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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 12 Dec 2012 07:58:32 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/12/t13553171806kfzrynv9928n2m.htm/, Retrieved Sun, 28 Apr 2024 21:32:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198858, Retrieved Sun, 28 Apr 2024 21:32:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [Exponential Smoothing] [Paper Triple Expo...] [2012-12-10 21:28:15] [86dcce9422b96d4554cb918e531c1d5d]
- R P     [Exponential Smoothing] [PAPER SINGLE SMOO...] [2012-12-12 12:54:46] [86dcce9422b96d4554cb918e531c1d5d]
-   P         [Exponential Smoothing] [PAPER Double SMOO...] [2012-12-12 12:58:32] [c63d55528b56cf8bb48e0b5d1a959d8e] [Current]
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Dataseries X:
68.897
38.683
44.720
39.525
45.315
50.380
40.600
36.279
42.438
38.064
31.879
11.379
70.249
39.253
47.060
41.697
38.708
49.267
39.018
32.228
40.870
39.383
34.571
12.066
70.938
34.077
45.409
40.809
37.013
44.953
37.848
32.745
43.412
34.931
33.008
8.620
68.906
39.556
50.669
36.432
40.891
48.428
36.222
33.425
39.401
37.967
34.801
12.657
69.116
41.519
51.321
38.529
41.547
52.073
38.401
40.898
40.439
41.888
37.898
8.771
68.184
50.530
47.221
41.756
45.633
48.138
39.486
39.341
41.117
41.629
29.722
7.054
56.676
34.870
35.117
30.169
30.936
35.699
33.228
27.733
33.666
35.429
27.438
8.170
63.410
38.040
45.389
37.353
37.024
50.957
37.994
36.454
46.080
43.373
37.395
10.963
76.058
50.179
57.452
47.568
50.050
50.856
41.992
39.284
44.521
43.832
41.153
17.100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198858&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198858&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198858&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 time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.396545148452336
beta0.452593371751002
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.396545148452336 \tabularnewline
beta & 0.452593371751002 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198858&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]0.396545148452336[/C][/ROW]
[ROW][C]beta[/C][C]0.452593371751002[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198858&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198858&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
alpha0.396545148452336
beta0.452593371751002
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
344.728.4689999999999936.251
439.525-0.86374051487759540.3887405148776
545.315-1.3069631706484146.6219631706484
650.389.0889848783698241.2910151216302
740.624.781622841589515.8183771584105
836.27933.21219257040833.06680742959175
942.43837.1366004824445.30139951755601
1038.06442.8985868630186-4.83458686301862
1131.87943.77351579933-11.89451579933
1211.37939.7141113384508-28.3351113384508
1370.24924.04986104299546.1991389570049
1439.25346.2333367686341-6.98033676863415
1547.0646.07596249050650.984037509493497
1641.69749.2534310512937-7.55643105129366
1738.70847.6880375554721-8.98003755547212
1849.26743.94643918890355.32056081109646
1939.01846.8305744902093-7.81257449020925
2032.22843.1046770082994-10.8766770082994
2140.8736.21164700912484.65835299087518
2239.38336.31500966133263.06799033866738
2334.57136.3383453149348-1.76734531493479
2412.06634.1270600608813-22.0610600608813
2570.93819.90902047747551.028979522525
2634.07743.832841548624-9.75584154862399
2745.40941.90181968863843.50718031136162
2840.80945.8596314483995-5.05063144839954
2937.01345.5174289308376-8.50442893083758
3044.95342.27931840203672.67368159796332
3137.84843.9536889167836-6.10568891678356
3232.74541.0508320311488-8.30583203114877
3343.41235.78484061331597.62715938668412
3434.93138.205874202333-3.27487420233304
3533.00835.7160054542737-2.70800545427374
368.6232.9649099838898-24.3449099838898
