Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 22 Dec 2010 14:12:30 +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/Dec/22/t12930271468ni6uky2g9fy43o.htm/, Retrieved Sun, 05 May 2024 23:20:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114227, Retrieved Sun, 05 May 2024 23:20:18 +0000
QR Codes:

Original text written by user:voorspelling 10.2 boeken
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [voorspelling 10.2...] [2010-12-22 14:12:30] [d2d436c33b2083ac16b3a67b544ba71f] [Current]
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Dataseries X:
90
69.3
87.3
57.4
56.2
61.6
77.7
177.2
97.6
81.6
96.8
191.3
106
75.1
72
63.5
57.4
62.3
79.4
178.1
109.3
85.2
102.7
193.7
108.4
73.4
85.9
58.5
58.6
62.7
77.5
180.5
102.2
82.6
97.8
197.8
93.8
72.4
77.7
58.7
53.1
64.3
76.4
188.4
105.5
79.8
96.1
202.5
97.3
89.5
64.7
61.2
57.8
62
76.3
195
110.9
81.4
101.7
202.2
97.4
68.5
86.8
59.1
62.4
66.2
68
198.5
120.4
90.2
103.2
207.3
106.4
75.5
97.3
60
67.5
71.2
73.7
213.3
114.6
96.1
117
229.2
105.6
99.9
79.3
72.5
67.4
78.3
85.7
177.4
113.6
94.1
105.7
228.3
100.3
70.3
94.2
66.5
64.4
73.7
87.9
152.2
97.3
89.3
107.6
228.4




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=114227&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=114227&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114227&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
alpha0.388480381575032
beta0.079378799348397
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.388480381575032 \tabularnewline
beta & 0.079378799348397 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114227&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]0.388480381575032[/C][/ROW]
[ROW][C]beta[/C][C]0.079378799348397[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114227&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114227&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
alpha0.388480381575032
beta0.079378799348397
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
387.348.638.7
457.444.127586779209313.2724132207907
556.230.186337760713126.013662239287
661.621.99700008934539.602999910655
777.720.308095418355157.3919045816449
8177.227.2996314817916149.900368518208
997.674.851384506608522.7486154933915
1081.673.70867747164417.8913225283559
1196.867.037549147788129.7624508522119
12191.369.780712960143121.519287039857
13106111.916910673859-5.91691067385916
1475.1104.3641852701-29.2641852700999
157286.8390789316744-14.8390789316744
1663.574.4602491540468-10.9602491540468
1757.463.250286280699-5.850286280699
1862.353.84503783453528.45496216546477
1979.450.257824329982129.1421756700179
20178.155.605847789181122.494152210819
21109.3100.9966479036678.30335209633299
2285.2102.282613768227-17.0826137682267
23102.793.1798515511059.52014844889507
24193.794.705314380368598.9946856196315
25108.4134.04258919058-25.6425891905805
2673.4124.169984676402-50.769984676402
2785.9102.970280563629-17.0702805636285
2858.594.3358523079252-35.8358523079252
2958.677.3062935949926-18.7062935949926
3062.766.3543844237556-3.65438442375563
3177.561.137156030003916.3628439699961
32180.564.2008109189472116.299189081053
33102.2109.674105741473-7.47410574147283
3482.6106.833423969598-24.2334239695977
3597.896.73478718753311.06521281246687
36197.896.4970225565805101.302977443419
3793.8138.323553657549-44.5235536575489
3872.4122.126360757447-49.7263607574465
3977.7102.374562299322-24.6745622993225
4058.791.5940039658122-32.8940039658122
4153.176.6059979017651-23.5059979017651
4264.364.5401910606676-0.240191060667613
4376.461.505286941590214.8947130584098
44188.464.8093059990854123.590694000915
45105.5114.15076057243-8.65076057243009
4679.8111.852239990084-32.0522399900841
