Free Statistics

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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 Dec 2016 15:08:14 +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/Dec/16/t148189732238fdsoxma6hywpt.htm/, Retrieved Fri, 03 May 2024 01:19:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300287, Retrieved Fri, 03 May 2024 01:19:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Exponential Smoothing] [] [2016-12-16 14:08:14] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataseries X:
4838
5531
5367.5
5013.5
5959.5
6334
5919
6248.5
5701
6530.5
7145.5
6819
7037
7809
6300
7143.5
7234.5
6567.5
6090
5654
6608
7566
6352.5
8592
6631.5
6852
7538
8407
7541
9904.5
9371
8091.5
8303.5
8617.5
10453.5
9990.5
8337
8336.5
10345.5
11060.5
9384.5
8357
8366
8404.5
8068
6518.5
9355
7298.5
8012
7189
6992
10277
7146.5
7102
7257
7088.5
9070.5
9606.5
6280
6248
6311.5
6434
7096.5
6601.5
5905
7006.5
6113.5
6911.5
6450.5
6504
7710
7045
6302.5
6810
7567
7051
7820
8514
8180
8140
8349.5
8474
7880
8130.5
8020.5
8232.5
8457
7468.5
6763
7877.5
7438
7131
7270
7203.5
7010
6564.5
6734.5
7571.5
6491
6489.5
6883.5
6958.5
5731.5
7157.5
6336
6862.5
7175.5
7408.5
7052
6685.5
7098.5
7048
7017
7099
7310
7868




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300287&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300287&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300287&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.342569555142985
beta0.256595190287573
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.342569555142985 \tabularnewline
beta & 0.256595190287573 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300287&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]0.342569555142985[/C][/ROW]
[ROW][C]beta[/C][C]0.256595190287573[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300287&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300287&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
alpha0.342569555142985
beta0.256595190287573
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
35367.56224-856.5
45013.56548.30136980846-1534.80136980846
55959.56505.32569125074-545.825691250736
663346753.16396467618-419.163964676182
759197007.54746427507-1088.54746427507
86248.56936.93538335049-688.43538335049
957016942.87487932905-1241.87487932905
106530.56650.05994005709-119.559940057091
117145.56731.20640825638414.293591743621
1268197031.65195444767-212.651954447673
1370377098.63257543695-61.6325754369509
1478097211.93022974399597.069770256011
1563007603.36270152345-1303.36270152345
167143.57229.19706943977-85.6970694397651
177234.57264.63369314695-30.1336931469496
186567.57316.45583509243-748.955835092426
1960907056.19690437388-966.196904373884
2056546636.58744658134-982.587446581338
2166086124.99198089771483.008019102286
2275666157.922127996741408.07787200326
236352.56631.52548202734-279.025482027339
2485926502.651776321282089.34822367872
256631.57368.76805853877-737.268058538765
2668527201.76454255675-349.764542556753
2775387136.7630357046401.236964295401
2884077364.301192306591042.69880769341
2975417903.23964522356-362.239645223564
309904.57929.047476630611975.45252336939
3193718929.3231097399441.676890260096
328091.59442.99805611369-1351.49805611369
338303.59223.58688188062-920.086881880623
348617.59071.08684044972-453.586840449716
3510453.59038.524456227251414.97554377275
369990.59770.45341274777220.046587252231
37833710112.3785573458-1775.37855734576
388336.59614.67300416854-1278.17300416854
3910345.59174.941355956221170.55864404378
4011060.59676.96471411851383.5352858815
419384.510373.5624896309-989.062489630942
42835710170.4402262215-1813.44022622148
4383669525.50676924307-1159.50676924307
448404.59002.66838931816-598.168389318158
4580688619.54743006864-551.547430068638
466518.58203.91543525186-1685.41543525186
4793557251.703900025782103.29609997422
487298.57782.27289317507-483.772893175065
4980127384.06635240173627.933647598275
5071897421.8930619802-232.893061980199
