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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 Dec 2016 00:55:50 +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/21/t148227818518jc6dtylnnbn5d.htm/, Retrieved Mon, 06 May 2024 11:04:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301836, Retrieved Mon, 06 May 2024 11:04:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-20 23:55:50] [2a4cd29e98d45e730e96e92769c461dd] [Current]
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Dataseries X:
3404
3425
3631
4141
3238
5390
1994
4343
4424
2762
3504
4279
3531
3210
4489
2395
2869
3193
3044
4209
5590
6703
4496
6277
5524
4478
2899
2265
2565
6319
1926
2591
5863
4287
4809
4455
3047
2757
2986
3158
1961
1364
2094
2497
2727
2949
3479
1858
2552
1843
2639
1495
2197
2861
1831
2516
2136
2432
1623
1535
2926
1548
1913
2092
1574
1371
2570
2775
1943
3431
1779
2628
3108
1188
1614
1078
1433
3167
1218
1922
3111
3443
2094
750
1297
2586
601
1846
1174
2420
742
1388
1878
1342
1605
1796
1842
1213
798
1948
832
1588
453
1111
1390
2262
1822
2100




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301836&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301836&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301836&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.172425397757574
beta0.0583108584272008
gamma0.366032410042517

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.172425397757574 \tabularnewline
beta & 0.0583108584272008 \tabularnewline
gamma & 0.366032410042517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301836&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]0.172425397757574[/C][/ROW]
[ROW][C]beta[/C][C]0.0583108584272008[/C][/ROW]
[ROW][C]gamma[/C][C]0.366032410042517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301836&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301836&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
alpha0.172425397757574
beta0.0583108584272008
gamma0.366032410042517







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1335313936.24457573788-405.244575737882
1432103490.62005260082-280.620052600819
1544894770.87580992331-281.875809923315
1623952383.044243818211.9557561818037
1728692716.23764584266152.762354157335
1831932968.84427219374224.155727806262
1930442071.97937425216972.020625747844
2042094921.82541405062-712.825414050624
2155904885.71942023759704.280579762412
2267033182.16059743683520.8394025632
2344965002.70356404652-506.703564046516
2462776277.56446408363-0.564464083634448
2555245159.54558345623364.454416543769
2644784800.93310030685-322.933100306853
2728996693.91386892937-3794.91386892937
2822653128.99527785106-863.995277851059
2925653459.46162657363-894.46162657363
3063193601.585575457222717.41442454278
3119263122.8049548538-1196.8049548538
3225915404.12103442729-2813.12103442729
3358635441.33071418045421.669285819554
3442874284.571236112032.42876388796685
3548094220.78177212844588.218227871559
3644555636.09019369837-1181.09019369837
3730474501.8499863382-1454.8499863382
3827573687.26354542412-930.263545424124
3929864038.09585199587-1052.09585199587
4031582214.38999757847943.610002421532
4119612751.1166565537-790.116656553698
4213643693.58741014303-2329.58741014303
4320941795.47129306315298.528706936852
4424973170.30283769315-673.302837693146
4527274111.47305276036-1384.47305276036
4629492876.6222786236972.3777213763133
4734792897.00759832204581.992401677963
4818583432.22801712098-1574.22801712098
4925522447.95551906187104.044480938127
5018432145.66577695385-302.665776953845
5126392335.41609245239303.583907547609
5214951642.878306586-147.878306585998
5321971479.92530146912717.07469853088
