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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 16 Jan 2011 14:23:51 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Jan/16/t12951878187bhin2fdlb8a068.htm/, Retrieved Mon, 27 May 2024 07:57:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117409, Retrieved Mon, 27 May 2024 07:57:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2011-01-16 14:23:51] [e2eb61add35e149c3ec50f04fb8f2afe] [Current]
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Dataseries X:
2981,85
3080,58
3106,22
3119,31
3061,26
3097,31
3161,69
3257,16
3277,01
3295,32
3363,99
3494,17
3667,03
3813,06
3917,96
3895,51
3801,06
3570,12
3701,61
3862,27
3970,1
4138,52
4199,75
4290,89
4443,91
4502,64
4356,98
4591,27
4696,96
4621,4
4562,84
4202,52
4296,49
4435,23
4105,18
4116,68
3844,49
3720,98
3674,4
3857,62
3801,06
3504,37
3032,6
3047,03
2962,34
2197,82
2014,45
1862,83
1905,41
1810,99
1670,07
1864,44
2052,02
2029,6
2070,83
2293,41
2443,27
2513,17
2466,92
2502,66




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117409&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117409&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 time1 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.99995731091006
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99995731091006 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117409&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]0.99995731091006[/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=117409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117409&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
alpha0.99995731091006
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23080.582981.8598.73
33106.223080.5757853061525.6442146938498
43119.313106.2189052718113.0910947281877
53061.263119.30944115308-58.0494411530794
63097.313061.2624780778136.0475219221853
73161.693097.3084611640964.3815388359058
83257.163161.687251610795.4727483893016
93277.013257.1559243552619.8540756447433
103295.323277.0091524475818.3108475524209
113363.993295.3192183265868.6707816734179
123494.173363.98706850682130.182931493176
133667.033494.16444260913172.865557390871
143813.063667.02262052667146.037379473327
153917.963813.05376579717104.906234202827
163895.513917.95552164833-22.4455216483325
173801.063895.51095817889-94.4509581788925
183570.123801.06403202545-230.944032025448
193701.613570.12985879055131.480141209446
203862.273701.60438723243160.665612767573
213970.13862.26314133121107.836858668793
224138.523970.09539654264168.424603457359
234199.754138.5128101069561.2371898930451
244290.894199.7473858400991.1426141599077
254443.914290.88610920475153.023890795253
264502.644443.9034675493658.7365324506372
274356.984502.63749259088-145.657492590884
284591.274356.9862179858234.283782014199
294696.964591.25999863856105.700001361442
304621.44696.95548776314-75.5554877631357
314562.844621.40322539501-58.5632253950125
324202.524562.8425000108-360.322500010796
334296.494202.5353818396193.9546181603891
344435.234296.48598916285138.744010837145
354105.184435.22407714444-330.044077144442
364116.684105.1940892812911.4859107187067
373844.494116.67950967692-272.189509676925
383720.983844.50161952246-123.521619522459
393674.43720.98527302553-46.5852730255251
403857.623674.40198868291183.21801131709
413801.063857.61217858984-56.5521785898363
423504.373801.06241416104-296.692414161038
433032.63504.38266552915-471.782665529153
443047.033032.6201399726414.4098600273592
452962.343047.02938485619-84.6893848561895
462197.822962.34361531277-764.523615312767
472014.452197.85263681738-183.402636817376
481862.832014.45782929166-151.627829291658
491905.411862.8364728540442.5735271459582
501810.991905.40818257487-94.4181825748706
511670.071810.99403062629-140.924030626288
521864.441670.07601591862194.363984081382
532052.021864.4317027784187.588297221597
