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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 27 May 2015 07:57:36 +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/2015/May/27/t1432709980v873vb35eqb6kvj.htm/, Retrieved Sat, 04 May 2024 13:20:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279460, Retrieved Sat, 04 May 2024 13:20:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bootstrap Plot - Central Tendency] [] [2015-04-23 17:50:34] [f74af3e606ffe601bae5db8023a85a50]
- RMPD    [Exponential Smoothing] [] [2015-05-27 06:57:36] [bad5dfd772bc354c7f8aa9414b1d4071] [Current]
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Dataseries X:
1329
1385
1681
1591
1598
1557
1190
932
1664
1717
1567
1355
1430
1863
1868
1711
1873
2095
1379
1021
1999
2094
2026
1390
1744
2117
1823
1963
1816
1966
1309
1250
2184
2295
1870
1222
1640
2194
2179
1976
1850
2077
1658
1156
2400
2218
1802
1444
1804
1541
2206
1972
1815
1749
1492
1307
1916
2035
1855
1086
1951
1733
1868
1532
1894
1586
1247
1212
2119
1931
1649
1296
1625
1454
1562
1612
1648
1412
1219
1207
1614
1537
1497
1141
1135
1368
1203
1201
1190
1347
607
914
1606
1518
1120
910




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279460&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279460&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279460&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.162466318251236
beta0.132864661249093
gamma0.438624241690765

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.162466318251236 \tabularnewline
beta & 0.132864661249093 \tabularnewline
gamma & 0.438624241690765 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279460&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]0.162466318251236[/C][/ROW]
[ROW][C]beta[/C][C]0.132864661249093[/C][/ROW]
[ROW][C]gamma[/C][C]0.438624241690765[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279460&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279460&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
alpha0.162466318251236
beta0.132864661249093
gamma0.438624241690765







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1314301297.38278750865132.617212491347
1418631736.41286117381126.587138826187
1518681775.5762816311292.423718368882
1617111642.3332039269468.6667960730608
1718731808.2973049057864.7026950942197
1820952050.5819823408944.4180176591126
1913791403.22076968936-24.2207696893586
2010211099.10988172347-78.1098817234749
2119991938.0493372444360.9506627555679
2220942029.0594204416964.9405795583052
2320261875.27629346904150.723706530962
2413901638.79850085064-248.79850085064
2517441744.05803160016-0.0580316001614847
2621172268.68815570267-151.688155702675
2718232241.34260117625-418.342601176245
2819631968.65079093051-5.65079093051372
2918162127.20539809845-311.205398098452
3019662299.90232385046-333.902323850465
3113091485.92715960943-176.927159609435
3212501101.85216367244148.147836327561
3321842059.35681324565124.643186754348
3422952140.25820111887154.741798881133
3518702002.94867323961-132.948673239613
3612221544.61240494916-322.612404949156