5428611927.44398861513933.556011384868
5518311517.28720971237313.712790287627
5625162395.23835914339120.761640856612
5721363112.24256233687-976.24256233687
5824322475.59180939685-43.5918093968471
5916232604.31584815875-981.315848158755
6015352221.3367801472-686.336780147199
6129261932.77530835654993.224691643459
6215481730.94880907063-182.948809070629
6319132063.19976927427-150.199769274269
6420921311.23354708865780.766452911346
6515741558.3440902548615.6559097451363
6613711880.58786718272-509.587867182723
6725701206.983141604381363.01685839562
6827752110.24241837642664.757581623581
6919432554.84246246572-611.84246246572
7034312294.421109612681136.57889038732
7117792350.60932113874-571.609321138738
7226282143.33723673981484.662763260189
7331082659.38739420947448.61260579053
7411881942.95939316917-754.959393169169
7516142262.47698948677-648.476989486772
7610781672.69588395201-594.695883952009
7714331463.25648403897-30.2564840389671
7831671604.777089274211562.22291072579
7912181807.81264576643-589.812645766427
8019222118.12151261133-196.121512611326
8131112020.555657534161090.44434246584
8234432559.82590300781883.174096992188
8320942082.2565534956611.7434465043393
847502304.01712830255-1554.01712830255
8512972383.43936833784-1086.43936833784
8625861282.039146386481303.96085361352
876011961.67578179182-1360.67578179182
8818461305.9556782335540.044321766497
8911741474.38771468714-300.387714687142
9024201984.15399255499435.846007445009
917421415.80615794633-673.80615794633
9213881741.84344320578-353.843443205785
9318781914.85334024946-36.8533402494634
9413422085.99821954211-743.998219542108
9516051339.96238295756265.037617042437
9617961151.90875305677644.091246943226
9718421625.71234947267216.287650527326
9812131443.93673001879-230.936730018794
997981090.09472633118-292.094726331177
10019481145.72299710359802.277002896407
1018321130.47750249206-298.47750249206
10215881703.79861844972-115.798618449718
103453909.990466949003-456.990466949003
10411111226.06335207237-115.063352072369
10513901447.29585012647-57.2958501264679
10622621386.02859670612875.971403293882
10718221263.57915299085558.420847009145
10821001243.08694676138856.913053238619

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3531 & 3936.24457573788 & -405.244575737882 \tabularnewline
14 & 3210 & 3490.62005260082 & -280.620052600819 \tabularnewline
15 & 4489 & 4770.87580992331 & -281.875809923315 \tabularnewline
16 & 2395 & 2383.0442438182 & 11.9557561818037 \tabularnewline
17 & 2869 & 2716.23764584266 & 152.762354157335 \tabularnewline
18 & 3193 & 2968.84427219374 & 224.155727806262 \tabularnewline
19 & 3044 & 2071.97937425216 & 972.020625747844 \tabularnewline
20 & 4209 & 4921.82541405062 & -712.825414050624 \tabularnewline
21 & 5590 & 4885.71942023759 & 704.280579762412 \tabularnewline
22 & 6703 & 3182.1605974368 & 3520.8394025632 \tabularnewline
23 & 4496 & 5002.70356404652 & -506.703564046516 \tabularnewline
24 & 6277 & 6277.56446408363 & -0.564464083634448 \tabularnewline
25 & 5524 & 5159.54558345623 & 364.454416543769 \tabularnewline
26 & 4478 & 4800.93310030685 & -322.933100306853 \tabularnewline
27 & 2899 & 6693.91386892937 & -3794.91386892937 \tabularnewline
28 & 2265 & 3128.99527785106 & -863.995277851059 \tabularnewline
29 & 2565 & 3459.46162657363 & -894.46162657363 \tabularnewline
30 & 6319 & 3601.58557545722 & 2717.41442454278 \tabularnewline
31 & 1926 & 3122.8049548538 & -1196.8049548538 \tabularnewline
32 & 2591 & 5404.12103442729 & -2813.12103442729 \tabularnewline
33 & 5863 & 5441.33071418045 & 421.669285819554 \tabularnewline
34 & 4287 & 4284.57123611203 & 2.42876388796685 \tabularnewline