5169927144.35505249298-152.355052492979
52102776881.014644941433395.98535505857
537146.58131.74051882608-985.24051882608
5471027794.98747741358-692.987477413575
5572577497.43665291284-240.436652912844
567088.57333.78117246221-245.281172462213
579070.57146.905475020981923.59452497902
589606.57872.107789631841734.39221036816
5962808684.95117557974-2404.95117557974
6062487868.38224201527-1620.38224201527
616311.57178.14838497236-866.648384972364
6264346669.94093352804-235.940933528036
637096.56357.05504394915739.444956050852
646601.56443.30513348883158.19486651117
6559056344.34223615553-439.342236155531
667006.56002.062389857521004.43761014248
676113.56242.66933689517-129.169336895167
686911.56083.58285205381827.917147946194
696450.56325.14038347772125.359616522283
7065046337.04241732669166.957582673312
7177106377.870503311241332.12949668876
7270456934.94746117555110.05253882445
736302.57083.05186450654-780.551864506536
7468106857.4504776045-47.4504776045014
7575676878.816329032688.183670967996
7670517212.68055820412-161.680558204122
7778207241.19518050322578.804819496778
7885147574.25547694235939.744523057647
7981808113.567868383566.4321316164951
8081408359.54951970405-219.549519704049
818349.58488.26378789507-138.763787895074
8284748632.45521541321-158.455215413205
8378808755.97247652774-875.972476527741
848130.58556.69069868961-426.190698689612
858020.58474.02757737751-453.527577377508
868232.58342.13382856038-109.633828560376
8784578318.41060836333138.589391636666
887468.58391.90334943833-923.403349438326
8967638020.42098526266-1257.42098526266
907877.57423.98490571527453.515094284727
9174387453.52818566536-15.5281856653583
9271317321.02656393931-190.026563939306
9372707112.0434523435157.956547656497
947203.57036.15340957928167.346590420719
9570106978.1901594063331.8098405936744
966564.56876.59228421051-312.092284210507
976734.56629.75056870993104.749431290069
987571.56534.913787357621036.58621264238
9964916850.41360814241-359.413608142409
1006489.56656.09332411461-166.593324114615
1016883.56513.18356257901370.316437420987
1026958.56586.75418366169371.745816338305
1035731.56693.49155573837-961.991555738366
1047157.56258.77041626864898.729583731363
10563366540.47554821202-204.475548212021
1066862.56426.28244053926436.217559460741
1077175.56569.91555087387605.584449126129
1087408.56824.8005039431583.699496056904
10970527123.49651647773-71.4965164777286
1106685.57191.45765711096-505.957657110956
1117098.57066.1110997870332.3889002129717
11270487128.03272251428-80.0327225142773
11370177144.40710757567-127.407107575668
11470997133.35316924939-34.3531692493889
11573107151.15697519596158.843024804045
11678687249.10648733811618.893512661894

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5367.5 & 6224 & -856.5 \tabularnewline
4 & 5013.5 & 6548.30136980846 & -1534.80136980846 \tabularnewline
5 & 5959.5 & 6505.32569125074 & -545.825691250736 \tabularnewline
6 & 6334 & 6753.16396467618 & -419.163964676182 \tabularnewline
7 & 5919 & 7007.54746427507 & -1088.54746427507 \tabularnewline
8 & 6248.5 & 6936.93538335049 & -688.43538335049 \tabularnewline
9 & 5701 & 6942.87487932905 & -1241.87487932905 \tabularnewline
10 & 6530.5 & 6650.05994005709 & -119.559940057091 \tabularnewline
11 & 7145.5 & 6731.20640825638 & 414.293591743621 \tabularnewline
12 & 6819 & 7031.65195444767 & -212.651954447673 \tabularnewline
13 & 7037 & 7098.63257543695 & -61.6325754369509 \tabularnewline
14 & 7809 & 7211.93022974399 & 597.069770256011 \tabularnewline
15 & 6300 & 7603.36270152345 & -1303.36270152345 \tabularnewline
16 & 7143.5 & 7229.19706943977 & -85.6970694397651 \tabularnewline
17 & 7234.5 & 7264.63369314695 & -30.1336931469496 \tabularnewline
18 & 6567.5 & 7316.45583509243 & -748.955835092426 \tabularnewline
19 & 6090 & 7056.19690437388 & -966.196904373884 \tabularnewline
20 & 5654 & 6636.58744658134 & -982.587446581338 \tabularnewline
21 & 6608 & 6124.99198089771 & 483.008019102286 \tabularnewline