4796.199.4743054237077-3.37430542370771
48202.598.133132005557104.366867994443
4997.3141.865662946582-44.5656629465819
5089.5126.366551354878-36.8665513548784
5164.7112.721535810545-48.0215358105447
5261.293.26218244586-32.06218244586
5357.879.0140198389737-21.2140198389737
546268.3259765970259-6.32597659702591
5576.363.226571262095913.0734287379041
5619566.0666010251793128.933398974821
57110.9117.8918891598-6.9918891598
5881.4116.697259865209-35.2972598652093
59101.7103.418084005214-1.71808400521401
60202.2103.13077845725399.0692215427473
6197.4145.052371938275-47.6523719382755
6268.5128.5060435415-60.0060435415
6386.8105.31014334553-18.5101433455298
6459.197.6637870342588-38.5637870342588
6562.481.0377879722635-18.6377879722635
6666.271.577913180987-5.37791318098701
676867.10340032804450.896599671955514
68198.565.0940611617671133.405938838233
69120.4118.6758537487081.72414625129198
7090.2121.155020986148-30.9550209861484
71103.2109.984409594208-6.78440959420841
72207.3107.99439497914499.3056050208558
73106.4150.280567217266-43.8805672172662
7475.5135.588570914034-60.0885709140336
7597.3112.747125503834-15.4471255038337
7660106.771661190078-46.7716611900785
7767.587.1849266142028-19.6849266142028
7871.277.5138308482658-6.31383084826578
7973.772.84244319478170.857556805218323
80213.370.9834435236719142.316556476328
81114.6128.467120796611-13.8671207966114
8296.1124.848881649245-28.7488816492445
83117114.5628380490692.43716195093079
84229.2116.467115588559112.732884411441
85105.6164.695473411175-59.0954734111746
8699.9144.349551828394-44.4495518283938
8779.3128.322587897676-49.0225878976756
8872.5109.007374417674-36.5073744176737
8967.493.4282940616907-26.0282940616907
9078.381.1174935712128-2.81749357121281
9185.777.73675036329587.96324963670418
92177.478.789677965673598.6103220343265
93113.6118.098071820628-4.49807182062801
9494.1117.212169968524-23.112169968524
95105.7108.382343724036-2.6823437240355
96228.3107.406388456074120.893611543926
97100.3158.165276589424-57.8652765894245
9870.3137.69544596786-67.3954459678596
9994.2111.445050980946-17.2450509809459
10066.5104.145313105131-37.6453131051313
10164.487.7596010946749-23.3596010946749
10273.776.2032654359678-2.50326543596778
10387.972.672013549966715.2279864500333
104152.276.498592198725275.7014078012747
10597.3106.152321005549-8.85232100554869
10689.3102.685605018411-13.3856050184113
107107.697.045023803864110.5549761961359
108228.4101.030373637203127.369626362797

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 87.3 & 48.6 & 38.7 \tabularnewline
4 & 57.4 & 44.1275867792093 & 13.2724132207907 \tabularnewline
5 & 56.2 & 30.1863377607131 & 26.013662239287 \tabularnewline
6 & 61.6 & 21.997000089345 & 39.602999910655 \tabularnewline
7 & 77.7 & 20.3080954183551 & 57.3919045816449 \tabularnewline
8 & 177.2 & 27.2996314817916 & 149.900368518208 \tabularnewline
9 & 97.6 & 74.8513845066085 & 22.7486154933915 \tabularnewline
10 & 81.6 & 73.7086774716441 & 7.8913225283559 \tabularnewline
11 & 96.8 & 67.0375491477881 & 29.7624508522119 \tabularnewline
12 & 191.3 & 69.780712960143 & 121.519287039857 \tabularnewline
13 & 106 & 111.916910673859 & -5.91691067385916 \tabularnewline
14 & 75.1 & 104.3641852701 & -29.2641852700999 \tabularnewline
15 & 72 & 86.8390789316744 & -14.8390789316744 \tabularnewline
16 & 63.5 & 74.4602491540468 & -10.9602491540468 \tabularnewline
17 & 57.4 & 63.250286280699 & -5.850286280699 \tabularnewline
18 & 62.3 & 53.8450378345352 & 8.45496216546477 \tabularnewline
19 & 79.4 & 50.2578243299821 & 29.1421756700179 \tabularnewline
20 & 178.1 & 55.605847789181 & 122.494152210819 \tabularnewline