35 & 4809 & 4220.78177212844 & 588.218227871559 \tabularnewline
36 & 4455 & 5636.09019369837 & -1181.09019369837 \tabularnewline
37 & 3047 & 4501.8499863382 & -1454.8499863382 \tabularnewline
38 & 2757 & 3687.26354542412 & -930.263545424124 \tabularnewline
39 & 2986 & 4038.09585199587 & -1052.09585199587 \tabularnewline
40 & 3158 & 2214.38999757847 & 943.610002421532 \tabularnewline
41 & 1961 & 2751.1166565537 & -790.116656553698 \tabularnewline
42 & 1364 & 3693.58741014303 & -2329.58741014303 \tabularnewline
43 & 2094 & 1795.47129306315 & 298.528706936852 \tabularnewline
44 & 2497 & 3170.30283769315 & -673.302837693146 \tabularnewline
45 & 2727 & 4111.47305276036 & -1384.47305276036 \tabularnewline
46 & 2949 & 2876.62227862369 & 72.3777213763133 \tabularnewline
47 & 3479 & 2897.00759832204 & 581.992401677963 \tabularnewline
48 & 1858 & 3432.22801712098 & -1574.22801712098 \tabularnewline
49 & 2552 & 2447.95551906187 & 104.044480938127 \tabularnewline
50 & 1843 & 2145.66577695385 & -302.665776953845 \tabularnewline
51 & 2639 & 2335.41609245239 & 303.583907547609 \tabularnewline
52 & 1495 & 1642.878306586 & -147.878306585998 \tabularnewline
53 & 2197 & 1479.92530146912 & 717.07469853088 \tabularnewline
54 & 2861 & 1927.44398861513 & 933.556011384868 \tabularnewline
55 & 1831 & 1517.28720971237 & 313.712790287627 \tabularnewline
56 & 2516 & 2395.23835914339 & 120.761640856612 \tabularnewline
57 & 2136 & 3112.24256233687 & -976.24256233687 \tabularnewline
58 & 2432 & 2475.59180939685 & -43.5918093968471 \tabularnewline
59 & 1623 & 2604.31584815875 & -981.315848158755 \tabularnewline
60 & 1535 & 2221.3367801472 & -686.336780147199 \tabularnewline
61 & 2926 & 1932.77530835654 & 993.224691643459 \tabularnewline
62 & 1548 & 1730.94880907063 & -182.948809070629 \tabularnewline
63 & 1913 & 2063.19976927427 & -150.199769274269 \tabularnewline
64 & 2092 & 1311.23354708865 & 780.766452911346 \tabularnewline
65 & 1574 & 1558.34409025486 & 15.6559097451363 \tabularnewline
66 & 1371 & 1880.58786718272 & -509.587867182723 \tabularnewline
67 & 2570 & 1206.98314160438 & 1363.01685839562 \tabularnewline
68 & 2775 & 2110.24241837642 & 664.757581623581 \tabularnewline
69 & 1943 & 2554.84246246572 & -611.84246246572 \tabularnewline
70 & 3431 & 2294.42110961268 & 1136.57889038732 \tabularnewline
71 & 1779 & 2350.60932113874 & -571.609321138738 \tabularnewline
72 & 2628 & 2143.33723673981 & 484.662763260189 \tabularnewline
73 & 3108 & 2659.38739420947 & 448.61260579053 \tabularnewline
74 & 1188 & 1942.95939316917 & -754.959393169169 \tabularnewline
75 & 1614 & 2262.47698948677 & -648.476989486772 \tabularnewline
76 & 1078 & 1672.69588395201 & -594.695883952009 \tabularnewline
77 & 1433 & 1463.25648403897 & -30.2564840389671 \tabularnewline
78 & 3167 & 1604.77708927421 & 1562.22291072579 \tabularnewline
79 & 1218 & 1807.81264576643 & -589.812645766427 \tabularnewline
80 & 1922 & 2118.12151261133 & -196.121512611326 \tabularnewline
81 & 3111 & 2020.55565753416 & 1090.44434246584 \tabularnewline
82 & 3443 & 2559.82590300781 & 883.174096992188 \tabularnewline
83 & 2094 & 2082.25655349566 & 11.7434465043393 \tabularnewline
84 & 750 & 2304.01712830255 & -1554.01712830255 \tabularnewline
85 & 1297 & 2383.43936833784 & -1086.43936833784 \tabularnewline
86 & 2586 & 1282.03914638648 & 1303.96085361352 \tabularnewline
87 & 601 & 1961.67578179182 & -1360.67578179182 \tabularnewline
88 & 1846 & 1305.9556782335 & 540.044321766497 \tabularnewline
89 & 1174 & 1474.38771468714 & -300.387714687142 \tabularnewline
90 & 2420 & 1984.15399255499 & 435.846007445009 \tabularnewline