22 & 7566 & 6157.92212799674 & 1408.07787200326 \tabularnewline
23 & 6352.5 & 6631.52548202734 & -279.025482027339 \tabularnewline
24 & 8592 & 6502.65177632128 & 2089.34822367872 \tabularnewline
25 & 6631.5 & 7368.76805853877 & -737.268058538765 \tabularnewline
26 & 6852 & 7201.76454255675 & -349.764542556753 \tabularnewline
27 & 7538 & 7136.7630357046 & 401.236964295401 \tabularnewline
28 & 8407 & 7364.30119230659 & 1042.69880769341 \tabularnewline
29 & 7541 & 7903.23964522356 & -362.239645223564 \tabularnewline
30 & 9904.5 & 7929.04747663061 & 1975.45252336939 \tabularnewline
31 & 9371 & 8929.3231097399 & 441.676890260096 \tabularnewline
32 & 8091.5 & 9442.99805611369 & -1351.49805611369 \tabularnewline
33 & 8303.5 & 9223.58688188062 & -920.086881880623 \tabularnewline
34 & 8617.5 & 9071.08684044972 & -453.586840449716 \tabularnewline
35 & 10453.5 & 9038.52445622725 & 1414.97554377275 \tabularnewline
36 & 9990.5 & 9770.45341274777 & 220.046587252231 \tabularnewline
37 & 8337 & 10112.3785573458 & -1775.37855734576 \tabularnewline
38 & 8336.5 & 9614.67300416854 & -1278.17300416854 \tabularnewline
39 & 10345.5 & 9174.94135595622 & 1170.55864404378 \tabularnewline
40 & 11060.5 & 9676.9647141185 & 1383.5352858815 \tabularnewline
41 & 9384.5 & 10373.5624896309 & -989.062489630942 \tabularnewline
42 & 8357 & 10170.4402262215 & -1813.44022622148 \tabularnewline
43 & 8366 & 9525.50676924307 & -1159.50676924307 \tabularnewline
44 & 8404.5 & 9002.66838931816 & -598.168389318158 \tabularnewline
45 & 8068 & 8619.54743006864 & -551.547430068638 \tabularnewline
46 & 6518.5 & 8203.91543525186 & -1685.41543525186 \tabularnewline
47 & 9355 & 7251.70390002578 & 2103.29609997422 \tabularnewline
48 & 7298.5 & 7782.27289317507 & -483.772893175065 \tabularnewline
49 & 8012 & 7384.06635240173 & 627.933647598275 \tabularnewline
50 & 7189 & 7421.8930619802 & -232.893061980199 \tabularnewline
51 & 6992 & 7144.35505249298 & -152.355052492979 \tabularnewline
52 & 10277 & 6881.01464494143 & 3395.98535505857 \tabularnewline
53 & 7146.5 & 8131.74051882608 & -985.24051882608 \tabularnewline
54 & 7102 & 7794.98747741358 & -692.987477413575 \tabularnewline
55 & 7257 & 7497.43665291284 & -240.436652912844 \tabularnewline
56 & 7088.5 & 7333.78117246221 & -245.281172462213 \tabularnewline
57 & 9070.5 & 7146.90547502098 & 1923.59452497902 \tabularnewline
58 & 9606.5 & 7872.10778963184 & 1734.39221036816 \tabularnewline
59 & 6280 & 8684.95117557974 & -2404.95117557974 \tabularnewline
60 & 6248 & 7868.38224201527 & -1620.38224201527 \tabularnewline
61 & 6311.5 & 7178.14838497236 & -866.648384972364 \tabularnewline
62 & 6434 & 6669.94093352804 & -235.940933528036 \tabularnewline
63 & 7096.5 & 6357.05504394915 & 739.444956050852 \tabularnewline
64 & 6601.5 & 6443.30513348883 & 158.19486651117 \tabularnewline
65 & 5905 & 6344.34223615553 & -439.342236155531 \tabularnewline
66 & 7006.5 & 6002.06238985752 & 1004.43761014248 \tabularnewline
67 & 6113.5 & 6242.66933689517 & -129.169336895167 \tabularnewline
68 & 6911.5 & 6083.58285205381 & 827.917147946194 \tabularnewline
69 & 6450.5 & 6325.14038347772 & 125.359616522283 \tabularnewline
70 & 6504 & 6337.04241732669 & 166.957582673312 \tabularnewline
71 & 7710 & 6377.87050331124 & 1332.12949668876 \tabularnewline
72 & 7045 & 6934.94746117555 & 110.05253882445 \tabularnewline
73 & 6302.5 & 7083.05186450654 & -780.551864506536 \tabularnewline
74 & 6810 & 6857.4504776045 & -47.4504776045014 \tabularnewline
75 & 7567 & 6878.816329032 & 688.183670967996 \tabularnewline
76 & 7051 & 7212.68055820412 & -161.680558204122 \tabularnewline
77 & 7820 & 7241.19518050322 & 578.804819496778 \tabularnewline
78 & 8514 & 7574.25547694235 & 939.744523057647 \tabularnewline
79 & 8180 & 8113.5678683835 & 66.4321316164951 \tabularnewline
80 & 8140 & 8359.54951970405 & -219.549519704049 \tabularnewline
81 & 8349.5 & 8488.26378789507 & -138.763787895074 \tabularnewline
82 & 8474 & 8632.45521541321 & -158.455215413205 \tabularnewline
