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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Aug 2011 05:17:38 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/18/t1313659225sso60mntpxc6k2e.htm/, Retrieved Wed, 15 May 2024 20:14:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124011, Retrieved Wed, 15 May 2024 20:14:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsYannick De Pelsmaeker
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Tijdreeks B - Sta...] [2011-08-15 17:47:36] [73148e40994d778578e43e2ad3ecd67d]
- R PD    [Exponential Smoothing] [Tijdreeks B stap 27] [2011-08-18 09:17:38] [d41d8cd98f00b204e9800998ecf8427e] [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'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124011&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124011&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124011&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0101407480697986
beta0.135508570798047
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0101407480697986 \tabularnewline
beta & 0.135508570798047 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124011&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]0.0101407480697986[/C][/ROW]
[ROW][C]beta[/C][C]0.135508570798047[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124011&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124011&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
alpha0.0101407480697986
beta0.135508570798047
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311801190.27777777778-10.2777777777776
1410801090.8791270989-10.8791270989022
1511901197.29276197884-7.29276197883519
1611401142.89941054136-2.89941054136284
1711601158.5466267251.45337327499601
1812001201.73998055765-1.73998055764537
199801066.14856038489-86.148560384886
2012601193.7494589784766.2505410215344
2111001085.4868371948214.5131628051777
2212101127.1361697423782.8638302576333
2311501140.842497207229.15750279277518
2411401241.31397123238-101.313971232378
2511101172.85240701571-62.852407015705
2611201072.1894715768747.8105284231287
2711001182.69302153777-82.6930215377727
2811701131.7250041153838.2749958846218
2911201151.99613254951-31.9961325495058
3012501191.54107725558.4589227449992
31910972.94199285212-62.9419928521204
3212601251.598260952178.40173904782591
3310901091.42317017198-1.42317017197729
3412401200.4334215196639.5665784803416
3511301140.5472796029-10.5472796029042
3612001131.2461315736768.7538684263302
3711201102.592827604817.4071723951977
3811201112.406914143737.59308585626604
3911201093.3896169942926.6103830057066
4010701163.48866345317-93.4886634531711
4111001112.90135342533-12.9013534253304
4212301242.24021632752-12.2402163275187
43930902.71972794778227.2802720522184
4412401253.0005077449-13.0005077448993
459801082.94303215665-102.943032156653
4612701231.4183010143538.5816989856457
4711401121.8355751455318.1644248544667
4811601191.28108430601-31.2810843060142
4911601110.6084090652249.3915909347784
5012201110.89728893278109.102711067215
5111601111.7383248989748.2616751010285
5210901063.2100337229426.7899662770612
5310601093.81206962316-33.8120696231608
5412301223.76411648636.23588351370381
551070923.746901322187146.253098677813
5612401235.721530197014.27846980299478
571050977.19225865895172.807741341049
5813501268.1642679350481.8357320649641
