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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 04 Jun 2010 12:18:00 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/04/t12756539108jp94jq6d9fxfv8.htm/, Retrieved Mon, 29 Apr 2024 03:19:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77430, Retrieved Mon, 29 Apr 2024 03:19:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact162
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-06-04 12:18:00] [917a4afc20628654d1f716afbd7d9cc1] [Current]
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Dataseries X:
2953
2635
2404
2413
2136
1565
1451
2037
2477
2785
2994
2681
3098
2708
2517
2445
2087
1801
1216
2173
2286
3121
3458
3511
3524
2767
2744
2603
2527
1846
1066
2327
3066
3048
3806
4042
3583
3438
2957
2885
2744
1837
1447
2504
3248
3098
4318
3561
3316
3379
2717
2354
2445
1542
1606
2590
3588
3202
4704
4005
3810
3488
2781
2944
2817
1960
1937
2903
3357
3552
4581
3905
4581
4037
3345
3175
2808
2050
1719
3143
3756
4776
4540
4309
4563
3506
3665
3361
3094
2440
1633
2935
4159
4159
4894
4921
4577
4155
3851
3429
3370
2726




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77430&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77430&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77430&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0739209572408732
beta0.0457595802441608
gamma0.330408735129191

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0739209572408732 \tabularnewline
beta & 0.0457595802441608 \tabularnewline
gamma & 0.330408735129191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77430&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]0.0739209572408732[/C][/ROW]
[ROW][C]beta[/C][C]0.0457595802441608[/C][/ROW]
[ROW][C]gamma[/C][C]0.330408735129191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77430&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77430&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
alpha0.0739209572408732
beta0.0457595802441608
gamma0.330408735129191







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1330983043.7513395881554.248660411848
1427082676.1476047433131.8523952566948
1525172499.0315056382217.968494361784
1624452429.6729784390915.3270215609109
1720872052.4833123189834.5166876810194
1818011740.22968219760.7703178030013
1912161479.02638528787-263.026385287868
2021732046.24268410856126.757315891436
2122862498.10879770803-212.108797708034
2231212790.63405895328330.365941046718
2334583035.43251390506422.56748609494
2435112745.82958857622765.170411423783
2535243268.87831897298255.121681027018
2627672885.73433583387-118.734335833874
2727442683.6500813541360.3499186458675
2826032614.73872898148-11.7387289814774
2925272216.85245011382310.147549886176
3018461910.12665563092-64.1266556309245
3110661512.13470404602-446.134704046022
3223272238.3636353224288.636364677583
3330662610.05431782677455.945682173229
3430483166.8416959311-118.841695931104
3538063430.05153765498375.948462345018
3640423222.6200002145819.379999785502
3735833622.01234825892-39.0123482589183
3834383065.99529840135372.004701598646
3929572946.197059666110.8029403338951
4028852846.3452049444338.6547950555669
4127442525.2917641732218.708235826795
4218372059.96935124306-222.969351243057