3716401701.35378435438-61.3537843543752
3821942112.688465781.3115342999986
3921791997.08705932813181.912940671873
4019761958.9344644999417.0655355000615
4118501992.08426536006-142.084265360055
4220772169.81719719382-92.8171971938191
4316581436.13035458094221.869645419056
4411561224.50868791566-68.5086879156556
4524002160.32577735821239.674222641786
4622182271.74412868332-53.7441286833159
4718021984.62330993-182.623309930003
4814441434.19730477839.80269522169783
4918041757.5010696473146.498930352692
5015412272.6639313138-731.663931313795
5122062050.77670024485155.22329975515
5219721938.5655903108833.4344096891218
5318151905.97626418081-90.976264180809
5417492097.29633612934-348.296336129335
5514921447.6693312921644.3306687078393
5613071111.63389087575195.366109124254
5719162151.22964502364-235.229645023643
5820352060.13787586909-25.1378758690871
5918551739.91177179898115.088228201021
6010861331.18106929626-245.181069296257
6119511575.37010811761375.629891882394
6217331815.75422186031-82.7542218603094
6318682015.28417364628-147.284173646276
6415321815.79132704241-283.791327042411
6518941681.85164835787212.148351642129
6615861810.35350933393-224.353509333927
6712471354.48477181037-107.484771810367
6812121068.44190530663143.55809469337
6921191843.11740515411275.882594845889
7019311910.5616266188520.4383733811469
7116491666.87537335907-17.8753733590738
7212961142.81889530367153.181104696325
7316251670.41454378358-45.414543783583
7414541673.35671269195-219.356712691946
7515621808.81866116684-246.818661166836
7616121555.0057774090656.9942225909438
7716481653.25372154206-5.25372154206434
7814121586.8847713835-174.884771383499
7912191209.238439549719.76156045028824
8012071045.70256848906161.297431510941
8116141820.55522393566-206.555223935656
8215371714.28294482372-177.282944823723
8314971445.0487022752451.9512977247646
8411411043.295103959497.7048960406
8511351419.92961849867-284.929618498667
8613681311.495861906456.5041380935957
8712031443.43302905474-240.433029054737
8812011306.38701822004-105.387018220038
8911901326.20779047328-136.207790473284
9013471183.58538145815163.414618541852
91607972.495869824646-365.495869824646
92914812.7160999657101.2839000343
9316061250.31906666772355.680933332279
9415181244.13167977876273.86832022124
9511201158.42569125398-38.4256912539834
96910838.16728213725671.8327178627441

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1430 & 1297.38278750865 & 132.617212491347 \tabularnewline
14 & 1863 & 1736.41286117381 & 126.587138826187 \tabularnewline
15 & 1868 & 1775.57628163112 & 92.423718368882 \tabularnewline
16 & 1711 & 1642.33320392694 & 68.6667960730608 \tabularnewline
17 & 1873 & 1808.29730490578 & 64.7026950942197 \tabularnewline
18 & 2095 & 2050.58198234089 & 44.4180176591126 \tabularnewline
19 & 1379 & 1403.22076968936 & -24.2207696893586 \tabularnewline
20 & 1021 & 1099.10988172347 & -78.1098817234749 \tabularnewline
21 & 1999 & 1938.04933724443 & 60.9506627555679 \tabularnewline
22 & 2094 & 2029.05942044169 & 64.9405795583052 \tabularnewline
23 & 2026 & 1875.27629346904 & 150.723706530962 \tabularnewline