5911001139.49431211147-39.4943121114673
6011301160.0161610975-30.0161610975001
6111701159.817782554110.1822174459023
6213601219.36765032894140.632349671056
6311501160.90068036228-10.9006803622783
6411801091.0334928631188.9665071368884
6510101062.8790237397-52.8790237396995
6611901232.85381760654-42.8538176065383
6710001071.44293823956-71.4429382395599
6812701240.8827239352629.1172760647382
699901050.68145980323-60.6814598032286
7014701349.29458344352120.70541655648
7111301101.0308962101328.9691037898685
7211501131.8348981682118.1651018317909
7311501172.18790651595-22.1879065159485
7414101360.7643615718149.2356384281866
7511901151.4761695377238.5238304622844
7611801181.13454086947-1.13454086946899
779901011.70535334118-21.7053533411818
7811701192.00873685351-22.0087368535101
7910801002.6276033402277.372396659785
8013501273.4390088899776.5609911100253
81960995.218007711652-35.2180077116523
8214901474.0590760639315.9409239360746
8311201134.20524609543-14.2052460954269
8410901154.09594368309-64.0959436830899
8512201153.7768822703766.2231177296283
8613701414.17655619341-44.1765561934142
8711801193.43695744169-13.4369574416864
8811901183.339844422386.66015557761671
891000993.6658457366516.33415426334886
9012501174.0301484109775.9698515890334
9110901084.227448199035.77255180097109
9213701353.6227335945216.3772664054759
93980964.17637943223115.8236205677688
9415301494.2757603256335.7242396743707
9511501124.9098385064625.0901614935376
9611201095.9960062843924.0039937156112
9712901225.8706899962964.1293100037146
9813701377.2689324889-7.26893248890315
9911301187.6821377817-57.6821377816952
10012001197.319515819352.68048418065223
1019101007.56685319796-97.5668531979584
10212201255.94867309083-35.9486730908293
10310401095.51340678989-55.5134067898932
10413401374.687983107-34.6879831069978
105950984.009187446754-34.0091874467537
10615001533.06698995186-33.0669899518609
10711201152.14765451455-32.1476545145538
10811501121.1700025614428.8299974385632

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1180 & 1190.27777777778 & -10.2777777777776 \tabularnewline
14 & 1080 & 1090.8791270989 & -10.8791270989022 \tabularnewline
15 & 1190 & 1197.29276197884 & -7.29276197883519 \tabularnewline
16 & 1140 & 1142.89941054136 & -2.89941054136284 \tabularnewline
17 & 1160 & 1158.546626725 & 1.45337327499601 \tabularnewline
18 & 1200 & 1201.73998055765 & -1.73998055764537 \tabularnewline
19 & 980 & 1066.14856038489 & -86.148560384886 \tabularnewline
20 & 1260 & 1193.74945897847 & 66.2505410215344 \tabularnewline
21 & 1100 & 1085.48683719482 & 14.5131628051777 \tabularnewline
22 & 1210 & 1127.13616974237 & 82.8638302576333 \tabularnewline
23 & 1150 & 1140.84249720722 & 9.15750279277518 \tabularnewline
24 & 1140 & 1241.31397123238 & -101.313971232378 \tabularnewline
25 & 1110 & 1172.85240701571 & -62.852407015705 \tabularnewline
26 & 1120 & 1072.18947157687 & 47.8105284231287 \tabularnewline
27 & 1100 & 1182.69302153777 & -82.6930215377727 \tabularnewline
28 & 1170 & 1131.72500411538 & 38.2749958846218 \tabularnewline
29 & 1120 & 1151.99613254951 & -31.9961325495058 \tabularnewline
30 & 1250 & 1191.541077255 & 58.4589227449992 \tabularnewline
31 & 910 & 972.94199285212 & -62.9419928521204 \tabularnewline
32 & 1260 & 1251.59826095217 & 8.40173904782591 \tabularnewline
33 & 1090 & 1091.42317017198 & -1.42317017197729 \tabularnewline
