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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 10 Aug 2016 14:16:12 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/10/t1470835018fu2hlrbv6ykg00f.htm/, Retrieved Tue, 30 Apr 2024 06:57:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296200, Retrieved Tue, 30 Apr 2024 06:57:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-08-10 13:16:12] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296200&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296200&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296200&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0240970395417507
beta0.141764472832465
gamma0.959889360460358

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0240970395417507 \tabularnewline
beta & 0.141764472832465 \tabularnewline
gamma & 0.959889360460358 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296200&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]0.0240970395417507[/C][/ROW]
[ROW][C]beta[/C][C]0.141764472832465[/C][/ROW]
[ROW][C]gamma[/C][C]0.959889360460358[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296200&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296200&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
alpha0.0240970395417507
beta0.141764472832465
gamma0.959889360460358







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311301147.95673076923-17.9567307692312
1413401354.50085481928-14.5008548192773
1511401153.57871881903-13.5787188190311
1612901304.29908391598-14.2990839159806
1712601269.95324318741-9.95324318740609
1812801290.26145637311-10.2614563731083
1913301295.9438549968934.0561450031105
2012701250.3105159502619.6894840497412
2113001334.39824423389-34.3982442338872
2211501173.31511040693-23.3151104069252
2314101322.0027337829487.9972662170558
2412501386.58993038919-136.589930389194
2510301105.1441748838-75.1441748837963
2613201312.897495764417.10250423558728
2711601112.7834776492647.2165223507393
2813001263.9254243679636.0745756320434
2911901234.66793089913-44.6679308991318
3013101253.5357988097756.4642011902326
3112901302.25383352132-12.2538335213167
3213201241.8011034785278.1988965214812
3313001276.5860899285223.4139100714806
3412301127.43028780357102.569712196425
3513301384.00626040259-54.0062604025927
3612201234.88448707973-14.8844870797313
3710101014.44403018423-4.44403018422554
3812901301.70054170217-11.7005417021724
3911701139.4005752851630.5994247148365
4012401280.33800322316-40.3380032231598
4112601173.9751219109286.0248780890779
4212601291.54736963852-31.5473696385156
4313101274.290349308535.7096506914984
4413601300.4076342607959.5923657392109
4512501284.04221459826-34.042214598257
4611701208.07379162014-38.0737916201433
4713601314.5282903701445.4717096298627
4811401204.73268600498-64.7326860049845
491030992.98231530606137.0176846939391
5012601274.69305705018-14.6930570501804
5112101152.1883529732557.8116470267473
5211901227.6657143759-37.6657143759014
5312301240.08337006302-10.0833700630201
5413501245.21912501502104.780874984976
5513001294.732810770365.26718922964346
5613401342.86686174947-2.86686174946863
5712701237.4479629489732.5520370510251
5812201159.6997685270660.3002314729406
5914001347.5149549027352.4850450972699
6011201135.40554015063-15.4055401506344
6110001021.08001039454-21.0800103945431
