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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 11 May 2014 05:56:04 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/11/t13998022342jllpyu3wzlx2og.htm/, Retrieved Tue, 14 May 2024 08:50:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234784, Retrieved Tue, 14 May 2024 08:50:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-05-11 09:56:04] [6f0aa55da9581424a24c59d08ba9c929] [Current]
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Dataseries X:
3477
2685
2438
1692
4054
3946
3623
2455
2362
2791
2369
3438
3682
2801
2563
3108
2890
3940
4036
1514
3461
2980
2728
3891
3715
2843
1416
2657
1856
2441
3172
2813
3335
2608
5784
4726
3817
2755
2541
3154
2684
3732
4286
2394
1698
3945
2549
3943
3899
2783
2660
1848
4482
4157
4404
2686
2593
3254
2664
4203
3985
2861
2758
1968
4666
4226
4748
2767
2723
3297
2758
4338




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234784&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234784&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234784&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0372822610063326
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0372822610063326 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234784&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]0.0372822610063326[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234784&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234784&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
alpha0.0372822610063326
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
226853477-792
324383447.47244928298-1009.47244928298
416923409.83703395011-1717.83703395011
540543345.79218528404708.207814715958
639463372.19577387901573.804226120993
736233393.58849280379229.411507196214
824553402.14147249293-947.141472492932
923623366.82989690553-1004.82989690553
1027913329.36756642213-538.36756642213
1123693309.29600629344-940.296006293436
1234383274.23964516359163.760354836408
1336823280.34500145509401.654998544907
1428013295.31960794534-494.319607945342
1525633276.89025530138-713.890255301376
1631083250.27481247335-142.274812473353
1728903244.97048578009-354.970485780094
1839403231.7363834797708.263616520304
1940363258.14205249209777.857947507905
2015143287.14235551693-1773.14235551693
2134613221.03559941717239.964400582831
2229803229.98201483193-249.982014831926
2327283220.66212010807-492.662120108073
2438913202.29456235827688.70543764173
2537153227.97105824091487.02894175909
2628433246.12859836521-403.12859836521
2714163231.09905274184-1815.09905274184
2826573163.42805610517-506.428056105173
2918563144.54727313653-1288.54727313653
3024413096.50731738046-655.507317380456
3131723072.0685224823299.9314775176831
3228133075.79419390988-262.79419390988
3333353065.99663218158269.003367818417
3426083076.02568595217-468.025685952171
3557843058.576630170832725.42336982917
3647263160.186575597561565.81342440244
3738173218.56364037336598.436359626645
3827553240.87470092864-485.874700928635
3925413222.76019351224-681.76019351224
4031543197.34263203399-43.342632033989
4126843195.7267207138-511.726720713797
4237323176.64839154823555.35160845177
4342863197.353155164821088.64684483518
4423943237.94037097768-843.940370977682
4516983206.47636579311-1508.47636579311
4639453150.23695620173794.763043798273
4725493179.8675194388-630.867519438802
4839433156.34735191867786.652648081333
4938993185.67554126576713.324458734242
5027833212.26988991849-429.269889918489
5126603196.26573784039-536.265737840388