83 & 7880 & 8755.97247652774 & -875.972476527741 \tabularnewline
84 & 8130.5 & 8556.69069868961 & -426.190698689612 \tabularnewline
85 & 8020.5 & 8474.02757737751 & -453.527577377508 \tabularnewline
86 & 8232.5 & 8342.13382856038 & -109.633828560376 \tabularnewline
87 & 8457 & 8318.41060836333 & 138.589391636666 \tabularnewline
88 & 7468.5 & 8391.90334943833 & -923.403349438326 \tabularnewline
89 & 6763 & 8020.42098526266 & -1257.42098526266 \tabularnewline
90 & 7877.5 & 7423.98490571527 & 453.515094284727 \tabularnewline
91 & 7438 & 7453.52818566536 & -15.5281856653583 \tabularnewline
92 & 7131 & 7321.02656393931 & -190.026563939306 \tabularnewline
93 & 7270 & 7112.0434523435 & 157.956547656497 \tabularnewline
94 & 7203.5 & 7036.15340957928 & 167.346590420719 \tabularnewline
95 & 7010 & 6978.19015940633 & 31.8098405936744 \tabularnewline
96 & 6564.5 & 6876.59228421051 & -312.092284210507 \tabularnewline
97 & 6734.5 & 6629.75056870993 & 104.749431290069 \tabularnewline
98 & 7571.5 & 6534.91378735762 & 1036.58621264238 \tabularnewline
99 & 6491 & 6850.41360814241 & -359.413608142409 \tabularnewline
100 & 6489.5 & 6656.09332411461 & -166.593324114615 \tabularnewline
101 & 6883.5 & 6513.18356257901 & 370.316437420987 \tabularnewline
102 & 6958.5 & 6586.75418366169 & 371.745816338305 \tabularnewline
103 & 5731.5 & 6693.49155573837 & -961.991555738366 \tabularnewline
104 & 7157.5 & 6258.77041626864 & 898.729583731363 \tabularnewline
105 & 6336 & 6540.47554821202 & -204.475548212021 \tabularnewline
106 & 6862.5 & 6426.28244053926 & 436.217559460741 \tabularnewline
107 & 7175.5 & 6569.91555087387 & 605.584449126129 \tabularnewline
108 & 7408.5 & 6824.8005039431 & 583.699496056904 \tabularnewline
109 & 7052 & 7123.49651647773 & -71.4965164777286 \tabularnewline
110 & 6685.5 & 7191.45765711096 & -505.957657110956 \tabularnewline
111 & 7098.5 & 7066.11109978703 & 32.3889002129717 \tabularnewline
112 & 7048 & 7128.03272251428 & -80.0327225142773 \tabularnewline
113 & 7017 & 7144.40710757567 & -127.407107575668 \tabularnewline
114 & 7099 & 7133.35316924939 & -34.3531692493889 \tabularnewline
115 & 7310 & 7151.15697519596 & 158.843024804045 \tabularnewline
116 & 7868 & 7249.10648733811 & 618.893512661894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300287&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]3[/C][C]5367.5[/C][C]6224[/C][C]-856.5[/C][/ROW]
[ROW][C]4[/C][C]5013.5[/C][C]6548.30136980846[/C][C]-1534.80136980846[/C][/ROW]
[ROW][C]5[/C][C]5959.5[/C][C]6505.32569125074[/C][C]-545.825691250736[/C][/ROW]
[ROW][C]6[/C][C]6334[/C][C]6753.16396467618[/C][C]-419.163964676182[/C][/ROW]
[ROW][C]7[/C][C]5919[/C][C]7007.54746427507[/C][C]-1088.54746427507[/C][/ROW]
[ROW][C]8[/C][C]6248.5[/C][C]6936.93538335049[/C][C]-688.43538335049[/C][/ROW]
[ROW][C]9[/C][C]5701[/C][C]6942.87487932905[/C][C]-1241.87487932905[/C][/ROW]
[ROW][C]10[/C][C]6530.5[/C][C]6650.05994005709[/C][C]-119.559940057091[/C][/ROW]
[ROW][C]11[/C][C]7145.5[/C][C]6731.20640825638[/C][C]414.293591743621[/C][/ROW]
[ROW][C]12[/C][C]6819[/C][C]7031.65195444767[/C][C]-212.651954447673[/C][/ROW]
[ROW][C]13[/C][C]7037[/C][C]7098.63257543695[/C][C]-61.6325754369509[/C][/ROW]
[ROW][C]14[/C][C]7809[/C][C]7211.93022974399[/C][C]597.069770256011[/C][/ROW]
[ROW][C]15[/C][C]6300[/C][C]7603.36270152345[/C][C]-1303.36270152345[/C][/ROW]
[ROW][C]16[/C][C]7143.5[/C][C]7229.19706943977[/C][C]-85.6970694397651[/C][/ROW]
[ROW][C]17[/C][C]7234.5[/C][C]7264.63369314695[/C][C]-30.1336931469496[/C][/ROW]
[ROW][C]18[/C][C]6567.5[/C][C]7316.45583509243[/C][C]-748.955835092426[/C][/ROW]
[ROW][C]19[/C][C]6090[/C][C]7056.19690437388[/C][C]-966.196904373884[/C][/ROW]
[ROW][C]20[/C][C]5654[/C][C]6636.58744658134[/C][C]-982.587446581338[/C][/ROW]
[ROW][C]21[/C][C]6608[/C][C]6124.99198089771[/C][C]483.008019102286[/C][/ROW]
[ROW][C]22[/C][C]7566[/C][C]6157.92212799674[/C][C]1408.07787200326[/C][/ROW]
[ROW][C]23[/C][C]6352.5[/C][C]6631.52548202734[/C][C]-279.025482027339[/C][/ROW]