34 & 1240 & 1200.43342151966 & 39.5665784803416 \tabularnewline
35 & 1130 & 1140.5472796029 & -10.5472796029042 \tabularnewline
36 & 1200 & 1131.24613157367 & 68.7538684263302 \tabularnewline
37 & 1120 & 1102.5928276048 & 17.4071723951977 \tabularnewline
38 & 1120 & 1112.40691414373 & 7.59308585626604 \tabularnewline
39 & 1120 & 1093.38961699429 & 26.6103830057066 \tabularnewline
40 & 1070 & 1163.48866345317 & -93.4886634531711 \tabularnewline
41 & 1100 & 1112.90135342533 & -12.9013534253304 \tabularnewline
42 & 1230 & 1242.24021632752 & -12.2402163275187 \tabularnewline
43 & 930 & 902.719727947782 & 27.2802720522184 \tabularnewline
44 & 1240 & 1253.0005077449 & -13.0005077448993 \tabularnewline
45 & 980 & 1082.94303215665 & -102.943032156653 \tabularnewline
46 & 1270 & 1231.41830101435 & 38.5816989856457 \tabularnewline
47 & 1140 & 1121.83557514553 & 18.1644248544667 \tabularnewline
48 & 1160 & 1191.28108430601 & -31.2810843060142 \tabularnewline
49 & 1160 & 1110.60840906522 & 49.3915909347784 \tabularnewline
50 & 1220 & 1110.89728893278 & 109.102711067215 \tabularnewline
51 & 1160 & 1111.73832489897 & 48.2616751010285 \tabularnewline
52 & 1090 & 1063.21003372294 & 26.7899662770612 \tabularnewline
53 & 1060 & 1093.81206962316 & -33.8120696231608 \tabularnewline
54 & 1230 & 1223.7641164863 & 6.23588351370381 \tabularnewline
55 & 1070 & 923.746901322187 & 146.253098677813 \tabularnewline
56 & 1240 & 1235.72153019701 & 4.27846980299478 \tabularnewline
57 & 1050 & 977.192258658951 & 72.807741341049 \tabularnewline
58 & 1350 & 1268.16426793504 & 81.8357320649641 \tabularnewline
59 & 1100 & 1139.49431211147 & -39.4943121114673 \tabularnewline
60 & 1130 & 1160.0161610975 & -30.0161610975001 \tabularnewline
61 & 1170 & 1159.8177825541 & 10.1822174459023 \tabularnewline
62 & 1360 & 1219.36765032894 & 140.632349671056 \tabularnewline
63 & 1150 & 1160.90068036228 & -10.9006803622783 \tabularnewline
64 & 1180 & 1091.03349286311 & 88.9665071368884 \tabularnewline
65 & 1010 & 1062.8790237397 & -52.8790237396995 \tabularnewline
66 & 1190 & 1232.85381760654 & -42.8538176065383 \tabularnewline
67 & 1000 & 1071.44293823956 & -71.4429382395599 \tabularnewline
68 & 1270 & 1240.88272393526 & 29.1172760647382 \tabularnewline
69 & 990 & 1050.68145980323 & -60.6814598032286 \tabularnewline
70 & 1470 & 1349.29458344352 & 120.70541655648 \tabularnewline
71 & 1130 & 1101.03089621013 & 28.9691037898685 \tabularnewline
72 & 1150 & 1131.83489816821 & 18.1651018317909 \tabularnewline
73 & 1150 & 1172.18790651595 & -22.1879065159485 \tabularnewline
74 & 1410 & 1360.76436157181 & 49.2356384281866 \tabularnewline
75 & 1190 & 1151.47616953772 & 38.5238304622844 \tabularnewline
76 & 1180 & 1181.13454086947 & -1.13454086946899 \tabularnewline
77 & 990 & 1011.70535334118 & -21.7053533411818 \tabularnewline
78 & 1170 & 1192.00873685351 & -22.0087368535101 \tabularnewline
79 & 1080 & 1002.62760334022 & 77.372396659785 \tabularnewline
80 & 1350 & 1273.43900888997 & 76.5609911100253 \tabularnewline
81 & 960 & 995.218007711652 & -35.2180077116523 \tabularnewline
82 & 1490 & 1474.05907606393 & 15.9409239360746 \tabularnewline
83 & 1120 & 1134.20524609543 & -14.2052460954269 \tabularnewline
84 & 1090 & 1154.09594368309 & -64.0959436830899 \tabularnewline
85 & 1220 & 1153.77688227037 & 66.2231177296283 \tabularnewline