5218483176.27253863347-1328.27253863347
5344823126.751535160591355.24846483941
5441573177.27826215517979.721737844833
5544043213.804503699081190.19549630092
5626863258.17768284073-572.177682840728
5725933236.84560512706-643.845605127062
5832543212.8415852289341.1584147710655
5926643214.37606399104-550.376063991036
6042033193.856799921681009.14320007832
6139853231.47994009977753.52005990023
6228613259.57287164648-398.572871646478
6327583244.71317381571-486.71317381571
6419683226.56740623429-1258.56740623429
6546663179.6451677011486.354832299
6642263235.0598365068990.940163493202
6747483272.004326323811475.99567367619
6827673327.03278227402-560.032782274022
6927233306.15349391318-583.15349391318
7032973284.4122131463512.5877868536463
7127583284.88151430132-526.881514301323
7243383265.238180165731072.76181983427

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2685 & 3477 & -792 \tabularnewline
3 & 2438 & 3447.47244928298 & -1009.47244928298 \tabularnewline
4 & 1692 & 3409.83703395011 & -1717.83703395011 \tabularnewline
5 & 4054 & 3345.79218528404 & 708.207814715958 \tabularnewline
6 & 3946 & 3372.19577387901 & 573.804226120993 \tabularnewline
7 & 3623 & 3393.58849280379 & 229.411507196214 \tabularnewline
8 & 2455 & 3402.14147249293 & -947.141472492932 \tabularnewline
9 & 2362 & 3366.82989690553 & -1004.82989690553 \tabularnewline
10 & 2791 & 3329.36756642213 & -538.36756642213 \tabularnewline
11 & 2369 & 3309.29600629344 & -940.296006293436 \tabularnewline
12 & 3438 & 3274.23964516359 & 163.760354836408 \tabularnewline
13 & 3682 & 3280.34500145509 & 401.654998544907 \tabularnewline
14 & 2801 & 3295.31960794534 & -494.319607945342 \tabularnewline
15 & 2563 & 3276.89025530138 & -713.890255301376 \tabularnewline
16 & 3108 & 3250.27481247335 & -142.274812473353 \tabularnewline
17 & 2890 & 3244.97048578009 & -354.970485780094 \tabularnewline
18 & 3940 & 3231.7363834797 & 708.263616520304 \tabularnewline
19 & 4036 & 3258.14205249209 & 777.857947507905 \tabularnewline
20 & 1514 & 3287.14235551693 & -1773.14235551693 \tabularnewline
21 & 3461 & 3221.03559941717 & 239.964400582831 \tabularnewline
22 & 2980 & 3229.98201483193 & -249.982014831926 \tabularnewline
23 & 2728 & 3220.66212010807 & -492.662120108073 \tabularnewline
24 & 3891 & 3202.29456235827 & 688.70543764173 \tabularnewline
25 & 3715 & 3227.97105824091 & 487.02894175909 \tabularnewline
26 & 2843 & 3246.12859836521 & -403.12859836521 \tabularnewline
27 & 1416 & 3231.09905274184 & -1815.09905274184 \tabularnewline
28 & 2657 & 3163.42805610517 & -506.428056105173 \tabularnewline
29 & 1856 & 3144.54727313653 & -1288.54727313653 \tabularnewline
30 & 2441 & 3096.50731738046 & -655.507317380456 \tabularnewline
31 & 3172 & 3072.06852248232 & 99.9314775176831 \tabularnewline
32 & 2813 & 3075.79419390988 & -262.79419390988 \tabularnewline
33 & 3335 & 3065.99663218158 & 269.003367818417 \tabularnewline
34 & 2608 & 3076.02568595217 & -468.025685952171 \tabularnewline
35 & 5784 & 3058.57663017083 & 2725.42336982917 \tabularnewline
36 & 4726 & 3160.18657559756 & 1565.81342440244 \tabularnewline
37 & 3817 & 3218.56364037336 & 598.436359626645 \tabularnewline
38 & 2755 & 3240.87470092864 & -485.874700928635 \tabularnewline
39 & 2541 & 3222.76019351224 & -681.76019351224 \tabularnewline
40 & 3154 & 3197.34263203399 & -43.342632033989 \tabularnewline
41 & 2684 & 3195.7267207138 & -511.726720713797 \tabularnewline
42 & 3732 & 3176.64839154823 & 555.35160845177 \tabularnewline
