054 \tabularnewline
71 & 1370 & 1393.63459987862 & -23.6345998786205 \tabularnewline
72 & 1060 & 1116.26263369766 & -56.2626336976564 \tabularnewline
73 & 1040 & 995.666201021915 & 44.3337989780853 \tabularnewline
74 & 1260 & 1255.76189761636 & 4.2381023836374 \tabularnewline
75 & 1210 & 1252.58732430053 & -42.5873243005337 \tabularnewline
76 & 1200 & 1146.14795915054 & 53.8520408494633 \tabularnewline
77 & 1200 & 1235.33035467898 & -35.3303546789773 \tabularnewline
78 & 1290 & 1353.82270016911 & -63.8227001691068 \tabularnewline
79 & 1400 & 1339.34705533962 & 60.6529446603815 \tabularnewline
80 & 1280 & 1276.38053024541 & 3.61946975459068 \tabularnewline
81 & 1280 & 1310.70150287949 & -30.7015028794901 \tabularnewline
82 & 1220 & 1202.0840887164 & 17.9159112836046 \tabularnewline
83 & 1350 & 1363.61208250377 & -13.6120825037683 \tabularnewline
84 & 1000 & 1055.7199052762 & -55.7199052761966 \tabularnewline
85 & 980 & 1029.17588122188 & -49.1758812218754 \tabularnewline
86 & 1240 & 1248.94356319303 & -8.94356319303211 \tabularnewline
87 & 1190 & 1201.0274783117 & -11.0274783116984 \tabularnewline
88 & 1200 & 1185.23711559444 & 14.7628844055619 \tabularnewline
89 & 1150 & 1189.34971860632 & -39.34971860632 \tabularnewline
90 & 1270 & 1280.45556179892 & -10.4555617989174 \tabularnewline
91 & 1410 & 1383.45268872766 & 26.5473112723409 \tabularnewline
92 & 1420 & 1265.70431451813 & 154.295685481871 \tabularnewline
93 & 1260 & 1271.48699713102 & -11.4869971310191 \tabularnewline
94 & 1300 & 1208.9223630534 & 91.0776369466009 \tabularnewline
95 & 1410 & 1342.97611161571 & 67.0238883842858 \tabularnewline
96 & 1000 & 998.154508587389 & 1.84549141261095 \tabularnewline
97 & 950 & 979.896824569382 & -29.8968245693818 \tabularnewline
98 & 1280 & 1238.65192653973 & 41.3480734602731 \tabularnewline
99 & 1330 & 1191.00226780488 & 138.997732195121 \tabularnewline
100 & 1190 & 1204.50559381239 & -14.5055938123871 \tabularnewline
101 & 1170 & 1158.64164250185 & 11.3583574981503 \tabularnewline
102 & 1270 & 1279.6286720433 & -9.6286720433045 \tabularnewline
103 & 1340 & 1418.90373301569 & -78.9037330156857 \tabularnewline
104 & 1470 & 1419.51873050034 & 50.4812694996642 \tabularnewline
105 & 1270 & 1268.38176117026 & 1.61823882974113 \tabularnewline
106 & 1280 & 1303.13639024446 & -23.1363902444646 \tabularnewline
107 & 1430 & 1412.44032477017 & 17.5596752298345 \tabularnewline
108 & 980 & 1005.73633251781 & -25.7363325178142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211078&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]1130[/C][C]1147.95673076923[/C][C]-17.9567307692312[/C][/ROW]
[ROW][C]14[/C][C]1340[/C][C]1354.50085481934[/C][C]-14.5008548193391[/C][/ROW]
[ROW][C]15[/C][C]1140[/C][C]1153.57871881914[/C][C]-13.5787188191368[/C][/ROW]
[ROW][C]16[/C][C]1290[/C][C]1304.29908391612[/C][C]-14.2990839161218[/C][/ROW]
[ROW][C]17[/C][C]1260[/C][C]1269.95324318758[/C][C]-9.95324318758026[/C][/ROW]
