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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 07 Jun 2009 12:28:21 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/07/t12443993569d804ty2o7q3244.htm/, Retrieved Sun, 12 May 2024 17:12:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42226, Retrieved Sun, 12 May 2024 17:12:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2009-06-07 18:28:21] [1f24ecf252e89ff3a946a11432983a6a] [Current]
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Dataseries X:
260288
261544
259886
257006
259670
258873
264416
263596
262586
260237
261690
259295
264170
264451
265538
261723
266189
265073
267007
266376
267406
262742
260300
263074
265940
264771
268403
264264
264118
266817
269296
269001
266707
267507
267510
267420
270845
270671
273653
271567
268372
268160
267879
271142
271323
269478
271008
269145
271684
273582
279475
276188
278422
281084
278618
280738
288897
282129
286406
284288
286139
288275
287670
286864
288798
288316
286915
288006
293338
303730
306248
305700
314849




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42226&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42226&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.75041612949919
beta0.0902646656756738
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.75041612949919 \tabularnewline
beta & 0.0902646656756738 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42226&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]0.75041612949919[/C][/ROW]
[ROW][C]beta[/C][C]0.0902646656756738[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42226&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
alpha0.75041612949919
beta0.0902646656756738
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3259886262800-2914
4257006261671.904516749-4665.90451674876
5259670258913.101633601756.898366398615
6258873260274.926815015-1401.92681501515
7264416259921.7737592024494.2262407981
8263596264297.610241472-701.610241472023
9262586264726.882907059-2140.88290705887
10260237263931.087174355-3694.08717435523
11261690261719.518992711-29.5189927108877
12259295262255.902381930-2960.90238192963
13264170260391.9685296363778.03147036358
14264451263840.948306046610.051693954272
15265538264953.947459094584.052540906356
16261723266086.997846907-4363.99784690654
17266189263211.3513895632977.64861043659
18265073266046.689038944-973.68903894379
19267007265850.9253229491156.07467705081
20266376267331.678596359-955.678596358513
21267406267163.004248135242.995751865325
22262742267910.294039917-5168.29403991741
23260300264246.784809956-3946.78480995598
24263074261232.5761516641841.4238483363
25265940262686.6634296653253.33657033514
26264771265420.640992233-649.640992233355
27268403265181.7571168693221.24288313149
28264264268065.841241574-3801.84124157444
29264118265422.168009842-1304.16800984152
30266817264564.4498534892252.55014651071
31269296266528.3292439822767.67075601837
32269001269066.234563773-65.2345637732651
33266707269473.863305855-2766.86330585508
34267507267666.729842166-159.729842166358
35267510267805.211911047-295.211911046703
36267420267822.029558153-402.02955815295
37270845267731.4576212623113.54237873817
38270671270489.926666867181.073333133303
39273653271060.0888357402592.91116426029
40271567273615.766603738-2048.76660373819
41268372272549.479126951-4177.47912695119
42268160269602.805456513-1442.80545651302
43267879268610.545058807-731.5450588073
44271142268102.4739550523039.52604494797
45271323270630.160954777692.83904522279
46269478271443.786366885-1965.78636688541
47271008270129.181762099878.818237901316
48269145271008.742020603-1863.74202060321