21 & 109.3 & 100.996647903667 & 8.30335209633299 \tabularnewline
22 & 85.2 & 102.282613768227 & -17.0826137682267 \tabularnewline
23 & 102.7 & 93.179851551105 & 9.52014844889507 \tabularnewline
24 & 193.7 & 94.7053143803685 & 98.9946856196315 \tabularnewline
25 & 108.4 & 134.04258919058 & -25.6425891905805 \tabularnewline
26 & 73.4 & 124.169984676402 & -50.769984676402 \tabularnewline
27 & 85.9 & 102.970280563629 & -17.0702805636285 \tabularnewline
28 & 58.5 & 94.3358523079252 & -35.8358523079252 \tabularnewline
29 & 58.6 & 77.3062935949926 & -18.7062935949926 \tabularnewline
30 & 62.7 & 66.3543844237556 & -3.65438442375563 \tabularnewline
31 & 77.5 & 61.1371560300039 & 16.3628439699961 \tabularnewline
32 & 180.5 & 64.2008109189472 & 116.299189081053 \tabularnewline
33 & 102.2 & 109.674105741473 & -7.47410574147283 \tabularnewline
34 & 82.6 & 106.833423969598 & -24.2334239695977 \tabularnewline
35 & 97.8 & 96.7347871875331 & 1.06521281246687 \tabularnewline
36 & 197.8 & 96.4970225565805 & 101.302977443419 \tabularnewline
37 & 93.8 & 138.323553657549 & -44.5235536575489 \tabularnewline
38 & 72.4 & 122.126360757447 & -49.7263607574465 \tabularnewline
39 & 77.7 & 102.374562299322 & -24.6745622993225 \tabularnewline
40 & 58.7 & 91.5940039658122 & -32.8940039658122 \tabularnewline
41 & 53.1 & 76.6059979017651 & -23.5059979017651 \tabularnewline
42 & 64.3 & 64.5401910606676 & -0.240191060667613 \tabularnewline
43 & 76.4 & 61.5052869415902 & 14.8947130584098 \tabularnewline
44 & 188.4 & 64.8093059990854 & 123.590694000915 \tabularnewline
45 & 105.5 & 114.15076057243 & -8.65076057243009 \tabularnewline
46 & 79.8 & 111.852239990084 & -32.0522399900841 \tabularnewline
47 & 96.1 & 99.4743054237077 & -3.37430542370771 \tabularnewline
48 & 202.5 & 98.133132005557 & 104.366867994443 \tabularnewline
49 & 97.3 & 141.865662946582 & -44.5656629465819 \tabularnewline
50 & 89.5 & 126.366551354878 & -36.8665513548784 \tabularnewline
51 & 64.7 & 112.721535810545 & -48.0215358105447 \tabularnewline
52 & 61.2 & 93.26218244586 & -32.06218244586 \tabularnewline
53 & 57.8 & 79.0140198389737 & -21.2140198389737 \tabularnewline
54 & 62 & 68.3259765970259 & -6.32597659702591 \tabularnewline
55 & 76.3 & 63.2265712620959 & 13.0734287379041 \tabularnewline
56 & 195 & 66.0666010251793 & 128.933398974821 \tabularnewline
57 & 110.9 & 117.8918891598 & -6.9918891598 \tabularnewline
58 & 81.4 & 116.697259865209 & -35.2972598652093 \tabularnewline
59 & 101.7 & 103.418084005214 & -1.71808400521401 \tabularnewline
60 & 202.2 & 103.130778457253 & 99.0692215427473 \tabularnewline
61 & 97.4 & 145.052371938275 & -47.6523719382755 \tabularnewline
62 & 68.5 & 128.5060435415 & -60.0060435415 \tabularnewline
63 & 86.8 & 105.31014334553 & -18.5101433455298 \tabularnewline
64 & 59.1 & 97.6637870342588 & -38.5637870342588 \tabularnewline
65 & 62.4 & 81.0377879722635 & -18.6377879722635 \tabularnewline
66 & 66.2 & 71.577913180987 & -5.37791318098701 \tabularnewline
67 & 68 & 67.1034003280445 & 0.896599671955514 \tabularnewline
68 & 198.5 & 65.0940611617671 & 133.405938838233 \tabularnewline
69 & 120.4 & 118.675853748708 & 1.72414625129198 \tabularnewline
70 & 90.2 & 121.155020986148 & -30.9550209861484 \tabularnewline
71 & 103.2 & 109.984409594208 & -6.78440959420841 \tabularnewline
72 & 207.3 & 107.994394979144 & 99.3056050208558 \tabularnewline
73 & 106.4 & 150.280567217266 & -43.8805672172662 \tabularnewline
74 & 75.5 & 135.588570914034 & -60.0885709140336 \tabularnewline
75 & 97.3 & 112.747125503834 & -15.4471255038337 \tabularnewline
76 & 60 & 106.771661190078 & -46.7716611900785 \tabularnewline
77 & 67.5 & 87.1849266142028 & -19.6849266142028 \tabularnewline