[ROW][C]24[/C][C]8592[/C][C]6502.65177632128[/C][C]2089.34822367872[/C][/ROW]
[ROW][C]25[/C][C]6631.5[/C][C]7368.76805853877[/C][C]-737.268058538765[/C][/ROW]
[ROW][C]26[/C][C]6852[/C][C]7201.76454255675[/C][C]-349.764542556753[/C][/ROW]
[ROW][C]27[/C][C]7538[/C][C]7136.7630357046[/C][C]401.236964295401[/C][/ROW]
[ROW][C]28[/C][C]8407[/C][C]7364.30119230659[/C][C]1042.69880769341[/C][/ROW]
[ROW][C]29[/C][C]7541[/C][C]7903.23964522356[/C][C]-362.239645223564[/C][/ROW]
[ROW][C]30[/C][C]9904.5[/C][C]7929.04747663061[/C][C]1975.45252336939[/C][/ROW]
[ROW][C]31[/C][C]9371[/C][C]8929.3231097399[/C][C]441.676890260096[/C][/ROW]
[ROW][C]32[/C][C]8091.5[/C][C]9442.99805611369[/C][C]-1351.49805611369[/C][/ROW]
[ROW][C]33[/C][C]8303.5[/C][C]9223.58688188062[/C][C]-920.086881880623[/C][/ROW]
[ROW][C]34[/C][C]8617.5[/C][C]9071.08684044972[/C][C]-453.586840449716[/C][/ROW]
[ROW][C]35[/C][C]10453.5[/C][C]9038.52445622725[/C][C]1414.97554377275[/C][/ROW]
[ROW][C]36[/C][C]9990.5[/C][C]9770.45341274777[/C][C]220.046587252231[/C][/ROW]
[ROW][C]37[/C][C]8337[/C][C]10112.3785573458[/C][C]-1775.37855734576[/C][/ROW]
[ROW][C]38[/C][C]8336.5[/C][C]9614.67300416854[/C][C]-1278.17300416854[/C][/ROW]
[ROW][C]39[/C][C]10345.5[/C][C]9174.94135595622[/C][C]1170.55864404378[/C][/ROW]
[ROW][C]40[/C][C]11060.5[/C][C]9676.9647141185[/C][C]1383.5352858815[/C][/ROW]
[ROW][C]41[/C][C]9384.5[/C][C]10373.5624896309[/C][C]-989.062489630942[/C][/ROW]
[ROW][C]42[/C][C]8357[/C][C]10170.4402262215[/C][C]-1813.44022622148[/C][/ROW]
[ROW][C]43[/C][C]8366[/C][C]9525.50676924307[/C][C]-1159.50676924307[/C][/ROW]
[ROW][C]44[/C][C]8404.5[/C][C]9002.66838931816[/C][C]-598.168389318158[/C][/ROW]
[ROW][C]45[/C][C]8068[/C][C]8619.54743006864[/C][C]-551.547430068638[/C][/ROW]
[ROW][C]46[/C][C]6518.5[/C][C]8203.91543525186[/C][C]-1685.41543525186[/C][/ROW]
[ROW][C]47[/C][C]9355[/C][C]7251.70390002578[/C][C]2103.29609997422[/C][/ROW]
[ROW][C]48[/C][C]7298.5[/C][C]7782.27289317507[/C][C]-483.772893175065[/C][/ROW]
[ROW][C]49[/C][C]8012[/C][C]7384.06635240173[/C][C]627.933647598275[/C][/ROW]
[ROW][C]50[/C][C]7189[/C][C]7421.8930619802[/C][C]-232.893061980199[/C][/ROW]
[ROW][C]51[/C][C]6992[/C][C]7144.35505249298[/C][C]-152.355052492979[/C][/ROW]
[ROW][C]52[/C][C]10277[/C][C]6881.01464494143[/C][C]3395.98535505857[/C][/ROW]
[ROW][C]53[/C][C]7146.5[/C][C]8131.74051882608[/C][C]-985.24051882608[/C][/ROW]
[ROW][C]54[/C][C]7102[/C][C]7794.98747741358[/C][C]-692.987477413575[/C][/ROW]
[ROW][C]55[/C][C]7257[/C][C]7497.43665291284[/C][C]-240.436652912844[/C][/ROW]
[ROW][C]56[/C][C]7088.5[/C][C]7333.78117246221[/C][C]-245.281172462213[/C][/ROW]
[ROW][C]57[/C][C]9070.5[/C][C]7146.90547502098[/C][C]1923.59452497902[/C][/ROW]
[ROW][C]58[/C][C]9606.5[/C][C]7872.10778963184[/C][C]1734.39221036816[/C][/ROW]
[ROW][C]59[/C][C]6280[/C][C]8684.95117557974[/C][C]-2404.95117557974[/C][/ROW]
[ROW][C]60[/C][C]6248[/C][C]7868.38224201527[/C][C]-1620.38224201527[/C][/ROW]
[ROW][C]61[/C][C]6311.5[/C][C]7178.14838497236[/C][C]-866.648384972364[/C][/ROW]
[ROW][C]62[/C][C]6434[/C][C]6669.94093352804[/C][C]-235.940933528036[/C][/ROW]
[ROW][C]63[/C][C]7096.5[/C][C]6357.05504394915[/C][C]739.444956050852[/C][/ROW]
[ROW][C]64[/C][C]6601.5[/C][C]6443.30513348883[/C][C]158.19486651117[/C][/ROW]
[ROW][C]65[/C][C]5905[/C][C]6344.34223615553[/C][C]-439.342236155531[/C][/ROW]
[ROW][C]66[/C][C]7006.5[/C][C]6002.06238985752[/C][C]1004.43761014248[/C][/ROW]
[ROW][C]67[/C][C]6113.5[/C][C]6242.66933689517[/C][C]-129.169336895167[/C][/ROW]
[ROW][C]68[/C][C]6911.5[/C][C]6083.58285205381[/C][C]827.917147946194[/C][/ROW]
[ROW][C]69[/C][C]6450.5[/C][C]6325.14038347772[/C][C]125.359616522283[/C][/ROW]
[ROW][C]70[/C][C]6504[/C][C]6337.04241732669[/C][C]166.957582673312[/C][/ROW]
[ROW][C]71[/C][C]7710[/C][C]6377.87050331124[/C][C]1332.12949668876[/C][/ROW]
[ROW][C]72[/C][C]7045[/C][C]6934.94746117555[/C][C]110.05253882445[/C][/ROW]
