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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 05:40:20 -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/21/t1356086485ujom1rb709ygeiz.htm/, Retrieved Tue, 23 Apr 2024 14:42:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203437, Retrieved Tue, 23 Apr 2024 14:42:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-21 10:40:20] [b5e28e8a989acbea90caf9c77474d9fd] [Current]
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Dataseries X:
369.82
373.1
374.55
375.01
374.81
375.31
375.31
375.39
375.59
376.26
377.18
377.26
377.26
381.87
387.09
387.14
388.78
389.16
389.16
389.42
389.49
388.97
388.97
389.09
389.09
391.76
390.96
391.76
392.8
393.06
393.06
393.26
393.87
394.47
394.57
394.57
394.57
399.57
406.13
407.03
409.46
409.9
409.9
410.14
410.54
410.69
410.79
410.97
410.97
413.8
423.31
423.85
426.6
426.26
426.26
426.32
427.14
427.55
428.29
428.8
428.8
434.87
435.66
440.75
440.99
441.04
441.04
441.88
441.92
442.48
442.81
442.81




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203437&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]4 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=203437&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203437&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 time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.833089234526611
beta0
gamma0.237425830595833

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.833089234526611 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.237425830595833 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203437&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]0.833089234526611[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.237425830595833[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203437&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203437&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
alpha0.833089234526611
beta0
gamma0.237425830595833







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13377.26370.9308680555556.32913194444461
14381.87380.7321414090371.13785859096265
15387.09386.8165374849150.273462515084645
16387.14387.0658144956120.0741855043877422
17388.78388.826992640676-0.0469926406756258
18389.16389.263885244294-0.103885244293508
19389.16387.838797898981.32120210102028
20389.42389.42426881264-0.00426881264036183
21389.49389.813004177452-0.323004177452162
22388.97390.266204541176-1.29620454117639
23388.97390.099058825511-1.12905882551115
24389.09389.159493739497-0.0694937394972044
25389.09389.278457628531-0.188457628531012
26391.76393.444272680278-1.6842726802779
27390.96397.143326486564-6.18332648656389
28391.76392.005624956242-0.245624956242409
29392.8393.495570289586-0.695570289585532
30393.06393.389885243299-0.329885243299202
31393.06391.8329944143691.22700558563088
32393.26393.287464234881-0.027464234881279
33393.87393.6442446025890.225755397411319
34394.47394.51604377418-0.0460437741801911
35394.57395.397017340313-0.827017340312921
36394.57394.751069191579-0.181069191578899
37394.57394.772366361357-0.20236636135661
38399.57398.8673166518380.702683348161941
39406.13404.3766251532721.75337484672815
40407.03406.0862088026210.94379119737863
41409.46408.5492130780920.910786921908311
42409.9409.7962586375560.103741362443884