6212601253.672446602666.32755339733512
6312601200.3876830085959.6123169914076
6411501187.26930290303-37.2693029030268
6512401226.3360034869513.6639965130501
6613601340.5267102813519.47328971865
6713501295.3555988908354.6444011091735
6812801337.81971858764-57.8197185876368
6913201264.8277299927155.1722700072937
7012101214.26740030429-4.26740030428823
7113701393.63459987826-23.634599878262
7210601116.2626336964-56.262633696399
731040995.66620102054344.3337989794568
7412601255.761897615464.23810238454166
7512101252.58732430012-42.5873243001224
7612001146.1479591489353.8520408510735
7712001235.33035467818-35.3303546781817
7812901353.82270016827-63.8227001682717
7914001339.3470553387860.6529446612201
8012801276.380530243723.61946975628393
8112801310.70150287904-30.7015028790395
8212201202.0840887152117.9159112847926
8313501363.61208250257-13.6120825025673
8410001055.71990527478-55.7199052747817
859801029.17588122136-49.1758812213579
8612401248.94356319192-8.94356319192002
8711901201.02747831027-11.0274783102657
8812001185.2371155939614.7628844060434
8911501189.34971860506-39.3497186050574
9012701280.4555617975-10.4555617974986
9114101383.4526887275726.5473112724305
9214201265.70431451745154.295685482554
9312601271.4869971307-11.4869971307039
9413001208.9223630535591.0776369464534
9514101342.9761116158567.0238883841516
961000998.1545085874111.8454914125889
97950979.896824569661-29.8968245696608
9812801238.6519265403141.3480734596853
9913301191.00226780551138.997732194485
10011901204.5055938137-14.5055938136998
10111701158.641642502411.3583574975971
10212701279.62867204411-9.62867204410918
10313401418.9037330167-78.9037330167009
10414701419.5187305018550.4812694981467
10512701268.381761169891.61823883011448
10612801303.13639024493-23.1363902449348
10714301412.4403247699417.5596752300632
1089801005.73633251681-25.7363325168083

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1130 & 1147.95673076923 & -17.9567307692312 \tabularnewline
14 & 1340 & 1354.50085481928 & -14.5008548192773 \tabularnewline
15 & 1140 & 1153.57871881903 & -13.5787188190311 \tabularnewline
16 & 1290 & 1304.29908391598 & -14.2990839159806 \tabularnewline
17 & 1260 & 1269.95324318741 & -9.95324318740609 \tabularnewline
18 & 1280 & 1290.26145637311 & -10.2614563731083 \tabularnewline
19 & 1330 & 1295.94385499689 & 34.0561450031105 \tabularnewline
20 & 1270 & 1250.31051595026 & 19.6894840497412 \tabularnewline
21 & 1300 & 1334.39824423389 & -34.3982442338872 \tabularnewline
22 & 1150 & 1173.31511040693 & -23.3151104069252 \tabularnewline
23 & 1410 & 1322.00273378294 & 87.9972662170558 \tabularnewline
24 & 1250 & 1386.58993038919 & -136.589930389194 \tabularnewline
25 & 1030 & 1105.1441748838 & -75.1441748837963 \tabularnewline
26 & 1320 & 1312.89749576441 & 7.10250423558728 \tabularnewline
27 & 1160 & 1112.78347764926 & 47.2165223507393 \tabularnewline
28 & 1300 & 1263.92542436796 & 36.0745756320434 \tabularnewline
29 & 1190 & 1234.66793089913 & -44.6679308991318 \tabularnewline
30 & 1310 & 1253.53579880977 & 56.4642011902326 \tabularnewline
31 & 1290 & 1302.25383352132 & -12.2538335213167 \tabularnewline
32 & 1320 & 1241.80110347852 & 78.1988965214812 \tabularnewline
33 & 1300 & 1276.58608992852 & 23.4139100714806 \tabularnewline
34 & 1230 & 1127.43028780357 & 102.569712196425 \tabularnewline