43 & 4286 & 3197.35315516482 & 1088.64684483518 \tabularnewline
44 & 2394 & 3237.94037097768 & -843.940370977682 \tabularnewline
45 & 1698 & 3206.47636579311 & -1508.47636579311 \tabularnewline
46 & 3945 & 3150.23695620173 & 794.763043798273 \tabularnewline
47 & 2549 & 3179.8675194388 & -630.867519438802 \tabularnewline
48 & 3943 & 3156.34735191867 & 786.652648081333 \tabularnewline
49 & 3899 & 3185.67554126576 & 713.324458734242 \tabularnewline
50 & 2783 & 3212.26988991849 & -429.269889918489 \tabularnewline
51 & 2660 & 3196.26573784039 & -536.265737840388 \tabularnewline
52 & 1848 & 3176.27253863347 & -1328.27253863347 \tabularnewline
53 & 4482 & 3126.75153516059 & 1355.24846483941 \tabularnewline
54 & 4157 & 3177.27826215517 & 979.721737844833 \tabularnewline
55 & 4404 & 3213.80450369908 & 1190.19549630092 \tabularnewline
56 & 2686 & 3258.17768284073 & -572.177682840728 \tabularnewline
57 & 2593 & 3236.84560512706 & -643.845605127062 \tabularnewline
58 & 3254 & 3212.84158522893 & 41.1584147710655 \tabularnewline
59 & 2664 & 3214.37606399104 & -550.376063991036 \tabularnewline
60 & 4203 & 3193.85679992168 & 1009.14320007832 \tabularnewline
61 & 3985 & 3231.47994009977 & 753.52005990023 \tabularnewline
62 & 2861 & 3259.57287164648 & -398.572871646478 \tabularnewline
63 & 2758 & 3244.71317381571 & -486.71317381571 \tabularnewline
64 & 1968 & 3226.56740623429 & -1258.56740623429 \tabularnewline
65 & 4666 & 3179.645167701 & 1486.354832299 \tabularnewline
66 & 4226 & 3235.0598365068 & 990.940163493202 \tabularnewline
67 & 4748 & 3272.00432632381 & 1475.99567367619 \tabularnewline
68 & 2767 & 3327.03278227402 & -560.032782274022 \tabularnewline
69 & 2723 & 3306.15349391318 & -583.15349391318 \tabularnewline
70 & 3297 & 3284.41221314635 & 12.5877868536463 \tabularnewline
71 & 2758 & 3284.88151430132 & -526.881514301323 \tabularnewline
72 & 4338 & 3265.23818016573 & 1072.76181983427 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234784&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]2[/C][C]2685[/C][C]3477[/C][C]-792[/C][/ROW]
[ROW][C]3[/C][C]2438[/C][C]3447.47244928298[/C][C]-1009.47244928298[/C][/ROW]
[ROW][C]4[/C][C]1692[/C][C]3409.83703395011[/C][C]-1717.83703395011[/C][/ROW]
[ROW][C]5[/C][C]4054[/C][C]3345.79218528404[/C][C]708.207814715958[/C][/ROW]
[ROW][C]6[/C][C]3946[/C][C]3372.19577387901[/C][C]573.804226120993[/C][/ROW]
[ROW][C]7[/C][C]3623[/C][C]3393.58849280379[/C][C]229.411507196214[/C][/ROW]
[ROW][C]8[/C][C]2455[/C][C]3402.14147249293[/C][C]-947.141472492932[/C][/ROW]
[ROW][C]9[/C][C]2362[/C][C]3366.82989690553[/C][C]-1004.82989690553[/C][/ROW]
[ROW][C]10[/C][C]2791[/C][C]3329.36756642213[/C][C]-538.36756642213[/C][/ROW]
[ROW][C]11[/C][C]2369[/C][C]3309.29600629344[/C][C]-940.296006293436[/C][/ROW]
[ROW][C]12[/C][C]3438[/C][C]3274.23964516359[/C][C]163.760354836408[/C][/ROW]
[ROW][C]13[/C][C]3682[/C][C]3280.34500145509[/C][C]401.654998544907[/C][/ROW]
[ROW][C]14[/C][C]2801[/C][C]3295.31960794534[/C][C]-494.319607945342[/C][/ROW]
[ROW][C]15[/C][C]2563[/C][C]3276.89025530138[/C][C]-713.890255301376[/C][/ROW]
[ROW][C]16[/C][C]3108[/C][C]3250.27481247335[/C][C]-142.274812473353[/C][/ROW]
[ROW][C]17[/C][C]2890[/C][C]3244.97048578009[/C][C]-354.970485780094[/C][/ROW]
[ROW][C]18[/C][C]3940[/C][C]3231.7363834797[/C][C]708.263616520304[/C][/ROW]
[ROW][C]19[/C][C]4036[/C][C]3258.14205249209[/C][C]777.857947507905[/C][/ROW]
[ROW][C]20[/C][C]1514[/C][C]3287.14235551693[/C][C]-1773.14235551693[/C][/ROW]
[ROW][C]21[/C][C]3461[/C][C]3221.03559941717[/C][C]239.964400582831[/C][/ROW]