3768.90617.264533782838751.6414662171614
3839.55640.9644717271879-1.40847172718792
3950.66943.37493051362987.29406948637024
4036.43250.5454334785199-14.1134334785199
4140.89146.6939047943997-5.80290479439967
4248.42845.09640711324653.33159288675353
4336.22247.7190834926714-11.4970834926714
4433.42542.3980960156641-8.97309601566413
4539.40136.46754873308192.93345126691813
4637.96735.78496237985282.1820376201472
4734.80135.1960249683759-0.395024968375857
4812.65733.5142692952083-20.8572692952083
4969.11619.974978494727449.1410215052726
5041.51943.012691546968-1.49369154696803
5151.32145.70337643782565.61762356217442
5238.52952.2222345527635-13.6932345527634
5341.54748.6258900203414-7.07889002034141
5452.07346.38195709761635.69104290238374
5538.40150.2232716809576-11.8222716809576
5640.89844.9979794235232-4.09997942352317
5740.43942.0990861949048-1.66008619490481
5841.88839.86977896750712.01822103249286
5937.89839.4613042334551-1.56330423345506
608.77137.3520210270772-28.5810210270772
6168.18419.399451544950948.7845484550491
6250.5340.88136699471119.64863300528891
6347.22148.5758009638906-1.35480096389059
6441.75651.6637254266796-9.90772542667963
6545.63349.5818529903989-3.94885299039888
6648.13849.1542272291666-1.01622722916661
6739.48649.7071339190346-10.2211339190346
6839.34144.7754547372586-5.43445473725858
6941.11740.76656823157230.350431768427676
7041.62939.11454369216942.51445630783057
7129.72238.7719313766108-9.04993137661081
727.05432.2192925086636-25.1652925086636
7356.67614.759677064435841.9163229355642
7434.8731.42382858527883.4461714147212
7535.11733.45132531489131.66567468510873
7630.16935.071719512917-4.90271951291696
7730.93633.2075396191632-2.27153961916318
7835.69931.97905971368383.71994028631619
7933.22833.7941035652729-0.566103565272918
8027.73333.8079368167402-6.0749368167402
8133.66630.54697754576753.11902245423247
8235.42931.49162073706933.93737926293066
8327.43833.4674353979804-6.02943539798043
848.1730.4088329448894-22.2388329448894
8563.4116.931186774182546.4788132258175
8638.0439.0449146558712-1.00491465587125
8745.38942.1488448583543.24015514164605
8837.35347.5176595444879-10.1646595444879
8937.02445.7465708843946-8.72257088439456
9050.95742.98186336546517.97513663453493
9137.99448.2698780794211-10.2758780794211
9236.45444.4762915350704-8.02229153507041
9346.0840.13656341077635.94343658922373
9443.37342.40156760856850.971432391431527
9537.39542.8692942348557-5.47429423485573
9610.96339.7985073663269-28.8355073663269
9776.05822.288729403195753.7692705968043
9850.17947.18564563193592.99335436806409
9957.45252.48484702312474.96715297687525
10047.56859.458222028643-11.890222028643
10150.0557.6129045499403-7.56290454994026
10250.85656.1262213171197-5.27022131711971
10341.99254.6028243470976-12.6108243470976
10439.28447.9052354801887-8.62123548018867
10544.52141.24241364265813.27858635734186
10643.83239.88682846555073.9451715344493
10741.15339.50362896171851.64937103828151
10817.138.5060596417788-21.4060596417788

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 44.72 & 8.46899999999999 & 36.251 \tabularnewline
4 & 39.525 & -0.863740514877595 & 40.3887405148776 \tabularnewline
5 & 45.315 & -1.30696317064841 & 46.6219631706484 \tabularnewline
6 & 50.38 & 9.08898487836982 & 41.2910151216302 \tabularnewline
7 & 40.6 & 24.7816228415895 & 15.8183771584105 \tabularnewline
8 & 36.279 & 33.2121925704083 & 3.06680742959175 \tabularnewline
9 & 42.438 & 37.136600482444 & 5.30139951755601 \tabularnewline
10 & 38.064 & 42.8985868630186 & -4.83458686301862 \tabularnewline
11 & 31.879 & 43.77351579933 & -11.89451579933 \tabularnewline
12 & 11.379 & 39.7141113384508 & -28.3351113384508 \tabularnewline
13 & 70.249 & 24.049861042995 & 46.1991389570049 \tabularnewline
14 & 39.253 & 46.2333367686341 & -6.98033676863415 \tabularnewline
15 & 47.06 & 46.0759624905065 & 0.984037509493497 \tabularnewline