91 & 742 & 1415.80615794633 & -673.80615794633 \tabularnewline
92 & 1388 & 1741.84344320578 & -353.843443205785 \tabularnewline
93 & 1878 & 1914.85334024946 & -36.8533402494634 \tabularnewline
94 & 1342 & 2085.99821954211 & -743.998219542108 \tabularnewline
95 & 1605 & 1339.96238295756 & 265.037617042437 \tabularnewline
96 & 1796 & 1151.90875305677 & 644.091246943226 \tabularnewline
97 & 1842 & 1625.71234947267 & 216.287650527326 \tabularnewline
98 & 1213 & 1443.93673001879 & -230.936730018794 \tabularnewline
99 & 798 & 1090.09472633118 & -292.094726331177 \tabularnewline
100 & 1948 & 1145.72299710359 & 802.277002896407 \tabularnewline
101 & 832 & 1130.47750249206 & -298.47750249206 \tabularnewline
102 & 1588 & 1703.79861844972 & -115.798618449718 \tabularnewline
103 & 453 & 909.990466949003 & -456.990466949003 \tabularnewline
104 & 1111 & 1226.06335207237 & -115.063352072369 \tabularnewline
105 & 1390 & 1447.29585012647 & -57.2958501264679 \tabularnewline
106 & 2262 & 1386.02859670612 & 875.971403293882 \tabularnewline
107 & 1822 & 1263.57915299085 & 558.420847009145 \tabularnewline
108 & 2100 & 1243.08694676138 & 856.913053238619 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301836&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]3531[/C][C]3936.24457573788[/C][C]-405.244575737882[/C][/ROW]
[ROW][C]14[/C][C]3210[/C][C]3490.62005260082[/C][C]-280.620052600819[/C][/ROW]
[ROW][C]15[/C][C]4489[/C][C]4770.87580992331[/C][C]-281.875809923315[/C][/ROW]
[ROW][C]16[/C][C]2395[/C][C]2383.0442438182[/C][C]11.9557561818037[/C][/ROW]
[ROW][C]17[/C][C]2869[/C][C]2716.23764584266[/C][C]152.762354157335[/C][/ROW]
[ROW][C]18[/C][C]3193[/C][C]2968.84427219374[/C][C]224.155727806262[/C][/ROW]
[ROW][C]19[/C][C]3044[/C][C]2071.97937425216[/C][C]972.020625747844[/C][/ROW]
[ROW][C]20[/C][C]4209[/C][C]4921.82541405062[/C][C]-712.825414050624[/C][/ROW]
[ROW][C]21[/C][C]5590[/C][C]4885.71942023759[/C][C]704.280579762412[/C][/ROW]
[ROW][C]22[/C][C]6703[/C][C]3182.1605974368[/C][C]3520.8394025632[/C][/ROW]
[ROW][C]23[/C][C]4496[/C][C]5002.70356404652[/C][C]-506.703564046516[/C][/ROW]
[ROW][C]24[/C][C]6277[/C][C]6277.56446408363[/C][C]-0.564464083634448[/C][/ROW]
[ROW][C]25[/C][C]5524[/C][C]5159.54558345623[/C][C]364.454416543769[/C][/ROW]
[ROW][C]26[/C][C]4478[/C][C]4800.93310030685[/C][C]-322.933100306853[/C][/ROW]
[ROW][C]27[/C][C]2899[/C][C]6693.91386892937[/C][C]-3794.91386892937[/C][/ROW]
[ROW][C]28[/C][C]2265[/C][C]3128.99527785106[/C][C]-863.995277851059[/C][/ROW]
[ROW][C]29[/C][C]2565[/C][C]3459.46162657363[/C][C]-894.46162657363[/C][/ROW]
[ROW][C]30[/C][C]6319[/C][C]3601.58557545722[/C][C]2717.41442454278[/C][/ROW]
[ROW][C]31[/C][C]1926[/C][C]3122.8049548538[/C][C]-1196.8049548538[/C][/ROW]
[ROW][C]32[/C][C]2591[/C][C]5404.12103442729[/C][C]-2813.12103442729[/C][/ROW]
[ROW][C]33[/C][C]5863[/C][C]5441.33071418045[/C][C]421.669285819554[/C][/ROW]
[ROW][C]34[/C][C]4287[/C][C]4284.57123611203[/C][C]2.42876388796685[/C][/ROW]
[ROW][C]35[/C][C]4809[/C][C]4220.78177212844[/C][C]588.218227871559[/C][/ROW]
[ROW][C]36[/C][C]4455[/C][C]5636.09019369837[/C][C]-1181.09019369837[/C][/ROW]
[ROW][C]37[/C][C]3047[/C][C]4501.8499863382[/C][C]-1454.8499863382[/C][/ROW]
[ROW][C]38[/C][C]2757[/C][C]3687.26354542412[/C][C]-930.263545424124[/C][/ROW]
[ROW][C]39[/C][C]2986[/C][C]4038.09585199587[/C][C]-1052.09585199587[/C][/ROW]
[ROW][C]40[/C][C]3158[/C][C]2214.38999757847[/C][C]943.610002421532[/C][/ROW]
[ROW][C]41[/C][C]1961[/C][C]2751.1166565537[/C][C]-790.116656553698[/C][/ROW]
[ROW][C]42[/C][C]1364[/C][C]3693.58741014303[/C][C]-2329.58741014303[/C][/ROW]
[ROW][C]43[/C][C]2094[/C][C]1795.47129306315[/C][C]298.528706936852[/C][/ROW]
