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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, 14 Dec 2016 11:19:46 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/14/t1481711067zyf2ukazyig74a7.htm/, Retrieved Fri, 03 May 2024 15:41:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299282, Retrieved Fri, 03 May 2024 15:41:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsF1 competition
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-14 10:19:46] [00d6a26c230b6c589ee3bbc701d55499] [Current]
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Dataseries X:
3840
3140
4580
4740
3920
4900
3400
3440
2600
2220
2190
2550
2720
3720
4710
5070
6030
5280
4420
3940
2750
2980
2690
2650
4000
4150
6050
6280
5520
4800
4610
3530
2790
2750
2470
2610
3680
3820
4460
4760
3290
3610
3650
3130
2850
2720
2740
2760
3330
3850
5430
5180
4770
5360
4950
3720
3330
3000
2760
3040
3260
3780
4670
4320
4080
4210
3350
3390
2630
2350
2330
2230
2830
3230
4240
3750
4160
3960
3000
2890
2300
2320
2270
1970
2920
3310
4370
3990
3970
3850
3510
2840
2130
2280
1960
1740
2370
1980
2680
3510
3350
3290
3150
2490
2490
2930
3590
2040
2480
2760
3400
3470
3130
3670
3080
2430




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299282&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299282&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299282&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.542267548655652
beta0.033070281059321
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.542267548655652 \tabularnewline
beta & 0.033070281059321 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299282&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]0.542267548655652[/C][/ROW]
[ROW][C]beta[/C][C]0.033070281059321[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299282&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299282&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
alpha0.542267548655652
beta0.033070281059321
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1327202476.97542343771243.024576562291
1437203566.82696843054153.173031569458
1547104665.8029043688744.1970956311261
1650705081.77979765692-11.7797976569245
1760306052.55658053516-22.5565805351644
1852805339.895125659-59.8951256590017
1944203975.77221221872444.227787781282
2039404365.48915376169-425.48915376169
2127503145.49415746267-395.494157462665
2229802522.93996234276457.060037657239
2326902695.53116683943-5.53116683942926
2426503091.78380661496-441.783806614956
2540003163.68211239099836.317887609011
2641504828.88176573392-678.88176573392
2760505602.5991631388447.400836861196
2862806286.49055573292-6.4905557329248
2955207472.40304467952-1952.40304467952
3048005621.86614529858-821.866145298579
3146104058.25992296137551.740077038631
3235304076.92594975124-546.92594975124
3327902813.10024590433-23.1002459043284
3427502748.944800492911.05519950708958
3524702467.815227956482.18477204351575
3626102619.14744418666-9.14744418665714
3736803433.93947328818246.060526711823
3838203980.81983432188-160.819834321882
3944605411.36351694304-951.363516943044
4047605040.64584577211-280.645845772108
4132904959.76611460911-1669.76611460911
4236103782.1207556568-172.120755656802
4336503262.7977099676387.202290032395
4431302837.50759852689292.492401473106
4528502362.0384340248487.961565975203
4627202578.98812460154141.011875398457
4727402377.25279496561362.747205034389
4827602723.1288286795636.8711713204393
4933303721.36100101204-391.361001012036
5038503713.48362359554136.516376404463
5154304879.34289364245550.657106357549
5251805711.58708391369-531.587083913687
5347704594.02216219354175.977837806464
5453605321.4320092489438.5679907510576
5549505123.62296538391-173.622965383915
5637204112.81213269911-392.812132699113
5733303204.88051295802125.119487041982
5830003036.64680365398-36.6468036539814