24 & 1390 & 1638.79850085064 & -248.79850085064 \tabularnewline
25 & 1744 & 1744.05803160016 & -0.0580316001614847 \tabularnewline
26 & 2117 & 2268.68815570267 & -151.688155702675 \tabularnewline
27 & 1823 & 2241.34260117625 & -418.342601176245 \tabularnewline
28 & 1963 & 1968.65079093051 & -5.65079093051372 \tabularnewline
29 & 1816 & 2127.20539809845 & -311.205398098452 \tabularnewline
30 & 1966 & 2299.90232385046 & -333.902323850465 \tabularnewline
31 & 1309 & 1485.92715960943 & -176.927159609435 \tabularnewline
32 & 1250 & 1101.85216367244 & 148.147836327561 \tabularnewline
33 & 2184 & 2059.35681324565 & 124.643186754348 \tabularnewline
34 & 2295 & 2140.25820111887 & 154.741798881133 \tabularnewline
35 & 1870 & 2002.94867323961 & -132.948673239613 \tabularnewline
36 & 1222 & 1544.61240494916 & -322.612404949156 \tabularnewline
37 & 1640 & 1701.35378435438 & -61.3537843543752 \tabularnewline
38 & 2194 & 2112.6884657 & 81.3115342999986 \tabularnewline
39 & 2179 & 1997.08705932813 & 181.912940671873 \tabularnewline
40 & 1976 & 1958.93446449994 & 17.0655355000615 \tabularnewline
41 & 1850 & 1992.08426536006 & -142.084265360055 \tabularnewline
42 & 2077 & 2169.81719719382 & -92.8171971938191 \tabularnewline
43 & 1658 & 1436.13035458094 & 221.869645419056 \tabularnewline
44 & 1156 & 1224.50868791566 & -68.5086879156556 \tabularnewline
45 & 2400 & 2160.32577735821 & 239.674222641786 \tabularnewline
46 & 2218 & 2271.74412868332 & -53.7441286833159 \tabularnewline
47 & 1802 & 1984.62330993 & -182.623309930003 \tabularnewline
48 & 1444 & 1434.1973047783 & 9.80269522169783 \tabularnewline
49 & 1804 & 1757.50106964731 & 46.498930352692 \tabularnewline
50 & 1541 & 2272.6639313138 & -731.663931313795 \tabularnewline
51 & 2206 & 2050.77670024485 & 155.22329975515 \tabularnewline
52 & 1972 & 1938.56559031088 & 33.4344096891218 \tabularnewline
53 & 1815 & 1905.97626418081 & -90.976264180809 \tabularnewline
54 & 1749 & 2097.29633612934 & -348.296336129335 \tabularnewline
55 & 1492 & 1447.66933129216 & 44.3306687078393 \tabularnewline
56 & 1307 & 1111.63389087575 & 195.366109124254 \tabularnewline
57 & 1916 & 2151.22964502364 & -235.229645023643 \tabularnewline
58 & 2035 & 2060.13787586909 & -25.1378758690871 \tabularnewline
59 & 1855 & 1739.91177179898 & 115.088228201021 \tabularnewline
60 & 1086 & 1331.18106929626 & -245.181069296257 \tabularnewline
61 & 1951 & 1575.37010811761 & 375.629891882394 \tabularnewline
62 & 1733 & 1815.75422186031 & -82.7542218603094 \tabularnewline
63 & 1868 & 2015.28417364628 & -147.284173646276 \tabularnewline
64 & 1532 & 1815.79132704241 & -283.791327042411 \tabularnewline
65 & 1894 & 1681.85164835787 & 212.148351642129 \tabularnewline
66 & 1586 & 1810.35350933393 & -224.353509333927 \tabularnewline
67 & 1247 & 1354.48477181037 & -107.484771810367 \tabularnewline
68 & 1212 & 1068.44190530663 & 143.55809469337 \tabularnewline
69 & 2119 & 1843.11740515411 & 275.882594845889 \tabularnewline
70 & 1931 & 1910.56162661885 & 20.4383733811469 \tabularnewline
71 & 1649 & 1666.87537335907 & -17.8753733590738 \tabularnewline