4314471488.53965796715-41.5396579671487
4425042510.41768909839-6.41768909838584
4532483039.95282066349208.047179336514
4630983440.21107317002-342.211073170018
4743183880.64978432776437.35021567224
4835613802.38664979137-241.386649791374
4933163865.93410822792-549.934108227915
5033793369.510646790669.48935320933651
5127173096.84754101386-379.847541013864
5223542969.45203176324-615.45203176324
5324452643.90816159447-198.908161594466
5415422002.43623879537-460.436238795372
5516061466.69192742223139.308072577772
5625902509.8619949996680.1380050003377
5735883106.16889657423481.831103425772
5832023352.77704040259-150.777040402587
5947044044.55265104991659.447348950087
6040053765.26463767186239.735362328138
6138103763.6505830362546.3494169637484
6234883471.6696762223716.3303237776299
6327813065.73113731036-284.731137310358
6429442863.3517076119180.648292388094
6528172709.43587516602107.564124833983
6619601968.08867639479-8.0886763947949
6719371626.66791923682310.332080763182
6829032755.36853261452147.631467385484
6933573546.86017041421-189.860170414209
7035523554.69355056176-2.69355056176073
7145814582.35179879189-1.35179879189491
7239054097.16659814172-192.166598141725
7345814000.65408916199580.345910838008
7440373720.09301337571316.906986624292
7533453208.18326799286136.816732007139
7631753146.5290951154628.4709048845352
7728082987.08280068018-179.082800680183
7820502127.23032372058-77.2303237205765
7917191858.74341484165-139.743414841654
8031432966.90568577197176.094314228026
8137563697.4496866781258.5503133218754
8247763786.76089529729989.239104702712
8345404981.53083543739-441.530835437393
8443094364.64607760225-55.6460776022477
8545634528.98569643534.0143035649944
8635064098.53767225567-592.537672255672
8736653430.0431700927234.956829907297
8833613335.5910326636225.4089673363828
8930943098.50112839995-4.50112839995199
9024402232.42957136688207.570428633124
9116331946.07136552366-313.071365523663
9229353216.87679167235-281.876791672346
9341593912.437485424246.562514576004
9441594314.22352711335-155.223527113348
9548945002.97302409231-108.973024092307
9649214506.96988076895414.030119231046
9745774739.32609311007-162.326093110073
9841554072.1335387119282.8664612880757
9938513685.92421974168165.07578025832
10034293512.22381455546-83.2238145554611
10133703244.77846622642125.22153377358
10227262411.44519592482314.554804075179

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3098 & 3043.75133958815 & 54.248660411848 \tabularnewline
14 & 2708 & 2676.14760474331 & 31.8523952566948 \tabularnewline
15 & 2517 & 2499.03150563822 & 17.968494361784 \tabularnewline
16 & 2445 & 2429.67297843909 & 15.3270215609109 \tabularnewline
17 & 2087 & 2052.48331231898 & 34.5166876810194 \tabularnewline
18 & 1801 & 1740.229682197 & 60.7703178030013 \tabularnewline
19 & 1216 & 1479.02638528787 & -263.026385287868 \tabularnewline
20 & 2173 & 2046.24268410856 & 126.757315891436 \tabularnewline
21 & 2286 & 2498.10879770803 & -212.108797708034 \tabularnewline
22 & 3121 & 2790.63405895328 & 330.365941046718 \tabularnewline
23 & 3458 & 3035.43251390506 & 422.56748609494 \tabularnewline
24 & 3511 & 2745.82958857622 & 765.170411423783 \tabularnewline
25 & 3524 & 3268.87831897298 & 255.121681027018 \tabularnewline