86 & 1370 & 1414.17655619341 & -44.1765561934142 \tabularnewline
87 & 1180 & 1193.43695744169 & -13.4369574416864 \tabularnewline
88 & 1190 & 1183.33984442238 & 6.66015557761671 \tabularnewline
89 & 1000 & 993.665845736651 & 6.33415426334886 \tabularnewline
90 & 1250 & 1174.03014841097 & 75.9698515890334 \tabularnewline
91 & 1090 & 1084.22744819903 & 5.77255180097109 \tabularnewline
92 & 1370 & 1353.62273359452 & 16.3772664054759 \tabularnewline
93 & 980 & 964.176379432231 & 15.8236205677688 \tabularnewline
94 & 1530 & 1494.27576032563 & 35.7242396743707 \tabularnewline
95 & 1150 & 1124.90983850646 & 25.0901614935376 \tabularnewline
96 & 1120 & 1095.99600628439 & 24.0039937156112 \tabularnewline
97 & 1290 & 1225.87068999629 & 64.1293100037146 \tabularnewline
98 & 1370 & 1377.2689324889 & -7.26893248890315 \tabularnewline
99 & 1130 & 1187.6821377817 & -57.6821377816952 \tabularnewline
100 & 1200 & 1197.31951581935 & 2.68048418065223 \tabularnewline
101 & 910 & 1007.56685319796 & -97.5668531979584 \tabularnewline
102 & 1220 & 1255.94867309083 & -35.9486730908293 \tabularnewline
103 & 1040 & 1095.51340678989 & -55.5134067898932 \tabularnewline
104 & 1340 & 1374.687983107 & -34.6879831069978 \tabularnewline
105 & 950 & 984.009187446754 & -34.0091874467537 \tabularnewline
106 & 1500 & 1533.06698995186 & -33.0669899518609 \tabularnewline
107 & 1120 & 1152.14765451455 & -32.1476545145538 \tabularnewline
108 & 1150 & 1121.17000256144 & 28.8299974385632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124011&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]1190.27777777778[/C][C]-10.2777777777776[/C][/ROW]
[ROW][C]14[/C][C]1080[/C][C]1090.8791270989[/C][C]-10.8791270989022[/C][/ROW]
[ROW][C]15[/C][C]1190[/C][C]1197.29276197884[/C][C]-7.29276197883519[/C][/ROW]
[ROW][C]16[/C][C]1140[/C][C]1142.89941054136[/C][C]-2.89941054136284[/C][/ROW]
[ROW][C]17[/C][C]1160[/C][C]1158.546626725[/C][C]1.45337327499601[/C][/ROW]
[ROW][C]18[/C][C]1200[/C][C]1201.73998055765[/C][C]-1.73998055764537[/C][/ROW]
[ROW][C]19[/C][C]980[/C][C]1066.14856038489[/C][C]-86.148560384886[/C][/ROW]
[ROW][C]20[/C][C]1260[/C][C]1193.74945897847[/C][C]66.2505410215344[/C][/ROW]
[ROW][C]21[/C][C]1100[/C][C]1085.48683719482[/C][C]14.5131628051777[/C][/ROW]
[ROW][C]22[/C][C]1210[/C][C]1127.13616974237[/C][C]82.8638302576333[/C][/ROW]
[ROW][C]23[/C][C]1150[/C][C]1140.84249720722[/C][C]9.15750279277518[/C][/ROW]
[ROW][C]24[/C][C]1140[/C][C]1241.31397123238[/C][C]-101.313971232378[/C][/ROW]
[ROW][C]25[/C][C]1110[/C][C]1172.85240701571[/C][C]-62.852407015705[/C][/ROW]
[ROW][C]26[/C][C]1120[/C][C]1072.18947157687[/C][C]47.8105284231287[/C][/ROW]
[ROW][C]27[/C][C]1100[/C][C]1182.69302153777[/C][C]-82.6930215377727[/C][/ROW]
[ROW][C]28[/C][C]1170[/C][C]1131.72500411538[/C][C]38.2749958846218[/C][/ROW]
[ROW][C]29[/C][C]1120[/C][C]1151.99613254951[/C][C]-31.9961325495058[/C][/ROW]
[ROW][C]30[/C][C]1250[/C][C]1191.541077255[/C][C]58.4589227449992[/C][/ROW]
[ROW][C]31[/C][C]910[/C][C]972.94199285212[/C][C]-62.9419928521204[/C][/ROW]
[ROW][C]32[/C][C]1260[/C][C]1251.59826095217[/C][C]8.40173904782591[/C][/ROW]
[ROW][C]33[/C][C]1090[/C][C]1091.42317017198[/C][C]-1.42317017197729[/C][/ROW]
[ROW][C]34[/C][C]1240[/C][C]1200.43342151966[/C][C]39.5665784803416[/C][/ROW]
[ROW][C]35[/C][C]1130[/C][C]1140.5472796029[/C][C]-10.5472796029042[/C][/ROW]