35 & 1330 & 1384.00626040259 & -54.0062604025927 \tabularnewline
36 & 1220 & 1234.88448707973 & -14.8844870797313 \tabularnewline
37 & 1010 & 1014.44403018423 & -4.44403018422554 \tabularnewline
38 & 1290 & 1301.70054170217 & -11.7005417021724 \tabularnewline
39 & 1170 & 1139.40057528516 & 30.5994247148365 \tabularnewline
40 & 1240 & 1280.33800322316 & -40.3380032231598 \tabularnewline
41 & 1260 & 1173.97512191092 & 86.0248780890779 \tabularnewline
42 & 1260 & 1291.54736963852 & -31.5473696385156 \tabularnewline
43 & 1310 & 1274.2903493085 & 35.7096506914984 \tabularnewline
44 & 1360 & 1300.40763426079 & 59.5923657392109 \tabularnewline
45 & 1250 & 1284.04221459826 & -34.042214598257 \tabularnewline
46 & 1170 & 1208.07379162014 & -38.0737916201433 \tabularnewline
47 & 1360 & 1314.52829037014 & 45.4717096298627 \tabularnewline
48 & 1140 & 1204.73268600498 & -64.7326860049845 \tabularnewline
49 & 1030 & 992.982315306061 & 37.0176846939391 \tabularnewline
50 & 1260 & 1274.69305705018 & -14.6930570501804 \tabularnewline
51 & 1210 & 1152.18835297325 & 57.8116470267473 \tabularnewline
52 & 1190 & 1227.6657143759 & -37.6657143759014 \tabularnewline
53 & 1230 & 1240.08337006302 & -10.0833700630201 \tabularnewline
54 & 1350 & 1245.21912501502 & 104.780874984976 \tabularnewline
55 & 1300 & 1294.73281077036 & 5.26718922964346 \tabularnewline
56 & 1340 & 1342.86686174947 & -2.86686174946863 \tabularnewline
57 & 1270 & 1237.44796294897 & 32.5520370510251 \tabularnewline
58 & 1220 & 1159.69976852706 & 60.3002314729406 \tabularnewline
59 & 1400 & 1347.51495490273 & 52.4850450972699 \tabularnewline
60 & 1120 & 1135.40554015063 & -15.4055401506344 \tabularnewline
61 & 1000 & 1021.08001039454 & -21.0800103945431 \tabularnewline
62 & 1260 & 1253.67244660266 & 6.32755339733512 \tabularnewline
63 & 1260 & 1200.38768300859 & 59.6123169914076 \tabularnewline
64 & 1150 & 1187.26930290303 & -37.2693029030268 \tabularnewline
65 & 1240 & 1226.33600348695 & 13.6639965130501 \tabularnewline
66 & 1360 & 1340.52671028135 & 19.47328971865 \tabularnewline
67 & 1350 & 1295.35559889083 & 54.6444011091735 \tabularnewline
68 & 1280 & 1337.81971858764 & -57.8197185876368 \tabularnewline
69 & 1320 & 1264.82772999271 & 55.1722700072937 \tabularnewline
70 & 1210 & 1214.26740030429 & -4.26740030428823 \tabularnewline
71 & 1370 & 1393.63459987826 & -23.634599878262 \tabularnewline
72 & 1060 & 1116.2626336964 & -56.262633696399 \tabularnewline
73 & 1040 & 995.666201020543 & 44.3337989794568 \tabularnewline
74 & 1260 & 1255.76189761546 & 4.23810238454166 \tabularnewline
75 & 1210 & 1252.58732430012 & -42.5873243001224 \tabularnewline
76 & 1200 & 1146.14795914893 & 53.8520408510735 \tabularnewline
77 & 1200 & 1235.33035467818 & -35.3303546781817 \tabularnewline
78 & 1290 & 1353.82270016827 & -63.8227001682717 \tabularnewline
79 & 1400 & 1339.34705533878 & 60.6529446612201 \tabularnewline
80 & 1280 & 1276.38053024372 & 3.61946975628393 \tabularnewline
81 & 1280 & 1310.70150287904 & -30.7015028790395 \tabularnewline
82 & 1220 & 1202.08408871521 & 17.9159112847926 \tabularnewline
83 & 1350 & 1363.61208250257 & -13.6120825025673 \tabularnewline
84 & 1000 & 1055.71990527478 & -55.7199052747817 \tabularnewline
85 & 980 & 1029.17588122136 & -49.1758812213579 \tabularnewline