[ROW][C]44[/C][C]2497[/C][C]3170.30283769315[/C][C]-673.302837693146[/C][/ROW]
[ROW][C]45[/C][C]2727[/C][C]4111.47305276036[/C][C]-1384.47305276036[/C][/ROW]
[ROW][C]46[/C][C]2949[/C][C]2876.62227862369[/C][C]72.3777213763133[/C][/ROW]
[ROW][C]47[/C][C]3479[/C][C]2897.00759832204[/C][C]581.992401677963[/C][/ROW]
[ROW][C]48[/C][C]1858[/C][C]3432.22801712098[/C][C]-1574.22801712098[/C][/ROW]
[ROW][C]49[/C][C]2552[/C][C]2447.95551906187[/C][C]104.044480938127[/C][/ROW]
[ROW][C]50[/C][C]1843[/C][C]2145.66577695385[/C][C]-302.665776953845[/C][/ROW]
[ROW][C]51[/C][C]2639[/C][C]2335.41609245239[/C][C]303.583907547609[/C][/ROW]
[ROW][C]52[/C][C]1495[/C][C]1642.878306586[/C][C]-147.878306585998[/C][/ROW]
[ROW][C]53[/C][C]2197[/C][C]1479.92530146912[/C][C]717.07469853088[/C][/ROW]
[ROW][C]54[/C][C]2861[/C][C]1927.44398861513[/C][C]933.556011384868[/C][/ROW]
[ROW][C]55[/C][C]1831[/C][C]1517.28720971237[/C][C]313.712790287627[/C][/ROW]
[ROW][C]56[/C][C]2516[/C][C]2395.23835914339[/C][C]120.761640856612[/C][/ROW]
[ROW][C]57[/C][C]2136[/C][C]3112.24256233687[/C][C]-976.24256233687[/C][/ROW]
[ROW][C]58[/C][C]2432[/C][C]2475.59180939685[/C][C]-43.5918093968471[/C][/ROW]
[ROW][C]59[/C][C]1623[/C][C]2604.31584815875[/C][C]-981.315848158755[/C][/ROW]
[ROW][C]60[/C][C]1535[/C][C]2221.3367801472[/C][C]-686.336780147199[/C][/ROW]
[ROW][C]61[/C][C]2926[/C][C]1932.77530835654[/C][C]993.224691643459[/C][/ROW]
[ROW][C]62[/C][C]1548[/C][C]1730.94880907063[/C][C]-182.948809070629[/C][/ROW]
[ROW][C]63[/C][C]1913[/C][C]2063.19976927427[/C][C]-150.199769274269[/C][/ROW]
[ROW][C]64[/C][C]2092[/C][C]1311.23354708865[/C][C]780.766452911346[/C][/ROW]
[ROW][C]65[/C][C]1574[/C][C]1558.34409025486[/C][C]15.6559097451363[/C][/ROW]
[ROW][C]66[/C][C]1371[/C][C]1880.58786718272[/C][C]-509.587867182723[/C][/ROW]
[ROW][C]67[/C][C]2570[/C][C]1206.98314160438[/C][C]1363.01685839562[/C][/ROW]
[ROW][C]68[/C][C]2775[/C][C]2110.24241837642[/C][C]664.757581623581[/C][/ROW]
[ROW][C]69[/C][C]1943[/C][C]2554.84246246572[/C][C]-611.84246246572[/C][/ROW]
[ROW][C]70[/C][C]3431[/C][C]2294.42110961268[/C][C]1136.57889038732[/C][/ROW]
[ROW][C]71[/C][C]1779[/C][C]2350.60932113874[/C][C]-571.609321138738[/C][/ROW]
[ROW][C]72[/C][C]2628[/C][C]2143.33723673981[/C][C]484.662763260189[/C][/ROW]
[ROW][C]73[/C][C]3108[/C][C]2659.38739420947[/C][C]448.61260579053[/C][/ROW]
[ROW][C]74[/C][C]1188[/C][C]1942.95939316917[/C][C]-754.959393169169[/C][/ROW]
[ROW][C]75[/C][C]1614[/C][C]2262.47698948677[/C][C]-648.476989486772[/C][/ROW]
[ROW][C]76[/C][C]1078[/C][C]1672.69588395201[/C][C]-594.695883952009[/C][/ROW]
[ROW][C]77[/C][C]1433[/C][C]1463.25648403897[/C][C]-30.2564840389671[/C][/ROW]
[ROW][C]78[/C][C]3167[/C][C]1604.77708927421[/C][C]1562.22291072579[/C][/ROW]
[ROW][C]79[/C][C]1218[/C][C]1807.81264576643[/C][C]-589.812645766427[/C][/ROW]
[ROW][C]80[/C][C]1922[/C][C]2118.12151261133[/C][C]-196.121512611326[/C][/ROW]
[ROW][C]81[/C][C]3111[/C][C]2020.55565753416[/C][C]1090.44434246584[/C][/ROW]
[ROW][C]82[/C][C]3443[/C][C]2559.82590300781[/C][C]883.174096992188[/C][/ROW]
[ROW][C]83[/C][C]2094[/C][C]2082.25655349566[/C][C]11.7434465043393[/C][/ROW]
[ROW][C]84[/C][C]750[/C][C]2304.01712830255[/C][C]-1554.01712830255[/C][/ROW]
[ROW][C]85[/C][C]1297[/C][C]2383.43936833784[/C][C]-1086.43936833784[/C][/ROW]
[ROW][C]86[/C][C]2586[/C][C]1282.03914638648[/C][C]1303.96085361352[/C][/ROW]
[ROW][C]87[/C][C]601[/C][C]1961.67578179182[/C][C]-1360.67578179182[/C][/ROW]
[ROW][C]88[/C][C]1846[/C][C]1305.9556782335[/C][C]540.044321766497[/C][/ROW]
[ROW][C]89[/C][C]1174[/C][C]1474.38771468714[/C][C]-300.387714687142[/C][/ROW]