[ROW][C]18[/C][C]1280[/C][C]1290.2614563733[/C][C]-10.2614563732952[/C][/ROW]
[ROW][C]19[/C][C]1330[/C][C]1295.94385499709[/C][C]34.0561450029129[/C][/ROW]
[ROW][C]20[/C][C]1270[/C][C]1250.31051595031[/C][C]19.68948404969[/C][/ROW]
[ROW][C]21[/C][C]1300[/C][C]1334.39824423385[/C][C]-34.3982442338538[/C][/ROW]
[ROW][C]22[/C][C]1150[/C][C]1173.315110407[/C][C]-23.3151104070014[/C][/ROW]
[ROW][C]23[/C][C]1410[/C][C]1322.00273378308[/C][C]87.99726621692[/C][/ROW]
[ROW][C]24[/C][C]1250[/C][C]1386.589930389[/C][C]-136.589930388996[/C][/ROW]
[ROW][C]25[/C][C]1030[/C][C]1105.14417488422[/C][C]-75.1441748842233[/C][/ROW]
[ROW][C]26[/C][C]1320[/C][C]1312.89749576496[/C][C]7.1025042350368[/C][/ROW]
[ROW][C]27[/C][C]1160[/C][C]1112.78347764966[/C][C]47.2165223503362[/C][/ROW]
[ROW][C]28[/C][C]1300[/C][C]1263.9254243681[/C][C]36.0745756319004[/C][/ROW]
[ROW][C]29[/C][C]1190[/C][C]1234.66793089903[/C][C]-44.6679308990308[/C][/ROW]
[ROW][C]30[/C][C]1310[/C][C]1253.53579880978[/C][C]56.4642011902247[/C][/ROW]
[ROW][C]31[/C][C]1290[/C][C]1302.2538335207[/C][C]-12.2538335206987[/C][/ROW]
[ROW][C]32[/C][C]1320[/C][C]1241.80110347818[/C][C]78.1988965218179[/C][/ROW]
[ROW][C]33[/C][C]1300[/C][C]1276.58608992842[/C][C]23.413910071584[/C][/ROW]
[ROW][C]34[/C][C]1230[/C][C]1127.43028780318[/C][C]102.569712196818[/C][/ROW]
[ROW][C]35[/C][C]1330[/C][C]1384.00626040086[/C][C]-54.0062604008613[/C][/ROW]
[ROW][C]36[/C][C]1220[/C][C]1234.88448708044[/C][C]-14.8844870804435[/C][/ROW]
[ROW][C]37[/C][C]1010[/C][C]1014.44403018403[/C][C]-4.44403018403136[/C][/ROW]
[ROW][C]38[/C][C]1290[/C][C]1301.70054170111[/C][C]-11.7005417011135[/C][/ROW]
[ROW][C]39[/C][C]1170[/C][C]1139.40057528393[/C][C]30.5994247160679[/C][/ROW]
[ROW][C]40[/C][C]1240[/C][C]1280.33800322217[/C][C]-40.338003222171[/C][/ROW]
[ROW][C]41[/C][C]1260[/C][C]1173.97512191095[/C][C]86.0248780890472[/C][/ROW]
[ROW][C]42[/C][C]1260[/C][C]1291.5473696373[/C][C]-31.5473696373008[/C][/ROW]
[ROW][C]43[/C][C]1310[/C][C]1274.29034930824[/C][C]35.7096506917583[/C][/ROW]
[ROW][C]44[/C][C]1360[/C][C]1300.40763425968[/C][C]59.5923657403209[/C][/ROW]
[ROW][C]45[/C][C]1250[/C][C]1284.04221459778[/C][C]-34.04221459778[/C][/ROW]
[ROW][C]46[/C][C]1170[/C][C]1208.07379161927[/C][C]-38.0737916192681[/C][/ROW]
[ROW][C]47[/C][C]1360[/C][C]1314.52829037104[/C][C]45.4717096289551[/C][/ROW]
[ROW][C]48[/C][C]1140[/C][C]1204.73268600533[/C][C]-64.7326860053272[/C][/ROW]
[ROW][C]49[/C][C]1030[/C][C]992.982315306483[/C][C]37.0176846935174[/C][/ROW]
[ROW][C]50[/C][C]1260[/C][C]1274.69305705048[/C][C]-14.6930570504771[/C][/ROW]
[ROW][C]51[/C][C]1210[/C][C]1152.1883529732[/C][C]57.8116470268042[/C][/ROW]
[ROW][C]52[/C][C]1190[/C][C]1227.66571437636[/C][C]-37.6657143763591[/C][/ROW]
[ROW][C]53[/C][C]1230[/C][C]1240.08337006247[/C][C]-10.0833700624726[/C][/ROW]
[ROW][C]54[/C][C]1350[/C][C]1245.21912501576[/C][C]104.78087498424[/C][/ROW]
[ROW][C]55[/C][C]1300[/C][C]1294.73281077007[/C][C]5.26718922992609[/C][/ROW]