26 & 2767 & 2885.73433583387 & -118.734335833874 \tabularnewline
27 & 2744 & 2683.65008135413 & 60.3499186458675 \tabularnewline
28 & 2603 & 2614.73872898148 & -11.7387289814774 \tabularnewline
29 & 2527 & 2216.85245011382 & 310.147549886176 \tabularnewline
30 & 1846 & 1910.12665563092 & -64.1266556309245 \tabularnewline
31 & 1066 & 1512.13470404602 & -446.134704046022 \tabularnewline
32 & 2327 & 2238.36363532242 & 88.636364677583 \tabularnewline
33 & 3066 & 2610.05431782677 & 455.945682173229 \tabularnewline
34 & 3048 & 3166.8416959311 & -118.841695931104 \tabularnewline
35 & 3806 & 3430.05153765498 & 375.948462345018 \tabularnewline
36 & 4042 & 3222.6200002145 & 819.379999785502 \tabularnewline
37 & 3583 & 3622.01234825892 & -39.0123482589183 \tabularnewline
38 & 3438 & 3065.99529840135 & 372.004701598646 \tabularnewline
39 & 2957 & 2946.1970596661 & 10.8029403338951 \tabularnewline
40 & 2885 & 2846.34520494443 & 38.6547950555669 \tabularnewline
41 & 2744 & 2525.2917641732 & 218.708235826795 \tabularnewline
42 & 1837 & 2059.96935124306 & -222.969351243057 \tabularnewline
43 & 1447 & 1488.53965796715 & -41.5396579671487 \tabularnewline
44 & 2504 & 2510.41768909839 & -6.41768909838584 \tabularnewline
45 & 3248 & 3039.95282066349 & 208.047179336514 \tabularnewline
46 & 3098 & 3440.21107317002 & -342.211073170018 \tabularnewline
47 & 4318 & 3880.64978432776 & 437.35021567224 \tabularnewline
48 & 3561 & 3802.38664979137 & -241.386649791374 \tabularnewline
49 & 3316 & 3865.93410822792 & -549.934108227915 \tabularnewline
50 & 3379 & 3369.51064679066 & 9.48935320933651 \tabularnewline
51 & 2717 & 3096.84754101386 & -379.847541013864 \tabularnewline
52 & 2354 & 2969.45203176324 & -615.45203176324 \tabularnewline
53 & 2445 & 2643.90816159447 & -198.908161594466 \tabularnewline
54 & 1542 & 2002.43623879537 & -460.436238795372 \tabularnewline
55 & 1606 & 1466.69192742223 & 139.308072577772 \tabularnewline
56 & 2590 & 2509.86199499966 & 80.1380050003377 \tabularnewline
57 & 3588 & 3106.16889657423 & 481.831103425772 \tabularnewline
58 & 3202 & 3352.77704040259 & -150.777040402587 \tabularnewline
59 & 4704 & 4044.55265104991 & 659.447348950087 \tabularnewline
60 & 4005 & 3765.26463767186 & 239.735362328138 \tabularnewline
61 & 3810 & 3763.65058303625 & 46.3494169637484 \tabularnewline
62 & 3488 & 3471.66967622237 & 16.3303237776299 \tabularnewline
63 & 2781 & 3065.73113731036 & -284.731137310358 \tabularnewline
64 & 2944 & 2863.35170761191 & 80.648292388094 \tabularnewline
65 & 2817 & 2709.43587516602 & 107.564124833983 \tabularnewline
66 & 1960 & 1968.08867639479 & -8.0886763947949 \tabularnewline
67 & 1937 & 1626.66791923682 & 310.332080763182 \tabularnewline
68 & 2903 & 2755.36853261452 & 147.631467385484 \tabularnewline
69 & 3357 & 3546.86017041421 & -189.860170414209 \tabularnewline
70 & 3552 & 3554.69355056176 & -2.69355056176073 \tabularnewline
71 & 4581 & 4582.35179879189 & -1.35179879189491 \tabularnewline
72 & 3905 & 4097.16659814172 & -192.166598141725 \tabularnewline
73 & 4581 & 4000.65408916199 & 580.345910838008 \tabularnewline
74 & 4037 & 3720.09301337571 & 316.906986624292 \tabularnewline
75 & 3345 & 3208.18326799286 & 136.816732007139 \tabularnewline