[ROW][C]73[/C][C]6302.5[/C][C]7083.05186450654[/C][C]-780.551864506536[/C][/ROW]
[ROW][C]74[/C][C]6810[/C][C]6857.4504776045[/C][C]-47.4504776045014[/C][/ROW]
[ROW][C]75[/C][C]7567[/C][C]6878.816329032[/C][C]688.183670967996[/C][/ROW]
[ROW][C]76[/C][C]7051[/C][C]7212.68055820412[/C][C]-161.680558204122[/C][/ROW]
[ROW][C]77[/C][C]7820[/C][C]7241.19518050322[/C][C]578.804819496778[/C][/ROW]
[ROW][C]78[/C][C]8514[/C][C]7574.25547694235[/C][C]939.744523057647[/C][/ROW]
[ROW][C]79[/C][C]8180[/C][C]8113.5678683835[/C][C]66.4321316164951[/C][/ROW]
[ROW][C]80[/C][C]8140[/C][C]8359.54951970405[/C][C]-219.549519704049[/C][/ROW]
[ROW][C]81[/C][C]8349.5[/C][C]8488.26378789507[/C][C]-138.763787895074[/C][/ROW]
[ROW][C]82[/C][C]8474[/C][C]8632.45521541321[/C][C]-158.455215413205[/C][/ROW]
[ROW][C]83[/C][C]7880[/C][C]8755.97247652774[/C][C]-875.972476527741[/C][/ROW]
[ROW][C]84[/C][C]8130.5[/C][C]8556.69069868961[/C][C]-426.190698689612[/C][/ROW]
[ROW][C]85[/C][C]8020.5[/C][C]8474.02757737751[/C][C]-453.527577377508[/C][/ROW]
[ROW][C]86[/C][C]8232.5[/C][C]8342.13382856038[/C][C]-109.633828560376[/C][/ROW]
[ROW][C]87[/C][C]8457[/C][C]8318.41060836333[/C][C]138.589391636666[/C][/ROW]
[ROW][C]88[/C][C]7468.5[/C][C]8391.90334943833[/C][C]-923.403349438326[/C][/ROW]
[ROW][C]89[/C][C]6763[/C][C]8020.42098526266[/C][C]-1257.42098526266[/C][/ROW]
[ROW][C]90[/C][C]7877.5[/C][C]7423.98490571527[/C][C]453.515094284727[/C][/ROW]
[ROW][C]91[/C][C]7438[/C][C]7453.52818566536[/C][C]-15.5281856653583[/C][/ROW]
[ROW][C]92[/C][C]7131[/C][C]7321.02656393931[/C][C]-190.026563939306[/C][/ROW]
[ROW][C]93[/C][C]7270[/C][C]7112.0434523435[/C][C]157.956547656497[/C][/ROW]
[ROW][C]94[/C][C]7203.5[/C][C]7036.15340957928[/C][C]167.346590420719[/C][/ROW]
[ROW][C]95[/C][C]7010[/C][C]6978.19015940633[/C][C]31.8098405936744[/C][/ROW]
[ROW][C]96[/C][C]6564.5[/C][C]6876.59228421051[/C][C]-312.092284210507[/C][/ROW]
[ROW][C]97[/C][C]6734.5[/C][C]6629.75056870993[/C][C]104.749431290069[/C][/ROW]
[ROW][C]98[/C][C]7571.5[/C][C]6534.91378735762[/C][C]1036.58621264238[/C][/ROW]
[ROW][C]99[/C][C]6491[/C][C]6850.41360814241[/C][C]-359.413608142409[/C][/ROW]
[ROW][C]100[/C][C]6489.5[/C][C]6656.09332411461[/C][C]-166.593324114615[/C][/ROW]
[ROW][C]101[/C][C]6883.5[/C][C]6513.18356257901[/C][C]370.316437420987[/C][/ROW]
[ROW][C]102[/C][C]6958.5[/C][C]6586.75418366169[/C][C]371.745816338305[/C][/ROW]
[ROW][C]103[/C][C]5731.5[/C][C]6693.49155573837[/C][C]-961.991555738366[/C][/ROW]
[ROW][C]104[/C][C]7157.5[/C][C]6258.77041626864[/C][C]898.729583731363[/C][/ROW]
[ROW][C]105[/C][C]6336[/C][C]6540.47554821202[/C][C]-204.475548212021[/C][/ROW]
[ROW][C]106[/C][C]6862.5[/C][C]6426.28244053926[/C][C]436.217559460741[/C][/ROW]
[ROW][C]107[/C][C]7175.5[/C][C]6569.91555087387[/C][C]605.584449126129[/C][/ROW]
[ROW][C]108[/C][C]7408.5[/C][C]6824.8005039431[/C][C]583.699496056904[/C][/ROW]
[ROW][C]109[/C][C]7052[/C][C]7123.49651647773[/C][C]-71.4965164777286[/C][/ROW]
[ROW][C]110[/C][C]6685.5[/C][C]7191.45765711096[/C][C]-505.957657110956[/C][/ROW]
[ROW][C]111[/C][C]7098.5[/C][C]7066.11109978703[/C][C]32.3889002129717[/C][/ROW]
[ROW][C]112[/C][C]7048[/C][C]7128.03272251428[/C][C]-80.0327225142773[/C][/ROW]
[ROW][C]113[/C][C]7017[/C][C]7144.40710757567[/C][C]-127.407107575668[/C][/ROW]
[ROW][C]114[/C][C]7099[/C][C]7133.35316924939[/C][C]-34.3531692493889[/C][/ROW]
[ROW][C]115[/C][C]7310[/C][C]7151.15697519596[/C][C]158.843024804045[/C][/ROW]
[ROW][C]116[/C][C]7868[/C][C]7249.10648733811[/C][C]618.893512661894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300287&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300287&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
35367.56224-856.5
45013.56548.30136980846-1534.80136980846
55959.56505.32569125074-545.825691250736
663346753.16396467618-419.163964676182
759197007.54746427507-1088.54746427507
86248.56936.93538335049-688.43538335049
957016942.87487932905-1241.87487932905
106530.56650.05994005709-119.559940057091
117145.56731.20640825638414.293591743621