16 & 41.697 & 49.2534310512937 & -7.55643105129366 \tabularnewline
17 & 38.708 & 47.6880375554721 & -8.98003755547212 \tabularnewline
18 & 49.267 & 43.9464391889035 & 5.32056081109646 \tabularnewline
19 & 39.018 & 46.8305744902093 & -7.81257449020925 \tabularnewline
20 & 32.228 & 43.1046770082994 & -10.8766770082994 \tabularnewline
21 & 40.87 & 36.2116470091248 & 4.65835299087518 \tabularnewline
22 & 39.383 & 36.3150096613326 & 3.06799033866738 \tabularnewline
23 & 34.571 & 36.3383453149348 & -1.76734531493479 \tabularnewline
24 & 12.066 & 34.1270600608813 & -22.0610600608813 \tabularnewline
25 & 70.938 & 19.909020477475 & 51.028979522525 \tabularnewline
26 & 34.077 & 43.832841548624 & -9.75584154862399 \tabularnewline
27 & 45.409 & 41.9018196886384 & 3.50718031136162 \tabularnewline
28 & 40.809 & 45.8596314483995 & -5.05063144839954 \tabularnewline
29 & 37.013 & 45.5174289308376 & -8.50442893083758 \tabularnewline
30 & 44.953 & 42.2793184020367 & 2.67368159796332 \tabularnewline
31 & 37.848 & 43.9536889167836 & -6.10568891678356 \tabularnewline
32 & 32.745 & 41.0508320311488 & -8.30583203114877 \tabularnewline
33 & 43.412 & 35.7848406133159 & 7.62715938668412 \tabularnewline
34 & 34.931 & 38.205874202333 & -3.27487420233304 \tabularnewline
35 & 33.008 & 35.7160054542737 & -2.70800545427374 \tabularnewline
36 & 8.62 & 32.9649099838898 & -24.3449099838898 \tabularnewline
37 & 68.906 & 17.2645337828387 & 51.6414662171614 \tabularnewline
38 & 39.556 & 40.9644717271879 & -1.40847172718792 \tabularnewline
39 & 50.669 & 43.3749305136298 & 7.29406948637024 \tabularnewline
40 & 36.432 & 50.5454334785199 & -14.1134334785199 \tabularnewline
41 & 40.891 & 46.6939047943997 & -5.80290479439967 \tabularnewline
42 & 48.428 & 45.0964071132465 & 3.33159288675353 \tabularnewline
43 & 36.222 & 47.7190834926714 & -11.4970834926714 \tabularnewline
44 & 33.425 & 42.3980960156641 & -8.97309601566413 \tabularnewline
45 & 39.401 & 36.4675487330819 & 2.93345126691813 \tabularnewline
46 & 37.967 & 35.7849623798528 & 2.1820376201472 \tabularnewline
47 & 34.801 & 35.1960249683759 & -0.395024968375857 \tabularnewline
48 & 12.657 & 33.5142692952083 & -20.8572692952083 \tabularnewline
49 & 69.116 & 19.9749784947274 & 49.1410215052726 \tabularnewline
50 & 41.519 & 43.012691546968 & -1.49369154696803 \tabularnewline
51 & 51.321 & 45.7033764378256 & 5.61762356217442 \tabularnewline
52 & 38.529 & 52.2222345527635 & -13.6932345527634 \tabularnewline
53 & 41.547 & 48.6258900203414 & -7.07889002034141 \tabularnewline
54 & 52.073 & 46.3819570976163 & 5.69104290238374 \tabularnewline
55 & 38.401 & 50.2232716809576 & -11.8222716809576 \tabularnewline
56 & 40.898 & 44.9979794235232 & -4.09997942352317 \tabularnewline
57 & 40.439 & 42.0990861949048 & -1.66008619490481 \tabularnewline
58 & 41.888 & 39.8697789675071 & 2.01822103249286 \tabularnewline
59 & 37.898 & 39.4613042334551 & -1.56330423345506 \tabularnewline
60 & 8.771 & 37.3520210270772 & -28.5810210270772 \tabularnewline
61 & 68.184 & 19.3994515449509 & 48.7845484550491 \tabularnewline
62 & 50.53 & 40.8813669947111 & 9.64863300528891 \tabularnewline
63 & 47.221 & 48.5758009638906 & -1.35480096389059 \tabularnewline
64 & 41.756 & 51.6637254266796 & -9.90772542667963 \tabularnewline
65 & 45.633 & 49.5818529903989 & -3.94885299039888 \tabularnewline
66 & 48.138 & 49.1542272291666 & -1.01622722916661 \tabularnewline
67 & 39.486 & 49.7071339190346 & -10.2211339190346 \tabularnewline
68 & 39.341 & 44.7754547372586 & -5.43445473725858 \tabularnewline
69 & 41.117 & 40.7665682315723 & 0.350431768427676 \tabularnewline
70 & 41.629 & 39.1145436921694 & 2.51445630783057 \tabularnewline
71 & 29.722 & 38.7719313766108 & -9.04993137661081 \tabularnewline
72 & 7.054 & 32.2192925086636 & -25.1652925086636 \tabularnewline