76 & 3175 & 3146.52909511546 & 28.4709048845352 \tabularnewline
77 & 2808 & 2987.08280068018 & -179.082800680183 \tabularnewline
78 & 2050 & 2127.23032372058 & -77.2303237205765 \tabularnewline
79 & 1719 & 1858.74341484165 & -139.743414841654 \tabularnewline
80 & 3143 & 2966.90568577197 & 176.094314228026 \tabularnewline
81 & 3756 & 3697.44968667812 & 58.5503133218754 \tabularnewline
82 & 4776 & 3786.76089529729 & 989.239104702712 \tabularnewline
83 & 4540 & 4981.53083543739 & -441.530835437393 \tabularnewline
84 & 4309 & 4364.64607760225 & -55.6460776022477 \tabularnewline
85 & 4563 & 4528.985696435 & 34.0143035649944 \tabularnewline
86 & 3506 & 4098.53767225567 & -592.537672255672 \tabularnewline
87 & 3665 & 3430.0431700927 & 234.956829907297 \tabularnewline
88 & 3361 & 3335.59103266362 & 25.4089673363828 \tabularnewline
89 & 3094 & 3098.50112839995 & -4.50112839995199 \tabularnewline
90 & 2440 & 2232.42957136688 & 207.570428633124 \tabularnewline
91 & 1633 & 1946.07136552366 & -313.071365523663 \tabularnewline
92 & 2935 & 3216.87679167235 & -281.876791672346 \tabularnewline
93 & 4159 & 3912.437485424 & 246.562514576004 \tabularnewline
94 & 4159 & 4314.22352711335 & -155.223527113348 \tabularnewline
95 & 4894 & 5002.97302409231 & -108.973024092307 \tabularnewline
96 & 4921 & 4506.96988076895 & 414.030119231046 \tabularnewline
97 & 4577 & 4739.32609311007 & -162.326093110073 \tabularnewline
98 & 4155 & 4072.13353871192 & 82.8664612880757 \tabularnewline
99 & 3851 & 3685.92421974168 & 165.07578025832 \tabularnewline
100 & 3429 & 3512.22381455546 & -83.2238145554611 \tabularnewline
101 & 3370 & 3244.77846622642 & 125.22153377358 \tabularnewline
102 & 2726 & 2411.44519592482 & 314.554804075179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77430&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]3098[/C][C]3043.75133958815[/C][C]54.248660411848[/C][/ROW]
[ROW][C]14[/C][C]2708[/C][C]2676.14760474331[/C][C]31.8523952566948[/C][/ROW]
[ROW][C]15[/C][C]2517[/C][C]2499.03150563822[/C][C]17.968494361784[/C][/ROW]
[ROW][C]16[/C][C]2445[/C][C]2429.67297843909[/C][C]15.3270215609109[/C][/ROW]
[ROW][C]17[/C][C]2087[/C][C]2052.48331231898[/C][C]34.5166876810194[/C][/ROW]
[ROW][C]18[/C][C]1801[/C][C]1740.229682197[/C][C]60.7703178030013[/C][/ROW]
[ROW][C]19[/C][C]1216[/C][C]1479.02638528787[/C][C]-263.026385287868[/C][/ROW]
[ROW][C]20[/C][C]2173[/C][C]2046.24268410856[/C][C]126.757315891436[/C][/ROW]
[ROW][C]21[/C][C]2286[/C][C]2498.10879770803[/C][C]-212.108797708034[/C][/ROW]
[ROW][C]22[/C][C]3121[/C][C]2790.63405895328[/C][C]330.365941046718[/C][/ROW]
[ROW][C]23[/C][C]3458[/C][C]3035.43251390506[/C][C]422.56748609494[/C][/ROW]
[ROW][C]24[/C][C]3511[/C][C]2745.82958857622[/C][C]765.170411423783[/C][/ROW]
[ROW][C]25[/C][C]3524[/C][C]3268.87831897298[/C][C]255.121681027018[/C][/ROW]
[ROW][C]26[/C][C]2767[/C][C]2885.73433583387[/C][C]-118.734335833874[/C][/ROW]
[ROW][C]27[/C][C]2744[/C][C]2683.65008135413[/C][C]60.3499186458675[/C][/ROW]
[ROW][C]28[/C][C]2603[/C][C]2614.73872898148[/C][C]-11.7387289814774[/C][/ROW]
[ROW][C]29[/C][C]2527[/C][C]2216.85245011382[/C][C]310.147549886176[/C][/ROW]
[ROW][C]30[/C][C]1846[/C][C]1910.12665563092[/C][C]-64.1266556309245[/C][/ROW]
[ROW][C]31[/C][C]1066[/C][C]1512.13470404602[/C][C]-446.134704046022[/C][/ROW]