[ROW][C]36[/C][C]1200[/C][C]1131.24613157367[/C][C]68.7538684263302[/C][/ROW]
[ROW][C]37[/C][C]1120[/C][C]1102.5928276048[/C][C]17.4071723951977[/C][/ROW]
[ROW][C]38[/C][C]1120[/C][C]1112.40691414373[/C][C]7.59308585626604[/C][/ROW]
[ROW][C]39[/C][C]1120[/C][C]1093.38961699429[/C][C]26.6103830057066[/C][/ROW]
[ROW][C]40[/C][C]1070[/C][C]1163.48866345317[/C][C]-93.4886634531711[/C][/ROW]
[ROW][C]41[/C][C]1100[/C][C]1112.90135342533[/C][C]-12.9013534253304[/C][/ROW]
[ROW][C]42[/C][C]1230[/C][C]1242.24021632752[/C][C]-12.2402163275187[/C][/ROW]
[ROW][C]43[/C][C]930[/C][C]902.719727947782[/C][C]27.2802720522184[/C][/ROW]
[ROW][C]44[/C][C]1240[/C][C]1253.0005077449[/C][C]-13.0005077448993[/C][/ROW]
[ROW][C]45[/C][C]980[/C][C]1082.94303215665[/C][C]-102.943032156653[/C][/ROW]
[ROW][C]46[/C][C]1270[/C][C]1231.41830101435[/C][C]38.5816989856457[/C][/ROW]
[ROW][C]47[/C][C]1140[/C][C]1121.83557514553[/C][C]18.1644248544667[/C][/ROW]
[ROW][C]48[/C][C]1160[/C][C]1191.28108430601[/C][C]-31.2810843060142[/C][/ROW]
[ROW][C]49[/C][C]1160[/C][C]1110.60840906522[/C][C]49.3915909347784[/C][/ROW]
[ROW][C]50[/C][C]1220[/C][C]1110.89728893278[/C][C]109.102711067215[/C][/ROW]
[ROW][C]51[/C][C]1160[/C][C]1111.73832489897[/C][C]48.2616751010285[/C][/ROW]
[ROW][C]52[/C][C]1090[/C][C]1063.21003372294[/C][C]26.7899662770612[/C][/ROW]
[ROW][C]53[/C][C]1060[/C][C]1093.81206962316[/C][C]-33.8120696231608[/C][/ROW]
[ROW][C]54[/C][C]1230[/C][C]1223.7641164863[/C][C]6.23588351370381[/C][/ROW]
[ROW][C]55[/C][C]1070[/C][C]923.746901322187[/C][C]146.253098677813[/C][/ROW]
[ROW][C]56[/C][C]1240[/C][C]1235.72153019701[/C][C]4.27846980299478[/C][/ROW]
[ROW][C]57[/C][C]1050[/C][C]977.192258658951[/C][C]72.807741341049[/C][/ROW]
[ROW][C]58[/C][C]1350[/C][C]1268.16426793504[/C][C]81.8357320649641[/C][/ROW]
[ROW][C]59[/C][C]1100[/C][C]1139.49431211147[/C][C]-39.4943121114673[/C][/ROW]
[ROW][C]60[/C][C]1130[/C][C]1160.0161610975[/C][C]-30.0161610975001[/C][/ROW]
[ROW][C]61[/C][C]1170[/C][C]1159.8177825541[/C][C]10.1822174459023[/C][/ROW]
[ROW][C]62[/C][C]1360[/C][C]1219.36765032894[/C][C]140.632349671056[/C][/ROW]
[ROW][C]63[/C][C]1150[/C][C]1160.90068036228[/C][C]-10.9006803622783[/C][/ROW]
[ROW][C]64[/C][C]1180[/C][C]1091.03349286311[/C][C]88.9665071368884[/C][/ROW]
[ROW][C]65[/C][C]1010[/C][C]1062.8790237397[/C][C]-52.8790237396995[/C][/ROW]
[ROW][C]66[/C][C]1190[/C][C]1232.85381760654[/C][C]-42.8538176065383[/C][/ROW]
[ROW][C]67[/C][C]1000[/C][C]1071.44293823956[/C][C]-71.4429382395599[/C][/ROW]
[ROW][C]68[/C][C]1270[/C][C]1240.88272393526[/C][C]29.1172760647382[/C][/ROW]
[ROW][C]69[/C][C]990[/C][C]1050.68145980323[/C][C]-60.6814598032286[/C][/ROW]
[ROW][C]70[/C][C]1470[/C][C]1349.29458344352[/C][C]120.70541655648[/C][/ROW]
[ROW][C]71[/C][C]1130[/C][C]1101.03089621013[/C][C]28.9691037898685[/C][/ROW]
[ROW][C]72[/C][C]1150[/C][C]1131.83489816821[/C][C]18.1651018317909[/C][/ROW]
[ROW][C]73[/C][C]1150[/C][C]1172.18790651595[/C][C]-22.1879065159485[/C][/ROW]
[ROW][C]74[/C][C]1410[/C][C]1360.76436157181[/C][C]49.2356384281866[/C][/ROW]
[ROW][C]75[/C][C]1190[/C][C]1151.47616953772[/C][C]38.5238304622844[/C][/ROW]
[ROW][C]76[/C][C]1180[/C][C]1181.13454086947[/C][C]-1.13454086946899[/C][/ROW]
[ROW][C]77[/C][C]990[/C][C]1011.70535334118[/C][C]-21.7053533411818[/C][/ROW]