86 & 1240 & 1248.94356319192 & -8.94356319192002 \tabularnewline
87 & 1190 & 1201.02747831027 & -11.0274783102657 \tabularnewline
88 & 1200 & 1185.23711559396 & 14.7628844060434 \tabularnewline
89 & 1150 & 1189.34971860506 & -39.3497186050574 \tabularnewline
90 & 1270 & 1280.4555617975 & -10.4555617974986 \tabularnewline
91 & 1410 & 1383.45268872757 & 26.5473112724305 \tabularnewline
92 & 1420 & 1265.70431451745 & 154.295685482554 \tabularnewline
93 & 1260 & 1271.4869971307 & -11.4869971307039 \tabularnewline
94 & 1300 & 1208.92236305355 & 91.0776369464534 \tabularnewline
95 & 1410 & 1342.97611161585 & 67.0238883841516 \tabularnewline
96 & 1000 & 998.154508587411 & 1.8454914125889 \tabularnewline
97 & 950 & 979.896824569661 & -29.8968245696608 \tabularnewline
98 & 1280 & 1238.65192654031 & 41.3480734596853 \tabularnewline
99 & 1330 & 1191.00226780551 & 138.997732194485 \tabularnewline
100 & 1190 & 1204.5055938137 & -14.5055938136998 \tabularnewline
101 & 1170 & 1158.6416425024 & 11.3583574975971 \tabularnewline
102 & 1270 & 1279.62867204411 & -9.62867204410918 \tabularnewline
103 & 1340 & 1418.9037330167 & -78.9037330167009 \tabularnewline
104 & 1470 & 1419.51873050185 & 50.4812694981467 \tabularnewline
105 & 1270 & 1268.38176116989 & 1.61823883011448 \tabularnewline
106 & 1280 & 1303.13639024493 & -23.1363902449348 \tabularnewline
107 & 1430 & 1412.44032476994 & 17.5596752300632 \tabularnewline
108 & 980 & 1005.73633251681 & -25.7363325168083 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296200&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]1354.50085481928[/C][C]-14.5008548192773[/C][/ROW]
[ROW][C]15[/C][C]1140[/C][C]1153.57871881903[/C][C]-13.5787188190311[/C][/ROW]
[ROW][C]16[/C][C]1290[/C][C]1304.29908391598[/C][C]-14.2990839159806[/C][/ROW]
[ROW][C]17[/C][C]1260[/C][C]1269.95324318741[/C][C]-9.95324318740609[/C][/ROW]
[ROW][C]18[/C][C]1280[/C][C]1290.26145637311[/C][C]-10.2614563731083[/C][/ROW]
[ROW][C]19[/C][C]1330[/C][C]1295.94385499689[/C][C]34.0561450031105[/C][/ROW]
[ROW][C]20[/C][C]1270[/C][C]1250.31051595026[/C][C]19.6894840497412[/C][/ROW]
[ROW][C]21[/C][C]1300[/C][C]1334.39824423389[/C][C]-34.3982442338872[/C][/ROW]
[ROW][C]22[/C][C]1150[/C][C]1173.31511040693[/C][C]-23.3151104069252[/C][/ROW]
[ROW][C]23[/C][C]1410[/C][C]1322.00273378294[/C][C]87.9972662170558[/C][/ROW]
[ROW][C]24[/C][C]1250[/C][C]1386.58993038919[/C][C]-136.589930389194[/C][/ROW]
[ROW][C]25[/C][C]1030[/C][C]1105.1441748838[/C][C]-75.1441748837963[/C][/ROW]
[ROW][C]26[/C][C]1320[/C][C]1312.89749576441[/C][C]7.10250423558728[/C][/ROW]
[ROW][C]27[/C][C]1160[/C][C]1112.78347764926[/C][C]47.2165223507393[/C][/ROW]
[ROW][C]28[/C][C]1300[/C][C]1263.92542436796[/C][C]36.0745756320434[/C][/ROW]
[ROW][C]29[/C][C]1190[/C][C]1234.66793089913[/C][C]-44.6679308991318[/C][/ROW]
[ROW][C]30[/C][C]1310[/C][C]1253.53579880977[/C][C]56.4642011902326[/C][/ROW]
[ROW][C]31[/C][C]1290[/C][C]1302.25383352132[/C][C]-12.2538335213167[/C][/ROW]
[ROW][C]32[/C][C]1320[/C][C]1241.80110347852[/C][C]78.1988965214812[/C][/ROW]
[ROW][C]33[/C][C]1300[/C][C]1276.58608992852[/C][C]23.4139100714806[/C][/ROW]
[ROW][C]34[/C][C]1230[/C][C]1127.43028780357[/C][C]102.569712196425[/C][/ROW]
[ROW][C]35[/C][C]1330[/C][C]1384.00626040259[/C][C]-54.0062604025927[/C][/ROW]
[ROW][C]36[/C][C]1220[/C][C]1234.88448707973[/C][C]-14.8844870797313[/C][/ROW]