49271684269703.9982817191980.00171828072
50273582271417.7793594182164.22064058227
51279475273416.3970692006058.60293080035
52276188278747.807961977-2559.80796197668
53278422277438.433001782983.56699821842
54281084278854.6867188152229.31328118459
55278618281356.773440358-2738.77344035765
56280738279945.214028354792.785971645731
57288897281237.4939603757659.50603962463
58282129288201.496156853-6072.49615685252
59286406284449.4554443871956.54455561255
60284288286855.065008422-2567.06500842172
61286139285692.202119926446.797880073835
62288275286821.2548835371453.74511646305
63287670288804.408062844-1134.40806284419
64286864288768.529016988-1904.52901698783
65288798288025.733491716772.266508283501
66288316289343.958795330-1027.95879532956
67286915289241.636114665-2326.63611466473
68288006288007.167860659-1.16786065918859
69293338288517.6893868174820.31061318319
70303730292972.83498173810757.1650182616
71306248302611.7398670873636.26013291255
72305700307153.308808186-1453.30880818627
73314849307777.1417095357071.85829046485

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 259886 & 262800 & -2914 \tabularnewline
4 & 257006 & 261671.904516749 & -4665.90451674876 \tabularnewline
5 & 259670 & 258913.101633601 & 756.898366398615 \tabularnewline
6 & 258873 & 260274.926815015 & -1401.92681501515 \tabularnewline
7 & 264416 & 259921.773759202 & 4494.2262407981 \tabularnewline
8 & 263596 & 264297.610241472 & -701.610241472023 \tabularnewline
9 & 262586 & 264726.882907059 & -2140.88290705887 \tabularnewline
10 & 260237 & 263931.087174355 & -3694.08717435523 \tabularnewline
11 & 261690 & 261719.518992711 & -29.5189927108877 \tabularnewline
12 & 259295 & 262255.902381930 & -2960.90238192963 \tabularnewline
13 & 264170 & 260391.968529636 & 3778.03147036358 \tabularnewline
14 & 264451 & 263840.948306046 & 610.051693954272 \tabularnewline
15 & 265538 & 264953.947459094 & 584.052540906356 \tabularnewline
16 & 261723 & 266086.997846907 & -4363.99784690654 \tabularnewline
17 & 266189 & 263211.351389563 & 2977.64861043659 \tabularnewline
18 & 265073 & 266046.689038944 & -973.68903894379 \tabularnewline
19 & 267007 & 265850.925322949 & 1156.07467705081 \tabularnewline
20 & 266376 & 267331.678596359 & -955.678596358513 \tabularnewline
21 & 267406 & 267163.004248135 & 242.995751865325 \tabularnewline
22 & 262742 & 267910.294039917 & -5168.29403991741 \tabularnewline
23 & 260300 & 264246.784809956 & -3946.78480995598 \tabularnewline
24 & 263074 & 261232.576151664 & 1841.4238483363 \tabularnewline
25 & 265940 & 262686.663429665 & 3253.33657033514 \tabularnewline
26 & 264771 & 265420.640992233 & -649.640992233355 \tabularnewline
27 & 268403 & 265181.757116869 & 3221.24288313149 \tabularnewline
28 & 264264 & 268065.841241574 & -3801.84124157444 \tabularnewline
29 & 264118 & 265422.168009842 & -1304.16800984152 \tabularnewline
30 & 266817 & 264564.449853489 & 2252.55014651071 \tabularnewline
31 & 269296 & 266528.329243982 & 2767.67075601837 \tabularnewline
32 & 269001 & 269066.234563773 & -65.2345637732651 \tabularnewline
33 & 266707 & 269473.863305855 & -2766.86330585508 \tabularnewline
34 & 267507 & 267666.729842166 & -159.729842166358 \tabularnewline
35 & 267510 & 267805.211911047 & -295.211911046703 \tabularnewline
36 & 267420 & 267822.029558153 & -402.02955815295 \tabularnewline
37 & 270845 & 267731.457621262 & 3113.54237873817 \tabularnewline
38 & 270671 & 270489.926666867 & 181.073333133303 \tabularnewline
39 & 273653 & 271060.088835740 & 2592.91116426029 \tabularnewline
40 & 271567 & 273615.766603738 & -2048.76660373819 \tabularnewline
41 & 268372 & 272549.479126951 & -4177.47912695119 \tabularnewline