[ROW][C]78[/C][C]1170[/C][C]1192.00873685351[/C][C]-22.0087368535101[/C][/ROW]
[ROW][C]79[/C][C]1080[/C][C]1002.62760334022[/C][C]77.372396659785[/C][/ROW]
[ROW][C]80[/C][C]1350[/C][C]1273.43900888997[/C][C]76.5609911100253[/C][/ROW]
[ROW][C]81[/C][C]960[/C][C]995.218007711652[/C][C]-35.2180077116523[/C][/ROW]
[ROW][C]82[/C][C]1490[/C][C]1474.05907606393[/C][C]15.9409239360746[/C][/ROW]
[ROW][C]83[/C][C]1120[/C][C]1134.20524609543[/C][C]-14.2052460954269[/C][/ROW]
[ROW][C]84[/C][C]1090[/C][C]1154.09594368309[/C][C]-64.0959436830899[/C][/ROW]
[ROW][C]85[/C][C]1220[/C][C]1153.77688227037[/C][C]66.2231177296283[/C][/ROW]
[ROW][C]86[/C][C]1370[/C][C]1414.17655619341[/C][C]-44.1765561934142[/C][/ROW]
[ROW][C]87[/C][C]1180[/C][C]1193.43695744169[/C][C]-13.4369574416864[/C][/ROW]
[ROW][C]88[/C][C]1190[/C][C]1183.33984442238[/C][C]6.66015557761671[/C][/ROW]
[ROW][C]89[/C][C]1000[/C][C]993.665845736651[/C][C]6.33415426334886[/C][/ROW]
[ROW][C]90[/C][C]1250[/C][C]1174.03014841097[/C][C]75.9698515890334[/C][/ROW]
[ROW][C]91[/C][C]1090[/C][C]1084.22744819903[/C][C]5.77255180097109[/C][/ROW]
[ROW][C]92[/C][C]1370[/C][C]1353.62273359452[/C][C]16.3772664054759[/C][/ROW]
[ROW][C]93[/C][C]980[/C][C]964.176379432231[/C][C]15.8236205677688[/C][/ROW]
[ROW][C]94[/C][C]1530[/C][C]1494.27576032563[/C][C]35.7242396743707[/C][/ROW]
[ROW][C]95[/C][C]1150[/C][C]1124.90983850646[/C][C]25.0901614935376[/C][/ROW]
[ROW][C]96[/C][C]1120[/C][C]1095.99600628439[/C][C]24.0039937156112[/C][/ROW]
[ROW][C]97[/C][C]1290[/C][C]1225.87068999629[/C][C]64.1293100037146[/C][/ROW]
[ROW][C]98[/C][C]1370[/C][C]1377.2689324889[/C][C]-7.26893248890315[/C][/ROW]
[ROW][C]99[/C][C]1130[/C][C]1187.6821377817[/C][C]-57.6821377816952[/C][/ROW]
[ROW][C]100[/C][C]1200[/C][C]1197.31951581935[/C][C]2.68048418065223[/C][/ROW]
[ROW][C]101[/C][C]910[/C][C]1007.56685319796[/C][C]-97.5668531979584[/C][/ROW]
[ROW][C]102[/C][C]1220[/C][C]1255.94867309083[/C][C]-35.9486730908293[/C][/ROW]
[ROW][C]103[/C][C]1040[/C][C]1095.51340678989[/C][C]-55.5134067898932[/C][/ROW]
[ROW][C]104[/C][C]1340[/C][C]1374.687983107[/C][C]-34.6879831069978[/C][/ROW]
[ROW][C]105[/C][C]950[/C][C]984.009187446754[/C][C]-34.0091874467537[/C][/ROW]
[ROW][C]106[/C][C]1500[/C][C]1533.06698995186[/C][C]-33.0669899518609[/C][/ROW]
[ROW][C]107[/C][C]1120[/C][C]1152.14765451455[/C][C]-32.1476545145538[/C][/ROW]
[ROW][C]108[/C][C]1150[/C][C]1121.17000256144[/C][C]28.8299974385632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124011&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124011&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
1311801190.27777777778-10.2777777777776
1410801090.8791270989-10.8791270989022
1511901197.29276197884-7.29276197883519
1611401142.89941054136-2.89941054136284
1711601158.5466267251.45337327499601
1812001201.73998055765-1.73998055764537
199801066.14856038489-86.148560384886
2012601193.7494589784766.2505410215344
2111001085.4868371948214.5131628051777
2212101127.1361697423782.8638302576333
2311501140.842497207229.15750279277518
2411401241.31397123238-101.313971232378
2511101172.85240701571-62.852407015705
2611201072.1894715768747.8105284231287
2711001182.69302153777-82.6930215377727
2811701131.7250041153838.2749958846218
2911201151.99613254951-31.9961325495058
3012501191.54107725558.4589227449992
31910972.94199285212-62.9419928521204
3212601251.598260952178.40173904782591