43409.9408.6623153788811.23768462111929
44410.14410.0759684957920.0640315042078328
45410.54410.5190078010950.0209921989048212
46410.69411.209449846819-0.519449846819327
47410.79411.665084765736-0.875084765735721
48410.97411.004690394465-0.0346903944652013
49410.97411.147090180292-0.177090180292168
50413.8415.298963934094-1.49896393409404
51423.31419.0157415632864.29425843671379
52423.85422.8100250461941.03997495380594
53426.6425.3518510496531.24814895034723
54426.26426.847966933483-0.587966933482846
55426.26425.1827058948031.0772941051967
56426.32426.416228785736-0.0962287857359456
57427.14426.7240513672710.415948632728771
58427.55427.722110227674-0.172110227674239
59428.29428.453016613739-0.163016613739103
60428.8428.4191424814440.380857518556013
61428.8428.902087609303-0.102087609303339
62434.87433.0640607588961.80593924110389
63435.66439.763696831667-4.10369683166692
64440.75436.4327704254534.31722957454696
65440.99441.713091684393-0.723091684392557
66441.04441.494224914201-0.454224914200722
67441.04440.006375420341.03362457966023
68441.88441.1570122465430.72298775345655
69441.92442.167612349219-0.247612349219082
70442.48442.589561557384-0.109561557383586
71442.81443.372936937466-0.562936937465508
72442.81443.027446637161-0.217446637160947

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 377.26 & 370.930868055555 & 6.32913194444461 \tabularnewline
14 & 381.87 & 380.732141409037 & 1.13785859096265 \tabularnewline
15 & 387.09 & 386.816537484915 & 0.273462515084645 \tabularnewline
16 & 387.14 & 387.065814495612 & 0.0741855043877422 \tabularnewline
17 & 388.78 & 388.826992640676 & -0.0469926406756258 \tabularnewline
18 & 389.16 & 389.263885244294 & -0.103885244293508 \tabularnewline
19 & 389.16 & 387.83879789898 & 1.32120210102028 \tabularnewline
20 & 389.42 & 389.42426881264 & -0.00426881264036183 \tabularnewline
21 & 389.49 & 389.813004177452 & -0.323004177452162 \tabularnewline
22 & 388.97 & 390.266204541176 & -1.29620454117639 \tabularnewline
23 & 388.97 & 390.099058825511 & -1.12905882551115 \tabularnewline
24 & 389.09 & 389.159493739497 & -0.0694937394972044 \tabularnewline
25 & 389.09 & 389.278457628531 & -0.188457628531012 \tabularnewline
26 & 391.76 & 393.444272680278 & -1.6842726802779 \tabularnewline
27 & 390.96 & 397.143326486564 & -6.18332648656389 \tabularnewline
28 & 391.76 & 392.005624956242 & -0.245624956242409 \tabularnewline
29 & 392.8 & 393.495570289586 & -0.695570289585532 \tabularnewline
30 & 393.06 & 393.389885243299 & -0.329885243299202 \tabularnewline
31 & 393.06 & 391.832994414369 & 1.22700558563088 \tabularnewline
32 & 393.26 & 393.287464234881 & -0.027464234881279 \tabularnewline
33 & 393.87 & 393.644244602589 & 0.225755397411319 \tabularnewline
34 & 394.47 & 394.51604377418 & -0.0460437741801911 \tabularnewline
35 & 394.57 & 395.397017340313 & -0.827017340312921 \tabularnewline
36 & 394.57 & 394.751069191579 & -0.181069191578899 \tabularnewline
37 & 394.57 & 394.772366361357 & -0.20236636135661 \tabularnewline
38 & 399.57 & 398.867316651838 & 0.702683348161941 \tabularnewline
39 & 406.13 & 404.376625153272 & 1.75337484672815 \tabularnewline
40 & 407.03 & 406.086208802621 & 0.94379119737863 \tabularnewline
41 & 409.46 & 408.549213078092 & 0.910786921908311 \tabularnewline
42 & 409.9 & 409.796258637556 & 0.103741362443884 \tabularnewline