[ROW][C]56[/C][C]1340[/C][C]1342.86686174908[/C][C]-2.86686174907572[/C][/ROW]
[ROW][C]57[/C][C]1270[/C][C]1237.44796294963[/C][C]32.5520370503698[/C][/ROW]
[ROW][C]58[/C][C]1220[/C][C]1159.69976852747[/C][C]60.3002314725277[/C][/ROW]
[ROW][C]59[/C][C]1400[/C][C]1347.51495490221[/C][C]52.4850450977945[/C][/ROW]
[ROW][C]60[/C][C]1120[/C][C]1135.40554015106[/C][C]-15.4055401510554[/C][/ROW]
[ROW][C]61[/C][C]1000[/C][C]1021.080010394[/C][C]-21.080010393998[/C][/ROW]
[ROW][C]62[/C][C]1260[/C][C]1253.67244660284[/C][C]6.32755339716391[/C][/ROW]
[ROW][C]63[/C][C]1260[/C][C]1200.38768300812[/C][C]59.612316991881[/C][/ROW]
[ROW][C]64[/C][C]1150[/C][C]1187.26930290345[/C][C]-37.2693029034476[/C][/ROW]
[ROW][C]65[/C][C]1240[/C][C]1226.33600348714[/C][C]13.6639965128632[/C][/ROW]
[ROW][C]66[/C][C]1360[/C][C]1340.52671028062[/C][C]19.4732897193835[/C][/ROW]
[ROW][C]67[/C][C]1350[/C][C]1295.35559889126[/C][C]54.6444011087397[/C][/ROW]
[ROW][C]68[/C][C]1280[/C][C]1337.81971858799[/C][C]-57.8197185879878[/C][/ROW]
[ROW][C]69[/C][C]1320[/C][C]1264.82772999306[/C][C]55.1722700069449[/C][/ROW]
[ROW][C]70[/C][C]1210[/C][C]1214.26740030436[/C][C]-4.26740030436054[/C][/ROW]
[ROW][C]71[/C][C]1370[/C][C]1393.63459987862[/C][C]-23.6345998786205[/C][/ROW]
[ROW][C]72[/C][C]1060[/C][C]1116.26263369766[/C][C]-56.2626336976564[/C][/ROW]
[ROW][C]73[/C][C]1040[/C][C]995.666201021915[/C][C]44.3337989780853[/C][/ROW]
[ROW][C]74[/C][C]1260[/C][C]1255.76189761636[/C][C]4.2381023836374[/C][/ROW]
[ROW][C]75[/C][C]1210[/C][C]1252.58732430053[/C][C]-42.5873243005337[/C][/ROW]
[ROW][C]76[/C][C]1200[/C][C]1146.14795915054[/C][C]53.8520408494633[/C][/ROW]
[ROW][C]77[/C][C]1200[/C][C]1235.33035467898[/C][C]-35.3303546789773[/C][/ROW]
[ROW][C]78[/C][C]1290[/C][C]1353.82270016911[/C][C]-63.8227001691068[/C][/ROW]
[ROW][C]79[/C][C]1400[/C][C]1339.34705533962[/C][C]60.6529446603815[/C][/ROW]
[ROW][C]80[/C][C]1280[/C][C]1276.38053024541[/C][C]3.61946975459068[/C][/ROW]
[ROW][C]81[/C][C]1280[/C][C]1310.70150287949[/C][C]-30.7015028794901[/C][/ROW]
[ROW][C]82[/C][C]1220[/C][C]1202.0840887164[/C][C]17.9159112836046[/C][/ROW]
[ROW][C]83[/C][C]1350[/C][C]1363.61208250377[/C][C]-13.6120825037683[/C][/ROW]
[ROW][C]84[/C][C]1000[/C][C]1055.7199052762[/C][C]-55.7199052761966[/C][/ROW]
[ROW][C]85[/C][C]980[/C][C]1029.17588122188[/C][C]-49.1758812218754[/C][/ROW]
[ROW][C]86[/C][C]1240[/C][C]1248.94356319303[/C][C]-8.94356319303211[/C][/ROW]
[ROW][C]87[/C][C]1190[/C][C]1201.0274783117[/C][C]-11.0274783116984[/C][/ROW]
[ROW][C]88[/C][C]1200[/C][C]1185.23711559444[/C][C]14.7628844055619[/C][/ROW]
[ROW][C]89[/C][C]1150[/C][C]1189.34971860632[/C][C]-39.34971860632[/C][/ROW]
[ROW][C]90[/C][C]1270[/C][C]1280.45556179892[/C][C]-10.4555617989174[/C][/ROW]
[ROW][C]91[/C][C]1410[/C][C]1383.45268872766[/C][C]26.5473112723409[/C][/ROW]
[ROW][C]92[/C][C]1420[/C][C]1265.70431451813[/C][C]154.295685481871[/C][/ROW]