78 & 71.2 & 77.5138308482658 & -6.31383084826578 \tabularnewline
79 & 73.7 & 72.8424431947817 & 0.857556805218323 \tabularnewline
80 & 213.3 & 70.9834435236719 & 142.316556476328 \tabularnewline
81 & 114.6 & 128.467120796611 & -13.8671207966114 \tabularnewline
82 & 96.1 & 124.848881649245 & -28.7488816492445 \tabularnewline
83 & 117 & 114.562838049069 & 2.43716195093079 \tabularnewline
84 & 229.2 & 116.467115588559 & 112.732884411441 \tabularnewline
85 & 105.6 & 164.695473411175 & -59.0954734111746 \tabularnewline
86 & 99.9 & 144.349551828394 & -44.4495518283938 \tabularnewline
87 & 79.3 & 128.322587897676 & -49.0225878976756 \tabularnewline
88 & 72.5 & 109.007374417674 & -36.5073744176737 \tabularnewline
89 & 67.4 & 93.4282940616907 & -26.0282940616907 \tabularnewline
90 & 78.3 & 81.1174935712128 & -2.81749357121281 \tabularnewline
91 & 85.7 & 77.7367503632958 & 7.96324963670418 \tabularnewline
92 & 177.4 & 78.7896779656735 & 98.6103220343265 \tabularnewline
93 & 113.6 & 118.098071820628 & -4.49807182062801 \tabularnewline
94 & 94.1 & 117.212169968524 & -23.112169968524 \tabularnewline
95 & 105.7 & 108.382343724036 & -2.6823437240355 \tabularnewline
96 & 228.3 & 107.406388456074 & 120.893611543926 \tabularnewline
97 & 100.3 & 158.165276589424 & -57.8652765894245 \tabularnewline
98 & 70.3 & 137.69544596786 & -67.3954459678596 \tabularnewline
99 & 94.2 & 111.445050980946 & -17.2450509809459 \tabularnewline
100 & 66.5 & 104.145313105131 & -37.6453131051313 \tabularnewline
101 & 64.4 & 87.7596010946749 & -23.3596010946749 \tabularnewline
102 & 73.7 & 76.2032654359678 & -2.50326543596778 \tabularnewline
103 & 87.9 & 72.6720135499667 & 15.2279864500333 \tabularnewline
104 & 152.2 & 76.4985921987252 & 75.7014078012747 \tabularnewline
105 & 97.3 & 106.152321005549 & -8.85232100554869 \tabularnewline
106 & 89.3 & 102.685605018411 & -13.3856050184113 \tabularnewline
107 & 107.6 & 97.0450238038641 & 10.5549761961359 \tabularnewline
108 & 228.4 & 101.030373637203 & 127.369626362797 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114227&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]87.3[/C][C]48.6[/C][C]38.7[/C][/ROW]
[ROW][C]4[/C][C]57.4[/C][C]44.1275867792093[/C][C]13.2724132207907[/C][/ROW]
[ROW][C]5[/C][C]56.2[/C][C]30.1863377607131[/C][C]26.013662239287[/C][/ROW]
[ROW][C]6[/C][C]61.6[/C][C]21.997000089345[/C][C]39.602999910655[/C][/ROW]
[ROW][C]7[/C][C]77.7[/C][C]20.3080954183551[/C][C]57.3919045816449[/C][/ROW]
[ROW][C]8[/C][C]177.2[/C][C]27.2996314817916[/C][C]149.900368518208[/C][/ROW]
[ROW][C]9[/C][C]97.6[/C][C]74.8513845066085[/C][C]22.7486154933915[/C][/ROW]
[ROW][C]10[/C][C]81.6[/C][C]73.7086774716441[/C][C]7.8913225283559[/C][/ROW]
[ROW][C]11[/C][C]96.8[/C][C]67.0375491477881[/C][C]29.7624508522119[/C][/ROW]
[ROW][C]12[/C][C]191.3[/C][C]69.780712960143[/C][C]121.519287039857[/C][/ROW]
[ROW][C]13[/C][C]106[/C][C]111.916910673859[/C][C]-5.91691067385916[/C][/ROW]
[ROW][C]14[/C][C]75.1[/C][C]104.3641852701[/C][C]-29.2641852700999[/C][/ROW]
[ROW][C]15[/C][C]72[/C][C]86.8390789316744[/C][C]-14.8390789316744[/C][/ROW]
[ROW][C]16[/C][C]63.5[/C][C]74.4602491540468[/C][C]-10.9602491540468[/C][/ROW]
[ROW][C]17[/C][C]57.4[/C][C]63.250286280699[/C][C]-5.850286280699[/C][/ROW]
[ROW][C]18[/C][C]62.3[/C][C]53.8450378345352[/C][C]8.45496216546477[/C][/ROW]
[ROW][C]19[/C][C]79.4[/C][C]50.2578243299821[/C][C]29.1421756700179[/C][/ROW]
[ROW][C]20[/C][C]178.1[/C][C]55.605847789181[/C][C]122.494152210819[/C][/ROW]
[ROW][C]21[/C][C]109.3[/C][C]100.996647903667[/C][C]8.30335209633299[/C][/ROW]
[ROW][C]22[/C][C]85.2[/C][C]102.282613768227[/C][C]-17.0826137682267[/C][/ROW]
[ROW][C]23[/C][C]102.7[/C][C]93.179851551105[/C][C]9.52014844889507[/C][/ROW]