3310901091.42317017198-1.42317017197729
3412401200.4334215196639.5665784803416
3511301140.5472796029-10.5472796029042
3612001131.2461315736768.7538684263302
3711201102.592827604817.4071723951977
3811201112.406914143737.59308585626604
3911201093.3896169942926.6103830057066
4010701163.48866345317-93.4886634531711
4111001112.90135342533-12.9013534253304
4212301242.24021632752-12.2402163275187
43930902.71972794778227.2802720522184
4412401253.0005077449-13.0005077448993
459801082.94303215665-102.943032156653
4612701231.4183010143538.5816989856457
4711401121.8355751455318.1644248544667
4811601191.28108430601-31.2810843060142
4911601110.6084090652249.3915909347784
5012201110.89728893278109.102711067215
5111601111.7383248989748.2616751010285
5210901063.2100337229426.7899662770612
5310601093.81206962316-33.8120696231608
5412301223.76411648636.23588351370381
551070923.746901322187146.253098677813
5612401235.721530197014.27846980299478
571050977.19225865895172.807741341049
5813501268.1642679350481.8357320649641
5911001139.49431211147-39.4943121114673
6011301160.0161610975-30.0161610975001
6111701159.817782554110.1822174459023
6213601219.36765032894140.632349671056
6311501160.90068036228-10.9006803622783
6411801091.0334928631188.9665071368884
6510101062.8790237397-52.8790237396995
6611901232.85381760654-42.8538176065383
6710001071.44293823956-71.4429382395599
6812701240.8827239352629.1172760647382
699901050.68145980323-60.6814598032286
7014701349.29458344352120.70541655648
7111301101.0308962101328.9691037898685
7211501131.8348981682118.1651018317909
7311501172.18790651595-22.1879065159485
7414101360.7643615718149.2356384281866
7511901151.4761695377238.5238304622844
7611801181.13454086947-1.13454086946899
779901011.70535334118-21.7053533411818
7811701192.00873685351-22.0087368535101
7910801002.6276033402277.372396659785
8013501273.4390088899776.5609911100253
81960995.218007711652-35.2180077116523
8214901474.0590760639315.9409239360746
8311201134.20524609543-14.2052460954269
8410901154.09594368309-64.0959436830899
8512201153.7768822703766.2231177296283
8613701414.17655619341-44.1765561934142
8711801193.43695744169-13.4369574416864
8811901183.339844422386.66015557761671
891000993.6658457366516.33415426334886
9012501174.0301484109775.9698515890334
9110901084.227448199035.77255180097109
9213701353.6227335945216.3772664054759
93980964.17637943223115.8236205677688
9415301494.2757603256335.7242396743707
9511501124.9098385064625.0901614935376
9611201095.9960062843924.0039937156112
9712901225.8706899962964.1293100037146
9813701377.2689324889-7.26893248890315
9911301187.6821377817-57.6821377816952
10012001197.319515819352.68048418065223
1019101007.56685319796-97.5668531979584
10212201255.94867309083-35.9486730908293
10310401095.51340678989-55.5134067898932
10413401374.687983107-34.6879831069978
105950984.009187446754-34.0091874467537
10615001533.06698995186-33.0669899518609
10711201152.14765451455-32.1476545145538
10811501121.1700025614428.8299974385632







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091290.410440583931188.172335187521392.64854598034
1101369.99442863311267.749545429321472.23931183688
1111130.099632960291027.846258366751232.35300755383
1121199.671979532431097.408207384541301.93575168033
113910.257225688079807.9809574171141012.53349395904
1141220.35168970171118.060634550451322.64274485294