5927602806.81348447151-46.8134844715055
6030402774.90888840745265.091111592553
6132603730.28808419925-470.288084199251
6237803933.55035984723-153.550359847231
6346705103.90714557503-433.907145575032
6443204864.52980066324-544.529800663241
6540804096.98102876192-16.9810287619239
6642104545.12020267912-335.120202679117
6733504072.17595528463-722.175955284631
6833902884.81906031274505.180939687258
6926302751.2977241666-121.297724166603
7023502416.42107849927-66.4210784992651
7123302192.09381653975137.906183460253
7222302358.10236201247-128.102362012467
7328302610.63938298359219.360617016405
7432303215.6012820781814.3987179218248
7542404154.7696213473285.2303786526791
7637504124.76438217745-374.764382177452
7741603701.66473948364458.335260516357
7839604243.67259746948-283.672597469475
7930003599.23297224442-599.232972244421
8028903025.44364114347-135.443641143465
8123002335.99634590164-35.996345901639
8223202092.9698879599227.030112040104
8322702122.11180737634147.888192623663
8419702169.43047465831-199.430474658313
8529202497.143552001422.856447998997
8633103103.30871563496206.691284365039
8743704177.7322513319192.2677486681
8839903988.313246264641.68675373535689
8939704159.30818755552-189.308187555523
9038504006.65523636105-156.655236361047
9135103267.38117221177242.618827788226
9228403373.23936054622-533.239360546224
9321302482.8382228896-352.838222889597
9422802184.0742126025395.9257873974739
9519602106.56640118197-146.566401181969
9617401844.78911182674-104.789111826741
9723702419.930915314-49.9309153140039
9819802600.45152277958-620.451522779581
9926802875.43726161858-195.437261618583
10035102485.607975678191024.39202432181
10133503077.42714926914272.572850730859
10232903178.07194052955111.928059470451
10331502826.96304727423323.03695272577
10424902648.41641308592-158.416413085925
10524902079.59014715199410.409852848009
10629302419.50472961221510.495270387785
10735902427.511542701671162.48845729833
10820402844.28577613651-804.285776136508
10924803358.17261736541-878.172617365406
11027602788.12382985798-28.1238298579819
11134003952.42059613783-552.420596137828
11234703963.42032317831-493.420323178307
11331303372.6447342307-242.644734230705
11436703119.16775206827550.832247931728
11530803085.84543816814-5.84543816814221
11624302516.3913040034-86.3913040033963

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2720 & 2476.97542343771 & 243.024576562291 \tabularnewline
14 & 3720 & 3566.82696843054 & 153.173031569458 \tabularnewline
15 & 4710 & 4665.80290436887 & 44.1970956311261 \tabularnewline
16 & 5070 & 5081.77979765692 & -11.7797976569245 \tabularnewline
17 & 6030 & 6052.55658053516 & -22.5565805351644 \tabularnewline
18 & 5280 & 5339.895125659 & -59.8951256590017 \tabularnewline
19 & 4420 & 3975.77221221872 & 444.227787781282 \tabularnewline
20 & 3940 & 4365.48915376169 & -425.48915376169 \tabularnewline
21 & 2750 & 3145.49415746267 & -395.494157462665 \tabularnewline
22 & 2980 & 2522.93996234276 & 457.060037657239 \tabularnewline
23 & 2690 & 2695.53116683943 & -5.53116683942926 \tabularnewline
24 & 2650 & 3091.78380661496 & -441.783806614956 \tabularnewline
25 & 4000 & 3163.68211239099 & 836.317887609011 \tabularnewline
26 & 4150 & 4828.88176573392 & -678.88176573392 \tabularnewline
27 & 6050 & 5602.5991631388 & 447.400836861196 \tabularnewline
28 & 6280 & 6286.49055573292 & -6.4905557329248 \tabularnewline
29 & 5520 & 7472.40304467952 & -1952.40304467952 \tabularnewline
30 & 4800 & 5621.86614529858 & -821.866145298579 \tabularnewline
31 & 4610 & 4058.25992296137 & 551.740077038631 \tabularnewline
32 & 3530 & 4076.92594975124 & -546.92594975124 \tabularnewline
33 & 2790 & 2813.10024590433 & -23.1002459043284 \tabularnewline
34 & 2750 & 2748.94480049291 & 1.05519950708958 \tabularnewline
35 & 2470 & 2467.81522795648 & 2.18477204351575 \tabularnewline