[ROW][C]37[/C][C]1010[/C][C]1014.44403018423[/C][C]-4.44403018422554[/C][/ROW]
[ROW][C]38[/C][C]1290[/C][C]1301.70054170217[/C][C]-11.7005417021724[/C][/ROW]
[ROW][C]39[/C][C]1170[/C][C]1139.40057528516[/C][C]30.5994247148365[/C][/ROW]
[ROW][C]40[/C][C]1240[/C][C]1280.33800322316[/C][C]-40.3380032231598[/C][/ROW]
[ROW][C]41[/C][C]1260[/C][C]1173.97512191092[/C][C]86.0248780890779[/C][/ROW]
[ROW][C]42[/C][C]1260[/C][C]1291.54736963852[/C][C]-31.5473696385156[/C][/ROW]
[ROW][C]43[/C][C]1310[/C][C]1274.2903493085[/C][C]35.7096506914984[/C][/ROW]
[ROW][C]44[/C][C]1360[/C][C]1300.40763426079[/C][C]59.5923657392109[/C][/ROW]
[ROW][C]45[/C][C]1250[/C][C]1284.04221459826[/C][C]-34.042214598257[/C][/ROW]
[ROW][C]46[/C][C]1170[/C][C]1208.07379162014[/C][C]-38.0737916201433[/C][/ROW]
[ROW][C]47[/C][C]1360[/C][C]1314.52829037014[/C][C]45.4717096298627[/C][/ROW]
[ROW][C]48[/C][C]1140[/C][C]1204.73268600498[/C][C]-64.7326860049845[/C][/ROW]
[ROW][C]49[/C][C]1030[/C][C]992.982315306061[/C][C]37.0176846939391[/C][/ROW]
[ROW][C]50[/C][C]1260[/C][C]1274.69305705018[/C][C]-14.6930570501804[/C][/ROW]
[ROW][C]51[/C][C]1210[/C][C]1152.18835297325[/C][C]57.8116470267473[/C][/ROW]
[ROW][C]52[/C][C]1190[/C][C]1227.6657143759[/C][C]-37.6657143759014[/C][/ROW]
[ROW][C]53[/C][C]1230[/C][C]1240.08337006302[/C][C]-10.0833700630201[/C][/ROW]
[ROW][C]54[/C][C]1350[/C][C]1245.21912501502[/C][C]104.780874984976[/C][/ROW]
[ROW][C]55[/C][C]1300[/C][C]1294.73281077036[/C][C]5.26718922964346[/C][/ROW]
[ROW][C]56[/C][C]1340[/C][C]1342.86686174947[/C][C]-2.86686174946863[/C][/ROW]
[ROW][C]57[/C][C]1270[/C][C]1237.44796294897[/C][C]32.5520370510251[/C][/ROW]
[ROW][C]58[/C][C]1220[/C][C]1159.69976852706[/C][C]60.3002314729406[/C][/ROW]
[ROW][C]59[/C][C]1400[/C][C]1347.51495490273[/C][C]52.4850450972699[/C][/ROW]
[ROW][C]60[/C][C]1120[/C][C]1135.40554015063[/C][C]-15.4055401506344[/C][/ROW]
[ROW][C]61[/C][C]1000[/C][C]1021.08001039454[/C][C]-21.0800103945431[/C][/ROW]
[ROW][C]62[/C][C]1260[/C][C]1253.67244660266[/C][C]6.32755339733512[/C][/ROW]
[ROW][C]63[/C][C]1260[/C][C]1200.38768300859[/C][C]59.6123169914076[/C][/ROW]
[ROW][C]64[/C][C]1150[/C][C]1187.26930290303[/C][C]-37.2693029030268[/C][/ROW]
[ROW][C]65[/C][C]1240[/C][C]1226.33600348695[/C][C]13.6639965130501[/C][/ROW]
[ROW][C]66[/C][C]1360[/C][C]1340.52671028135[/C][C]19.47328971865[/C][/ROW]
[ROW][C]67[/C][C]1350[/C][C]1295.35559889083[/C][C]54.6444011091735[/C][/ROW]
[ROW][C]68[/C][C]1280[/C][C]1337.81971858764[/C][C]-57.8197185876368[/C][/ROW]
[ROW][C]69[/C][C]1320[/C][C]1264.82772999271[/C][C]55.1722700072937[/C][/ROW]
[ROW][C]70[/C][C]1210[/C][C]1214.26740030429[/C][C]-4.26740030428823[/C][/ROW]
[ROW][C]71[/C][C]1370[/C][C]1393.63459987826[/C][C]-23.634599878262[/C][/ROW]
[ROW][C]72[/C][C]1060[/C][C]1116.2626336964[/C][C]-56.262633696399[/C][/ROW]
[ROW][C]73[/C][C]1040[/C][C]995.666201020543[/C][C]44.3337989794568[/C][/ROW]
[ROW][C]74[/C][C]1260[/C][C]1255.76189761546[/C][C]4.23810238454166[/C][/ROW]
[ROW][C]75[/C][C]1210[/C][C]1252.58732430012[/C][C]-42.5873243001224[/C][/ROW]
[ROW][C]76[/C][C]1200[/C][C]1146.14795914893[/C][C]53.8520408510735[/C][/ROW]
[ROW][C]77[/C][C]1200[/C][C]1235.33035467818[/C][C]-35.3303546781817[/C][/ROW]
[ROW][C]78[/C][C]1290[/C][C]1353.82270016827[/C][C]-63.8227001682717[/C][/ROW]