[ROW][C]32[/C][C]2327[/C][C]2238.36363532242[/C][C]88.636364677583[/C][/ROW]
[ROW][C]33[/C][C]3066[/C][C]2610.05431782677[/C][C]455.945682173229[/C][/ROW]
[ROW][C]34[/C][C]3048[/C][C]3166.8416959311[/C][C]-118.841695931104[/C][/ROW]
[ROW][C]35[/C][C]3806[/C][C]3430.05153765498[/C][C]375.948462345018[/C][/ROW]
[ROW][C]36[/C][C]4042[/C][C]3222.6200002145[/C][C]819.379999785502[/C][/ROW]
[ROW][C]37[/C][C]3583[/C][C]3622.01234825892[/C][C]-39.0123482589183[/C][/ROW]
[ROW][C]38[/C][C]3438[/C][C]3065.99529840135[/C][C]372.004701598646[/C][/ROW]
[ROW][C]39[/C][C]2957[/C][C]2946.1970596661[/C][C]10.8029403338951[/C][/ROW]
[ROW][C]40[/C][C]2885[/C][C]2846.34520494443[/C][C]38.6547950555669[/C][/ROW]
[ROW][C]41[/C][C]2744[/C][C]2525.2917641732[/C][C]218.708235826795[/C][/ROW]
[ROW][C]42[/C][C]1837[/C][C]2059.96935124306[/C][C]-222.969351243057[/C][/ROW]
[ROW][C]43[/C][C]1447[/C][C]1488.53965796715[/C][C]-41.5396579671487[/C][/ROW]
[ROW][C]44[/C][C]2504[/C][C]2510.41768909839[/C][C]-6.41768909838584[/C][/ROW]
[ROW][C]45[/C][C]3248[/C][C]3039.95282066349[/C][C]208.047179336514[/C][/ROW]
[ROW][C]46[/C][C]3098[/C][C]3440.21107317002[/C][C]-342.211073170018[/C][/ROW]
[ROW][C]47[/C][C]4318[/C][C]3880.64978432776[/C][C]437.35021567224[/C][/ROW]
[ROW][C]48[/C][C]3561[/C][C]3802.38664979137[/C][C]-241.386649791374[/C][/ROW]
[ROW][C]49[/C][C]3316[/C][C]3865.93410822792[/C][C]-549.934108227915[/C][/ROW]
[ROW][C]50[/C][C]3379[/C][C]3369.51064679066[/C][C]9.48935320933651[/C][/ROW]
[ROW][C]51[/C][C]2717[/C][C]3096.84754101386[/C][C]-379.847541013864[/C][/ROW]
[ROW][C]52[/C][C]2354[/C][C]2969.45203176324[/C][C]-615.45203176324[/C][/ROW]
[ROW][C]53[/C][C]2445[/C][C]2643.90816159447[/C][C]-198.908161594466[/C][/ROW]
[ROW][C]54[/C][C]1542[/C][C]2002.43623879537[/C][C]-460.436238795372[/C][/ROW]
[ROW][C]55[/C][C]1606[/C][C]1466.69192742223[/C][C]139.308072577772[/C][/ROW]
[ROW][C]56[/C][C]2590[/C][C]2509.86199499966[/C][C]80.1380050003377[/C][/ROW]
[ROW][C]57[/C][C]3588[/C][C]3106.16889657423[/C][C]481.831103425772[/C][/ROW]
[ROW][C]58[/C][C]3202[/C][C]3352.77704040259[/C][C]-150.777040402587[/C][/ROW]
[ROW][C]59[/C][C]4704[/C][C]4044.55265104991[/C][C]659.447348950087[/C][/ROW]
[ROW][C]60[/C][C]4005[/C][C]3765.26463767186[/C][C]239.735362328138[/C][/ROW]
[ROW][C]61[/C][C]3810[/C][C]3763.65058303625[/C][C]46.3494169637484[/C][/ROW]
[ROW][C]62[/C][C]3488[/C][C]3471.66967622237[/C][C]16.3303237776299[/C][/ROW]
[ROW][C]63[/C][C]2781[/C][C]3065.73113731036[/C][C]-284.731137310358[/C][/ROW]
[ROW][C]64[/C][C]2944[/C][C]2863.35170761191[/C][C]80.648292388094[/C][/ROW]
[ROW][C]65[/C][C]2817[/C][C]2709.43587516602[/C][C]107.564124833983[/C][/ROW]
[ROW][C]66[/C][C]1960[/C][C]1968.08867639479[/C][C]-8.0886763947949[/C][/ROW]
[ROW][C]67[/C][C]1937[/C][C]1626.66791923682[/C][C]310.332080763182[/C][/ROW]
[ROW][C]68[/C][C]2903[/C][C]2755.36853261452[/C][C]147.631467385484[/C][/ROW]
[ROW][C]69[/C][C]3357[/C][C]3546.86017041421[/C][C]-189.860170414209[/C][/ROW]
[ROW][C]70[/C][C]3552[/C][C]3554.69355056176[/C][C]-2.69355056176073[/C][/ROW]
[ROW][C]71[/C][C]4581[/C][C]4582.35179879189[/C][C]-1.35179879189491[/C][/ROW]
[ROW][C]72[/C][C]3905[/C][C]4097.16659814172[/C][C]-192.166598141725[/C][/ROW]