[ROW][C]93[/C][C]1260[/C][C]1271.48699713102[/C][C]-11.4869971310191[/C][/ROW]
[ROW][C]94[/C][C]1300[/C][C]1208.9223630534[/C][C]91.0776369466009[/C][/ROW]
[ROW][C]95[/C][C]1410[/C][C]1342.97611161571[/C][C]67.0238883842858[/C][/ROW]
[ROW][C]96[/C][C]1000[/C][C]998.154508587389[/C][C]1.84549141261095[/C][/ROW]
[ROW][C]97[/C][C]950[/C][C]979.896824569382[/C][C]-29.8968245693818[/C][/ROW]
[ROW][C]98[/C][C]1280[/C][C]1238.65192653973[/C][C]41.3480734602731[/C][/ROW]
[ROW][C]99[/C][C]1330[/C][C]1191.00226780488[/C][C]138.997732195121[/C][/ROW]
[ROW][C]100[/C][C]1190[/C][C]1204.50559381239[/C][C]-14.5055938123871[/C][/ROW]
[ROW][C]101[/C][C]1170[/C][C]1158.64164250185[/C][C]11.3583574981503[/C][/ROW]
[ROW][C]102[/C][C]1270[/C][C]1279.6286720433[/C][C]-9.6286720433045[/C][/ROW]
[ROW][C]103[/C][C]1340[/C][C]1418.90373301569[/C][C]-78.9037330156857[/C][/ROW]
[ROW][C]104[/C][C]1470[/C][C]1419.51873050034[/C][C]50.4812694996642[/C][/ROW]
[ROW][C]105[/C][C]1270[/C][C]1268.38176117026[/C][C]1.61823882974113[/C][/ROW]
[ROW][C]106[/C][C]1280[/C][C]1303.13639024446[/C][C]-23.1363902444646[/C][/ROW]
[ROW][C]107[/C][C]1430[/C][C]1412.44032477017[/C][C]17.5596752298345[/C][/ROW]
[ROW][C]108[/C][C]980[/C][C]1005.73633251781[/C][C]-25.7363325178142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211078&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211078&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
1311301147.95673076923-17.9567307692312
1413401354.50085481934-14.5008548193391
1511401153.57871881914-13.5787188191368
1612901304.29908391612-14.2990839161218
1712601269.95324318758-9.95324318758026
1812801290.2614563733-10.2614563732952
1913301295.9438549970934.0561450029129
2012701250.3105159503119.68948404969
2113001334.39824423385-34.3982442338538
2211501173.315110407-23.3151104070014
2314101322.0027337830887.99726621692
2412501386.589930389-136.589930388996
2510301105.14417488422-75.1441748842233
2613201312.897495764967.1025042350368
2711601112.7834776496647.2165223503362
2813001263.925424368136.0745756319004
2911901234.66793089903-44.6679308990308
3013101253.5357988097856.4642011902247
3112901302.2538335207-12.2538335206987
3213201241.8011034781878.1988965218179
3313001276.5860899284223.413910071584
3412301127.43028780318102.569712196818
3513301384.00626040086-54.0062604008613
3612201234.88448708044-14.8844870804435
3710101014.44403018403-4.44403018403136
3812901301.70054170111-11.7005417011135
3911701139.4005752839330.5994247160679
4012401280.33800322217-40.338003222171
4112601173.9751219109586.0248780890472
4212601291.5473696373-31.5473696373008
4313101274.2903493082435.7096506917583
4413601300.4076342596859.5923657403209
4512501284.04221459778-34.04221459778
4611701208.07379161927-38.0737916192681
4713601314.5282903710445.4717096289551
4811401204.73268600533-64.7326860053272
491030992.98231530648337.0176846935174
5012601274.69305705048-14.6930570504771
5112101152.188352973257.8116470268042
5211901227.66571437636-37.6657143763591