[ROW][C]90[/C][C]2420[/C][C]1984.15399255499[/C][C]435.846007445009[/C][/ROW]
[ROW][C]91[/C][C]742[/C][C]1415.80615794633[/C][C]-673.80615794633[/C][/ROW]
[ROW][C]92[/C][C]1388[/C][C]1741.84344320578[/C][C]-353.843443205785[/C][/ROW]
[ROW][C]93[/C][C]1878[/C][C]1914.85334024946[/C][C]-36.8533402494634[/C][/ROW]
[ROW][C]94[/C][C]1342[/C][C]2085.99821954211[/C][C]-743.998219542108[/C][/ROW]
[ROW][C]95[/C][C]1605[/C][C]1339.96238295756[/C][C]265.037617042437[/C][/ROW]
[ROW][C]96[/C][C]1796[/C][C]1151.90875305677[/C][C]644.091246943226[/C][/ROW]
[ROW][C]97[/C][C]1842[/C][C]1625.71234947267[/C][C]216.287650527326[/C][/ROW]
[ROW][C]98[/C][C]1213[/C][C]1443.93673001879[/C][C]-230.936730018794[/C][/ROW]
[ROW][C]99[/C][C]798[/C][C]1090.09472633118[/C][C]-292.094726331177[/C][/ROW]
[ROW][C]100[/C][C]1948[/C][C]1145.72299710359[/C][C]802.277002896407[/C][/ROW]
[ROW][C]101[/C][C]832[/C][C]1130.47750249206[/C][C]-298.47750249206[/C][/ROW]
[ROW][C]102[/C][C]1588[/C][C]1703.79861844972[/C][C]-115.798618449718[/C][/ROW]
[ROW][C]103[/C][C]453[/C][C]909.990466949003[/C][C]-456.990466949003[/C][/ROW]
[ROW][C]104[/C][C]1111[/C][C]1226.06335207237[/C][C]-115.063352072369[/C][/ROW]
[ROW][C]105[/C][C]1390[/C][C]1447.29585012647[/C][C]-57.2958501264679[/C][/ROW]
[ROW][C]106[/C][C]2262[/C][C]1386.02859670612[/C][C]875.971403293882[/C][/ROW]
[ROW][C]107[/C][C]1822[/C][C]1263.57915299085[/C][C]558.420847009145[/C][/ROW]
[ROW][C]108[/C][C]2100[/C][C]1243.08694676138[/C][C]856.913053238619[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301836&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301836&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
1335313936.24457573788-405.244575737882
1432103490.62005260082-280.620052600819
1544894770.87580992331-281.875809923315
1623952383.044243818211.9557561818037
1728692716.23764584266152.762354157335
1831932968.84427219374224.155727806262
1930442071.97937425216972.020625747844
2042094921.82541405062-712.825414050624
2155904885.71942023759704.280579762412
2267033182.16059743683520.8394025632
2344965002.70356404652-506.703564046516
2462776277.56446408363-0.564464083634448
2555245159.54558345623364.454416543769
2644784800.93310030685-322.933100306853
2728996693.91386892937-3794.91386892937
2822653128.99527785106-863.995277851059
2925653459.46162657363-894.46162657363
3063193601.585575457222717.41442454278
3119263122.8049548538-1196.8049548538
3225915404.12103442729-2813.12103442729
3358635441.33071418045421.669285819554
3442874284.571236112032.42876388796685
3548094220.78177212844588.218227871559
3644555636.09019369837-1181.09019369837
3730474501.8499863382-1454.8499863382
3827573687.26354542412-930.263545424124
3929864038.09585199587-1052.09585199587
4031582214.38999757847943.610002421532
4119612751.1166565537-790.116656553698
4213643693.58741014303-2329.58741014303
4320941795.47129306315298.528706936852
4424973170.30283769315-673.302837693146
4527274111.47305276036-1384.47305276036
4629492876.6222786236972.3777213763133
4734792897.00759832204581.992401677963
4818583432.22801712098-1574.22801712098
4925522447.95551906187104.044480938127
5018432145.66577695385-302.665776953845
5126392335.41609245239303.583907547609
5214951642.878306586-147.878306585998
5321971479.92530146912717.07469853088
5428611927.44398861513933.556011384868
5518311517.28720971237313.712790287627
5625162395.23835914339120.761640856612
5721363112.24256233687-976.24256233687
5824322475.59180939685-43.5918093968471
5916232604.31584815875-981.315848158755
6015352221.3367801472-686.336780147199
6129261932.77530835654993.224691643459
6215481730.94880907063-182.948809070629