1151040.69395391751938.3856291970431143.00227863797
1161340.901316965771238.573048356711443.22958557484
117951.149463297384848.7983851992521053.50054139552
1181501.434789048021399.057844980021603.81173311602
1191121.756231327551019.350174384031224.16228827107
1201151.50349056631049.064883930261253.94209720234

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1290.41044058393 & 1188.17233518752 & 1392.64854598034 \tabularnewline
110 & 1369.9944286331 & 1267.74954542932 & 1472.23931183688 \tabularnewline
111 & 1130.09963296029 & 1027.84625836675 & 1232.35300755383 \tabularnewline
112 & 1199.67197953243 & 1097.40820738454 & 1301.93575168033 \tabularnewline
113 & 910.257225688079 & 807.980957417114 & 1012.53349395904 \tabularnewline
114 & 1220.3516897017 & 1118.06063455045 & 1322.64274485294 \tabularnewline
115 & 1040.69395391751 & 938.385629197043 & 1143.00227863797 \tabularnewline
116 & 1340.90131696577 & 1238.57304835671 & 1443.22958557484 \tabularnewline
117 & 951.149463297384 & 848.798385199252 & 1053.50054139552 \tabularnewline
118 & 1501.43478904802 & 1399.05784498002 & 1603.81173311602 \tabularnewline
119 & 1121.75623132755 & 1019.35017438403 & 1224.16228827107 \tabularnewline
120 & 1151.5034905663 & 1049.06488393026 & 1253.94209720234 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124011&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]1290.41044058393[/C][C]1188.17233518752[/C][C]1392.64854598034[/C][/ROW]
[ROW][C]110[/C][C]1369.9944286331[/C][C]1267.74954542932[/C][C]1472.23931183688[/C][/ROW]
[ROW][C]111[/C][C]1130.09963296029[/C][C]1027.84625836675[/C][C]1232.35300755383[/C][/ROW]
[ROW][C]112[/C][C]1199.67197953243[/C][C]1097.40820738454[/C][C]1301.93575168033[/C][/ROW]
[ROW][C]113[/C][C]910.257225688079[/C][C]807.980957417114[/C][C]1012.53349395904[/C][/ROW]
[ROW][C]114[/C][C]1220.3516897017[/C][C]1118.06063455045[/C][C]1322.64274485294[/C][/ROW]
[ROW][C]115[/C][C]1040.69395391751[/C][C]938.385629197043[/C][C]1143.00227863797[/C][/ROW]
[ROW][C]116[/C][C]1340.90131696577[/C][C]1238.57304835671[/C][C]1443.22958557484[/C][/ROW]
[ROW][C]117[/C][C]951.149463297384[/C][C]848.798385199252[/C][C]1053.50054139552[/C][/ROW]
[ROW][C]118[/C][C]1501.43478904802[/C][C]1399.05784498002[/C][C]1603.81173311602[/C][/ROW]
[ROW][C]119[/C][C]1121.75623132755[/C][C]1019.35017438403[/C][C]1224.16228827107[/C][/ROW]
[ROW][C]120[/C][C]1151.5034905663[/C][C]1049.06488393026[/C][C]1253.94209720234[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124011&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124011&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
1091290.410440583931188.172335187521392.64854598034
1101369.99442863311267.749545429321472.23931183688
1111130.099632960291027.846258366751232.35300755383
1121199.671979532431097.408207384541301.93575168033
113910.257225688079807.9809574171141012.53349395904
1141220.35168970171118.060634550451322.64274485294
1151040.69395391751938.3856291970431143.00227863797
1161340.901316965771238.573048356711443.22958557484
117951.149463297384848.7983851992521053.50054139552
1181501.434789048021399.057844980021603.81173311602
1191121.756231327551019.350174384031224.16228827107
1201151.50349056631049.064883930261253.94209720234



Parameters (Session):
par1 = 12 ;
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')