5312301240.08337006247-10.0833700624726
5413501245.21912501576104.78087498424
5513001294.732810770075.26718922992609
5613401342.86686174908-2.86686174907572
5712701237.4479629496332.5520370503698
5812201159.6997685274760.3002314725277
5914001347.5149549022152.4850450977945
6011201135.40554015106-15.4055401510554
6110001021.080010394-21.080010393998
6212601253.672446602846.32755339716391
6312601200.3876830081259.612316991881
6411501187.26930290345-37.2693029034476
6512401226.3360034871413.6639965128632
6613601340.5267102806219.4732897193835
6713501295.3555988912654.6444011087397
6812801337.81971858799-57.8197185879878
6913201264.8277299930655.1722700069449
7012101214.26740030436-4.26740030436054
7113701393.63459987862-23.6345998786205
7210601116.26263369766-56.2626336976564
731040995.66620102191544.3337989780853
7412601255.761897616364.2381023836374
7512101252.58732430053-42.5873243005337
7612001146.1479591505453.8520408494633
7712001235.33035467898-35.3303546789773
7812901353.82270016911-63.8227001691068
7914001339.3470553396260.6529446603815
8012801276.380530245413.61946975459068
8112801310.70150287949-30.7015028794901
8212201202.084088716417.9159112836046
8313501363.61208250377-13.6120825037683
8410001055.7199052762-55.7199052761966
859801029.17588122188-49.1758812218754
8612401248.94356319303-8.94356319303211
8711901201.0274783117-11.0274783116984
8812001185.2371155944414.7628844055619
8911501189.34971860632-39.34971860632
9012701280.45556179892-10.4555617989174
9114101383.4526887276626.5473112723409
9214201265.70431451813154.295685481871
9312601271.48699713102-11.4869971310191
9413001208.922363053491.0776369466009
9514101342.9761116157167.0238883842858
961000998.1545085873891.84549141261095
97950979.896824569382-29.8968245693818
9812801238.6519265397341.3480734602731
9913301191.00226780488138.997732195121
10011901204.50559381239-14.5055938123871
10111701158.6416425018511.3583574981503
10212701279.6286720433-9.6286720433045
10313401418.90373301569-78.9037330156857
10414701419.5187305003450.4812694996642
10512701268.381761170261.61823882974113
10612801303.13639024446-23.1363902444646
10714301412.4403247701717.5596752298345
1089801005.73633251781-25.7363325178142







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109957.350883089625861.7249251567591052.97684102249
1101283.939601655981188.27745743221379.60174587976
1111327.000412832091231.292558057171422.70826760701
1121193.116524512181097.352334236171288.88071478818
1131171.637774969091075.805529443071267.4700204951
1141272.459888474291176.546780298731368.37299664986
1151346.874409548141250.866552184811442.88226691146
1161470.664310688231374.546748434391566.78187294206
1171272.436574327481176.193293842411368.67985481256
1181283.856121682721187.470065147121380.24217821832
1191431.812042655611335.265122633541528.35896267769
120984.039076992143887.3121930529571080.76596093133