36 & 2610 & 2619.14744418666 & -9.14744418665714 \tabularnewline
37 & 3680 & 3433.93947328818 & 246.060526711823 \tabularnewline
38 & 3820 & 3980.81983432188 & -160.819834321882 \tabularnewline
39 & 4460 & 5411.36351694304 & -951.363516943044 \tabularnewline
40 & 4760 & 5040.64584577211 & -280.645845772108 \tabularnewline
41 & 3290 & 4959.76611460911 & -1669.76611460911 \tabularnewline
42 & 3610 & 3782.1207556568 & -172.120755656802 \tabularnewline
43 & 3650 & 3262.7977099676 & 387.202290032395 \tabularnewline
44 & 3130 & 2837.50759852689 & 292.492401473106 \tabularnewline
45 & 2850 & 2362.0384340248 & 487.961565975203 \tabularnewline
46 & 2720 & 2578.98812460154 & 141.011875398457 \tabularnewline
47 & 2740 & 2377.25279496561 & 362.747205034389 \tabularnewline
48 & 2760 & 2723.12882867956 & 36.8711713204393 \tabularnewline
49 & 3330 & 3721.36100101204 & -391.361001012036 \tabularnewline
50 & 3850 & 3713.48362359554 & 136.516376404463 \tabularnewline
51 & 5430 & 4879.34289364245 & 550.657106357549 \tabularnewline
52 & 5180 & 5711.58708391369 & -531.587083913687 \tabularnewline
53 & 4770 & 4594.02216219354 & 175.977837806464 \tabularnewline
54 & 5360 & 5321.43200924894 & 38.5679907510576 \tabularnewline
55 & 4950 & 5123.62296538391 & -173.622965383915 \tabularnewline
56 & 3720 & 4112.81213269911 & -392.812132699113 \tabularnewline
57 & 3330 & 3204.88051295802 & 125.119487041982 \tabularnewline
58 & 3000 & 3036.64680365398 & -36.6468036539814 \tabularnewline
59 & 2760 & 2806.81348447151 & -46.8134844715055 \tabularnewline
60 & 3040 & 2774.90888840745 & 265.091111592553 \tabularnewline
61 & 3260 & 3730.28808419925 & -470.288084199251 \tabularnewline
62 & 3780 & 3933.55035984723 & -153.550359847231 \tabularnewline
63 & 4670 & 5103.90714557503 & -433.907145575032 \tabularnewline
64 & 4320 & 4864.52980066324 & -544.529800663241 \tabularnewline
65 & 4080 & 4096.98102876192 & -16.9810287619239 \tabularnewline
66 & 4210 & 4545.12020267912 & -335.120202679117 \tabularnewline
67 & 3350 & 4072.17595528463 & -722.175955284631 \tabularnewline
68 & 3390 & 2884.81906031274 & 505.180939687258 \tabularnewline
69 & 2630 & 2751.2977241666 & -121.297724166603 \tabularnewline
70 & 2350 & 2416.42107849927 & -66.4210784992651 \tabularnewline
71 & 2330 & 2192.09381653975 & 137.906183460253 \tabularnewline
72 & 2230 & 2358.10236201247 & -128.102362012467 \tabularnewline
73 & 2830 & 2610.63938298359 & 219.360617016405 \tabularnewline
74 & 3230 & 3215.60128207818 & 14.3987179218248 \tabularnewline
75 & 4240 & 4154.76962134732 & 85.2303786526791 \tabularnewline
76 & 3750 & 4124.76438217745 & -374.764382177452 \tabularnewline
77 & 4160 & 3701.66473948364 & 458.335260516357 \tabularnewline
78 & 3960 & 4243.67259746948 & -283.672597469475 \tabularnewline
79 & 3000 & 3599.23297224442 & -599.232972244421 \tabularnewline
80 & 2890 & 3025.44364114347 & -135.443641143465 \tabularnewline
81 & 2300 & 2335.99634590164 & -35.996345901639 \tabularnewline
82 & 2320 & 2092.9698879599 & 227.030112040104 \tabularnewline
83 & 2270 & 2122.11180737634 & 147.888192623663 \tabularnewline
84 & 1970 & 2169.43047465831 & -199.430474658313 \tabularnewline
85 & 2920 & 2497.143552001 & 422.856447998997 \tabularnewline
86 & 3310 & 3103.30871563496 & 206.691284365039 \tabularnewline
87 & 4370 & 4177.7322513319 & 192.2677486681 \tabularnewline
88 & 3990 & 3988.31324626464 & 1.68675373535689 \tabularnewline
89 & 3970 & 4159.30818755552 & -189.308187555523 \tabularnewline
90 & 3850 & 4006.65523636105 & -156.655236361047 \tabularnewline
91 & 3510 & 3267.38117221177 & 242.618827788226 \tabularnewline
92 & 2840 & 3373.23936054622 & -533.239360546224 \tabularnewline
93 & 2130 & 2482.8382228896 & -352.838222889597 \tabularnewline
94 & 2280 & 2184.07421260253 & 95.9257873974739 \tabularnewline
95 & 1960 & 2106.56640118197 & -146.566401181969 \tabularnewline