72 & 1296 & 1142.81889530367 & 153.181104696325 \tabularnewline
73 & 1625 & 1670.41454378358 & -45.414543783583 \tabularnewline
74 & 1454 & 1673.35671269195 & -219.356712691946 \tabularnewline
75 & 1562 & 1808.81866116684 & -246.818661166836 \tabularnewline
76 & 1612 & 1555.00577740906 & 56.9942225909438 \tabularnewline
77 & 1648 & 1653.25372154206 & -5.25372154206434 \tabularnewline
78 & 1412 & 1586.8847713835 & -174.884771383499 \tabularnewline
79 & 1219 & 1209.23843954971 & 9.76156045028824 \tabularnewline
80 & 1207 & 1045.70256848906 & 161.297431510941 \tabularnewline
81 & 1614 & 1820.55522393566 & -206.555223935656 \tabularnewline
82 & 1537 & 1714.28294482372 & -177.282944823723 \tabularnewline
83 & 1497 & 1445.04870227524 & 51.9512977247646 \tabularnewline
84 & 1141 & 1043.2951039594 & 97.7048960406 \tabularnewline
85 & 1135 & 1419.92961849867 & -284.929618498667 \tabularnewline
86 & 1368 & 1311.4958619064 & 56.5041380935957 \tabularnewline
87 & 1203 & 1443.43302905474 & -240.433029054737 \tabularnewline
88 & 1201 & 1306.38701822004 & -105.387018220038 \tabularnewline
89 & 1190 & 1326.20779047328 & -136.207790473284 \tabularnewline
90 & 1347 & 1183.58538145815 & 163.414618541852 \tabularnewline
91 & 607 & 972.495869824646 & -365.495869824646 \tabularnewline
92 & 914 & 812.7160999657 & 101.2839000343 \tabularnewline
93 & 1606 & 1250.31906666772 & 355.680933332279 \tabularnewline
94 & 1518 & 1244.13167977876 & 273.86832022124 \tabularnewline
95 & 1120 & 1158.42569125398 & -38.4256912539834 \tabularnewline
96 & 910 & 838.167282137256 & 71.8327178627441 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279460&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]1430[/C][C]1297.38278750865[/C][C]132.617212491347[/C][/ROW]
[ROW][C]14[/C][C]1863[/C][C]1736.41286117381[/C][C]126.587138826187[/C][/ROW]
[ROW][C]15[/C][C]1868[/C][C]1775.57628163112[/C][C]92.423718368882[/C][/ROW]
[ROW][C]16[/C][C]1711[/C][C]1642.33320392694[/C][C]68.6667960730608[/C][/ROW]
[ROW][C]17[/C][C]1873[/C][C]1808.29730490578[/C][C]64.7026950942197[/C][/ROW]
[ROW][C]18[/C][C]2095[/C][C]2050.58198234089[/C][C]44.4180176591126[/C][/ROW]
[ROW][C]19[/C][C]1379[/C][C]1403.22076968936[/C][C]-24.2207696893586[/C][/ROW]
[ROW][C]20[/C][C]1021[/C][C]1099.10988172347[/C][C]-78.1098817234749[/C][/ROW]
[ROW][C]21[/C][C]1999[/C][C]1938.04933724443[/C][C]60.9506627555679[/C][/ROW]
[ROW][C]22[/C][C]2094[/C][C]2029.05942044169[/C][C]64.9405795583052[/C][/ROW]
[ROW][C]23[/C][C]2026[/C][C]1875.27629346904[/C][C]150.723706530962[/C][/ROW]
[ROW][C]24[/C][C]1390[/C][C]1638.79850085064[/C][C]-248.79850085064[/C][/ROW]
[ROW][C]25[/C][C]1744[/C][C]1744.05803160016[/C][C]-0.0580316001614847[/C][/ROW]
[ROW][C]26[/C][C]2117[/C][C]2268.68815570267[/C][C]-151.688155702675[/C][/ROW]
[ROW][C]27[/C][C]1823[/C][C]2241.34260117625[/C][C]-418.342601176245[/C][/ROW]
[ROW][C]28[/C][C]1963[/C][C]1968.65079093051[/C][C]-5.65079093051372[/C][/ROW]
[ROW][C]29[/C][C]1816[/C][C]2127.20539809845[/C][C]-311.205398098452[/C][/ROW]