73 & 56.676 & 14.7596770644358 & 41.9163229355642 \tabularnewline
74 & 34.87 & 31.4238285852788 & 3.4461714147212 \tabularnewline
75 & 35.117 & 33.4513253148913 & 1.66567468510873 \tabularnewline
76 & 30.169 & 35.071719512917 & -4.90271951291696 \tabularnewline
77 & 30.936 & 33.2075396191632 & -2.27153961916318 \tabularnewline
78 & 35.699 & 31.9790597136838 & 3.71994028631619 \tabularnewline
79 & 33.228 & 33.7941035652729 & -0.566103565272918 \tabularnewline
80 & 27.733 & 33.8079368167402 & -6.0749368167402 \tabularnewline
81 & 33.666 & 30.5469775457675 & 3.11902245423247 \tabularnewline
82 & 35.429 & 31.4916207370693 & 3.93737926293066 \tabularnewline
83 & 27.438 & 33.4674353979804 & -6.02943539798043 \tabularnewline
84 & 8.17 & 30.4088329448894 & -22.2388329448894 \tabularnewline
85 & 63.41 & 16.9311867741825 & 46.4788132258175 \tabularnewline
86 & 38.04 & 39.0449146558712 & -1.00491465587125 \tabularnewline
87 & 45.389 & 42.148844858354 & 3.24015514164605 \tabularnewline
88 & 37.353 & 47.5176595444879 & -10.1646595444879 \tabularnewline
89 & 37.024 & 45.7465708843946 & -8.72257088439456 \tabularnewline
90 & 50.957 & 42.9818633654651 & 7.97513663453493 \tabularnewline
91 & 37.994 & 48.2698780794211 & -10.2758780794211 \tabularnewline
92 & 36.454 & 44.4762915350704 & -8.02229153507041 \tabularnewline
93 & 46.08 & 40.1365634107763 & 5.94343658922373 \tabularnewline
94 & 43.373 & 42.4015676085685 & 0.971432391431527 \tabularnewline
95 & 37.395 & 42.8692942348557 & -5.47429423485573 \tabularnewline
96 & 10.963 & 39.7985073663269 & -28.8355073663269 \tabularnewline
97 & 76.058 & 22.2887294031957 & 53.7692705968043 \tabularnewline
98 & 50.179 & 47.1856456319359 & 2.99335436806409 \tabularnewline
99 & 57.452 & 52.4848470231247 & 4.96715297687525 \tabularnewline
100 & 47.568 & 59.458222028643 & -11.890222028643 \tabularnewline
101 & 50.05 & 57.6129045499403 & -7.56290454994026 \tabularnewline
102 & 50.856 & 56.1262213171197 & -5.27022131711971 \tabularnewline
103 & 41.992 & 54.6028243470976 & -12.6108243470976 \tabularnewline
104 & 39.284 & 47.9052354801887 & -8.62123548018867 \tabularnewline
105 & 44.521 & 41.2424136426581 & 3.27858635734186 \tabularnewline
106 & 43.832 & 39.8868284655507 & 3.9451715344493 \tabularnewline
107 & 41.153 & 39.5036289617185 & 1.64937103828151 \tabularnewline
108 & 17.1 & 38.5060596417788 & -21.4060596417788 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198858&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]44.72[/C][C]8.46899999999999[/C][C]36.251[/C][/ROW]
[ROW][C]4[/C][C]39.525[/C][C]-0.863740514877595[/C][C]40.3887405148776[/C][/ROW]
[ROW][C]5[/C][C]45.315[/C][C]-1.30696317064841[/C][C]46.6219631706484[/C][/ROW]
[ROW][C]6[/C][C]50.38[/C][C]9.08898487836982[/C][C]41.2910151216302[/C][/ROW]
[ROW][C]7[/C][C]40.6[/C][C]24.7816228415895[/C][C]15.8183771584105[/C][/ROW]
[ROW][C]8[/C][C]36.279[/C][C]33.2121925704083[/C][C]3.06680742959175[/C][/ROW]
[ROW][C]9[/C][C]42.438[/C][C]37.136600482444[/C][C]5.30139951755601[/C][/ROW]
[ROW][C]10[/C][C]38.064[/C][C]42.8985868630186[/C][C]-4.83458686301862[/C][/ROW]
[ROW][C]11[/C][C]31.879[/C][C]43.77351579933[/C][C]-11.89451579933[/C][/ROW]
[ROW][C]12[/C][C]11.379[/C][C]39.7141113384508[/C][C]-28.3351113384508[/C][/ROW]
[ROW][C]13[/C][C]70.249[/C][C]24.049861042995[/C][C]46.1991389570049[/C][/ROW]
[ROW][C]14[/C][C]39.253[/C][C]46.2333367686341[/C][C]-6.98033676863415[/C][/ROW]
[ROW][C]15[/C][C]47.06[/C][C]46.0759624905065[/C][C]0.984037509493497[/C][/ROW]
[ROW][C]16[/C][C]41.697[/C][C]49.2534310512937[/C][C]-7.55643105129366[/C][/ROW]
[ROW][C]17[/C][C]38.708[/C][C]47.6880375554721[/C][C]-8.98003755547212[/C][/ROW]
[ROW][C]18[/C][C]49.267[/C][C]43.9464391889035[/C][C]5.32056081109646[/C][/ROW]
[ROW][C]19[/C][C]39.018[/C][C]46.8305744902093[/C][C]-7.81257449020925[/C][/ROW]
[ROW][C]20[/C][C]32.228[/C][C]43.1046770082994[/C][C]-10.8766770082994[/C][/ROW]