96 & 1740 & 1844.78911182674 & -104.789111826741 \tabularnewline
97 & 2370 & 2419.930915314 & -49.9309153140039 \tabularnewline
98 & 1980 & 2600.45152277958 & -620.451522779581 \tabularnewline
99 & 2680 & 2875.43726161858 & -195.437261618583 \tabularnewline
100 & 3510 & 2485.60797567819 & 1024.39202432181 \tabularnewline
101 & 3350 & 3077.42714926914 & 272.572850730859 \tabularnewline
102 & 3290 & 3178.07194052955 & 111.928059470451 \tabularnewline
103 & 3150 & 2826.96304727423 & 323.03695272577 \tabularnewline
104 & 2490 & 2648.41641308592 & -158.416413085925 \tabularnewline
105 & 2490 & 2079.59014715199 & 410.409852848009 \tabularnewline
106 & 2930 & 2419.50472961221 & 510.495270387785 \tabularnewline
107 & 3590 & 2427.51154270167 & 1162.48845729833 \tabularnewline
108 & 2040 & 2844.28577613651 & -804.285776136508 \tabularnewline
109 & 2480 & 3358.17261736541 & -878.172617365406 \tabularnewline
110 & 2760 & 2788.12382985798 & -28.1238298579819 \tabularnewline
111 & 3400 & 3952.42059613783 & -552.420596137828 \tabularnewline
112 & 3470 & 3963.42032317831 & -493.420323178307 \tabularnewline
113 & 3130 & 3372.6447342307 & -242.644734230705 \tabularnewline
114 & 3670 & 3119.16775206827 & 550.832247931728 \tabularnewline
115 & 3080 & 3085.84543816814 & -5.84543816814221 \tabularnewline
116 & 2430 & 2516.3913040034 & -86.3913040033963 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299282&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]2720[/C][C]2476.97542343771[/C][C]243.024576562291[/C][/ROW]
[ROW][C]14[/C][C]3720[/C][C]3566.82696843054[/C][C]153.173031569458[/C][/ROW]
[ROW][C]15[/C][C]4710[/C][C]4665.80290436887[/C][C]44.1970956311261[/C][/ROW]
[ROW][C]16[/C][C]5070[/C][C]5081.77979765692[/C][C]-11.7797976569245[/C][/ROW]
[ROW][C]17[/C][C]6030[/C][C]6052.55658053516[/C][C]-22.5565805351644[/C][/ROW]
[ROW][C]18[/C][C]5280[/C][C]5339.895125659[/C][C]-59.8951256590017[/C][/ROW]
[ROW][C]19[/C][C]4420[/C][C]3975.77221221872[/C][C]444.227787781282[/C][/ROW]
[ROW][C]20[/C][C]3940[/C][C]4365.48915376169[/C][C]-425.48915376169[/C][/ROW]
[ROW][C]21[/C][C]2750[/C][C]3145.49415746267[/C][C]-395.494157462665[/C][/ROW]
[ROW][C]22[/C][C]2980[/C][C]2522.93996234276[/C][C]457.060037657239[/C][/ROW]
[ROW][C]23[/C][C]2690[/C][C]2695.53116683943[/C][C]-5.53116683942926[/C][/ROW]
[ROW][C]24[/C][C]2650[/C][C]3091.78380661496[/C][C]-441.783806614956[/C][/ROW]
[ROW][C]25[/C][C]4000[/C][C]3163.68211239099[/C][C]836.317887609011[/C][/ROW]
[ROW][C]26[/C][C]4150[/C][C]4828.88176573392[/C][C]-678.88176573392[/C][/ROW]
[ROW][C]27[/C][C]6050[/C][C]5602.5991631388[/C][C]447.400836861196[/C][/ROW]
[ROW][C]28[/C][C]6280[/C][C]6286.49055573292[/C][C]-6.4905557329248[/C][/ROW]
[ROW][C]29[/C][C]5520[/C][C]7472.40304467952[/C][C]-1952.40304467952[/C][/ROW]
[ROW][C]30[/C][C]4800[/C][C]5621.86614529858[/C][C]-821.866145298579[/C][/ROW]
[ROW][C]31[/C][C]4610[/C][C]4058.25992296137[/C][C]551.740077038631[/C][/ROW]
[ROW][C]32[/C][C]3530[/C][C]4076.92594975124[/C][C]-546.92594975124[/C][/ROW]
[ROW][C]33[/C][C]2790[/C][C]2813.10024590433[/C][C]-23.1002459043284[/C][/ROW]
[ROW][C]34[/C][C]2750[/C][C]2748.94480049291[/C][C]1.05519950708958[/C][/ROW]
[ROW][C]35[/C][C]2470[/C][C]2467.81522795648[/C][C]2.18477204351575[/C][/ROW]
[ROW][C]36[/C][C]2610[/C][C]2619.14744418666[/C][C]-9.14744418665714[/C][/ROW]
[ROW][C]37[/C][C]3680[/C][C]3433.93947328818[/C][C]246.060526711823[/C][/ROW]
[ROW][C]38[/C][C]3820[/C][C]3980.81983432188[/C][C]-160.819834321882[/C][/ROW]
[ROW][C]39[/C][C]4460[/C][C]5411.36351694304[/C][C]-951.363516943044[/C][/ROW]
[ROW][C]40[/C][C]4760[/C][C]5040.64584577211[/C][C]-280.645845772108[/C][/ROW]
[ROW][C]41[/C][C]3290[/C][C]4959.76611460911[/C][C]-1669.76611460911[/C][/ROW]
[ROW][C]42[/C][C]3610[/C][C]3782.1207556568[/C][C]-172.120755656802[/C][/ROW]
[ROW][C]43[/C][C]3650[/C][C]3262.7977099676[/C][C]387.202290032395[/C][/ROW]