43 & 409.9 & 408.662315378881 & 1.23768462111929 \tabularnewline
44 & 410.14 & 410.075968495792 & 0.0640315042078328 \tabularnewline
45 & 410.54 & 410.519007801095 & 0.0209921989048212 \tabularnewline
46 & 410.69 & 411.209449846819 & -0.519449846819327 \tabularnewline
47 & 410.79 & 411.665084765736 & -0.875084765735721 \tabularnewline
48 & 410.97 & 411.004690394465 & -0.0346903944652013 \tabularnewline
49 & 410.97 & 411.147090180292 & -0.177090180292168 \tabularnewline
50 & 413.8 & 415.298963934094 & -1.49896393409404 \tabularnewline
51 & 423.31 & 419.015741563286 & 4.29425843671379 \tabularnewline
52 & 423.85 & 422.810025046194 & 1.03997495380594 \tabularnewline
53 & 426.6 & 425.351851049653 & 1.24814895034723 \tabularnewline
54 & 426.26 & 426.847966933483 & -0.587966933482846 \tabularnewline
55 & 426.26 & 425.182705894803 & 1.0772941051967 \tabularnewline
56 & 426.32 & 426.416228785736 & -0.0962287857359456 \tabularnewline
57 & 427.14 & 426.724051367271 & 0.415948632728771 \tabularnewline
58 & 427.55 & 427.722110227674 & -0.172110227674239 \tabularnewline
59 & 428.29 & 428.453016613739 & -0.163016613739103 \tabularnewline
60 & 428.8 & 428.419142481444 & 0.380857518556013 \tabularnewline
61 & 428.8 & 428.902087609303 & -0.102087609303339 \tabularnewline
62 & 434.87 & 433.064060758896 & 1.80593924110389 \tabularnewline
63 & 435.66 & 439.763696831667 & -4.10369683166692 \tabularnewline
64 & 440.75 & 436.432770425453 & 4.31722957454696 \tabularnewline
65 & 440.99 & 441.713091684393 & -0.723091684392557 \tabularnewline
66 & 441.04 & 441.494224914201 & -0.454224914200722 \tabularnewline
67 & 441.04 & 440.00637542034 & 1.03362457966023 \tabularnewline
68 & 441.88 & 441.157012246543 & 0.72298775345655 \tabularnewline
69 & 441.92 & 442.167612349219 & -0.247612349219082 \tabularnewline
70 & 442.48 & 442.589561557384 & -0.109561557383586 \tabularnewline
71 & 442.81 & 443.372936937466 & -0.562936937465508 \tabularnewline
72 & 442.81 & 443.027446637161 & -0.217446637160947 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203437&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]377.26[/C][C]370.930868055555[/C][C]6.32913194444461[/C][/ROW]
[ROW][C]14[/C][C]381.87[/C][C]380.732141409037[/C][C]1.13785859096265[/C][/ROW]
[ROW][C]15[/C][C]387.09[/C][C]386.816537484915[/C][C]0.273462515084645[/C][/ROW]
[ROW][C]16[/C][C]387.14[/C][C]387.065814495612[/C][C]0.0741855043877422[/C][/ROW]
[ROW][C]17[/C][C]388.78[/C][C]388.826992640676[/C][C]-0.0469926406756258[/C][/ROW]
[ROW][C]18[/C][C]389.16[/C][C]389.263885244294[/C][C]-0.103885244293508[/C][/ROW]
[ROW][C]19[/C][C]389.16[/C][C]387.83879789898[/C][C]1.32120210102028[/C][/ROW]
[ROW][C]20[/C][C]389.42[/C][C]389.42426881264[/C][C]-0.00426881264036183[/C][/ROW]
[ROW][C]21[/C][C]389.49[/C][C]389.813004177452[/C][C]-0.323004177452162[/C][/ROW]
[ROW][C]22[/C][C]388.97[/C][C]390.266204541176[/C][C]-1.29620454117639[/C][/ROW]
[ROW][C]23[/C][C]388.97[/C][C]390.099058825511[/C][C]-1.12905882551115[/C][/ROW]
[ROW][C]24[/C][C]389.09[/C][C]389.159493739497[/C][C]-0.0694937394972044[/C][/ROW]
[ROW][C]25[/C][C]389.09[/C][C]389.278457628531[/C][C]-0.188457628531012[/C][/ROW]
[ROW][C]26[/C][C]391.76[/C][C]393.444272680278[/C][C]-1.6842726802779[/C][/ROW]
[ROW][C]27[/C][C]390.96[/C][C]397.143326486564[/C][C]-6.18332648656389[/C][/ROW]