[ROW][C]79[/C][C]1400[/C][C]1339.34705533878[/C][C]60.6529446612201[/C][/ROW]
[ROW][C]80[/C][C]1280[/C][C]1276.38053024372[/C][C]3.61946975628393[/C][/ROW]
[ROW][C]81[/C][C]1280[/C][C]1310.70150287904[/C][C]-30.7015028790395[/C][/ROW]
[ROW][C]82[/C][C]1220[/C][C]1202.08408871521[/C][C]17.9159112847926[/C][/ROW]
[ROW][C]83[/C][C]1350[/C][C]1363.61208250257[/C][C]-13.6120825025673[/C][/ROW]
[ROW][C]84[/C][C]1000[/C][C]1055.71990527478[/C][C]-55.7199052747817[/C][/ROW]
[ROW][C]85[/C][C]980[/C][C]1029.17588122136[/C][C]-49.1758812213579[/C][/ROW]
[ROW][C]86[/C][C]1240[/C][C]1248.94356319192[/C][C]-8.94356319192002[/C][/ROW]
[ROW][C]87[/C][C]1190[/C][C]1201.02747831027[/C][C]-11.0274783102657[/C][/ROW]
[ROW][C]88[/C][C]1200[/C][C]1185.23711559396[/C][C]14.7628844060434[/C][/ROW]
[ROW][C]89[/C][C]1150[/C][C]1189.34971860506[/C][C]-39.3497186050574[/C][/ROW]
[ROW][C]90[/C][C]1270[/C][C]1280.4555617975[/C][C]-10.4555617974986[/C][/ROW]
[ROW][C]91[/C][C]1410[/C][C]1383.45268872757[/C][C]26.5473112724305[/C][/ROW]
[ROW][C]92[/C][C]1420[/C][C]1265.70431451745[/C][C]154.295685482554[/C][/ROW]
[ROW][C]93[/C][C]1260[/C][C]1271.4869971307[/C][C]-11.4869971307039[/C][/ROW]
[ROW][C]94[/C][C]1300[/C][C]1208.92236305355[/C][C]91.0776369464534[/C][/ROW]
[ROW][C]95[/C][C]1410[/C][C]1342.97611161585[/C][C]67.0238883841516[/C][/ROW]
[ROW][C]96[/C][C]1000[/C][C]998.154508587411[/C][C]1.8454914125889[/C][/ROW]
[ROW][C]97[/C][C]950[/C][C]979.896824569661[/C][C]-29.8968245696608[/C][/ROW]
[ROW][C]98[/C][C]1280[/C][C]1238.65192654031[/C][C]41.3480734596853[/C][/ROW]
[ROW][C]99[/C][C]1330[/C][C]1191.00226780551[/C][C]138.997732194485[/C][/ROW]
[ROW][C]100[/C][C]1190[/C][C]1204.5055938137[/C][C]-14.5055938136998[/C][/ROW]
[ROW][C]101[/C][C]1170[/C][C]1158.6416425024[/C][C]11.3583574975971[/C][/ROW]
[ROW][C]102[/C][C]1270[/C][C]1279.62867204411[/C][C]-9.62867204410918[/C][/ROW]
[ROW][C]103[/C][C]1340[/C][C]1418.9037330167[/C][C]-78.9037330167009[/C][/ROW]
[ROW][C]104[/C][C]1470[/C][C]1419.51873050185[/C][C]50.4812694981467[/C][/ROW]
[ROW][C]105[/C][C]1270[/C][C]1268.38176116989[/C][C]1.61823883011448[/C][/ROW]
[ROW][C]106[/C][C]1280[/C][C]1303.13639024493[/C][C]-23.1363902449348[/C][/ROW]
[ROW][C]107[/C][C]1430[/C][C]1412.44032476994[/C][C]17.5596752300632[/C][/ROW]
[ROW][C]108[/C][C]980[/C][C]1005.73633251681[/C][C]-25.7363325168083[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296200&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296200&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
1413401354.50085481928-14.5008548192773
1511401153.57871881903-13.5787188190311
1612901304.29908391598-14.2990839159806
1712601269.95324318741-9.95324318740609
1812801290.26145637311-10.2614563731083
1913301295.9438549968934.0561450031105
2012701250.3105159502619.6894840497412
2113001334.39824423389-34.3982442338872
2211501173.31511040693-23.3151104069252
2314101322.0027337829487.9972662170558
2412501386.58993038919-136.589930389194
2510301105.1441748838-75.1441748837963
2613201312.897495764417.10250423558728
2711601112.7834776492647.2165223507393
2813001263.9254243679636.0745756320434
2911901234.66793089913-44.6679308991318
3013101253.5357988097756.4642011902326
3112901302.25383352132-12.2538335213167
3213201241.8011034785278.1988965214812
3313001276.5860899285223.4139100714806