[ROW][C]44[/C][C]3130[/C][C]2837.50759852689[/C][C]292.492401473106[/C][/ROW]
[ROW][C]45[/C][C]2850[/C][C]2362.0384340248[/C][C]487.961565975203[/C][/ROW]
[ROW][C]46[/C][C]2720[/C][C]2578.98812460154[/C][C]141.011875398457[/C][/ROW]
[ROW][C]47[/C][C]2740[/C][C]2377.25279496561[/C][C]362.747205034389[/C][/ROW]
[ROW][C]48[/C][C]2760[/C][C]2723.12882867956[/C][C]36.8711713204393[/C][/ROW]
[ROW][C]49[/C][C]3330[/C][C]3721.36100101204[/C][C]-391.361001012036[/C][/ROW]
[ROW][C]50[/C][C]3850[/C][C]3713.48362359554[/C][C]136.516376404463[/C][/ROW]
[ROW][C]51[/C][C]5430[/C][C]4879.34289364245[/C][C]550.657106357549[/C][/ROW]
[ROW][C]52[/C][C]5180[/C][C]5711.58708391369[/C][C]-531.587083913687[/C][/ROW]
[ROW][C]53[/C][C]4770[/C][C]4594.02216219354[/C][C]175.977837806464[/C][/ROW]
[ROW][C]54[/C][C]5360[/C][C]5321.43200924894[/C][C]38.5679907510576[/C][/ROW]
[ROW][C]55[/C][C]4950[/C][C]5123.62296538391[/C][C]-173.622965383915[/C][/ROW]
[ROW][C]56[/C][C]3720[/C][C]4112.81213269911[/C][C]-392.812132699113[/C][/ROW]
[ROW][C]57[/C][C]3330[/C][C]3204.88051295802[/C][C]125.119487041982[/C][/ROW]
[ROW][C]58[/C][C]3000[/C][C]3036.64680365398[/C][C]-36.6468036539814[/C][/ROW]
[ROW][C]59[/C][C]2760[/C][C]2806.81348447151[/C][C]-46.8134844715055[/C][/ROW]
[ROW][C]60[/C][C]3040[/C][C]2774.90888840745[/C][C]265.091111592553[/C][/ROW]
[ROW][C]61[/C][C]3260[/C][C]3730.28808419925[/C][C]-470.288084199251[/C][/ROW]
[ROW][C]62[/C][C]3780[/C][C]3933.55035984723[/C][C]-153.550359847231[/C][/ROW]
[ROW][C]63[/C][C]4670[/C][C]5103.90714557503[/C][C]-433.907145575032[/C][/ROW]
[ROW][C]64[/C][C]4320[/C][C]4864.52980066324[/C][C]-544.529800663241[/C][/ROW]
[ROW][C]65[/C][C]4080[/C][C]4096.98102876192[/C][C]-16.9810287619239[/C][/ROW]
[ROW][C]66[/C][C]4210[/C][C]4545.12020267912[/C][C]-335.120202679117[/C][/ROW]
[ROW][C]67[/C][C]3350[/C][C]4072.17595528463[/C][C]-722.175955284631[/C][/ROW]
[ROW][C]68[/C][C]3390[/C][C]2884.81906031274[/C][C]505.180939687258[/C][/ROW]
[ROW][C]69[/C][C]2630[/C][C]2751.2977241666[/C][C]-121.297724166603[/C][/ROW]
[ROW][C]70[/C][C]2350[/C][C]2416.42107849927[/C][C]-66.4210784992651[/C][/ROW]
[ROW][C]71[/C][C]2330[/C][C]2192.09381653975[/C][C]137.906183460253[/C][/ROW]
[ROW][C]72[/C][C]2230[/C][C]2358.10236201247[/C][C]-128.102362012467[/C][/ROW]
[ROW][C]73[/C][C]2830[/C][C]2610.63938298359[/C][C]219.360617016405[/C][/ROW]
[ROW][C]74[/C][C]3230[/C][C]3215.60128207818[/C][C]14.3987179218248[/C][/ROW]
[ROW][C]75[/C][C]4240[/C][C]4154.76962134732[/C][C]85.2303786526791[/C][/ROW]
[ROW][C]76[/C][C]3750[/C][C]4124.76438217745[/C][C]-374.764382177452[/C][/ROW]
[ROW][C]77[/C][C]4160[/C][C]3701.66473948364[/C][C]458.335260516357[/C][/ROW]
[ROW][C]78[/C][C]3960[/C][C]4243.67259746948[/C][C]-283.672597469475[/C][/ROW]
[ROW][C]79[/C][C]3000[/C][C]3599.23297224442[/C][C]-599.232972244421[/C][/ROW]
[ROW][C]80[/C][C]2890[/C][C]3025.44364114347[/C][C]-135.443641143465[/C][/ROW]
[ROW][C]81[/C][C]2300[/C][C]2335.99634590164[/C][C]-35.996345901639[/C][/ROW]
[ROW][C]82[/C][C]2320[/C][C]2092.9698879599[/C][C]227.030112040104[/C][/ROW]
[ROW][C]83[/C][C]2270[/C][C]2122.11180737634[/C][C]147.888192623663[/C][/ROW]
[ROW][C]84[/C][C]1970[/C][C]2169.43047465831[/C][C]-199.430474658313[/C][/ROW]
[ROW][C]85[/C][C]2920[/C][C]2497.143552001[/C][C]422.856447998997[/C][/ROW]
[ROW][C]86[/C][C]3310[/C][C]3103.30871563496[/C][C]206.691284365039[/C][/ROW]
[ROW][C]87[/C][C]4370[/C][C]4177.7322513319[/C][C]192.2677486681[/C][/ROW]
[ROW][C]88[/C][C]3990[/C][C]3988.31324626464[/C][C]1.68675373535689[/C][/ROW]
[ROW][C]89[/C][C]3970[/C][C]4159.30818755552[/C][C]-189.308187555523[/C][/ROW]
[ROW][C]90[/C][C]3850[/C][C]4006.65523636105[/C][C]-156.655236361047[/C][/ROW]
[ROW][C]91[/C][C]3510[/C][C]3267.38117221177[/C][C]242.618827788226[/C][/ROW]
[ROW][C]92[/C][C]2840[/C][C]3373.23936054622[/C][C]-533.239360546224[/C][/ROW]