[ROW][C]24[/C][C]193.7[/C][C]94.7053143803685[/C][C]98.9946856196315[/C][/ROW]
[ROW][C]25[/C][C]108.4[/C][C]134.04258919058[/C][C]-25.6425891905805[/C][/ROW]
[ROW][C]26[/C][C]73.4[/C][C]124.169984676402[/C][C]-50.769984676402[/C][/ROW]
[ROW][C]27[/C][C]85.9[/C][C]102.970280563629[/C][C]-17.0702805636285[/C][/ROW]
[ROW][C]28[/C][C]58.5[/C][C]94.3358523079252[/C][C]-35.8358523079252[/C][/ROW]
[ROW][C]29[/C][C]58.6[/C][C]77.3062935949926[/C][C]-18.7062935949926[/C][/ROW]
[ROW][C]30[/C][C]62.7[/C][C]66.3543844237556[/C][C]-3.65438442375563[/C][/ROW]
[ROW][C]31[/C][C]77.5[/C][C]61.1371560300039[/C][C]16.3628439699961[/C][/ROW]
[ROW][C]32[/C][C]180.5[/C][C]64.2008109189472[/C][C]116.299189081053[/C][/ROW]
[ROW][C]33[/C][C]102.2[/C][C]109.674105741473[/C][C]-7.47410574147283[/C][/ROW]
[ROW][C]34[/C][C]82.6[/C][C]106.833423969598[/C][C]-24.2334239695977[/C][/ROW]
[ROW][C]35[/C][C]97.8[/C][C]96.7347871875331[/C][C]1.06521281246687[/C][/ROW]
[ROW][C]36[/C][C]197.8[/C][C]96.4970225565805[/C][C]101.302977443419[/C][/ROW]
[ROW][C]37[/C][C]93.8[/C][C]138.323553657549[/C][C]-44.5235536575489[/C][/ROW]
[ROW][C]38[/C][C]72.4[/C][C]122.126360757447[/C][C]-49.7263607574465[/C][/ROW]
[ROW][C]39[/C][C]77.7[/C][C]102.374562299322[/C][C]-24.6745622993225[/C][/ROW]
[ROW][C]40[/C][C]58.7[/C][C]91.5940039658122[/C][C]-32.8940039658122[/C][/ROW]
[ROW][C]41[/C][C]53.1[/C][C]76.6059979017651[/C][C]-23.5059979017651[/C][/ROW]
[ROW][C]42[/C][C]64.3[/C][C]64.5401910606676[/C][C]-0.240191060667613[/C][/ROW]
[ROW][C]43[/C][C]76.4[/C][C]61.5052869415902[/C][C]14.8947130584098[/C][/ROW]
[ROW][C]44[/C][C]188.4[/C][C]64.8093059990854[/C][C]123.590694000915[/C][/ROW]
[ROW][C]45[/C][C]105.5[/C][C]114.15076057243[/C][C]-8.65076057243009[/C][/ROW]
[ROW][C]46[/C][C]79.8[/C][C]111.852239990084[/C][C]-32.0522399900841[/C][/ROW]
[ROW][C]47[/C][C]96.1[/C][C]99.4743054237077[/C][C]-3.37430542370771[/C][/ROW]
[ROW][C]48[/C][C]202.5[/C][C]98.133132005557[/C][C]104.366867994443[/C][/ROW]
[ROW][C]49[/C][C]97.3[/C][C]141.865662946582[/C][C]-44.5656629465819[/C][/ROW]
[ROW][C]50[/C][C]89.5[/C][C]126.366551354878[/C][C]-36.8665513548784[/C][/ROW]
[ROW][C]51[/C][C]64.7[/C][C]112.721535810545[/C][C]-48.0215358105447[/C][/ROW]
[ROW][C]52[/C][C]61.2[/C][C]93.26218244586[/C][C]-32.06218244586[/C][/ROW]
[ROW][C]53[/C][C]57.8[/C][C]79.0140198389737[/C][C]-21.2140198389737[/C][/ROW]
[ROW][C]54[/C][C]62[/C][C]68.3259765970259[/C][C]-6.32597659702591[/C][/ROW]
[ROW][C]55[/C][C]76.3[/C][C]63.2265712620959[/C][C]13.0734287379041[/C][/ROW]
[ROW][C]56[/C][C]195[/C][C]66.0666010251793[/C][C]128.933398974821[/C][/ROW]
[ROW][C]57[/C][C]110.9[/C][C]117.8918891598[/C][C]-6.9918891598[/C][/ROW]
[ROW][C]58[/C][C]81.4[/C][C]116.697259865209[/C][C]-35.2972598652093[/C][/ROW]
[ROW][C]59[/C][C]101.7[/C][C]103.418084005214[/C][C]-1.71808400521401[/C][/ROW]
[ROW][C]60[/C][C]202.2[/C][C]103.130778457253[/C][C]99.0692215427473[/C][/ROW]
[ROW][C]61[/C][C]97.4[/C][C]145.052371938275[/C][C]-47.6523719382755[/C][/ROW]
[ROW][C]62[/C][C]68.5[/C][C]128.5060435415[/C][C]-60.0060435415[/C][/ROW]
[ROW][C]63[/C][C]86.8[/C][C]105.31014334553[/C][C]-18.5101433455298[/C][/ROW]
[ROW][C]64[/C][C]59.1[/C][C]97.6637870342588[/C][C]-38.5637870342588[/C][/ROW]
[ROW][C]65[/C][C]62.4[/C][C]81.0377879722635[/C][C]-18.6377879722635[/C][/ROW]
[ROW][C]66[/C][C]66.2[/C][C]71.577913180987[/C][C]-5.37791318098701[/C][/ROW]
[ROW][C]67[/C][C]68[/C][C]67.1034003280445[/C][C]0.896599671955514[/C][/ROW]
[ROW][C]68[/C][C]198.5[/C][C]65.0940611617671[/C][C]133.405938838233[/C][/ROW]
[ROW][C]69[/C][C]120.4[/C][C]118.675853748708[/C][C]1.72414625129198[/C][/ROW]
[ROW][C]70[/C][C]90.2[/C][C]121.155020986148[/C][C]-30.9550209861484[/C][/ROW]