[ROW][C]22[/C][C]2980[/C][C]3229.98201483193[/C][C]-249.982014831926[/C][/ROW]
[ROW][C]23[/C][C]2728[/C][C]3220.66212010807[/C][C]-492.662120108073[/C][/ROW]
[ROW][C]24[/C][C]3891[/C][C]3202.29456235827[/C][C]688.70543764173[/C][/ROW]
[ROW][C]25[/C][C]3715[/C][C]3227.97105824091[/C][C]487.02894175909[/C][/ROW]
[ROW][C]26[/C][C]2843[/C][C]3246.12859836521[/C][C]-403.12859836521[/C][/ROW]
[ROW][C]27[/C][C]1416[/C][C]3231.09905274184[/C][C]-1815.09905274184[/C][/ROW]
[ROW][C]28[/C][C]2657[/C][C]3163.42805610517[/C][C]-506.428056105173[/C][/ROW]
[ROW][C]29[/C][C]1856[/C][C]3144.54727313653[/C][C]-1288.54727313653[/C][/ROW]
[ROW][C]30[/C][C]2441[/C][C]3096.50731738046[/C][C]-655.507317380456[/C][/ROW]
[ROW][C]31[/C][C]3172[/C][C]3072.06852248232[/C][C]99.9314775176831[/C][/ROW]
[ROW][C]32[/C][C]2813[/C][C]3075.79419390988[/C][C]-262.79419390988[/C][/ROW]
[ROW][C]33[/C][C]3335[/C][C]3065.99663218158[/C][C]269.003367818417[/C][/ROW]
[ROW][C]34[/C][C]2608[/C][C]3076.02568595217[/C][C]-468.025685952171[/C][/ROW]
[ROW][C]35[/C][C]5784[/C][C]3058.57663017083[/C][C]2725.42336982917[/C][/ROW]
[ROW][C]36[/C][C]4726[/C][C]3160.18657559756[/C][C]1565.81342440244[/C][/ROW]
[ROW][C]37[/C][C]3817[/C][C]3218.56364037336[/C][C]598.436359626645[/C][/ROW]
[ROW][C]38[/C][C]2755[/C][C]3240.87470092864[/C][C]-485.874700928635[/C][/ROW]
[ROW][C]39[/C][C]2541[/C][C]3222.76019351224[/C][C]-681.76019351224[/C][/ROW]
[ROW][C]40[/C][C]3154[/C][C]3197.34263203399[/C][C]-43.342632033989[/C][/ROW]
[ROW][C]41[/C][C]2684[/C][C]3195.7267207138[/C][C]-511.726720713797[/C][/ROW]
[ROW][C]42[/C][C]3732[/C][C]3176.64839154823[/C][C]555.35160845177[/C][/ROW]
[ROW][C]43[/C][C]4286[/C][C]3197.35315516482[/C][C]1088.64684483518[/C][/ROW]
[ROW][C]44[/C][C]2394[/C][C]3237.94037097768[/C][C]-843.940370977682[/C][/ROW]
[ROW][C]45[/C][C]1698[/C][C]3206.47636579311[/C][C]-1508.47636579311[/C][/ROW]
[ROW][C]46[/C][C]3945[/C][C]3150.23695620173[/C][C]794.763043798273[/C][/ROW]
[ROW][C]47[/C][C]2549[/C][C]3179.8675194388[/C][C]-630.867519438802[/C][/ROW]
[ROW][C]48[/C][C]3943[/C][C]3156.34735191867[/C][C]786.652648081333[/C][/ROW]
[ROW][C]49[/C][C]3899[/C][C]3185.67554126576[/C][C]713.324458734242[/C][/ROW]
[ROW][C]50[/C][C]2783[/C][C]3212.26988991849[/C][C]-429.269889918489[/C][/ROW]
[ROW][C]51[/C][C]2660[/C][C]3196.26573784039[/C][C]-536.265737840388[/C][/ROW]
[ROW][C]52[/C][C]1848[/C][C]3176.27253863347[/C][C]-1328.27253863347[/C][/ROW]
[ROW][C]53[/C][C]4482[/C][C]3126.75153516059[/C][C]1355.24846483941[/C][/ROW]
[ROW][C]54[/C][C]4157[/C][C]3177.27826215517[/C][C]979.721737844833[/C][/ROW]
[ROW][C]55[/C][C]4404[/C][C]3213.80450369908[/C][C]1190.19549630092[/C][/ROW]
[ROW][C]56[/C][C]2686[/C][C]3258.17768284073[/C][C]-572.177682840728[/C][/ROW]
[ROW][C]57[/C][C]2593[/C][C]3236.84560512706[/C][C]-643.845605127062[/C][/ROW]
[ROW][C]58[/C][C]3254[/C][C]3212.84158522893[/C][C]41.1584147710655[/C][/ROW]
[ROW][C]59[/C][C]2664[/C][C]3214.37606399104[/C][C]-550.376063991036[/C][/ROW]
[ROW][C]60[/C][C]4203[/C][C]3193.85679992168[/C][C]1009.14320007832[/C][/ROW]
[ROW][C]61[/C][C]3985[/C][C]3231.47994009977[/C][C]753.52005990023[/C][/ROW]
[ROW][C]62[/C][C]2861[/C][C]3259.57287164648[/C][C]-398.572871646478[/C][/ROW]
[ROW][C]63[/C][C]2758[/C][C]3244.71317381571[/C][C]-486.71317381571[/C][/ROW]
[ROW][C]64[/C][C]1968[/C][C]3226.56740623429[/C][C]-1258.56740623429[/C][/ROW]
[ROW][C]65[/C][C]4666[/C][C]3179.645167701[/C][C]1486.354832299[/C][/ROW]
[ROW][C]66[/C][C]4226[/C][C]3235.0598365068[/C][C]990.940163493202[/C][/ROW]