[ROW][C]28[/C][C]391.76[/C][C]392.005624956242[/C][C]-0.245624956242409[/C][/ROW]
[ROW][C]29[/C][C]392.8[/C][C]393.495570289586[/C][C]-0.695570289585532[/C][/ROW]
[ROW][C]30[/C][C]393.06[/C][C]393.389885243299[/C][C]-0.329885243299202[/C][/ROW]
[ROW][C]31[/C][C]393.06[/C][C]391.832994414369[/C][C]1.22700558563088[/C][/ROW]
[ROW][C]32[/C][C]393.26[/C][C]393.287464234881[/C][C]-0.027464234881279[/C][/ROW]
[ROW][C]33[/C][C]393.87[/C][C]393.644244602589[/C][C]0.225755397411319[/C][/ROW]
[ROW][C]34[/C][C]394.47[/C][C]394.51604377418[/C][C]-0.0460437741801911[/C][/ROW]
[ROW][C]35[/C][C]394.57[/C][C]395.397017340313[/C][C]-0.827017340312921[/C][/ROW]
[ROW][C]36[/C][C]394.57[/C][C]394.751069191579[/C][C]-0.181069191578899[/C][/ROW]
[ROW][C]37[/C][C]394.57[/C][C]394.772366361357[/C][C]-0.20236636135661[/C][/ROW]
[ROW][C]38[/C][C]399.57[/C][C]398.867316651838[/C][C]0.702683348161941[/C][/ROW]
[ROW][C]39[/C][C]406.13[/C][C]404.376625153272[/C][C]1.75337484672815[/C][/ROW]
[ROW][C]40[/C][C]407.03[/C][C]406.086208802621[/C][C]0.94379119737863[/C][/ROW]
[ROW][C]41[/C][C]409.46[/C][C]408.549213078092[/C][C]0.910786921908311[/C][/ROW]
[ROW][C]42[/C][C]409.9[/C][C]409.796258637556[/C][C]0.103741362443884[/C][/ROW]
[ROW][C]43[/C][C]409.9[/C][C]408.662315378881[/C][C]1.23768462111929[/C][/ROW]
[ROW][C]44[/C][C]410.14[/C][C]410.075968495792[/C][C]0.0640315042078328[/C][/ROW]
[ROW][C]45[/C][C]410.54[/C][C]410.519007801095[/C][C]0.0209921989048212[/C][/ROW]
[ROW][C]46[/C][C]410.69[/C][C]411.209449846819[/C][C]-0.519449846819327[/C][/ROW]
[ROW][C]47[/C][C]410.79[/C][C]411.665084765736[/C][C]-0.875084765735721[/C][/ROW]
[ROW][C]48[/C][C]410.97[/C][C]411.004690394465[/C][C]-0.0346903944652013[/C][/ROW]
[ROW][C]49[/C][C]410.97[/C][C]411.147090180292[/C][C]-0.177090180292168[/C][/ROW]
[ROW][C]50[/C][C]413.8[/C][C]415.298963934094[/C][C]-1.49896393409404[/C][/ROW]
[ROW][C]51[/C][C]423.31[/C][C]419.015741563286[/C][C]4.29425843671379[/C][/ROW]
[ROW][C]52[/C][C]423.85[/C][C]422.810025046194[/C][C]1.03997495380594[/C][/ROW]
[ROW][C]53[/C][C]426.6[/C][C]425.351851049653[/C][C]1.24814895034723[/C][/ROW]
[ROW][C]54[/C][C]426.26[/C][C]426.847966933483[/C][C]-0.587966933482846[/C][/ROW]
[ROW][C]55[/C][C]426.26[/C][C]425.182705894803[/C][C]1.0772941051967[/C][/ROW]
[ROW][C]56[/C][C]426.32[/C][C]426.416228785736[/C][C]-0.0962287857359456[/C][/ROW]
[ROW][C]57[/C][C]427.14[/C][C]426.724051367271[/C][C]0.415948632728771[/C][/ROW]
[ROW][C]58[/C][C]427.55[/C][C]427.722110227674[/C][C]-0.172110227674239[/C][/ROW]
[ROW][C]59[/C][C]428.29[/C][C]428.453016613739[/C][C]-0.163016613739103[/C][/ROW]
[ROW][C]60[/C][C]428.8[/C][C]428.419142481444[/C][C]0.380857518556013[/C][/ROW]
[ROW][C]61[/C][C]428.8[/C][C]428.902087609303[/C][C]-0.102087609303339[/C][/ROW]
[ROW][C]62[/C][C]434.87[/C][C]433.064060758896[/C][C]1.80593924110389[/C][/ROW]
[ROW][C]63[/C][C]435.66[/C][C]439.763696831667[/C][C]-4.10369683166692[/C][/ROW]
[ROW][C]64[/C][C]440.75[/C][C]436.432770425453[/C][C]4.31722957454696[/C][/ROW]
[ROW][C]65[/C][C]440.99[/C][C]441.713091684393[/C][C]-0.723091684392557[/C][/ROW]
[ROW][C]66[/C][C]441.04[/C][C]441.494224914201[/C][C]-0.454224914200722[/C][/ROW]
[ROW][C]67[/C][C]441.04[/C][C]440.00637542034[/C][C]1.03362457966023[/C][/ROW]
[ROW][C]68[/C][C]441.88[/C][C]441.157012246543[/C][C]0.72298775345655[/C][/ROW]