[ROW][C]93[/C][C]2130[/C][C]2482.8382228896[/C][C]-352.838222889597[/C][/ROW]
[ROW][C]94[/C][C]2280[/C][C]2184.07421260253[/C][C]95.9257873974739[/C][/ROW]
[ROW][C]95[/C][C]1960[/C][C]2106.56640118197[/C][C]-146.566401181969[/C][/ROW]
[ROW][C]96[/C][C]1740[/C][C]1844.78911182674[/C][C]-104.789111826741[/C][/ROW]
[ROW][C]97[/C][C]2370[/C][C]2419.930915314[/C][C]-49.9309153140039[/C][/ROW]
[ROW][C]98[/C][C]1980[/C][C]2600.45152277958[/C][C]-620.451522779581[/C][/ROW]
[ROW][C]99[/C][C]2680[/C][C]2875.43726161858[/C][C]-195.437261618583[/C][/ROW]
[ROW][C]100[/C][C]3510[/C][C]2485.60797567819[/C][C]1024.39202432181[/C][/ROW]
[ROW][C]101[/C][C]3350[/C][C]3077.42714926914[/C][C]272.572850730859[/C][/ROW]
[ROW][C]102[/C][C]3290[/C][C]3178.07194052955[/C][C]111.928059470451[/C][/ROW]
[ROW][C]103[/C][C]3150[/C][C]2826.96304727423[/C][C]323.03695272577[/C][/ROW]
[ROW][C]104[/C][C]2490[/C][C]2648.41641308592[/C][C]-158.416413085925[/C][/ROW]
[ROW][C]105[/C][C]2490[/C][C]2079.59014715199[/C][C]410.409852848009[/C][/ROW]
[ROW][C]106[/C][C]2930[/C][C]2419.50472961221[/C][C]510.495270387785[/C][/ROW]
[ROW][C]107[/C][C]3590[/C][C]2427.51154270167[/C][C]1162.48845729833[/C][/ROW]
[ROW][C]108[/C][C]2040[/C][C]2844.28577613651[/C][C]-804.285776136508[/C][/ROW]
[ROW][C]109[/C][C]2480[/C][C]3358.17261736541[/C][C]-878.172617365406[/C][/ROW]
[ROW][C]110[/C][C]2760[/C][C]2788.12382985798[/C][C]-28.1238298579819[/C][/ROW]
[ROW][C]111[/C][C]3400[/C][C]3952.42059613783[/C][C]-552.420596137828[/C][/ROW]
[ROW][C]112[/C][C]3470[/C][C]3963.42032317831[/C][C]-493.420323178307[/C][/ROW]
[ROW][C]113[/C][C]3130[/C][C]3372.6447342307[/C][C]-242.644734230705[/C][/ROW]
[ROW][C]114[/C][C]3670[/C][C]3119.16775206827[/C][C]550.832247931728[/C][/ROW]
[ROW][C]115[/C][C]3080[/C][C]3085.84543816814[/C][C]-5.84543816814221[/C][/ROW]
[ROW][C]116[/C][C]2430[/C][C]2516.3913040034[/C][C]-86.3913040033963[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299282&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299282&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
1327202476.97542343771243.024576562291
1437203566.82696843054153.173031569458
1547104665.8029043688744.1970956311261
1650705081.77979765692-11.7797976569245
1760306052.55658053516-22.5565805351644
1852805339.895125659-59.8951256590017
1944203975.77221221872444.227787781282
2039404365.48915376169-425.48915376169
2127503145.49415746267-395.494157462665
2229802522.93996234276457.060037657239
2326902695.53116683943-5.53116683942926
2426503091.78380661496-441.783806614956
2540003163.68211239099836.317887609011
2641504828.88176573392-678.88176573392
2760505602.5991631388447.400836861196
2862806286.49055573292-6.4905557329248
2955207472.40304467952-1952.40304467952
3048005621.86614529858-821.866145298579
3146104058.25992296137551.740077038631
3235304076.92594975124-546.92594975124
3327902813.10024590433-23.1002459043284
3427502748.944800492911.05519950708958
3524702467.815227956482.18477204351575
3626102619.14744418666-9.14744418665714
3736803433.93947328818246.060526711823
3838203980.81983432188-160.819834321882
3944605411.36351694304-951.363516943044
4047605040.64584577211-280.645845772108
4132904959.76611460911-1669.76611460911
4236103782.1207556568-172.120755656802
4336503262.7977099676387.202290032395
4431302837.50759852689292.492401473106
4528502362.0384340248487.961565975203
4627202578.98812460154141.011875398457
4727402377.25279496561362.747205034389
4827602723.1288286795636.8711713204393
4933303721.36100101204-391.361001012036
5038503713.48362359554136.516376404463
5154304879.34289364245550.657106357549
5251805711.58708391369-531.587083913687
5347704594.02216219354175.977837806464
5453605321.4320092489438.5679907510576
5549505123.62296538391-173.622965383915
5637204112.81213269911-392.812132699113