[ROW][C]21[/C][C]40.87[/C][C]36.2116470091248[/C][C]4.65835299087518[/C][/ROW]
[ROW][C]22[/C][C]39.383[/C][C]36.3150096613326[/C][C]3.06799033866738[/C][/ROW]
[ROW][C]23[/C][C]34.571[/C][C]36.3383453149348[/C][C]-1.76734531493479[/C][/ROW]
[ROW][C]24[/C][C]12.066[/C][C]34.1270600608813[/C][C]-22.0610600608813[/C][/ROW]
[ROW][C]25[/C][C]70.938[/C][C]19.909020477475[/C][C]51.028979522525[/C][/ROW]
[ROW][C]26[/C][C]34.077[/C][C]43.832841548624[/C][C]-9.75584154862399[/C][/ROW]
[ROW][C]27[/C][C]45.409[/C][C]41.9018196886384[/C][C]3.50718031136162[/C][/ROW]
[ROW][C]28[/C][C]40.809[/C][C]45.8596314483995[/C][C]-5.05063144839954[/C][/ROW]
[ROW][C]29[/C][C]37.013[/C][C]45.5174289308376[/C][C]-8.50442893083758[/C][/ROW]
[ROW][C]30[/C][C]44.953[/C][C]42.2793184020367[/C][C]2.67368159796332[/C][/ROW]
[ROW][C]31[/C][C]37.848[/C][C]43.9536889167836[/C][C]-6.10568891678356[/C][/ROW]
[ROW][C]32[/C][C]32.745[/C][C]41.0508320311488[/C][C]-8.30583203114877[/C][/ROW]
[ROW][C]33[/C][C]43.412[/C][C]35.7848406133159[/C][C]7.62715938668412[/C][/ROW]
[ROW][C]34[/C][C]34.931[/C][C]38.205874202333[/C][C]-3.27487420233304[/C][/ROW]
[ROW][C]35[/C][C]33.008[/C][C]35.7160054542737[/C][C]-2.70800545427374[/C][/ROW]
[ROW][C]36[/C][C]8.62[/C][C]32.9649099838898[/C][C]-24.3449099838898[/C][/ROW]
[ROW][C]37[/C][C]68.906[/C][C]17.2645337828387[/C][C]51.6414662171614[/C][/ROW]
[ROW][C]38[/C][C]39.556[/C][C]40.9644717271879[/C][C]-1.40847172718792[/C][/ROW]
[ROW][C]39[/C][C]50.669[/C][C]43.3749305136298[/C][C]7.29406948637024[/C][/ROW]
[ROW][C]40[/C][C]36.432[/C][C]50.5454334785199[/C][C]-14.1134334785199[/C][/ROW]
[ROW][C]41[/C][C]40.891[/C][C]46.6939047943997[/C][C]-5.80290479439967[/C][/ROW]
[ROW][C]42[/C][C]48.428[/C][C]45.0964071132465[/C][C]3.33159288675353[/C][/ROW]
[ROW][C]43[/C][C]36.222[/C][C]47.7190834926714[/C][C]-11.4970834926714[/C][/ROW]
[ROW][C]44[/C][C]33.425[/C][C]42.3980960156641[/C][C]-8.97309601566413[/C][/ROW]
[ROW][C]45[/C][C]39.401[/C][C]36.4675487330819[/C][C]2.93345126691813[/C][/ROW]
[ROW][C]46[/C][C]37.967[/C][C]35.7849623798528[/C][C]2.1820376201472[/C][/ROW]
[ROW][C]47[/C][C]34.801[/C][C]35.1960249683759[/C][C]-0.395024968375857[/C][/ROW]
[ROW][C]48[/C][C]12.657[/C][C]33.5142692952083[/C][C]-20.8572692952083[/C][/ROW]
[ROW][C]49[/C][C]69.116[/C][C]19.9749784947274[/C][C]49.1410215052726[/C][/ROW]
[ROW][C]50[/C][C]41.519[/C][C]43.012691546968[/C][C]-1.49369154696803[/C][/ROW]
[ROW][C]51[/C][C]51.321[/C][C]45.7033764378256[/C][C]5.61762356217442[/C][/ROW]
[ROW][C]52[/C][C]38.529[/C][C]52.2222345527635[/C][C]-13.6932345527634[/C][/ROW]
[ROW][C]53[/C][C]41.547[/C][C]48.6258900203414[/C][C]-7.07889002034141[/C][/ROW]
[ROW][C]54[/C][C]52.073[/C][C]46.3819570976163[/C][C]5.69104290238374[/C][/ROW]
[ROW][C]55[/C][C]38.401[/C][C]50.2232716809576[/C][C]-11.8222716809576[/C][/ROW]
[ROW][C]56[/C][C]40.898[/C][C]44.9979794235232[/C][C]-4.09997942352317[/C][/ROW]
[ROW][C]57[/C][C]40.439[/C][C]42.0990861949048[/C][C]-1.66008619490481[/C][/ROW]
[ROW][C]58[/C][C]41.888[/C][C]39.8697789675071[/C][C]2.01822103249286[/C][/ROW]
[ROW][C]59[/C][C]37.898[/C][C]39.4613042334551[/C][C]-1.56330423345506[/C][/ROW]
[ROW][C]60[/C][C]8.771[/C][C]37.3520210270772[/C][C]-28.5810210270772[/C][/ROW]
[ROW][C]61[/C][C]68.184[/C][C]19.3994515449509[/C][C]48.7845484550491[/C][/ROW]
[ROW][C]62[/C][C]50.53[/C][C]40.8813669947111[/C][C]9.64863300528891[/C][/ROW]
[ROW][C]63[/C][C]47.221[/C][C]48.5758009638906[/C][C]-1.35480096389059[/C][/ROW]
[ROW][C]64[/C][C]41.756[/C][C]51.6637254266796[/C][C]-9.90772542667963[/C][/ROW]
[ROW][C]65[/C][C]45.633[/C][C]49.5818529903989[/C][C]-3.94885299039888[/C][/ROW]
[ROW][C]66[/C][C]48.138[/C][C]49.1542272291666[/C][C]-1.01622722916661[/C][/ROW]
[ROW][C]67[/C][C]39.486[/C][C]49.7071339190346[/C][C]-10.2211339190346[/C][/ROW]