6319132063.19976927427-150.199769274269
6420921311.23354708865780.766452911346
6515741558.3440902548615.6559097451363
6613711880.58786718272-509.587867182723
6725701206.983141604381363.01685839562
6827752110.24241837642664.757581623581
6919432554.84246246572-611.84246246572
7034312294.421109612681136.57889038732
7117792350.60932113874-571.609321138738
7226282143.33723673981484.662763260189
7331082659.38739420947448.61260579053
7411881942.95939316917-754.959393169169
7516142262.47698948677-648.476989486772
7610781672.69588395201-594.695883952009
7714331463.25648403897-30.2564840389671
7831671604.777089274211562.22291072579
7912181807.81264576643-589.812645766427
8019222118.12151261133-196.121512611326
8131112020.555657534161090.44434246584
8234432559.82590300781883.174096992188
8320942082.2565534956611.7434465043393
847502304.01712830255-1554.01712830255
8512972383.43936833784-1086.43936833784
8625861282.039146386481303.96085361352
876011961.67578179182-1360.67578179182
8818461305.9556782335540.044321766497
8911741474.38771468714-300.387714687142
9024201984.15399255499435.846007445009
917421415.80615794633-673.80615794633
9213881741.84344320578-353.843443205785
9318781914.85334024946-36.8533402494634
9413422085.99821954211-743.998219542108
9516051339.96238295756265.037617042437
9617961151.90875305677644.091246943226
9718421625.71234947267216.287650527326
9812131443.93673001879-230.936730018794
997981090.09472633118-292.094726331177
10019481145.72299710359802.277002896407
1018321130.47750249206-298.47750249206
10215881703.79861844972-115.798618449718
103453909.990466949003-456.990466949003
10411111226.06335207237-115.063352072369
10513901447.29585012647-57.2958501264679
10622621386.02859670612875.971403293882
10718221263.57915299085558.420847009145
10821001243.08694676138856.913053238619







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091625.65849278882696.5682756488142554.74870992883
1101299.47287939006327.0200281662082271.92573061392
111980.46250537874-14.37163287806481975.29664363555
1121423.09170138275225.0000335324712621.18336923303
113969.994628210593-135.5879578021842075.57721422337
1141650.80232652063100.5088332504983201.09581979075
115766.661251848962-357.1472167553021890.46972045322
1161340.34714285095-278.582567739672959.27685344158
1171667.54918853523-356.6652624535733691.76363952404
1181947.74264883232-490.67791441084386.16321207545
1191554.38049130784-574.8931457281833683.65412834386
1201510.13831455129-479.5222417927453499.79887089532
1211486.4995392965-986.1164603458133959.11553893882
1221187.43672731064-1034.145925760973409.01938038224
123895.318612838386-1070.243340710452860.88056638722
1241298.6088040109-1291.165553156883888.38316117867
125884.522700385015-1212.521128586322981.56652935635
1261504.26440449093-1687.371724458584695.90053344043

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1625.65849278882 & 696.568275648814 & 2554.74870992883 \tabularnewline
110 & 1299.47287939006 & 327.020028166208 & 2271.92573061392 \tabularnewline
111 & 980.46250537874 & -14.3716328780648 & 1975.29664363555 \tabularnewline
112 & 1423.09170138275 & 225.000033532471 & 2621.18336923303 \tabularnewline
113 & 969.994628210593 & -135.587957802184 & 2075.57721422337 \tabularnewline
114 & 1650.80232652063 & 100.508833250498 & 3201.09581979075 \tabularnewline
115 & 766.661251848962 & -357.147216755302 & 1890.46972045322 \tabularnewline
116 & 1340.34714285095 & -278.58256773967 & 2959.27685344158 \tabularnewline
117 & 1667.54918853523 & -356.665262453573 & 3691.76363952404 \tabularnewline
118 & 1947.74264883232 & -490.6779144108 & 4386.16321207545 \tabularnewline