1268197031.65195444767-212.651954447673
1370377098.63257543695-61.6325754369509
1478097211.93022974399597.069770256011
1563007603.36270152345-1303.36270152345
167143.57229.19706943977-85.6970694397651
177234.57264.63369314695-30.1336931469496
186567.57316.45583509243-748.955835092426
1960907056.19690437388-966.196904373884
2056546636.58744658134-982.587446581338
2166086124.99198089771483.008019102286
2275666157.922127996741408.07787200326
236352.56631.52548202734-279.025482027339
2485926502.651776321282089.34822367872
256631.57368.76805853877-737.268058538765
2668527201.76454255675-349.764542556753
2775387136.7630357046401.236964295401
2884077364.301192306591042.69880769341
2975417903.23964522356-362.239645223564
309904.57929.047476630611975.45252336939
3193718929.3231097399441.676890260096
328091.59442.99805611369-1351.49805611369
338303.59223.58688188062-920.086881880623
348617.59071.08684044972-453.586840449716
3510453.59038.524456227251414.97554377275
369990.59770.45341274777220.046587252231
37833710112.3785573458-1775.37855734576
388336.59614.67300416854-1278.17300416854
3910345.59174.941355956221170.55864404378
4011060.59676.96471411851383.5352858815
419384.510373.5624896309-989.062489630942
42835710170.4402262215-1813.44022622148
4383669525.50676924307-1159.50676924307
448404.59002.66838931816-598.168389318158
4580688619.54743006864-551.547430068638
466518.58203.91543525186-1685.41543525186
4793557251.703900025782103.29609997422
487298.57782.27289317507-483.772893175065
4980127384.06635240173627.933647598275
5071897421.8930619802-232.893061980199
5169927144.35505249298-152.355052492979
52102776881.014644941433395.98535505857
537146.58131.74051882608-985.24051882608
5471027794.98747741358-692.987477413575
5572577497.43665291284-240.436652912844
567088.57333.78117246221-245.281172462213
579070.57146.905475020981923.59452497902
589606.57872.107789631841734.39221036816
5962808684.95117557974-2404.95117557974
6062487868.38224201527-1620.38224201527
616311.57178.14838497236-866.648384972364
6264346669.94093352804-235.940933528036
637096.56357.05504394915739.444956050852
646601.56443.30513348883158.19486651117
6559056344.34223615553-439.342236155531
667006.56002.062389857521004.43761014248
676113.56242.66933689517-129.169336895167
686911.56083.58285205381827.917147946194
696450.56325.14038347772125.359616522283
7065046337.04241732669166.957582673312
7177106377.870503311241332.12949668876
7270456934.94746117555110.05253882445
736302.57083.05186450654-780.551864506536
7468106857.4504776045-47.4504776045014
7575676878.816329032688.183670967996
7670517212.68055820412-161.680558204122
7778207241.19518050322578.804819496778
7885147574.25547694235939.744523057647
7981808113.567868383566.4321316164951
8081408359.54951970405-219.549519704049
818349.58488.26378789507-138.763787895074
8284748632.45521541321-158.455215413205
8378808755.97247652774-875.972476527741
848130.58556.69069868961-426.190698689612
858020.58474.02757737751-453.527577377508
868232.58342.13382856038-109.633828560376
8784578318.41060836333138.589391636666
887468.58391.90334943833-923.403349438326
8967638020.42098526266-1257.42098526266
907877.57423.98490571527453.515094284727
9174387453.52818566536-15.5281856653583
9271317321.02656393931-190.026563939306
9372707112.0434523435157.956547656497
947203.57036.15340957928167.346590420719
9570106978.1901594063331.8098405936744
966564.56876.59228421051-312.092284210507
976734.56629.75056870993104.749431290069
987571.56534.913787357621036.58621264238
9964916850.41360814241-359.413608142409
1006489.56656.09332411461-166.593324114615
1016883.56513.18356257901370.316437420987
1026958.56586.75418366169371.745816338305
1035731.56693.49155573837-961.991555738366
1047157.56258.77041626864898.729583731363
10563366540.47554821202-204.475548212021
1066862.56426.28244053926436.217559460741
1077175.56569.91555087387605.584449126129
1087408.56824.8005039431583.699496056904