42 & 268160 & 269602.805456513 & -1442.80545651302 \tabularnewline
43 & 267879 & 268610.545058807 & -731.5450588073 \tabularnewline
44 & 271142 & 268102.473955052 & 3039.52604494797 \tabularnewline
45 & 271323 & 270630.160954777 & 692.83904522279 \tabularnewline
46 & 269478 & 271443.786366885 & -1965.78636688541 \tabularnewline
47 & 271008 & 270129.181762099 & 878.818237901316 \tabularnewline
48 & 269145 & 271008.742020603 & -1863.74202060321 \tabularnewline
49 & 271684 & 269703.998281719 & 1980.00171828072 \tabularnewline
50 & 273582 & 271417.779359418 & 2164.22064058227 \tabularnewline
51 & 279475 & 273416.397069200 & 6058.60293080035 \tabularnewline
52 & 276188 & 278747.807961977 & -2559.80796197668 \tabularnewline
53 & 278422 & 277438.433001782 & 983.56699821842 \tabularnewline
54 & 281084 & 278854.686718815 & 2229.31328118459 \tabularnewline
55 & 278618 & 281356.773440358 & -2738.77344035765 \tabularnewline
56 & 280738 & 279945.214028354 & 792.785971645731 \tabularnewline
57 & 288897 & 281237.493960375 & 7659.50603962463 \tabularnewline
58 & 282129 & 288201.496156853 & -6072.49615685252 \tabularnewline
59 & 286406 & 284449.455444387 & 1956.54455561255 \tabularnewline
60 & 284288 & 286855.065008422 & -2567.06500842172 \tabularnewline
61 & 286139 & 285692.202119926 & 446.797880073835 \tabularnewline
62 & 288275 & 286821.254883537 & 1453.74511646305 \tabularnewline
63 & 287670 & 288804.408062844 & -1134.40806284419 \tabularnewline
64 & 286864 & 288768.529016988 & -1904.52901698783 \tabularnewline
65 & 288798 & 288025.733491716 & 772.266508283501 \tabularnewline
66 & 288316 & 289343.958795330 & -1027.95879532956 \tabularnewline
67 & 286915 & 289241.636114665 & -2326.63611466473 \tabularnewline
68 & 288006 & 288007.167860659 & -1.16786065918859 \tabularnewline
69 & 293338 & 288517.689386817 & 4820.31061318319 \tabularnewline
70 & 303730 & 292972.834981738 & 10757.1650182616 \tabularnewline
71 & 306248 & 302611.739867087 & 3636.26013291255 \tabularnewline
72 & 305700 & 307153.308808186 & -1453.30880818627 \tabularnewline
73 & 314849 & 307777.141709535 & 7071.85829046485 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42226&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]259886[/C][C]262800[/C][C]-2914[/C][/ROW]
[ROW][C]4[/C][C]257006[/C][C]261671.904516749[/C][C]-4665.90451674876[/C][/ROW]
[ROW][C]5[/C][C]259670[/C][C]258913.101633601[/C][C]756.898366398615[/C][/ROW]
[ROW][C]6[/C][C]258873[/C][C]260274.926815015[/C][C]-1401.92681501515[/C][/ROW]
[ROW][C]7[/C][C]264416[/C][C]259921.773759202[/C][C]4494.2262407981[/C][/ROW]
[ROW][C]8[/C][C]263596[/C][C]264297.610241472[/C][C]-701.610241472023[/C][/ROW]
[ROW][C]9[/C][C]262586[/C][C]264726.882907059[/C][C]-2140.88290705887[/C][/ROW]
[ROW][C]10[/C][C]260237[/C][C]263931.087174355[/C][C]-3694.08717435523[/C][/ROW]
[ROW][C]11[/C][C]261690[/C][C]261719.518992711[/C][C]-29.5189927108877[/C][/ROW]
[ROW][C]12[/C][C]259295[/C][C]262255.902381930[/C][C]-2960.90238192963[/C][/ROW]
[ROW][C]13[/C][C]264170[/C][C]260391.968529636[/C][C]3778.03147036358[/C][/ROW]
[ROW][C]14[/C][C]264451[/C][C]263840.948306046[/C][C]610.051693954272[/C][/ROW]
[ROW][C]15[/C][C]265538[/C][C]264953.947459094[/C][C]584.052540906356[/C][/ROW]
[ROW][C]16[/C][C]261723[/C][C]266086.997846907[/C][C]-4363.99784690654[/C][/ROW]
[ROW][C]17[/C][C]266189[/C][C]263211.351389563[/C][C]2977.64861043659[/C][/ROW]
[ROW][C]18[/C][C]265073[/C][C]266046.689038944[/C][C]-973.68903894379[/C][/ROW]
[ROW][C]19[/C][C]267007[/C][C]265850.925322949[/C][C]1156.07467705081[/C][/ROW]
[ROW][C]20[/C][C]266376[/C][C]267331.678596359[/C][C]-955.678596358513[/C][/ROW]