119 & 1554.38049130784 & -574.893145728183 & 3683.65412834386 \tabularnewline
120 & 1510.13831455129 & -479.522241792745 & 3499.79887089532 \tabularnewline
121 & 1486.4995392965 & -986.116460345813 & 3959.11553893882 \tabularnewline
122 & 1187.43672731064 & -1034.14592576097 & 3409.01938038224 \tabularnewline
123 & 895.318612838386 & -1070.24334071045 & 2860.88056638722 \tabularnewline
124 & 1298.6088040109 & -1291.16555315688 & 3888.38316117867 \tabularnewline
125 & 884.522700385015 & -1212.52112858632 & 2981.56652935635 \tabularnewline
126 & 1504.26440449093 & -1687.37172445858 & 4695.90053344043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301836&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]1625.65849278882[/C][C]696.568275648814[/C][C]2554.74870992883[/C][/ROW]
[ROW][C]110[/C][C]1299.47287939006[/C][C]327.020028166208[/C][C]2271.92573061392[/C][/ROW]
[ROW][C]111[/C][C]980.46250537874[/C][C]-14.3716328780648[/C][C]1975.29664363555[/C][/ROW]
[ROW][C]112[/C][C]1423.09170138275[/C][C]225.000033532471[/C][C]2621.18336923303[/C][/ROW]
[ROW][C]113[/C][C]969.994628210593[/C][C]-135.587957802184[/C][C]2075.57721422337[/C][/ROW]
[ROW][C]114[/C][C]1650.80232652063[/C][C]100.508833250498[/C][C]3201.09581979075[/C][/ROW]
[ROW][C]115[/C][C]766.661251848962[/C][C]-357.147216755302[/C][C]1890.46972045322[/C][/ROW]
[ROW][C]116[/C][C]1340.34714285095[/C][C]-278.58256773967[/C][C]2959.27685344158[/C][/ROW]
[ROW][C]117[/C][C]1667.54918853523[/C][C]-356.665262453573[/C][C]3691.76363952404[/C][/ROW]
[ROW][C]118[/C][C]1947.74264883232[/C][C]-490.6779144108[/C][C]4386.16321207545[/C][/ROW]
[ROW][C]119[/C][C]1554.38049130784[/C][C]-574.893145728183[/C][C]3683.65412834386[/C][/ROW]
[ROW][C]120[/C][C]1510.13831455129[/C][C]-479.522241792745[/C][C]3499.79887089532[/C][/ROW]
[ROW][C]121[/C][C]1486.4995392965[/C][C]-986.116460345813[/C][C]3959.11553893882[/C][/ROW]
[ROW][C]122[/C][C]1187.43672731064[/C][C]-1034.14592576097[/C][C]3409.01938038224[/C][/ROW]
[ROW][C]123[/C][C]895.318612838386[/C][C]-1070.24334071045[/C][C]2860.88056638722[/C][/ROW]
[ROW][C]124[/C][C]1298.6088040109[/C][C]-1291.16555315688[/C][C]3888.38316117867[/C][/ROW]
[ROW][C]125[/C][C]884.522700385015[/C][C]-1212.52112858632[/C][C]2981.56652935635[/C][/ROW]
[ROW][C]126[/C][C]1504.26440449093[/C][C]-1687.37172445858[/C][C]4695.90053344043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301836&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301836&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
1091625.65849278882696.5682756488142554.74870992883
1101299.47287939006327.0200281662082271.92573061392
111980.46250537874-14.37163287806481975.29664363555
1121423.09170138275225.0000335324712621.18336923303
113969.994628210593-135.5879578021842075.57721422337
1141650.80232652063100.5088332504983201.09581979075
115766.661251848962-357.1472167553021890.46972045322
1161340.34714285095-278.582567739672959.27685344158
1171667.54918853523-356.6652624535733691.76363952404
1181947.74264883232-490.67791441084386.16321207545
1191554.38049130784-574.8931457281833683.65412834386
1201510.13831455129-479.5222417927453499.79887089532
1211486.4995392965-986.1164603458133959.11553893882
1221187.43672731064-1034.145925760973409.01938038224
123895.318612838386-1070.243340710452860.88056638722
1241298.6088040109-1291.165553156883888.38316117867
125884.522700385015-1212.521128586322981.56652935635
1261504.26440449093-1687.371724458584695.90053344043



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):
par4 <- '12'
par3 <- 'multiplicative'
par2 <- 'Triple'
par1 <- '12'
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')