[ROW][C]73[/C][C]4581[/C][C]4000.65408916199[/C][C]580.345910838008[/C][/ROW]
[ROW][C]74[/C][C]4037[/C][C]3720.09301337571[/C][C]316.906986624292[/C][/ROW]
[ROW][C]75[/C][C]3345[/C][C]3208.18326799286[/C][C]136.816732007139[/C][/ROW]
[ROW][C]76[/C][C]3175[/C][C]3146.52909511546[/C][C]28.4709048845352[/C][/ROW]
[ROW][C]77[/C][C]2808[/C][C]2987.08280068018[/C][C]-179.082800680183[/C][/ROW]
[ROW][C]78[/C][C]2050[/C][C]2127.23032372058[/C][C]-77.2303237205765[/C][/ROW]
[ROW][C]79[/C][C]1719[/C][C]1858.74341484165[/C][C]-139.743414841654[/C][/ROW]
[ROW][C]80[/C][C]3143[/C][C]2966.90568577197[/C][C]176.094314228026[/C][/ROW]
[ROW][C]81[/C][C]3756[/C][C]3697.44968667812[/C][C]58.5503133218754[/C][/ROW]
[ROW][C]82[/C][C]4776[/C][C]3786.76089529729[/C][C]989.239104702712[/C][/ROW]
[ROW][C]83[/C][C]4540[/C][C]4981.53083543739[/C][C]-441.530835437393[/C][/ROW]
[ROW][C]84[/C][C]4309[/C][C]4364.64607760225[/C][C]-55.6460776022477[/C][/ROW]
[ROW][C]85[/C][C]4563[/C][C]4528.985696435[/C][C]34.0143035649944[/C][/ROW]
[ROW][C]86[/C][C]3506[/C][C]4098.53767225567[/C][C]-592.537672255672[/C][/ROW]
[ROW][C]87[/C][C]3665[/C][C]3430.0431700927[/C][C]234.956829907297[/C][/ROW]
[ROW][C]88[/C][C]3361[/C][C]3335.59103266362[/C][C]25.4089673363828[/C][/ROW]
[ROW][C]89[/C][C]3094[/C][C]3098.50112839995[/C][C]-4.50112839995199[/C][/ROW]
[ROW][C]90[/C][C]2440[/C][C]2232.42957136688[/C][C]207.570428633124[/C][/ROW]
[ROW][C]91[/C][C]1633[/C][C]1946.07136552366[/C][C]-313.071365523663[/C][/ROW]
[ROW][C]92[/C][C]2935[/C][C]3216.87679167235[/C][C]-281.876791672346[/C][/ROW]
[ROW][C]93[/C][C]4159[/C][C]3912.437485424[/C][C]246.562514576004[/C][/ROW]
[ROW][C]94[/C][C]4159[/C][C]4314.22352711335[/C][C]-155.223527113348[/C][/ROW]
[ROW][C]95[/C][C]4894[/C][C]5002.97302409231[/C][C]-108.973024092307[/C][/ROW]
[ROW][C]96[/C][C]4921[/C][C]4506.96988076895[/C][C]414.030119231046[/C][/ROW]
[ROW][C]97[/C][C]4577[/C][C]4739.32609311007[/C][C]-162.326093110073[/C][/ROW]
[ROW][C]98[/C][C]4155[/C][C]4072.13353871192[/C][C]82.8664612880757[/C][/ROW]
[ROW][C]99[/C][C]3851[/C][C]3685.92421974168[/C][C]165.07578025832[/C][/ROW]
[ROW][C]100[/C][C]3429[/C][C]3512.22381455546[/C][C]-83.2238145554611[/C][/ROW]
[ROW][C]101[/C][C]3370[/C][C]3244.77846622642[/C][C]125.22153377358[/C][/ROW]
[ROW][C]102[/C][C]2726[/C][C]2411.44519592482[/C][C]314.554804075179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77430&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77430&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
1330983043.7513395881554.248660411848
1427082676.1476047433131.8523952566948
1525172499.0315056382217.968494361784
1624452429.6729784390915.3270215609109
1720872052.4833123189834.5166876810194
1818011740.22968219760.7703178030013
1912161479.02638528787-263.026385287868
2021732046.24268410856126.757315891436
2122862498.10879770803-212.108797708034
2231212790.63405895328330.365941046718
2334583035.43251390506422.56748609494
2435112745.82958857622765.170411423783
2535243268.87831897298255.121681027018
2627672885.73433583387-118.734335833874
2727442683.6500813541360.3499186458675
2826032614.73872898148-11.7387289814774
2925272216.85245011382310.147549886176
3018461910.12665563092-64.1266556309245
3110661512.13470404602-446.134704046022