[ROW][C]68[/C][C]39.341[/C][C]44.7754547372586[/C][C]-5.43445473725858[/C][/ROW]
[ROW][C]69[/C][C]41.117[/C][C]40.7665682315723[/C][C]0.350431768427676[/C][/ROW]
[ROW][C]70[/C][C]41.629[/C][C]39.1145436921694[/C][C]2.51445630783057[/C][/ROW]
[ROW][C]71[/C][C]29.722[/C][C]38.7719313766108[/C][C]-9.04993137661081[/C][/ROW]
[ROW][C]72[/C][C]7.054[/C][C]32.2192925086636[/C][C]-25.1652925086636[/C][/ROW]
[ROW][C]73[/C][C]56.676[/C][C]14.7596770644358[/C][C]41.9163229355642[/C][/ROW]
[ROW][C]74[/C][C]34.87[/C][C]31.4238285852788[/C][C]3.4461714147212[/C][/ROW]
[ROW][C]75[/C][C]35.117[/C][C]33.4513253148913[/C][C]1.66567468510873[/C][/ROW]
[ROW][C]76[/C][C]30.169[/C][C]35.071719512917[/C][C]-4.90271951291696[/C][/ROW]
[ROW][C]77[/C][C]30.936[/C][C]33.2075396191632[/C][C]-2.27153961916318[/C][/ROW]
[ROW][C]78[/C][C]35.699[/C][C]31.9790597136838[/C][C]3.71994028631619[/C][/ROW]
[ROW][C]79[/C][C]33.228[/C][C]33.7941035652729[/C][C]-0.566103565272918[/C][/ROW]
[ROW][C]80[/C][C]27.733[/C][C]33.8079368167402[/C][C]-6.0749368167402[/C][/ROW]
[ROW][C]81[/C][C]33.666[/C][C]30.5469775457675[/C][C]3.11902245423247[/C][/ROW]
[ROW][C]82[/C][C]35.429[/C][C]31.4916207370693[/C][C]3.93737926293066[/C][/ROW]
[ROW][C]83[/C][C]27.438[/C][C]33.4674353979804[/C][C]-6.02943539798043[/C][/ROW]
[ROW][C]84[/C][C]8.17[/C][C]30.4088329448894[/C][C]-22.2388329448894[/C][/ROW]
[ROW][C]85[/C][C]63.41[/C][C]16.9311867741825[/C][C]46.4788132258175[/C][/ROW]
[ROW][C]86[/C][C]38.04[/C][C]39.0449146558712[/C][C]-1.00491465587125[/C][/ROW]
[ROW][C]87[/C][C]45.389[/C][C]42.148844858354[/C][C]3.24015514164605[/C][/ROW]
[ROW][C]88[/C][C]37.353[/C][C]47.5176595444879[/C][C]-10.1646595444879[/C][/ROW]
[ROW][C]89[/C][C]37.024[/C][C]45.7465708843946[/C][C]-8.72257088439456[/C][/ROW]
[ROW][C]90[/C][C]50.957[/C][C]42.9818633654651[/C][C]7.97513663453493[/C][/ROW]
[ROW][C]91[/C][C]37.994[/C][C]48.2698780794211[/C][C]-10.2758780794211[/C][/ROW]
[ROW][C]92[/C][C]36.454[/C][C]44.4762915350704[/C][C]-8.02229153507041[/C][/ROW]
[ROW][C]93[/C][C]46.08[/C][C]40.1365634107763[/C][C]5.94343658922373[/C][/ROW]
[ROW][C]94[/C][C]43.373[/C][C]42.4015676085685[/C][C]0.971432391431527[/C][/ROW]
[ROW][C]95[/C][C]37.395[/C][C]42.8692942348557[/C][C]-5.47429423485573[/C][/ROW]
[ROW][C]96[/C][C]10.963[/C][C]39.7985073663269[/C][C]-28.8355073663269[/C][/ROW]
[ROW][C]97[/C][C]76.058[/C][C]22.2887294031957[/C][C]53.7692705968043[/C][/ROW]
[ROW][C]98[/C][C]50.179[/C][C]47.1856456319359[/C][C]2.99335436806409[/C][/ROW]
[ROW][C]99[/C][C]57.452[/C][C]52.4848470231247[/C][C]4.96715297687525[/C][/ROW]
[ROW][C]100[/C][C]47.568[/C][C]59.458222028643[/C][C]-11.890222028643[/C][/ROW]
[ROW][C]101[/C][C]50.05[/C][C]57.6129045499403[/C][C]-7.56290454994026[/C][/ROW]
[ROW][C]102[/C][C]50.856[/C][C]56.1262213171197[/C][C]-5.27022131711971[/C][/ROW]
[ROW][C]103[/C][C]41.992[/C][C]54.6028243470976[/C][C]-12.6108243470976[/C][/ROW]
[ROW][C]104[/C][C]39.284[/C][C]47.9052354801887[/C][C]-8.62123548018867[/C][/ROW]
[ROW][C]105[/C][C]44.521[/C][C]41.2424136426581[/C][C]3.27858635734186[/C][/ROW]
[ROW][C]106[/C][C]43.832[/C][C]39.8868284655507[/C][C]3.9451715344493[/C][/ROW]
[ROW][C]107[/C][C]41.153[/C][C]39.5036289617185[/C][C]1.64937103828151[/C][/ROW]
[ROW][C]108[/C][C]17.1[/C][C]38.5060596417788[/C][C]-21.4060596417788[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198858&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198858&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
344.728.4689999999999936.251
439.525-0.86374051487759540.3887405148776
545.315-1.3069631706484146.6219631706484
650.389.0889848783698241.2910151216302
740.624.781622841589515.8183771584105
836.27933.21219257040833.06680742959175
942.43837.1366004824445.30139951755601
1038.06442.8985868630186-4.83458686301862
1131.87943.77351579933-11.89451579933
1211.37939.7141113384508-28.3351113384508