5733303204.88051295802125.119487041982
5830003036.64680365398-36.6468036539814
5927602806.81348447151-46.8134844715055
6030402774.90888840745265.091111592553
6132603730.28808419925-470.288084199251
6237803933.55035984723-153.550359847231
6346705103.90714557503-433.907145575032
6443204864.52980066324-544.529800663241
6540804096.98102876192-16.9810287619239
6642104545.12020267912-335.120202679117
6733504072.17595528463-722.175955284631
6833902884.81906031274505.180939687258
6926302751.2977241666-121.297724166603
7023502416.42107849927-66.4210784992651
7123302192.09381653975137.906183460253
7222302358.10236201247-128.102362012467
7328302610.63938298359219.360617016405
7432303215.6012820781814.3987179218248
7542404154.7696213473285.2303786526791
7637504124.76438217745-374.764382177452
7741603701.66473948364458.335260516357
7839604243.67259746948-283.672597469475
7930003599.23297224442-599.232972244421
8028903025.44364114347-135.443641143465
8123002335.99634590164-35.996345901639
8223202092.9698879599227.030112040104
8322702122.11180737634147.888192623663
8419702169.43047465831-199.430474658313
8529202497.143552001422.856447998997
8633103103.30871563496206.691284365039
8743704177.7322513319192.2677486681
8839903988.313246264641.68675373535689
8939704159.30818755552-189.308187555523
9038504006.65523636105-156.655236361047
9135103267.38117221177242.618827788226
9228403373.23936054622-533.239360546224
9321302482.8382228896-352.838222889597
9422802184.0742126025395.9257873974739
9519602106.56640118197-146.566401181969
9617401844.78911182674-104.789111826741
9723702419.930915314-49.9309153140039
9819802600.45152277958-620.451522779581
9926802875.43726161858-195.437261618583
10035102485.607975678191024.39202432181
10133503077.42714926914272.572850730859
10232903178.07194052955111.928059470451
10331502826.96304727423323.03695272577
10424902648.41641308592-158.416413085925
10524902079.59014715199410.409852848009
10629302419.50472961221510.495270387785
10735902427.511542701671162.48845729833
10820402844.28577613651-804.285776136508
10924803358.17261736541-878.172617365406
11027602788.12382985798-28.1238298579819
11134003952.42059613783-552.420596137828
11234703963.42032317831-493.420323178307
11331303372.6447342307-242.644734230705
11436703119.16775206827550.832247931728
11530803085.84543816814-5.84543816814221
11624302516.3913040034-86.3913040033963







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1172230.07966871281325.945088175053134.21424925054
1182345.575795339631295.054295279323396.09729539995
1192264.822925683941105.042305499783424.6035458681
1201499.74885224309413.890884362862585.60682012332
1212105.23589085121659.2443277235873551.22745397884
1222345.32822854215662.4725300898294028.18392699446
1233112.70273620318860.7631271625875364.64234524378
1243401.30301013727840.7203299254865961.88569034905
1253195.69862929802654.9616210085425736.43563758749
1263428.28685733582593.742095699516262.83161897212
1272877.43209271539344.5240736690395410.34011176175
1282311.17166747327307.6659882757074314.67734667084
1292120.58133931928-147.8089850818714388.97166372043
1302229.9333562686-231.0830134669744690.94972600417
1312152.70113844872-347.0035256617424652.40580255917
1321425.19507069192-537.1861982718033387.57633965564
1332000.14750140497-618.7312462566854619.02624906663
1342227.7659624308-747.6659947648875203.19791962649

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 2230.0796687128 & 1325.94508817505 & 3134.21424925054 \tabularnewline
118 & 2345.57579533963 & 1295.05429527932 & 3396.09729539995 \tabularnewline
119 & 2264.82292568394 & 1105.04230549978 & 3424.6035458681 \tabularnewline
120 & 1499.74885224309 & 413.89088436286 & 2585.60682012332 \tabularnewline
121 & 2105.23589085121 & 659.244327723587 & 3551.22745397884 \tabularnewline
122 & 2345.32822854215 & 662.472530089829 & 4028.18392699446 \tabularnewline