[ROW][C]71[/C][C]103.2[/C][C]109.984409594208[/C][C]-6.78440959420841[/C][/ROW]
[ROW][C]72[/C][C]207.3[/C][C]107.994394979144[/C][C]99.3056050208558[/C][/ROW]
[ROW][C]73[/C][C]106.4[/C][C]150.280567217266[/C][C]-43.8805672172662[/C][/ROW]
[ROW][C]74[/C][C]75.5[/C][C]135.588570914034[/C][C]-60.0885709140336[/C][/ROW]
[ROW][C]75[/C][C]97.3[/C][C]112.747125503834[/C][C]-15.4471255038337[/C][/ROW]
[ROW][C]76[/C][C]60[/C][C]106.771661190078[/C][C]-46.7716611900785[/C][/ROW]
[ROW][C]77[/C][C]67.5[/C][C]87.1849266142028[/C][C]-19.6849266142028[/C][/ROW]
[ROW][C]78[/C][C]71.2[/C][C]77.5138308482658[/C][C]-6.31383084826578[/C][/ROW]
[ROW][C]79[/C][C]73.7[/C][C]72.8424431947817[/C][C]0.857556805218323[/C][/ROW]
[ROW][C]80[/C][C]213.3[/C][C]70.9834435236719[/C][C]142.316556476328[/C][/ROW]
[ROW][C]81[/C][C]114.6[/C][C]128.467120796611[/C][C]-13.8671207966114[/C][/ROW]
[ROW][C]82[/C][C]96.1[/C][C]124.848881649245[/C][C]-28.7488816492445[/C][/ROW]
[ROW][C]83[/C][C]117[/C][C]114.562838049069[/C][C]2.43716195093079[/C][/ROW]
[ROW][C]84[/C][C]229.2[/C][C]116.467115588559[/C][C]112.732884411441[/C][/ROW]
[ROW][C]85[/C][C]105.6[/C][C]164.695473411175[/C][C]-59.0954734111746[/C][/ROW]
[ROW][C]86[/C][C]99.9[/C][C]144.349551828394[/C][C]-44.4495518283938[/C][/ROW]
[ROW][C]87[/C][C]79.3[/C][C]128.322587897676[/C][C]-49.0225878976756[/C][/ROW]
[ROW][C]88[/C][C]72.5[/C][C]109.007374417674[/C][C]-36.5073744176737[/C][/ROW]
[ROW][C]89[/C][C]67.4[/C][C]93.4282940616907[/C][C]-26.0282940616907[/C][/ROW]
[ROW][C]90[/C][C]78.3[/C][C]81.1174935712128[/C][C]-2.81749357121281[/C][/ROW]
[ROW][C]91[/C][C]85.7[/C][C]77.7367503632958[/C][C]7.96324963670418[/C][/ROW]
[ROW][C]92[/C][C]177.4[/C][C]78.7896779656735[/C][C]98.6103220343265[/C][/ROW]
[ROW][C]93[/C][C]113.6[/C][C]118.098071820628[/C][C]-4.49807182062801[/C][/ROW]
[ROW][C]94[/C][C]94.1[/C][C]117.212169968524[/C][C]-23.112169968524[/C][/ROW]
[ROW][C]95[/C][C]105.7[/C][C]108.382343724036[/C][C]-2.6823437240355[/C][/ROW]
[ROW][C]96[/C][C]228.3[/C][C]107.406388456074[/C][C]120.893611543926[/C][/ROW]
[ROW][C]97[/C][C]100.3[/C][C]158.165276589424[/C][C]-57.8652765894245[/C][/ROW]
[ROW][C]98[/C][C]70.3[/C][C]137.69544596786[/C][C]-67.3954459678596[/C][/ROW]
[ROW][C]99[/C][C]94.2[/C][C]111.445050980946[/C][C]-17.2450509809459[/C][/ROW]
[ROW][C]100[/C][C]66.5[/C][C]104.145313105131[/C][C]-37.6453131051313[/C][/ROW]
[ROW][C]101[/C][C]64.4[/C][C]87.7596010946749[/C][C]-23.3596010946749[/C][/ROW]
[ROW][C]102[/C][C]73.7[/C][C]76.2032654359678[/C][C]-2.50326543596778[/C][/ROW]
[ROW][C]103[/C][C]87.9[/C][C]72.6720135499667[/C][C]15.2279864500333[/C][/ROW]
[ROW][C]104[/C][C]152.2[/C][C]76.4985921987252[/C][C]75.7014078012747[/C][/ROW]
[ROW][C]105[/C][C]97.3[/C][C]106.152321005549[/C][C]-8.85232100554869[/C][/ROW]
[ROW][C]106[/C][C]89.3[/C][C]102.685605018411[/C][C]-13.3856050184113[/C][/ROW]
[ROW][C]107[/C][C]107.6[/C][C]97.0450238038641[/C][C]10.5549761961359[/C][/ROW]
[ROW][C]108[/C][C]228.4[/C][C]101.030373637203[/C][C]127.369626362797[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114227&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114227&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
387.348.638.7
457.444.127586779209313.2724132207907
556.230.186337760713126.013662239287
661.621.99700008934539.602999910655
777.720.308095418355157.3919045816449
8177.227.2996314817916149.900368518208
997.674.851384506608522.7486154933915
1081.673.70867747164417.8913225283559
1196.867.037549147788129.7624508522119
12191.369.780712960143121.519287039857
13106111.916910673859-5.91691067385916
1475.1104.3641852701-29.2641852700999
157286.8390789316744-14.8390789316744
1663.574.4602491540468-10.9602491540468