1370.24924.04986104299546.1991389570049
1439.25346.2333367686341-6.98033676863415
1547.0646.07596249050650.984037509493497
1641.69749.2534310512937-7.55643105129366
1738.70847.6880375554721-8.98003755547212
1849.26743.94643918890355.32056081109646
1939.01846.8305744902093-7.81257449020925
2032.22843.1046770082994-10.8766770082994
2140.8736.21164700912484.65835299087518
2239.38336.31500966133263.06799033866738
2334.57136.3383453149348-1.76734531493479
2412.06634.1270600608813-22.0610600608813
2570.93819.90902047747551.028979522525
2634.07743.832841548624-9.75584154862399
2745.40941.90181968863843.50718031136162
2840.80945.8596314483995-5.05063144839954
2937.01345.5174289308376-8.50442893083758
3044.95342.27931840203672.67368159796332
3137.84843.9536889167836-6.10568891678356
3232.74541.0508320311488-8.30583203114877
3343.41235.78484061331597.62715938668412
3434.93138.205874202333-3.27487420233304
3533.00835.7160054542737-2.70800545427374
368.6232.9649099838898-24.3449099838898
3768.90617.264533782838751.6414662171614
3839.55640.9644717271879-1.40847172718792
3950.66943.37493051362987.29406948637024
4036.43250.5454334785199-14.1134334785199
4140.89146.6939047943997-5.80290479439967
4248.42845.09640711324653.33159288675353
4336.22247.7190834926714-11.4970834926714
4433.42542.3980960156641-8.97309601566413
4539.40136.46754873308192.93345126691813
4637.96735.78496237985282.1820376201472
4734.80135.1960249683759-0.395024968375857
4812.65733.5142692952083-20.8572692952083
4969.11619.974978494727449.1410215052726
5041.51943.012691546968-1.49369154696803
5151.32145.70337643782565.61762356217442
5238.52952.2222345527635-13.6932345527634
5341.54748.6258900203414-7.07889002034141
5452.07346.38195709761635.69104290238374
5538.40150.2232716809576-11.8222716809576
5640.89844.9979794235232-4.09997942352317
5740.43942.0990861949048-1.66008619490481
5841.88839.86977896750712.01822103249286
5937.89839.4613042334551-1.56330423345506
608.77137.3520210270772-28.5810210270772
6168.18419.399451544950948.7845484550491
6250.5340.88136699471119.64863300528891
6347.22148.5758009638906-1.35480096389059
6441.75651.6637254266796-9.90772542667963
6545.63349.5818529903989-3.94885299039888
6648.13849.1542272291666-1.01622722916661
6739.48649.7071339190346-10.2211339190346
6839.34144.7754547372586-5.43445473725858
6941.11740.76656823157230.350431768427676
7041.62939.11454369216942.51445630783057
7129.72238.7719313766108-9.04993137661081
727.05432.2192925086636-25.1652925086636
7356.67614.759677064435841.9163229355642
7434.8731.42382858527883.4461714147212
7535.11733.45132531489131.66567468510873
7630.16935.071719512917-4.90271951291696
7730.93633.2075396191632-2.27153961916318
7835.69931.97905971368383.71994028631619
7933.22833.7941035652729-0.566103565272918
8027.73333.8079368167402-6.0749368167402
8133.66630.54697754576753.11902245423247
8235.42931.49162073706933.93737926293066
8327.43833.4674353979804-6.02943539798043
848.1730.4088329448894-22.2388329448894
8563.4116.931186774182546.4788132258175
8638.0439.0449146558712-1.00491465587125
8745.38942.1488448583543.24015514164605
8837.35347.5176595444879-10.1646595444879
8937.02445.7465708843946-8.72257088439456
9050.95742.98186336546517.97513663453493
9137.99448.2698780794211-10.2758780794211
9236.45444.4762915350704-8.02229153507041
9346.0840.13656341077635.94343658922373
9443.37342.40156760856850.971432391431527
9537.39542.8692942348557-5.47429423485573
9610.96339.7985073663269-28.8355073663269
9776.05822.288729403195753.7692705968043
9850.17947.18564563193592.99335436806409
9957.45252.48484702312474.96715297687525
10047.56859.458222028643-11.890222028643
10150.0557.6129045499403-7.56290454994026
10250.85656.1262213171197-5.27022131711971
10341.99254.6028243470976-12.6108243470976
10439.28447.9052354801887-8.62123548018867
10544.52141.24241364265813.27858635734186