[ROW][C]30[/C][C]1966[/C][C]2299.90232385046[/C][C]-333.902323850465[/C][/ROW]
[ROW][C]31[/C][C]1309[/C][C]1485.92715960943[/C][C]-176.927159609435[/C][/ROW]
[ROW][C]32[/C][C]1250[/C][C]1101.85216367244[/C][C]148.147836327561[/C][/ROW]
[ROW][C]33[/C][C]2184[/C][C]2059.35681324565[/C][C]124.643186754348[/C][/ROW]
[ROW][C]34[/C][C]2295[/C][C]2140.25820111887[/C][C]154.741798881133[/C][/ROW]
[ROW][C]35[/C][C]1870[/C][C]2002.94867323961[/C][C]-132.948673239613[/C][/ROW]
[ROW][C]36[/C][C]1222[/C][C]1544.61240494916[/C][C]-322.612404949156[/C][/ROW]
[ROW][C]37[/C][C]1640[/C][C]1701.35378435438[/C][C]-61.3537843543752[/C][/ROW]
[ROW][C]38[/C][C]2194[/C][C]2112.6884657[/C][C]81.3115342999986[/C][/ROW]
[ROW][C]39[/C][C]2179[/C][C]1997.08705932813[/C][C]181.912940671873[/C][/ROW]
[ROW][C]40[/C][C]1976[/C][C]1958.93446449994[/C][C]17.0655355000615[/C][/ROW]
[ROW][C]41[/C][C]1850[/C][C]1992.08426536006[/C][C]-142.084265360055[/C][/ROW]
[ROW][C]42[/C][C]2077[/C][C]2169.81719719382[/C][C]-92.8171971938191[/C][/ROW]
[ROW][C]43[/C][C]1658[/C][C]1436.13035458094[/C][C]221.869645419056[/C][/ROW]
[ROW][C]44[/C][C]1156[/C][C]1224.50868791566[/C][C]-68.5086879156556[/C][/ROW]
[ROW][C]45[/C][C]2400[/C][C]2160.32577735821[/C][C]239.674222641786[/C][/ROW]
[ROW][C]46[/C][C]2218[/C][C]2271.74412868332[/C][C]-53.7441286833159[/C][/ROW]
[ROW][C]47[/C][C]1802[/C][C]1984.62330993[/C][C]-182.623309930003[/C][/ROW]
[ROW][C]48[/C][C]1444[/C][C]1434.1973047783[/C][C]9.80269522169783[/C][/ROW]
[ROW][C]49[/C][C]1804[/C][C]1757.50106964731[/C][C]46.498930352692[/C][/ROW]
[ROW][C]50[/C][C]1541[/C][C]2272.6639313138[/C][C]-731.663931313795[/C][/ROW]
[ROW][C]51[/C][C]2206[/C][C]2050.77670024485[/C][C]155.22329975515[/C][/ROW]
[ROW][C]52[/C][C]1972[/C][C]1938.56559031088[/C][C]33.4344096891218[/C][/ROW]
[ROW][C]53[/C][C]1815[/C][C]1905.97626418081[/C][C]-90.976264180809[/C][/ROW]
[ROW][C]54[/C][C]1749[/C][C]2097.29633612934[/C][C]-348.296336129335[/C][/ROW]
[ROW][C]55[/C][C]1492[/C][C]1447.66933129216[/C][C]44.3306687078393[/C][/ROW]
[ROW][C]56[/C][C]1307[/C][C]1111.63389087575[/C][C]195.366109124254[/C][/ROW]
[ROW][C]57[/C][C]1916[/C][C]2151.22964502364[/C][C]-235.229645023643[/C][/ROW]
[ROW][C]58[/C][C]2035[/C][C]2060.13787586909[/C][C]-25.1378758690871[/C][/ROW]
[ROW][C]59[/C][C]1855[/C][C]1739.91177179898[/C][C]115.088228201021[/C][/ROW]
[ROW][C]60[/C][C]1086[/C][C]1331.18106929626[/C][C]-245.181069296257[/C][/ROW]
[ROW][C]61[/C][C]1951[/C][C]1575.37010811761[/C][C]375.629891882394[/C][/ROW]
[ROW][C]62[/C][C]1733[/C][C]1815.75422186031[/C][C]-82.7542218603094[/C][/ROW]
[ROW][C]63[/C][C]1868[/C][C]2015.28417364628[/C][C]-147.284173646276[/C][/ROW]
[ROW][C]64[/C][C]1532[/C][C]1815.79132704241[/C][C]-283.791327042411[/C][/ROW]
[ROW][C]65[/C][C]1894[/C][C]1681.85164835787[/C][C]212.148351642129[/C][/ROW]
[ROW][C]66[/C][C]1586[/C][C]1810.35350933393[/C][C]-224.353509333927[/C][/ROW]
[ROW][C]67[/C][C]1247[/C][C]1354.48477181037[/C][C]-107.484771810367[/C][/ROW]
[ROW][C]68[/C][C]1212[/C][C]1068.44190530663[/C][C]143.55809469337[/C][/ROW]
[ROW][C]69[/C][C]2119[/C][C]1843.11740515411[/C][C]275.882594845889[/C][/ROW]