1757.463.250286280699-5.850286280699
1862.353.84503783453528.45496216546477
1979.450.257824329982129.1421756700179
20178.155.605847789181122.494152210819
21109.3100.9966479036678.30335209633299
2285.2102.282613768227-17.0826137682267
23102.793.1798515511059.52014844889507
24193.794.705314380368598.9946856196315
25108.4134.04258919058-25.6425891905805
2673.4124.169984676402-50.769984676402
2785.9102.970280563629-17.0702805636285
2858.594.3358523079252-35.8358523079252
2958.677.3062935949926-18.7062935949926
3062.766.3543844237556-3.65438442375563
3177.561.137156030003916.3628439699961
32180.564.2008109189472116.299189081053
33102.2109.674105741473-7.47410574147283
3482.6106.833423969598-24.2334239695977
3597.896.73478718753311.06521281246687
36197.896.4970225565805101.302977443419
3793.8138.323553657549-44.5235536575489
3872.4122.126360757447-49.7263607574465
3977.7102.374562299322-24.6745622993225
4058.791.5940039658122-32.8940039658122
4153.176.6059979017651-23.5059979017651
4264.364.5401910606676-0.240191060667613
4376.461.505286941590214.8947130584098
44188.464.8093059990854123.590694000915
45105.5114.15076057243-8.65076057243009
4679.8111.852239990084-32.0522399900841
4796.199.4743054237077-3.37430542370771
48202.598.133132005557104.366867994443
4997.3141.865662946582-44.5656629465819
5089.5126.366551354878-36.8665513548784
5164.7112.721535810545-48.0215358105447
5261.293.26218244586-32.06218244586
5357.879.0140198389737-21.2140198389737
546268.3259765970259-6.32597659702591
5576.363.226571262095913.0734287379041
5619566.0666010251793128.933398974821
57110.9117.8918891598-6.9918891598
5881.4116.697259865209-35.2972598652093
59101.7103.418084005214-1.71808400521401
60202.2103.13077845725399.0692215427473
6197.4145.052371938275-47.6523719382755
6268.5128.5060435415-60.0060435415
6386.8105.31014334553-18.5101433455298
6459.197.6637870342588-38.5637870342588
6562.481.0377879722635-18.6377879722635
6666.271.577913180987-5.37791318098701
676867.10340032804450.896599671955514
68198.565.0940611617671133.405938838233
69120.4118.6758537487081.72414625129198
7090.2121.155020986148-30.9550209861484
71103.2109.984409594208-6.78440959420841
72207.3107.99439497914499.3056050208558
73106.4150.280567217266-43.8805672172662
7475.5135.588570914034-60.0885709140336
7597.3112.747125503834-15.4471255038337
7660106.771661190078-46.7716611900785
7767.587.1849266142028-19.6849266142028
7871.277.5138308482658-6.31383084826578
7973.772.84244319478170.857556805218323
80213.370.9834435236719142.316556476328
81114.6128.467120796611-13.8671207966114
8296.1124.848881649245-28.7488816492445
83117114.5628380490692.43716195093079
84229.2116.467115588559112.732884411441
85105.6164.695473411175-59.0954734111746
8699.9144.349551828394-44.4495518283938
8779.3128.322587897676-49.0225878976756
8872.5109.007374417674-36.5073744176737
8967.493.4282940616907-26.0282940616907
9078.381.1174935712128-2.81749357121281
9185.777.73675036329587.96324963670418
92177.478.789677965673598.6103220343265
93113.6118.098071820628-4.49807182062801
9494.1117.212169968524-23.112169968524
95105.7108.382343724036-2.6823437240355
96228.3107.406388456074120.893611543926
97100.3158.165276589424-57.8652765894245
9870.3137.69544596786-67.3954459678596
9994.2111.445050980946-17.2450509809459
10066.5104.145313105131-37.6453131051313
10164.487.7596010946749-23.3596010946749
10273.776.2032654359678-2.50326543596778
10387.972.672013549966715.2279864500333
104152.276.498592198725275.7014078012747
10597.3106.152321005549-8.85232100554869
10689.3102.685605018411-13.3856050184113
107107.697.045023803864110.5549761961359
108228.4101.030373637203127.369626362797