3223272238.3636353224288.636364677583
3330662610.05431782677455.945682173229
3430483166.8416959311-118.841695931104
3538063430.05153765498375.948462345018
3640423222.6200002145819.379999785502
3735833622.01234825892-39.0123482589183
3834383065.99529840135372.004701598646
3929572946.197059666110.8029403338951
4028852846.3452049444338.6547950555669
4127442525.2917641732218.708235826795
4218372059.96935124306-222.969351243057
4314471488.53965796715-41.5396579671487
4425042510.41768909839-6.41768909838584
4532483039.95282066349208.047179336514
4630983440.21107317002-342.211073170018
4743183880.64978432776437.35021567224
4835613802.38664979137-241.386649791374
4933163865.93410822792-549.934108227915
5033793369.510646790669.48935320933651
5127173096.84754101386-379.847541013864
5223542969.45203176324-615.45203176324
5324452643.90816159447-198.908161594466
5415422002.43623879537-460.436238795372
5516061466.69192742223139.308072577772
5625902509.8619949996680.1380050003377
5735883106.16889657423481.831103425772
5832023352.77704040259-150.777040402587
5947044044.55265104991659.447348950087
6040053765.26463767186239.735362328138
6138103763.6505830362546.3494169637484
6234883471.6696762223716.3303237776299
6327813065.73113731036-284.731137310358
6429442863.3517076119180.648292388094
6528172709.43587516602107.564124833983
6619601968.08867639479-8.0886763947949
6719371626.66791923682310.332080763182
6829032755.36853261452147.631467385484
6933573546.86017041421-189.860170414209
7035523554.69355056176-2.69355056176073
7145814582.35179879189-1.35179879189491
7239054097.16659814172-192.166598141725
7345814000.65408916199580.345910838008
7440373720.09301337571316.906986624292
7533453208.18326799286136.816732007139
7631753146.5290951154628.4709048845352
7728082987.08280068018-179.082800680183
7820502127.23032372058-77.2303237205765
7917191858.74341484165-139.743414841654
8031432966.90568577197176.094314228026
8137563697.4496866781258.5503133218754
8247763786.76089529729989.239104702712
8345404981.53083543739-441.530835437393
8443094364.64607760225-55.6460776022477
8545634528.98569643534.0143035649944
8635064098.53767225567-592.537672255672
8736653430.0431700927234.956829907297
8833613335.5910326636225.4089673363828
8930943098.50112839995-4.50112839995199
9024402232.42957136688207.570428633124
9116331946.07136552366-313.071365523663
9229353216.87679167235-281.876791672346
9341593912.437485424246.562514576004
9441594314.22352711335-155.223527113348
9548945002.97302409231-108.973024092307
9649214506.96988076895414.030119231046
9745774739.32609311007-162.326093110073
9841554072.1335387119282.8664612880757
9938513685.92421974168165.07578025832
10034293512.22381455546-83.2238145554611
10133703244.77846622642125.22153377358
10227262411.44519592482314.554804075179







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1031947.581908061761726.600268381292168.56354774222
1043337.575801942953103.661152444673571.49045144124
1054282.253223543324032.083126184554532.42332090209
1064562.614244115064302.009076719794823.21941151034
1075331.335921899445049.295643161045613.37620063784
1084980.993505402464699.381454065865262.60555673906
1095009.494023993844720.00003813815298.98800984958