[ROW][C]21[/C][C]267406[/C][C]267163.004248135[/C][C]242.995751865325[/C][/ROW]
[ROW][C]22[/C][C]262742[/C][C]267910.294039917[/C][C]-5168.29403991741[/C][/ROW]
[ROW][C]23[/C][C]260300[/C][C]264246.784809956[/C][C]-3946.78480995598[/C][/ROW]
[ROW][C]24[/C][C]263074[/C][C]261232.576151664[/C][C]1841.4238483363[/C][/ROW]
[ROW][C]25[/C][C]265940[/C][C]262686.663429665[/C][C]3253.33657033514[/C][/ROW]
[ROW][C]26[/C][C]264771[/C][C]265420.640992233[/C][C]-649.640992233355[/C][/ROW]
[ROW][C]27[/C][C]268403[/C][C]265181.757116869[/C][C]3221.24288313149[/C][/ROW]
[ROW][C]28[/C][C]264264[/C][C]268065.841241574[/C][C]-3801.84124157444[/C][/ROW]
[ROW][C]29[/C][C]264118[/C][C]265422.168009842[/C][C]-1304.16800984152[/C][/ROW]
[ROW][C]30[/C][C]266817[/C][C]264564.449853489[/C][C]2252.55014651071[/C][/ROW]
[ROW][C]31[/C][C]269296[/C][C]266528.329243982[/C][C]2767.67075601837[/C][/ROW]
[ROW][C]32[/C][C]269001[/C][C]269066.234563773[/C][C]-65.2345637732651[/C][/ROW]
[ROW][C]33[/C][C]266707[/C][C]269473.863305855[/C][C]-2766.86330585508[/C][/ROW]
[ROW][C]34[/C][C]267507[/C][C]267666.729842166[/C][C]-159.729842166358[/C][/ROW]
[ROW][C]35[/C][C]267510[/C][C]267805.211911047[/C][C]-295.211911046703[/C][/ROW]
[ROW][C]36[/C][C]267420[/C][C]267822.029558153[/C][C]-402.02955815295[/C][/ROW]
[ROW][C]37[/C][C]270845[/C][C]267731.457621262[/C][C]3113.54237873817[/C][/ROW]
[ROW][C]38[/C][C]270671[/C][C]270489.926666867[/C][C]181.073333133303[/C][/ROW]
[ROW][C]39[/C][C]273653[/C][C]271060.088835740[/C][C]2592.91116426029[/C][/ROW]
[ROW][C]40[/C][C]271567[/C][C]273615.766603738[/C][C]-2048.76660373819[/C][/ROW]
[ROW][C]41[/C][C]268372[/C][C]272549.479126951[/C][C]-4177.47912695119[/C][/ROW]
[ROW][C]42[/C][C]268160[/C][C]269602.805456513[/C][C]-1442.80545651302[/C][/ROW]
[ROW][C]43[/C][C]267879[/C][C]268610.545058807[/C][C]-731.5450588073[/C][/ROW]
[ROW][C]44[/C][C]271142[/C][C]268102.473955052[/C][C]3039.52604494797[/C][/ROW]
[ROW][C]45[/C][C]271323[/C][C]270630.160954777[/C][C]692.83904522279[/C][/ROW]
[ROW][C]46[/C][C]269478[/C][C]271443.786366885[/C][C]-1965.78636688541[/C][/ROW]
[ROW][C]47[/C][C]271008[/C][C]270129.181762099[/C][C]878.818237901316[/C][/ROW]
[ROW][C]48[/C][C]269145[/C][C]271008.742020603[/C][C]-1863.74202060321[/C][/ROW]
[ROW][C]49[/C][C]271684[/C][C]269703.998281719[/C][C]1980.00171828072[/C][/ROW]
[ROW][C]50[/C][C]273582[/C][C]271417.779359418[/C][C]2164.22064058227[/C][/ROW]
[ROW][C]51[/C][C]279475[/C][C]273416.397069200[/C][C]6058.60293080035[/C][/ROW]
[ROW][C]52[/C][C]276188[/C][C]278747.807961977[/C][C]-2559.80796197668[/C][/ROW]
[ROW][C]53[/C][C]278422[/C][C]277438.433001782[/C][C]983.56699821842[/C][/ROW]
[ROW][C]54[/C][C]281084[/C][C]278854.686718815[/C][C]2229.31328118459[/C][/ROW]
[ROW][C]55[/C][C]278618[/C][C]281356.773440358[/C][C]-2738.77344035765[/C][/ROW]
[ROW][C]56[/C][C]280738[/C][C]279945.214028354[/C][C]792.785971645731[/C][/ROW]
[ROW][C]57[/C][C]288897[/C][C]281237.493960375[/C][C]7659.50603962463[/C][/ROW]
[ROW][C]58[/C][C]282129[/C][C]288201.496156853[/C][C]-6072.49615685252[/C][/ROW]
[ROW][C]59[/C][C]286406[/C][C]284449.455444387[/C][C]1956.54455561255[/C][/ROW]
[ROW][C]60[/C][C]284288[/C][C]286855.065008422[/C][C]-2567.06500842172[/C][/ROW]
[ROW][C]61[/C][C]286139[/C][C]285692.202119926[/C][C]446.797880073835[/C][/ROW]
[ROW][C]62[/C][C]288275[/C][C]286821.254883537[/C][C]1453.74511646305[/C][/ROW]
[ROW][C]63[/C][C]287670[/C][C]288804.408062844[/C][C]-1134.40806284419[/C][/ROW]
[ROW][C]64[/C][C]286864[/C][C]288768.529016988[/C][C]-1904.52901698783[/C][/ROW]
[ROW][C]65[/C][C]288798[/C][C]288025.733491716[/C][C]772.266508283501[/C][/ROW]
[ROW][C]66[/C][C]288316[/C][C]289343.958795330[/C][C]-1027.95879532956[/C][/ROW]