10643.83239.88682846555073.9451715344493
10741.15339.50362896171851.64937103828151
10817.138.5060596417788-21.4060596417788







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10924.52414628992-11.299846046297460.3481386261374
11019.03070203649-22.311453537001360.3728576099813
11113.5372577830599-35.876050586581662.9505661527014
1128.04381352962984-51.651564082583967.7391911418436
1132.55036927619978-69.264942822301574.365681374701
114-2.94307497723027-88.41853289529182.5323829408304
115-8.43651923066034-108.89575824531692.0227197839954
116-13.9299634840904-130.540981294406102.681054326225
117-19.4234077375204-153.240231238947114.393415763906
118-24.9168519909505-176.907552584158127.073848602257
119-30.4102962443806-201.476067077743140.655474588981
120-35.9037404978106-226.892203331706155.084722336085

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 24.52414628992 & -11.2998460462974 & 60.3481386261374 \tabularnewline
110 & 19.03070203649 & -22.3114535370013 & 60.3728576099813 \tabularnewline
111 & 13.5372577830599 & -35.8760505865816 & 62.9505661527014 \tabularnewline
112 & 8.04381352962984 & -51.6515640825839 & 67.7391911418436 \tabularnewline
113 & 2.55036927619978 & -69.2649428223015 & 74.365681374701 \tabularnewline
114 & -2.94307497723027 & -88.418532895291 & 82.5323829408304 \tabularnewline
115 & -8.43651923066034 & -108.895758245316 & 92.0227197839954 \tabularnewline
116 & -13.9299634840904 & -130.540981294406 & 102.681054326225 \tabularnewline
117 & -19.4234077375204 & -153.240231238947 & 114.393415763906 \tabularnewline
118 & -24.9168519909505 & -176.907552584158 & 127.073848602257 \tabularnewline
119 & -30.4102962443806 & -201.476067077743 & 140.655474588981 \tabularnewline
120 & -35.9037404978106 & -226.892203331706 & 155.084722336085 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198858&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]24.52414628992[/C][C]-11.2998460462974[/C][C]60.3481386261374[/C][/ROW]
[ROW][C]110[/C][C]19.03070203649[/C][C]-22.3114535370013[/C][C]60.3728576099813[/C][/ROW]
[ROW][C]111[/C][C]13.5372577830599[/C][C]-35.8760505865816[/C][C]62.9505661527014[/C][/ROW]
[ROW][C]112[/C][C]8.04381352962984[/C][C]-51.6515640825839[/C][C]67.7391911418436[/C][/ROW]
[ROW][C]113[/C][C]2.55036927619978[/C][C]-69.2649428223015[/C][C]74.365681374701[/C][/ROW]
[ROW][C]114[/C][C]-2.94307497723027[/C][C]-88.418532895291[/C][C]82.5323829408304[/C][/ROW]
[ROW][C]115[/C][C]-8.43651923066034[/C][C]-108.895758245316[/C][C]92.0227197839954[/C][/ROW]
[ROW][C]116[/C][C]-13.9299634840904[/C][C]-130.540981294406[/C][C]102.681054326225[/C][/ROW]
[ROW][C]117[/C][C]-19.4234077375204[/C][C]-153.240231238947[/C][C]114.393415763906[/C][/ROW]
[ROW][C]118[/C][C]-24.9168519909505[/C][C]-176.907552584158[/C][C]127.073848602257[/C][/ROW]
[ROW][C]119[/C][C]-30.4102962443806[/C][C]-201.476067077743[/C][C]140.655474588981[/C][/ROW]
[ROW][C]120[/C][C]-35.9037404978106[/C][C]-226.892203331706[/C][C]155.084722336085[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198858&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198858&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
10924.52414628992-11.299846046297460.3481386261374
11019.03070203649-22.311453537001360.3728576099813
11113.5372577830599-35.876050586581662.9505661527014
1128.04381352962984-51.651564082583967.7391911418436
1132.55036927619978-69.264942822301574.365681374701
114-2.94307497723027-88.41853289529182.5323829408304
115-8.43651923066034-108.89575824531692.0227197839954
116-13.9299634840904-130.540981294406102.681054326225
117-19.4234077375204-153.240231238947114.393415763906
118-24.9168519909505-176.907552584158127.073848602257
119-30.4102962443806-201.476067077743140.655474588981
120-35.9037404978106-226.892203331706155.084722336085



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