[ROW][C]70[/C][C]1931[/C][C]1910.56162661885[/C][C]20.4383733811469[/C][/ROW]
[ROW][C]71[/C][C]1649[/C][C]1666.87537335907[/C][C]-17.8753733590738[/C][/ROW]
[ROW][C]72[/C][C]1296[/C][C]1142.81889530367[/C][C]153.181104696325[/C][/ROW]
[ROW][C]73[/C][C]1625[/C][C]1670.41454378358[/C][C]-45.414543783583[/C][/ROW]
[ROW][C]74[/C][C]1454[/C][C]1673.35671269195[/C][C]-219.356712691946[/C][/ROW]
[ROW][C]75[/C][C]1562[/C][C]1808.81866116684[/C][C]-246.818661166836[/C][/ROW]
[ROW][C]76[/C][C]1612[/C][C]1555.00577740906[/C][C]56.9942225909438[/C][/ROW]
[ROW][C]77[/C][C]1648[/C][C]1653.25372154206[/C][C]-5.25372154206434[/C][/ROW]
[ROW][C]78[/C][C]1412[/C][C]1586.8847713835[/C][C]-174.884771383499[/C][/ROW]
[ROW][C]79[/C][C]1219[/C][C]1209.23843954971[/C][C]9.76156045028824[/C][/ROW]
[ROW][C]80[/C][C]1207[/C][C]1045.70256848906[/C][C]161.297431510941[/C][/ROW]
[ROW][C]81[/C][C]1614[/C][C]1820.55522393566[/C][C]-206.555223935656[/C][/ROW]
[ROW][C]82[/C][C]1537[/C][C]1714.28294482372[/C][C]-177.282944823723[/C][/ROW]
[ROW][C]83[/C][C]1497[/C][C]1445.04870227524[/C][C]51.9512977247646[/C][/ROW]
[ROW][C]84[/C][C]1141[/C][C]1043.2951039594[/C][C]97.7048960406[/C][/ROW]
[ROW][C]85[/C][C]1135[/C][C]1419.92961849867[/C][C]-284.929618498667[/C][/ROW]
[ROW][C]86[/C][C]1368[/C][C]1311.4958619064[/C][C]56.5041380935957[/C][/ROW]
[ROW][C]87[/C][C]1203[/C][C]1443.43302905474[/C][C]-240.433029054737[/C][/ROW]
[ROW][C]88[/C][C]1201[/C][C]1306.38701822004[/C][C]-105.387018220038[/C][/ROW]
[ROW][C]89[/C][C]1190[/C][C]1326.20779047328[/C][C]-136.207790473284[/C][/ROW]
[ROW][C]90[/C][C]1347[/C][C]1183.58538145815[/C][C]163.414618541852[/C][/ROW]
[ROW][C]91[/C][C]607[/C][C]972.495869824646[/C][C]-365.495869824646[/C][/ROW]
[ROW][C]92[/C][C]914[/C][C]812.7160999657[/C][C]101.2839000343[/C][/ROW]
[ROW][C]93[/C][C]1606[/C][C]1250.31906666772[/C][C]355.680933332279[/C][/ROW]
[ROW][C]94[/C][C]1518[/C][C]1244.13167977876[/C][C]273.86832022124[/C][/ROW]
[ROW][C]95[/C][C]1120[/C][C]1158.42569125398[/C][C]-38.4256912539834[/C][/ROW]
[ROW][C]96[/C][C]910[/C][C]838.167282137256[/C][C]71.8327178627441[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279460&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279460&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
1314301297.38278750865132.617212491347
1418631736.41286117381126.587138826187
1518681775.5762816311292.423718368882
1617111642.3332039269468.6667960730608
1718731808.2973049057864.7026950942197
1820952050.5819823408944.4180176591126
1913791403.22076968936-24.2207696893586
2010211099.10988172347-78.1098817234749
2119991938.0493372444360.9506627555679
2220942029.0594204416964.9405795583052
2320261875.27629346904150.723706530962
2413901638.79850085064-248.79850085064
2517441744.05803160016-0.0580316001614847
2621172268.68815570267-151.688155702675
2718232241.34260117625-418.342601176245
2819631968.65079093051-5.65079093051372
2918162127.20539809845-311.205398098452
3019662299.90232385046-333.902323850465
3113091485.92715960943-176.927159609435
3212501101.85216367244148.147836327561