[ROW][C]67[/C][C]286915[/C][C]289241.636114665[/C][C]-2326.63611466473[/C][/ROW]
[ROW][C]68[/C][C]288006[/C][C]288007.167860659[/C][C]-1.16786065918859[/C][/ROW]
[ROW][C]69[/C][C]293338[/C][C]288517.689386817[/C][C]4820.31061318319[/C][/ROW]
[ROW][C]70[/C][C]303730[/C][C]292972.834981738[/C][C]10757.1650182616[/C][/ROW]
[ROW][C]71[/C][C]306248[/C][C]302611.739867087[/C][C]3636.26013291255[/C][/ROW]
[ROW][C]72[/C][C]305700[/C][C]307153.308808186[/C][C]-1453.30880818627[/C][/ROW]
[ROW][C]73[/C][C]314849[/C][C]307777.141709535[/C][C]7071.85829046485[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42226&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42226&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
3259886262800-2914
4257006261671.904516749-4665.90451674876
5259670258913.101633601756.898366398615
6258873260274.926815015-1401.92681501515
7264416259921.7737592024494.2262407981
8263596264297.610241472-701.610241472023
9262586264726.882907059-2140.88290705887
10260237263931.087174355-3694.08717435523
11261690261719.518992711-29.5189927108877
12259295262255.902381930-2960.90238192963
13264170260391.9685296363778.03147036358
14264451263840.948306046610.051693954272
15265538264953.947459094584.052540906356
16261723266086.997846907-4363.99784690654
17266189263211.3513895632977.64861043659
18265073266046.689038944-973.68903894379
19267007265850.9253229491156.07467705081
20266376267331.678596359-955.678596358513
21267406267163.004248135242.995751865325
22262742267910.294039917-5168.29403991741
23260300264246.784809956-3946.78480995598
24263074261232.5761516641841.4238483363
25265940262686.6634296653253.33657033514
26264771265420.640992233-649.640992233355
27268403265181.7571168693221.24288313149
28264264268065.841241574-3801.84124157444
29264118265422.168009842-1304.16800984152
30266817264564.4498534892252.55014651071
31269296266528.3292439822767.67075601837
32269001269066.234563773-65.2345637732651
33266707269473.863305855-2766.86330585508
34267507267666.729842166-159.729842166358
35267510267805.211911047-295.211911046703
36267420267822.029558153-402.02955815295
37270845267731.4576212623113.54237873817
38270671270489.926666867181.073333133303
39273653271060.0888357402592.91116426029
40271567273615.766603738-2048.76660373819
41268372272549.479126951-4177.47912695119
42268160269602.805456513-1442.80545651302
43267879268610.545058807-731.5450588073
44271142268102.4739550523039.52604494797
45271323270630.160954777692.83904522279
46269478271443.786366885-1965.78636688541
47271008270129.181762099878.818237901316
48269145271008.742020603-1863.74202060321
49271684269703.9982817191980.00171828072
50273582271417.7793594182164.22064058227
51279475273416.3970692006058.60293080035
52276188278747.807961977-2559.80796197668
53278422277438.433001782983.56699821842
54281084278854.6867188152229.31328118459
55278618281356.773440358-2738.77344035765
56280738279945.214028354792.785971645731
57288897281237.4939603757659.50603962463
58282129288201.496156853-6072.49615685252
59286406284449.4554443871956.54455561255
60284288286855.065008422-2567.06500842172
61286139285692.202119926446.797880073835
62288275286821.2548835371453.74511646305
63287670288804.408062844-1134.40806284419
64286864288768.529016988-1904.52901698783
65288798288025.733491716772.266508283501
66288316289343.958795330-1027.95879532956
67286915289241.636114665-2326.63611466473
68288006288007.167860659-1.16786065918859
69293338288517.6893868174820.31061318319
70303730292972.83498173810757.1650182616
71306248302611.7398670873636.26013291255
72305700307153.308808186-1453.30880818627