10970527123.49651647773-71.4965164777286
1106685.57191.45765711096-505.957657110956
1117098.57066.1110997870332.3889002129717
11270487128.03272251428-80.0327225142773
11370177144.40710757567-127.407107575668
11470997133.35316924939-34.3531692493889
11573107151.15697519596158.843024804045
11678687249.10648733811618.893512661894







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1177559.057082447745754.207797538169363.90636735731
1187656.99360224395692.022843880099621.96436060771
1197754.930122040075578.596167395039931.26407668511
1207852.866641836235416.9318401796610288.8014434928
1217950.80316163245211.5521832622510690.0541400026
1228048.739681428574967.194388914411130.2849739427
1238146.676201224734688.1513749729911605.2010274765
1248244.61272102094378.0570330232612111.1684090185
1258342.549240817064039.8945547525812645.2039268816
1268440.485760613233676.0879429334413204.883578293
1278538.42228040943288.608973717513788.2355871013
1288636.358800205562879.0733173178414393.6442830933

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 7559.05708244774 & 5754.20779753816 & 9363.90636735731 \tabularnewline
118 & 7656.9936022439 & 5692.02284388009 & 9621.96436060771 \tabularnewline
119 & 7754.93012204007 & 5578.59616739503 & 9931.26407668511 \tabularnewline
120 & 7852.86664183623 & 5416.93184017966 & 10288.8014434928 \tabularnewline
121 & 7950.8031616324 & 5211.55218326225 & 10690.0541400026 \tabularnewline
122 & 8048.73968142857 & 4967.1943889144 & 11130.2849739427 \tabularnewline
123 & 8146.67620122473 & 4688.15137497299 & 11605.2010274765 \tabularnewline
124 & 8244.6127210209 & 4378.05703302326 & 12111.1684090185 \tabularnewline
125 & 8342.54924081706 & 4039.89455475258 & 12645.2039268816 \tabularnewline
126 & 8440.48576061323 & 3676.08794293344 & 13204.883578293 \tabularnewline
127 & 8538.4222804094 & 3288.6089737175 & 13788.2355871013 \tabularnewline
128 & 8636.35880020556 & 2879.07331731784 & 14393.6442830933 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300287&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]117[/C][C]7559.05708244774[/C][C]5754.20779753816[/C][C]9363.90636735731[/C][/ROW]
[ROW][C]118[/C][C]7656.9936022439[/C][C]5692.02284388009[/C][C]9621.96436060771[/C][/ROW]
[ROW][C]119[/C][C]7754.93012204007[/C][C]5578.59616739503[/C][C]9931.26407668511[/C][/ROW]
[ROW][C]120[/C][C]7852.86664183623[/C][C]5416.93184017966[/C][C]10288.8014434928[/C][/ROW]
[ROW][C]121[/C][C]7950.8031616324[/C][C]5211.55218326225[/C][C]10690.0541400026[/C][/ROW]
[ROW][C]122[/C][C]8048.73968142857[/C][C]4967.1943889144[/C][C]11130.2849739427[/C][/ROW]
[ROW][C]123[/C][C]8146.67620122473[/C][C]4688.15137497299[/C][C]11605.2010274765[/C][/ROW]
[ROW][C]124[/C][C]8244.6127210209[/C][C]4378.05703302326[/C][C]12111.1684090185[/C][/ROW]
[ROW][C]125[/C][C]8342.54924081706[/C][C]4039.89455475258[/C][C]12645.2039268816[/C][/ROW]
[ROW][C]126[/C][C]8440.48576061323[/C][C]3676.08794293344[/C][C]13204.883578293[/C][/ROW]
[ROW][C]127[/C][C]8538.4222804094[/C][C]3288.6089737175[/C][C]13788.2355871013[/C][/ROW]
[ROW][C]128[/C][C]8636.35880020556[/C][C]2879.07331731784[/C][C]14393.6442830933[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300287&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300287&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
1177559.057082447745754.207797538169363.90636735731
1187656.99360224395692.022843880099621.96436060771
1197754.930122040075578.596167395039931.26407668511
1207852.866641836235416.9318401796610288.8014434928
1217950.80316163245211.5521832622510690.0541400026
1228048.739681428574967.194388914411130.2849739427
1238146.676201224734688.1513749729911605.2010274765
1248244.61272102094378.0570330232612111.1684090185
1258342.549240817064039.8945547525812645.2039268816
1268440.485760613233676.0879429334413204.883578293
1278538.42228040943288.608973717513788.2355871013
1288636.358800205562879.0733173178414393.6442830933



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')