[ROW][C]69[/C][C]441.92[/C][C]442.167612349219[/C][C]-0.247612349219082[/C][/ROW]
[ROW][C]70[/C][C]442.48[/C][C]442.589561557384[/C][C]-0.109561557383586[/C][/ROW]
[ROW][C]71[/C][C]442.81[/C][C]443.372936937466[/C][C]-0.562936937465508[/C][/ROW]
[ROW][C]72[/C][C]442.81[/C][C]443.027446637161[/C][C]-0.217446637160947[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203437&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203437&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
13377.26370.9308680555556.32913194444461
14381.87380.7321414090371.13785859096265
15387.09386.8165374849150.273462515084645
16387.14387.0658144956120.0741855043877422
17388.78388.826992640676-0.0469926406756258
18389.16389.263885244294-0.103885244293508
19389.16387.838797898981.32120210102028
20389.42389.42426881264-0.00426881264036183
21389.49389.813004177452-0.323004177452162
22388.97390.266204541176-1.29620454117639
23388.97390.099058825511-1.12905882551115
24389.09389.159493739497-0.0694937394972044
25389.09389.278457628531-0.188457628531012
26391.76393.444272680278-1.6842726802779
27390.96397.143326486564-6.18332648656389
28391.76392.005624956242-0.245624956242409
29392.8393.495570289586-0.695570289585532
30393.06393.389885243299-0.329885243299202
31393.06391.8329944143691.22700558563088
32393.26393.287464234881-0.027464234881279
33393.87393.6442446025890.225755397411319
34394.47394.51604377418-0.0460437741801911
35394.57395.397017340313-0.827017340312921
36394.57394.751069191579-0.181069191578899
37394.57394.772366361357-0.20236636135661
38399.57398.8673166518380.702683348161941
39406.13404.3766251532721.75337484672815
40407.03406.0862088026210.94379119737863
41409.46408.5492130780920.910786921908311
42409.9409.7962586375560.103741362443884
43409.9408.6623153788811.23768462111929
44410.14410.0759684957920.0640315042078328
45410.54410.5190078010950.0209921989048212
46410.69411.209449846819-0.519449846819327
47410.79411.665084765736-0.875084765735721
48410.97411.004690394465-0.0346903944652013
49410.97411.147090180292-0.177090180292168
50413.8415.298963934094-1.49896393409404
51423.31419.0157415632864.29425843671379
52423.85422.8100250461941.03997495380594
53426.6425.3518510496531.24814895034723
54426.26426.847966933483-0.587966933482846
55426.26425.1827058948031.0772941051967
56426.32426.416228785736-0.0962287857359456
57427.14426.7240513672710.415948632728771
58427.55427.722110227674-0.172110227674239
59428.29428.453016613739-0.163016613739103
60428.8428.4191424814440.380857518556013
61428.8428.902087609303-0.102087609303339
62434.87433.0640607588961.80593924110389
63435.66439.763696831667-4.10369683166692
64440.75436.4327704254534.31722957454696
65440.99441.713091684393-0.723091684392557
66441.04441.494224914201-0.454224914200722
67441.04440.006375420341.03362457966023
68441.88441.1570122465430.72298775345655
69441.92442.167612349219-0.247612349219082
70442.48442.589561557384-0.109561557383586
71442.81443.372936937466-0.562936937465508
72442.81443.027446637161-0.217446637160947







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73442.992812416641439.727339426115446.258285407168
74447.315446711536443.06526372951451.565629693562
75452.276381707054447.230116067044457.322647347064
76452.697913231964446.96506590813458.430760555798
77454.181854485497447.836282803825460.527426167168