73314849307777.1417095357071.85829046485







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74315277.417333265309182.784873738321372.049792793
75317470.856430298309596.334192698325345.378667898
76319664.295527331310116.569895423329212.021159239
77321857.734624364310680.154881908333035.314366821
78324051.173721397311257.166366084336845.18107671
79326244.61281843311831.253670205340657.971966655
80328438.051915463312392.677711358344483.426119568
81330631.491012496312935.31035912348327.671665872
82332824.930109529313455.157206776352194.703012282
83335018.369206562313949.559027087356087.179386036
84337211.808303594314416.728983543360006.887623646
85339405.247400627314855.469600057363955.025201198

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 315277.417333265 & 309182.784873738 & 321372.049792793 \tabularnewline
75 & 317470.856430298 & 309596.334192698 & 325345.378667898 \tabularnewline
76 & 319664.295527331 & 310116.569895423 & 329212.021159239 \tabularnewline
77 & 321857.734624364 & 310680.154881908 & 333035.314366821 \tabularnewline
78 & 324051.173721397 & 311257.166366084 & 336845.18107671 \tabularnewline
79 & 326244.61281843 & 311831.253670205 & 340657.971966655 \tabularnewline
80 & 328438.051915463 & 312392.677711358 & 344483.426119568 \tabularnewline
81 & 330631.491012496 & 312935.31035912 & 348327.671665872 \tabularnewline
82 & 332824.930109529 & 313455.157206776 & 352194.703012282 \tabularnewline
83 & 335018.369206562 & 313949.559027087 & 356087.179386036 \tabularnewline
84 & 337211.808303594 & 314416.728983543 & 360006.887623646 \tabularnewline
85 & 339405.247400627 & 314855.469600057 & 363955.025201198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42226&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]74[/C][C]315277.417333265[/C][C]309182.784873738[/C][C]321372.049792793[/C][/ROW]
[ROW][C]75[/C][C]317470.856430298[/C][C]309596.334192698[/C][C]325345.378667898[/C][/ROW]
[ROW][C]76[/C][C]319664.295527331[/C][C]310116.569895423[/C][C]329212.021159239[/C][/ROW]
[ROW][C]77[/C][C]321857.734624364[/C][C]310680.154881908[/C][C]333035.314366821[/C][/ROW]
[ROW][C]78[/C][C]324051.173721397[/C][C]311257.166366084[/C][C]336845.18107671[/C][/ROW]
[ROW][C]79[/C][C]326244.61281843[/C][C]311831.253670205[/C][C]340657.971966655[/C][/ROW]
[ROW][C]80[/C][C]328438.051915463[/C][C]312392.677711358[/C][C]344483.426119568[/C][/ROW]
[ROW][C]81[/C][C]330631.491012496[/C][C]312935.31035912[/C][C]348327.671665872[/C][/ROW]
[ROW][C]82[/C][C]332824.930109529[/C][C]313455.157206776[/C][C]352194.703012282[/C][/ROW]
[ROW][C]83[/C][C]335018.369206562[/C][C]313949.559027087[/C][C]356087.179386036[/C][/ROW]
[ROW][C]84[/C][C]337211.808303594[/C][C]314416.728983543[/C][C]360006.887623646[/C][/ROW]
[ROW][C]85[/C][C]339405.247400627[/C][C]314855.469600057[/C][C]363955.025201198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42226&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42226&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
74315277.417333265309182.784873738321372.049792793
75317470.856430298309596.334192698325345.378667898
76319664.295527331310116.569895423329212.021159239
77321857.734624364310680.154881908333035.314366821
78324051.173721397311257.166366084336845.18107671
79326244.61281843311831.253670205340657.971966655
80328438.051915463312392.677711358344483.426119568
81330631.491012496312935.31035912348327.671665872
82332824.930109529313455.157206776352194.703012282
83335018.369206562313949.559027087356087.179386036
84337211.808303594314416.728983543360006.887623646
85339405.247400627314855.469600057363955.025201198



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')