3412301127.43028780357102.569712196425
3513301384.00626040259-54.0062604025927
3612201234.88448707973-14.8844870797313
3710101014.44403018423-4.44403018422554
3812901301.70054170217-11.7005417021724
3911701139.4005752851630.5994247148365
4012401280.33800322316-40.3380032231598
4112601173.9751219109286.0248780890779
4212601291.54736963852-31.5473696385156
4313101274.290349308535.7096506914984
4413601300.4076342607959.5923657392109
4512501284.04221459826-34.042214598257
4611701208.07379162014-38.0737916201433
4713601314.5282903701445.4717096298627
4811401204.73268600498-64.7326860049845
491030992.98231530606137.0176846939391
5012601274.69305705018-14.6930570501804
5112101152.1883529732557.8116470267473
5211901227.6657143759-37.6657143759014
5312301240.08337006302-10.0833700630201
5413501245.21912501502104.780874984976
5513001294.732810770365.26718922964346
5613401342.86686174947-2.86686174946863
5712701237.4479629489732.5520370510251
5812201159.6997685270660.3002314729406
5914001347.5149549027352.4850450972699
6011201135.40554015063-15.4055401506344
6110001021.08001039454-21.0800103945431
6212601253.672446602666.32755339733512
6312601200.3876830085959.6123169914076
6411501187.26930290303-37.2693029030268
6512401226.3360034869513.6639965130501
6613601340.5267102813519.47328971865
6713501295.3555988908354.6444011091735
6812801337.81971858764-57.8197185876368
6913201264.8277299927155.1722700072937
7012101214.26740030429-4.26740030428823
7113701393.63459987826-23.634599878262
7210601116.2626336964-56.262633696399
731040995.66620102054344.3337989794568
7412601255.761897615464.23810238454166
7512101252.58732430012-42.5873243001224
7612001146.1479591489353.8520408510735
7712001235.33035467818-35.3303546781817
7812901353.82270016827-63.8227001682717
7914001339.3470553387860.6529446612201
8012801276.380530243723.61946975628393
8112801310.70150287904-30.7015028790395
8212201202.0840887152117.9159112847926
8313501363.61208250257-13.6120825025673
8410001055.71990527478-55.7199052747817
859801029.17588122136-49.1758812213579
8612401248.94356319192-8.94356319192002
8711901201.02747831027-11.0274783102657
8812001185.2371155939614.7628844060434
8911501189.34971860506-39.3497186050574
9012701280.4555617975-10.4555617974986
9114101383.4526887275726.5473112724305
9214201265.70431451745154.295685482554
9312601271.4869971307-11.4869971307039
9413001208.9223630535591.0776369464534
9514101342.9761116158567.0238883841516
961000998.1545085874111.8454914125889
97950979.896824569661-29.8968245696608
9812801238.6519265403141.3480734596853
9913301191.00226780551138.997732194485
10011901204.5055938137-14.5055938136998
10111701158.641642502411.3583574975971
10212701279.62867204411-9.62867204410918
10313401418.9037330167-78.9037330167009
10414701419.5187305018550.4812694981467
10512701268.381761169891.61823883011448
10612801303.13639024493-23.1363902449348
10714301412.4403247699417.5596752300632
1089801005.73633251681-25.7363325168083







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109957.350883088252861.7249251554151052.97684102109
1101283.939601655291188.277457431531379.60174587905
1111327.000412832051231.292558057141422.70826760696
1121193.11652451041097.352334234391288.88071478641
1131171.637774967571075.805529441541267.47002049359
1141272.45988847261176.546780297021368.37299664818