78454.576042514791447.671911758781461.480173270801
79453.525564786174446.10479912319460.946330449158
80453.802789898372445.899087945883461.70649185086
81454.172612846209445.81383027441462.531395418008
82454.806316041613446.015981144042463.596650939184
83455.662999195771446.461329285352464.864669106189
84455.80017700772446.204789018215465.395564997225

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 442.992812416641 & 439.727339426115 & 446.258285407168 \tabularnewline
74 & 447.315446711536 & 443.06526372951 & 451.565629693562 \tabularnewline
75 & 452.276381707054 & 447.230116067044 & 457.322647347064 \tabularnewline
76 & 452.697913231964 & 446.96506590813 & 458.430760555798 \tabularnewline
77 & 454.181854485497 & 447.836282803825 & 460.527426167168 \tabularnewline
78 & 454.576042514791 & 447.671911758781 & 461.480173270801 \tabularnewline
79 & 453.525564786174 & 446.10479912319 & 460.946330449158 \tabularnewline
80 & 453.802789898372 & 445.899087945883 & 461.70649185086 \tabularnewline
81 & 454.172612846209 & 445.81383027441 & 462.531395418008 \tabularnewline
82 & 454.806316041613 & 446.015981144042 & 463.596650939184 \tabularnewline
83 & 455.662999195771 & 446.461329285352 & 464.864669106189 \tabularnewline
84 & 455.80017700772 & 446.204789018215 & 465.395564997225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203437&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]73[/C][C]442.992812416641[/C][C]439.727339426115[/C][C]446.258285407168[/C][/ROW]
[ROW][C]74[/C][C]447.315446711536[/C][C]443.06526372951[/C][C]451.565629693562[/C][/ROW]
[ROW][C]75[/C][C]452.276381707054[/C][C]447.230116067044[/C][C]457.322647347064[/C][/ROW]
[ROW][C]76[/C][C]452.697913231964[/C][C]446.96506590813[/C][C]458.430760555798[/C][/ROW]
[ROW][C]77[/C][C]454.181854485497[/C][C]447.836282803825[/C][C]460.527426167168[/C][/ROW]
[ROW][C]78[/C][C]454.576042514791[/C][C]447.671911758781[/C][C]461.480173270801[/C][/ROW]
[ROW][C]79[/C][C]453.525564786174[/C][C]446.10479912319[/C][C]460.946330449158[/C][/ROW]
[ROW][C]80[/C][C]453.802789898372[/C][C]445.899087945883[/C][C]461.70649185086[/C][/ROW]
[ROW][C]81[/C][C]454.172612846209[/C][C]445.81383027441[/C][C]462.531395418008[/C][/ROW]
[ROW][C]82[/C][C]454.806316041613[/C][C]446.015981144042[/C][C]463.596650939184[/C][/ROW]
[ROW][C]83[/C][C]455.662999195771[/C][C]446.461329285352[/C][C]464.864669106189[/C][/ROW]
[ROW][C]84[/C][C]455.80017700772[/C][C]446.204789018215[/C][C]465.395564997225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203437&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203437&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
73442.992812416641439.727339426115446.258285407168
74447.315446711536443.06526372951451.565629693562
75452.276381707054447.230116067044457.322647347064
76452.697913231964446.96506590813458.430760555798
77454.181854485497447.836282803825460.527426167168
78454.576042514791447.671911758781461.480173270801
79453.525564786174446.10479912319460.946330449158
80453.802789898372445.899087945883461.70649185086
81454.172612846209445.81383027441462.531395418008
82454.806316041613446.015981144042463.596650939184
83455.662999195771446.461329285352464.864669106189
84455.80017700772446.204789018215465.395564997225



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')