[ROW][C]67[/C][C]4748[/C][C]3272.00432632381[/C][C]1475.99567367619[/C][/ROW]
[ROW][C]68[/C][C]2767[/C][C]3327.03278227402[/C][C]-560.032782274022[/C][/ROW]
[ROW][C]69[/C][C]2723[/C][C]3306.15349391318[/C][C]-583.15349391318[/C][/ROW]
[ROW][C]70[/C][C]3297[/C][C]3284.41221314635[/C][C]12.5877868536463[/C][/ROW]
[ROW][C]71[/C][C]2758[/C][C]3284.88151430132[/C][C]-526.881514301323[/C][/ROW]
[ROW][C]72[/C][C]4338[/C][C]3265.23818016573[/C][C]1072.76181983427[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234784&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234784&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
226853477-792
324383447.47244928298-1009.47244928298
416923409.83703395011-1717.83703395011
540543345.79218528404708.207814715958
639463372.19577387901573.804226120993
736233393.58849280379229.411507196214
824553402.14147249293-947.141472492932
923623366.82989690553-1004.82989690553
1027913329.36756642213-538.36756642213
1123693309.29600629344-940.296006293436
1234383274.23964516359163.760354836408
1336823280.34500145509401.654998544907
1428013295.31960794534-494.319607945342
1525633276.89025530138-713.890255301376
1631083250.27481247335-142.274812473353
1728903244.97048578009-354.970485780094
1839403231.7363834797708.263616520304
1940363258.14205249209777.857947507905
2015143287.14235551693-1773.14235551693
2134613221.03559941717239.964400582831
2229803229.98201483193-249.982014831926
2327283220.66212010807-492.662120108073
2438913202.29456235827688.70543764173
2537153227.97105824091487.02894175909
2628433246.12859836521-403.12859836521
2714163231.09905274184-1815.09905274184
2826573163.42805610517-506.428056105173
2918563144.54727313653-1288.54727313653
3024413096.50731738046-655.507317380456
3131723072.0685224823299.9314775176831
3228133075.79419390988-262.79419390988
3333353065.99663218158269.003367818417
3426083076.02568595217-468.025685952171
3557843058.576630170832725.42336982917
3647263160.186575597561565.81342440244
3738173218.56364037336598.436359626645
3827553240.87470092864-485.874700928635
3925413222.76019351224-681.76019351224
4031543197.34263203399-43.342632033989
4126843195.7267207138-511.726720713797
4237323176.64839154823555.35160845177
4342863197.353155164821088.64684483518
4423943237.94037097768-843.940370977682
4516983206.47636579311-1508.47636579311
4639453150.23695620173794.763043798273
4725493179.8675194388-630.867519438802
4839433156.34735191867786.652648081333
4938993185.67554126576713.324458734242
5027833212.26988991849-429.269889918489
5126603196.26573784039-536.265737840388
5218483176.27253863347-1328.27253863347
5344823126.751535160591355.24846483941
5441573177.27826215517979.721737844833
5544043213.804503699081190.19549630092
5626863258.17768284073-572.177682840728
5725933236.84560512706-643.845605127062
5832543212.8415852289341.1584147710655
5926643214.37606399104-550.376063991036
6042033193.856799921681009.14320007832
6139853231.47994009977753.52005990023
6228613259.57287164648-398.572871646478
6327583244.71317381571-486.71317381571
6419683226.56740623429-1258.56740623429
6546663179.6451677011486.354832299
6642263235.0598365068990.940163493202
6747483272.004326323811475.99567367619
6827673327.03278227402-560.032782274022
6927233306.15349391318-583.15349391318
7032973284.4122131463512.5877868536463
7127583284.88151430132-526.881514301323
7243383265.238180165731072.76181983427







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
733305.233166330421533.430598549215077.03573411163