3321842059.35681324565124.643186754348
3422952140.25820111887154.741798881133
3518702002.94867323961-132.948673239613
3612221544.61240494916-322.612404949156
3716401701.35378435438-61.3537843543752
3821942112.688465781.3115342999986
3921791997.08705932813181.912940671873
4019761958.9344644999417.0655355000615
4118501992.08426536006-142.084265360055
4220772169.81719719382-92.8171971938191
4316581436.13035458094221.869645419056
4411561224.50868791566-68.5086879156556
4524002160.32577735821239.674222641786
4622182271.74412868332-53.7441286833159
4718021984.62330993-182.623309930003
4814441434.19730477839.80269522169783
4918041757.5010696473146.498930352692
5015412272.6639313138-731.663931313795
5122062050.77670024485155.22329975515
5219721938.5655903108833.4344096891218
5318151905.97626418081-90.976264180809
5417492097.29633612934-348.296336129335
5514921447.6693312921644.3306687078393
5613071111.63389087575195.366109124254
5719162151.22964502364-235.229645023643
5820352060.13787586909-25.1378758690871
5918551739.91177179898115.088228201021
6010861331.18106929626-245.181069296257
6119511575.37010811761375.629891882394
6217331815.75422186031-82.7542218603094
6318682015.28417364628-147.284173646276
6415321815.79132704241-283.791327042411
6518941681.85164835787212.148351642129
6615861810.35350933393-224.353509333927
6712471354.48477181037-107.484771810367
6812121068.44190530663143.55809469337
6921191843.11740515411275.882594845889
7019311910.5616266188520.4383733811469
7116491666.87537335907-17.8753733590738
7212961142.81889530367153.181104696325
7316251670.41454378358-45.414543783583
7414541673.35671269195-219.356712691946
7515621808.81866116684-246.818661166836
7616121555.0057774090656.9942225909438
7716481653.25372154206-5.25372154206434
7814121586.8847713835-174.884771383499
7912191209.238439549719.76156045028824
8012071045.70256848906161.297431510941
8116141820.55522393566-206.555223935656
8215371714.28294482372-177.282944823723
8314971445.0487022752451.9512977247646
8411411043.295103959497.7048960406
8511351419.92961849867-284.929618498667
8613681311.495861906456.5041380935957
8712031443.43302905474-240.433029054737
8812011306.38701822004-105.387018220038
8911901326.20779047328-136.207790473284
9013471183.58538145815163.414618541852
91607972.495869824646-365.495869824646
92914812.7160999657101.2839000343
9316061250.31906666772355.680933332279
9415181244.13167977876273.86832022124
9511201158.42569125398-38.4256912539834
96910838.16728213725671.8327178627441







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
971010.70527780212810.9734671438831210.43708846036
981058.33636029998845.3727057089021271.30001489106
991063.31715059778835.1815619765251291.45273921903
1001024.22382344976781.5075141994431266.94013270008
1011047.07926837104782.129552339241312.02898440285
1021042.69818551249755.6113293177011329.78504170728
103682.256033102355428.112269019435936.399797185275
104753.042262548025465.0283626918861041.05616240416
1051206.74775057015772.8336427849061640.6618583554
1061127.95445092453678.131387449431577.77751439964