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 957.350883089625 & 861.724925156759 & 1052.97684102249 \tabularnewline
110 & 1283.93960165598 & 1188.2774574322 & 1379.60174587976 \tabularnewline
111 & 1327.00041283209 & 1231.29255805717 & 1422.70826760701 \tabularnewline
112 & 1193.11652451218 & 1097.35233423617 & 1288.88071478818 \tabularnewline
113 & 1171.63777496909 & 1075.80552944307 & 1267.4700204951 \tabularnewline
114 & 1272.45988847429 & 1176.54678029873 & 1368.37299664986 \tabularnewline
115 & 1346.87440954814 & 1250.86655218481 & 1442.88226691146 \tabularnewline
116 & 1470.66431068823 & 1374.54674843439 & 1566.78187294206 \tabularnewline
117 & 1272.43657432748 & 1176.19329384241 & 1368.67985481256 \tabularnewline
118 & 1283.85612168272 & 1187.47006514712 & 1380.24217821832 \tabularnewline
119 & 1431.81204265561 & 1335.26512263354 & 1528.35896267769 \tabularnewline
120 & 984.039076992143 & 887.312193052957 & 1080.76596093133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211078&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]957.350883089625[/C][C]861.724925156759[/C][C]1052.97684102249[/C][/ROW]
[ROW][C]110[/C][C]1283.93960165598[/C][C]1188.2774574322[/C][C]1379.60174587976[/C][/ROW]
[ROW][C]111[/C][C]1327.00041283209[/C][C]1231.29255805717[/C][C]1422.70826760701[/C][/ROW]
[ROW][C]112[/C][C]1193.11652451218[/C][C]1097.35233423617[/C][C]1288.88071478818[/C][/ROW]
[ROW][C]113[/C][C]1171.63777496909[/C][C]1075.80552944307[/C][C]1267.4700204951[/C][/ROW]
[ROW][C]114[/C][C]1272.45988847429[/C][C]1176.54678029873[/C][C]1368.37299664986[/C][/ROW]
[ROW][C]115[/C][C]1346.87440954814[/C][C]1250.86655218481[/C][C]1442.88226691146[/C][/ROW]
[ROW][C]116[/C][C]1470.66431068823[/C][C]1374.54674843439[/C][C]1566.78187294206[/C][/ROW]
[ROW][C]117[/C][C]1272.43657432748[/C][C]1176.19329384241[/C][C]1368.67985481256[/C][/ROW]
[ROW][C]118[/C][C]1283.85612168272[/C][C]1187.47006514712[/C][C]1380.24217821832[/C][/ROW]
[ROW][C]119[/C][C]1431.81204265561[/C][C]1335.26512263354[/C][C]1528.35896267769[/C][/ROW]
[ROW][C]120[/C][C]984.039076992143[/C][C]887.312193052957[/C][C]1080.76596093133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211078&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211078&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
109957.350883089625861.7249251567591052.97684102249
1101283.939601655981188.27745743221379.60174587976
1111327.000412832091231.292558057171422.70826760701
1121193.116524512181097.352334236171288.88071478818
1131171.637774969091075.805529443071267.4700204951
1141272.459888474291176.546780298731368.37299664986
1151346.874409548141250.866552184811442.88226691146
1161470.664310688231374.546748434391566.78187294206
1171272.436574327481176.193293842411368.67985481256
1181283.856121682721187.470065147121380.24217821832
1191431.812042655611335.265122633541528.35896267769
120984.039076992143887.3121930529571080.76596093133



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')