743305.233166330421532.199652606995078.26668005385
753305.233166330421530.96956066845079.49677199244
763305.233166330421529.740320958425080.72601170241
773305.233166330421528.51193170825081.95440095263
783305.233166330421527.284391154985083.18194150586
793305.233166330421526.057697542095084.40863511875
803305.233166330421524.83184911895085.63448354194
813305.233166330421523.606844140815086.85948852003
823305.233166330421522.382680869225088.08365179162
833305.233166330421521.15935757155089.30697508934
843305.233166330421519.936872520925090.52946013991

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 3305.23316633042 & 1533.43059854921 & 5077.03573411163 \tabularnewline
74 & 3305.23316633042 & 1532.19965260699 & 5078.26668005385 \tabularnewline
75 & 3305.23316633042 & 1530.9695606684 & 5079.49677199244 \tabularnewline
76 & 3305.23316633042 & 1529.74032095842 & 5080.72601170241 \tabularnewline
77 & 3305.23316633042 & 1528.5119317082 & 5081.95440095263 \tabularnewline
78 & 3305.23316633042 & 1527.28439115498 & 5083.18194150586 \tabularnewline
79 & 3305.23316633042 & 1526.05769754209 & 5084.40863511875 \tabularnewline
80 & 3305.23316633042 & 1524.8318491189 & 5085.63448354194 \tabularnewline
81 & 3305.23316633042 & 1523.60684414081 & 5086.85948852003 \tabularnewline
82 & 3305.23316633042 & 1522.38268086922 & 5088.08365179162 \tabularnewline
83 & 3305.23316633042 & 1521.1593575715 & 5089.30697508934 \tabularnewline
84 & 3305.23316633042 & 1519.93687252092 & 5090.52946013991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234784&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]3305.23316633042[/C][C]1533.43059854921[/C][C]5077.03573411163[/C][/ROW]
[ROW][C]74[/C][C]3305.23316633042[/C][C]1532.19965260699[/C][C]5078.26668005385[/C][/ROW]
[ROW][C]75[/C][C]3305.23316633042[/C][C]1530.9695606684[/C][C]5079.49677199244[/C][/ROW]
[ROW][C]76[/C][C]3305.23316633042[/C][C]1529.74032095842[/C][C]5080.72601170241[/C][/ROW]
[ROW][C]77[/C][C]3305.23316633042[/C][C]1528.5119317082[/C][C]5081.95440095263[/C][/ROW]
[ROW][C]78[/C][C]3305.23316633042[/C][C]1527.28439115498[/C][C]5083.18194150586[/C][/ROW]
[ROW][C]79[/C][C]3305.23316633042[/C][C]1526.05769754209[/C][C]5084.40863511875[/C][/ROW]
[ROW][C]80[/C][C]3305.23316633042[/C][C]1524.8318491189[/C][C]5085.63448354194[/C][/ROW]
[ROW][C]81[/C][C]3305.23316633042[/C][C]1523.60684414081[/C][C]5086.85948852003[/C][/ROW]
[ROW][C]82[/C][C]3305.23316633042[/C][C]1522.38268086922[/C][C]5088.08365179162[/C][/ROW]
[ROW][C]83[/C][C]3305.23316633042[/C][C]1521.1593575715[/C][C]5089.30697508934[/C][/ROW]
[ROW][C]84[/C][C]3305.23316633042[/C][C]1519.93687252092[/C][C]5090.52946013991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234784&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234784&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
733305.233166330421533.430598549215077.03573411163
743305.233166330421532.199652606995078.26668005385
753305.233166330421530.96956066845079.49677199244
763305.233166330421529.740320958425080.72601170241
773305.233166330421528.51193170825081.95440095263
783305.233166330421527.284391154985083.18194150586
793305.233166330421526.057697542095084.40863511875
803305.233166330421524.83184911895085.63448354194
813305.233166330421523.606844140815086.85948852003
823305.233166330421522.382680869225088.08365179162
833305.233166330421521.15935757155089.30697508934
843305.233166330421519.936872520925090.52946013991



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