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109154.32363404326447.272984601823261.374283484706
110158.13629339883742.0553178321554274.21726896552
111161.9489527544136.2628137538313287.63509175499
112165.76161210998429.9371870635074301.58603715646
113169.57427146555723.1147393626518316.033803568461
114173.3869308211315.8269079760202330.946953666239
115177.1995901767038.10089664849966346.298283704905
116181.012249532276-0.0397086291137612362.064207693665
117184.824908887849-8.57438260678703378.224200382484
118188.637568243422-17.4851774468497394.760313933693
119192.450227598995-26.7563131865662411.656768384555
120196.262886954568-36.3738354169099428.899609326045

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 154.323634043264 & 47.272984601823 & 261.374283484706 \tabularnewline
110 & 158.136293398837 & 42.0553178321554 & 274.21726896552 \tabularnewline
111 & 161.94895275441 & 36.2628137538313 & 287.63509175499 \tabularnewline
112 & 165.761612109984 & 29.9371870635074 & 301.58603715646 \tabularnewline
113 & 169.574271465557 & 23.1147393626518 & 316.033803568461 \tabularnewline
114 & 173.38693082113 & 15.8269079760202 & 330.946953666239 \tabularnewline
115 & 177.199590176703 & 8.10089664849966 & 346.298283704905 \tabularnewline
116 & 181.012249532276 & -0.0397086291137612 & 362.064207693665 \tabularnewline
117 & 184.824908887849 & -8.57438260678703 & 378.224200382484 \tabularnewline
118 & 188.637568243422 & -17.4851774468497 & 394.760313933693 \tabularnewline
119 & 192.450227598995 & -26.7563131865662 & 411.656768384555 \tabularnewline
120 & 196.262886954568 & -36.3738354169099 & 428.899609326045 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114227&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]154.323634043264[/C][C]47.272984601823[/C][C]261.374283484706[/C][/ROW]
[ROW][C]110[/C][C]158.136293398837[/C][C]42.0553178321554[/C][C]274.21726896552[/C][/ROW]
[ROW][C]111[/C][C]161.94895275441[/C][C]36.2628137538313[/C][C]287.63509175499[/C][/ROW]
[ROW][C]112[/C][C]165.761612109984[/C][C]29.9371870635074[/C][C]301.58603715646[/C][/ROW]
[ROW][C]113[/C][C]169.574271465557[/C][C]23.1147393626518[/C][C]316.033803568461[/C][/ROW]
[ROW][C]114[/C][C]173.38693082113[/C][C]15.8269079760202[/C][C]330.946953666239[/C][/ROW]
[ROW][C]115[/C][C]177.199590176703[/C][C]8.10089664849966[/C][C]346.298283704905[/C][/ROW]
[ROW][C]116[/C][C]181.012249532276[/C][C]-0.0397086291137612[/C][C]362.064207693665[/C][/ROW]
[ROW][C]117[/C][C]184.824908887849[/C][C]-8.57438260678703[/C][C]378.224200382484[/C][/ROW]
[ROW][C]118[/C][C]188.637568243422[/C][C]-17.4851774468497[/C][C]394.760313933693[/C][/ROW]
[ROW][C]119[/C][C]192.450227598995[/C][C]-26.7563131865662[/C][C]411.656768384555[/C][/ROW]
[ROW][C]120[/C][C]196.262886954568[/C][C]-36.3738354169099[/C][C]428.899609326045[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114227&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114227&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
109154.32363404326447.272984601823261.374283484706
110158.13629339883742.0553178321554274.21726896552
111161.9489527544136.2628137538313287.63509175499
112165.76161210998429.9371870635074301.58603715646
113169.57427146555723.1147393626518316.033803568461
114173.3869308211315.8269079760202330.946953666239
115177.1995901767038.10089664849966346.298283704905
116181.012249532276-0.0397086291137612362.064207693665
117184.824908887849-8.57438260678703378.224200382484
118188.637568243422-17.4851774468497394.760313933693
119192.450227598995-26.7563131865662411.656768384555
120196.262886954568-36.3738354169099428.899609326045



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')