107926.517169988762507.2420829569211345.7922570206
108702.158126246218391.2842113222551013.03204117018

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 1010.70527780212 & 810.973467143883 & 1210.43708846036 \tabularnewline
98 & 1058.33636029998 & 845.372705708902 & 1271.30001489106 \tabularnewline
99 & 1063.31715059778 & 835.181561976525 & 1291.45273921903 \tabularnewline
100 & 1024.22382344976 & 781.507514199443 & 1266.94013270008 \tabularnewline
101 & 1047.07926837104 & 782.12955233924 & 1312.02898440285 \tabularnewline
102 & 1042.69818551249 & 755.611329317701 & 1329.78504170728 \tabularnewline
103 & 682.256033102355 & 428.112269019435 & 936.399797185275 \tabularnewline
104 & 753.042262548025 & 465.028362691886 & 1041.05616240416 \tabularnewline
105 & 1206.74775057015 & 772.833642784906 & 1640.6618583554 \tabularnewline
106 & 1127.95445092453 & 678.13138744943 & 1577.77751439964 \tabularnewline
107 & 926.517169988762 & 507.242082956921 & 1345.7922570206 \tabularnewline
108 & 702.158126246218 & 391.284211322255 & 1013.03204117018 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279460&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]97[/C][C]1010.70527780212[/C][C]810.973467143883[/C][C]1210.43708846036[/C][/ROW]
[ROW][C]98[/C][C]1058.33636029998[/C][C]845.372705708902[/C][C]1271.30001489106[/C][/ROW]
[ROW][C]99[/C][C]1063.31715059778[/C][C]835.181561976525[/C][C]1291.45273921903[/C][/ROW]
[ROW][C]100[/C][C]1024.22382344976[/C][C]781.507514199443[/C][C]1266.94013270008[/C][/ROW]
[ROW][C]101[/C][C]1047.07926837104[/C][C]782.12955233924[/C][C]1312.02898440285[/C][/ROW]
[ROW][C]102[/C][C]1042.69818551249[/C][C]755.611329317701[/C][C]1329.78504170728[/C][/ROW]
[ROW][C]103[/C][C]682.256033102355[/C][C]428.112269019435[/C][C]936.399797185275[/C][/ROW]
[ROW][C]104[/C][C]753.042262548025[/C][C]465.028362691886[/C][C]1041.05616240416[/C][/ROW]
[ROW][C]105[/C][C]1206.74775057015[/C][C]772.833642784906[/C][C]1640.6618583554[/C][/ROW]
[ROW][C]106[/C][C]1127.95445092453[/C][C]678.13138744943[/C][C]1577.77751439964[/C][/ROW]
[ROW][C]107[/C][C]926.517169988762[/C][C]507.242082956921[/C][C]1345.7922570206[/C][/ROW]
[ROW][C]108[/C][C]702.158126246218[/C][C]391.284211322255[/C][C]1013.03204117018[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279460&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279460&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
971010.70527780212810.9734671438831210.43708846036
981058.33636029998845.3727057089021271.30001489106
991063.31715059778835.1815619765251291.45273921903
1001024.22382344976781.5075141994431266.94013270008
1011047.07926837104782.129552339241312.02898440285
1021042.69818551249755.6113293177011329.78504170728
103682.256033102355428.112269019435936.399797185275
104753.042262548025465.0283626918861041.05616240416
1051206.74775057015772.8336427849061640.6618583554
1061127.95445092453678.131387449431577.77751439964
107926.517169988762507.2420829569211345.7922570206
108702.158126246218391.2842113222551013.03204117018



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')