1104389.905538875474108.793051444984671.01802630597
1113998.28704417143720.500552464624276.07353587817
1123719.662543208563442.820903063823996.5041833533
1133509.417032880833232.098110929843786.73595483183
1142672.449291151052536.403441862982808.49514043912

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
103 & 1947.58190806176 & 1726.60026838129 & 2168.56354774222 \tabularnewline
104 & 3337.57580194295 & 3103.66115244467 & 3571.49045144124 \tabularnewline
105 & 4282.25322354332 & 4032.08312618455 & 4532.42332090209 \tabularnewline
106 & 4562.61424411506 & 4302.00907671979 & 4823.21941151034 \tabularnewline
107 & 5331.33592189944 & 5049.29564316104 & 5613.37620063784 \tabularnewline
108 & 4980.99350540246 & 4699.38145406586 & 5262.60555673906 \tabularnewline
109 & 5009.49402399384 & 4720.0000381381 & 5298.98800984958 \tabularnewline
110 & 4389.90553887547 & 4108.79305144498 & 4671.01802630597 \tabularnewline
111 & 3998.2870441714 & 3720.50055246462 & 4276.07353587817 \tabularnewline
112 & 3719.66254320856 & 3442.82090306382 & 3996.5041833533 \tabularnewline
113 & 3509.41703288083 & 3232.09811092984 & 3786.73595483183 \tabularnewline
114 & 2672.44929115105 & 2536.40344186298 & 2808.49514043912 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77430&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]103[/C][C]1947.58190806176[/C][C]1726.60026838129[/C][C]2168.56354774222[/C][/ROW]
[ROW][C]104[/C][C]3337.57580194295[/C][C]3103.66115244467[/C][C]3571.49045144124[/C][/ROW]
[ROW][C]105[/C][C]4282.25322354332[/C][C]4032.08312618455[/C][C]4532.42332090209[/C][/ROW]
[ROW][C]106[/C][C]4562.61424411506[/C][C]4302.00907671979[/C][C]4823.21941151034[/C][/ROW]
[ROW][C]107[/C][C]5331.33592189944[/C][C]5049.29564316104[/C][C]5613.37620063784[/C][/ROW]
[ROW][C]108[/C][C]4980.99350540246[/C][C]4699.38145406586[/C][C]5262.60555673906[/C][/ROW]
[ROW][C]109[/C][C]5009.49402399384[/C][C]4720.0000381381[/C][C]5298.98800984958[/C][/ROW]
[ROW][C]110[/C][C]4389.90553887547[/C][C]4108.79305144498[/C][C]4671.01802630597[/C][/ROW]
[ROW][C]111[/C][C]3998.2870441714[/C][C]3720.50055246462[/C][C]4276.07353587817[/C][/ROW]
[ROW][C]112[/C][C]3719.66254320856[/C][C]3442.82090306382[/C][C]3996.5041833533[/C][/ROW]
[ROW][C]113[/C][C]3509.41703288083[/C][C]3232.09811092984[/C][C]3786.73595483183[/C][/ROW]
[ROW][C]114[/C][C]2672.44929115105[/C][C]2536.40344186298[/C][C]2808.49514043912[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77430&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77430&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
1031947.581908061761726.600268381292168.56354774222
1043337.575801942953103.661152444673571.49045144124
1054282.253223543324032.083126184554532.42332090209
1064562.614244115064302.009076719794823.21941151034
1075331.335921899445049.295643161045613.37620063784
1084980.993505402464699.381454065865262.60555673906
1095009.494023993844720.00003813815298.98800984958
1104389.905538875474108.793051444984671.01802630597
1113998.28704417143720.500552464624276.07353587817
1123719.662543208563442.820903063823996.5041833533
1133509.417032880833232.098110929843786.73595483183
1142672.449291151052536.403441862982808.49514043912



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')