123 & 3112.70273620318 & 860.763127162587 & 5364.64234524378 \tabularnewline
124 & 3401.30301013727 & 840.720329925486 & 5961.88569034905 \tabularnewline
125 & 3195.69862929802 & 654.961621008542 & 5736.43563758749 \tabularnewline
126 & 3428.28685733582 & 593.74209569951 & 6262.83161897212 \tabularnewline
127 & 2877.43209271539 & 344.524073669039 & 5410.34011176175 \tabularnewline
128 & 2311.17166747327 & 307.665988275707 & 4314.67734667084 \tabularnewline
129 & 2120.58133931928 & -147.808985081871 & 4388.97166372043 \tabularnewline
130 & 2229.9333562686 & -231.083013466974 & 4690.94972600417 \tabularnewline
131 & 2152.70113844872 & -347.003525661742 & 4652.40580255917 \tabularnewline
132 & 1425.19507069192 & -537.186198271803 & 3387.57633965564 \tabularnewline
133 & 2000.14750140497 & -618.731246256685 & 4619.02624906663 \tabularnewline
134 & 2227.7659624308 & -747.665994764887 & 5203.19791962649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299282&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]117[/C][C]2230.0796687128[/C][C]1325.94508817505[/C][C]3134.21424925054[/C][/ROW]
[ROW][C]118[/C][C]2345.57579533963[/C][C]1295.05429527932[/C][C]3396.09729539995[/C][/ROW]
[ROW][C]119[/C][C]2264.82292568394[/C][C]1105.04230549978[/C][C]3424.6035458681[/C][/ROW]
[ROW][C]120[/C][C]1499.74885224309[/C][C]413.89088436286[/C][C]2585.60682012332[/C][/ROW]
[ROW][C]121[/C][C]2105.23589085121[/C][C]659.244327723587[/C][C]3551.22745397884[/C][/ROW]
[ROW][C]122[/C][C]2345.32822854215[/C][C]662.472530089829[/C][C]4028.18392699446[/C][/ROW]
[ROW][C]123[/C][C]3112.70273620318[/C][C]860.763127162587[/C][C]5364.64234524378[/C][/ROW]
[ROW][C]124[/C][C]3401.30301013727[/C][C]840.720329925486[/C][C]5961.88569034905[/C][/ROW]
[ROW][C]125[/C][C]3195.69862929802[/C][C]654.961621008542[/C][C]5736.43563758749[/C][/ROW]
[ROW][C]126[/C][C]3428.28685733582[/C][C]593.74209569951[/C][C]6262.83161897212[/C][/ROW]
[ROW][C]127[/C][C]2877.43209271539[/C][C]344.524073669039[/C][C]5410.34011176175[/C][/ROW]
[ROW][C]128[/C][C]2311.17166747327[/C][C]307.665988275707[/C][C]4314.67734667084[/C][/ROW]
[ROW][C]129[/C][C]2120.58133931928[/C][C]-147.808985081871[/C][C]4388.97166372043[/C][/ROW]
[ROW][C]130[/C][C]2229.9333562686[/C][C]-231.083013466974[/C][C]4690.94972600417[/C][/ROW]
[ROW][C]131[/C][C]2152.70113844872[/C][C]-347.003525661742[/C][C]4652.40580255917[/C][/ROW]
[ROW][C]132[/C][C]1425.19507069192[/C][C]-537.186198271803[/C][C]3387.57633965564[/C][/ROW]
[ROW][C]133[/C][C]2000.14750140497[/C][C]-618.731246256685[/C][C]4619.02624906663[/C][/ROW]
[ROW][C]134[/C][C]2227.7659624308[/C][C]-747.665994764887[/C][C]5203.19791962649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299282&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299282&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
1172230.07966871281325.945088175053134.21424925054
1182345.575795339631295.054295279323396.09729539995
1192264.822925683941105.042305499783424.6035458681
1201499.74885224309413.890884362862585.60682012332
1212105.23589085121659.2443277235873551.22745397884
1222345.32822854215662.4725300898294028.18392699446
1233112.70273620318860.7631271625875364.64234524378
1243401.30301013727840.7203299254865961.88569034905
1253195.69862929802654.9616210085425736.43563758749
1263428.28685733582593.742095699516262.83161897212
1272877.43209271539344.5240736690395410.34011176175
1282311.17166747327307.6659882757074314.67734667084
1292120.58133931928-147.8089850818714388.97166372043
1302229.9333562686-231.0830134669744690.94972600417
1312152.70113844872-347.0035256617424652.40580255917
1321425.19507069192-537.1861982718033387.57633965564
1332000.14750140497-618.7312462566854619.02624906663
1342227.7659624308-747.6659947648875203.19791962649



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')