1151346.874409545941250.866552182581442.88226690929
1161470.664310687451374.546748433581566.78187294132
1171272.436574326041176.193293840931368.67985481116
1181283.856121681121187.470065145471380.24217821678
1191431.812042654421335.265122632281528.35896267655
120984.039076990472887.3121930512241080.76596092972

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 957.350883088252 & 861.724925155415 & 1052.97684102109 \tabularnewline
110 & 1283.93960165529 & 1188.27745743153 & 1379.60174587905 \tabularnewline
111 & 1327.00041283205 & 1231.29255805714 & 1422.70826760696 \tabularnewline
112 & 1193.1165245104 & 1097.35233423439 & 1288.88071478641 \tabularnewline
113 & 1171.63777496757 & 1075.80552944154 & 1267.47002049359 \tabularnewline
114 & 1272.4598884726 & 1176.54678029702 & 1368.37299664818 \tabularnewline
115 & 1346.87440954594 & 1250.86655218258 & 1442.88226690929 \tabularnewline
116 & 1470.66431068745 & 1374.54674843358 & 1566.78187294132 \tabularnewline
117 & 1272.43657432604 & 1176.19329384093 & 1368.67985481116 \tabularnewline
118 & 1283.85612168112 & 1187.47006514547 & 1380.24217821678 \tabularnewline
119 & 1431.81204265442 & 1335.26512263228 & 1528.35896267655 \tabularnewline
120 & 984.039076990472 & 887.312193051224 & 1080.76596092972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296200&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]957.350883088252[/C][C]861.724925155415[/C][C]1052.97684102109[/C][/ROW]
[ROW][C]110[/C][C]1283.93960165529[/C][C]1188.27745743153[/C][C]1379.60174587905[/C][/ROW]
[ROW][C]111[/C][C]1327.00041283205[/C][C]1231.29255805714[/C][C]1422.70826760696[/C][/ROW]
[ROW][C]112[/C][C]1193.1165245104[/C][C]1097.35233423439[/C][C]1288.88071478641[/C][/ROW]
[ROW][C]113[/C][C]1171.63777496757[/C][C]1075.80552944154[/C][C]1267.47002049359[/C][/ROW]
[ROW][C]114[/C][C]1272.4598884726[/C][C]1176.54678029702[/C][C]1368.37299664818[/C][/ROW]
[ROW][C]115[/C][C]1346.87440954594[/C][C]1250.86655218258[/C][C]1442.88226690929[/C][/ROW]
[ROW][C]116[/C][C]1470.66431068745[/C][C]1374.54674843358[/C][C]1566.78187294132[/C][/ROW]
[ROW][C]117[/C][C]1272.43657432604[/C][C]1176.19329384093[/C][C]1368.67985481116[/C][/ROW]
[ROW][C]118[/C][C]1283.85612168112[/C][C]1187.47006514547[/C][C]1380.24217821678[/C][/ROW]
[ROW][C]119[/C][C]1431.81204265442[/C][C]1335.26512263228[/C][C]1528.35896267655[/C][/ROW]
[ROW][C]120[/C][C]984.039076990472[/C][C]887.312193051224[/C][C]1080.76596092972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296200&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296200&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
109957.350883088252861.7249251554151052.97684102109
1101283.939601655291188.277457431531379.60174587905
1111327.000412832051231.292558057141422.70826760696
1121193.11652451041097.352334234391288.88071478641
1131171.637774967571075.805529441541267.47002049359
1141272.45988847261176.546780297021368.37299664818
1151346.874409545941250.866552182581442.88226690929
1161470.664310687451374.546748433581566.78187294132
1171272.436574326041176.193293840931368.67985481116
1181283.856121681121187.470065145471380.24217821678
1191431.812042654421335.265122632281528.35896267655
120984.039076990472887.3121930512241080.76596092972



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')