542029.62052.01199202631-22.4119920263083
552070.832029.6009567475441.2290432524567
562293.412070.82823996966222.581760030335
572443.272293.40049818723149.869501812773
582513.172443.2636022073669.9063977926421
592466.922513.1670157595-46.2470157594971
602502.662466.9219742430235.7380257569844

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3080.58 & 2981.85 & 98.73 \tabularnewline
3 & 3106.22 & 3080.57578530615 & 25.6442146938498 \tabularnewline
4 & 3119.31 & 3106.21890527181 & 13.0910947281877 \tabularnewline
5 & 3061.26 & 3119.30944115308 & -58.0494411530794 \tabularnewline
6 & 3097.31 & 3061.26247807781 & 36.0475219221853 \tabularnewline
7 & 3161.69 & 3097.30846116409 & 64.3815388359058 \tabularnewline
8 & 3257.16 & 3161.6872516107 & 95.4727483893016 \tabularnewline
9 & 3277.01 & 3257.15592435526 & 19.8540756447433 \tabularnewline
10 & 3295.32 & 3277.00915244758 & 18.3108475524209 \tabularnewline
11 & 3363.99 & 3295.31921832658 & 68.6707816734179 \tabularnewline
12 & 3494.17 & 3363.98706850682 & 130.182931493176 \tabularnewline
13 & 3667.03 & 3494.16444260913 & 172.865557390871 \tabularnewline
14 & 3813.06 & 3667.02262052667 & 146.037379473327 \tabularnewline
15 & 3917.96 & 3813.05376579717 & 104.906234202827 \tabularnewline
16 & 3895.51 & 3917.95552164833 & -22.4455216483325 \tabularnewline
17 & 3801.06 & 3895.51095817889 & -94.4509581788925 \tabularnewline
18 & 3570.12 & 3801.06403202545 & -230.944032025448 \tabularnewline
19 & 3701.61 & 3570.12985879055 & 131.480141209446 \tabularnewline
20 & 3862.27 & 3701.60438723243 & 160.665612767573 \tabularnewline
21 & 3970.1 & 3862.26314133121 & 107.836858668793 \tabularnewline
22 & 4138.52 & 3970.09539654264 & 168.424603457359 \tabularnewline
23 & 4199.75 & 4138.51281010695 & 61.2371898930451 \tabularnewline
24 & 4290.89 & 4199.74738584009 & 91.1426141599077 \tabularnewline
25 & 4443.91 & 4290.88610920475 & 153.023890795253 \tabularnewline
26 & 4502.64 & 4443.90346754936 & 58.7365324506372 \tabularnewline
27 & 4356.98 & 4502.63749259088 & -145.657492590884 \tabularnewline
28 & 4591.27 & 4356.9862179858 & 234.283782014199 \tabularnewline
29 & 4696.96 & 4591.25999863856 & 105.700001361442 \tabularnewline
30 & 4621.4 & 4696.95548776314 & -75.5554877631357 \tabularnewline
31 & 4562.84 & 4621.40322539501 & -58.5632253950125 \tabularnewline
32 & 4202.52 & 4562.8425000108 & -360.322500010796 \tabularnewline
33 & 4296.49 & 4202.53538183961 & 93.9546181603891 \tabularnewline
34 & 4435.23 & 4296.48598916285 & 138.744010837145 \tabularnewline
35 & 4105.18 & 4435.22407714444 & -330.044077144442 \tabularnewline
36 & 4116.68 & 4105.19408928129 & 11.4859107187067 \tabularnewline
37 & 3844.49 & 4116.67950967692 & -272.189509676925 \tabularnewline
38 & 3720.98 & 3844.50161952246 & -123.521619522459 \tabularnewline
39 & 3674.4 & 3720.98527302553 & -46.5852730255251 \tabularnewline
40 & 3857.62 & 3674.40198868291 & 183.21801131709 \tabularnewline
41 & 3801.06 & 3857.61217858984 & -56.5521785898363 \tabularnewline
42 & 3504.37 & 3801.06241416104 & -296.692414161038 \tabularnewline
43 & 3032.6 & 3504.38266552915 & -471.782665529153 \tabularnewline
44 & 3047.03 & 3032.62013997264 & 14.4098600273592 \tabularnewline
45 & 2962.34 & 3047.02938485619 & -84.6893848561895 \tabularnewline
46 & 2197.82 & 2962.34361531277 & -764.523615312767 \tabularnewline
47 & 2014.45 & 2197.85263681738 & -183.402636817376 \tabularnewline
48 & 1862.83 & 2014.45782929166 & -151.627829291658 \tabularnewline
49 & 1905.41 & 1862.83647285404 & 42.5735271459582 \tabularnewline
50 & 1810.99 & 1905.40818257487 & -94.4181825748706 \tabularnewline
51 & 1670.07 & 1810.99403062629 & -140.924030626288 \tabularnewline
52 & 1864.44 & 1670.07601591862 & 194.363984081382 \tabularnewline
53 & 2052.02 & 1864.4317027784 & 187.588297221597 \tabularnewline
54 & 2029.6 & 2052.01199202631 & -22.4119920263083 \tabularnewline
55 & 2070.83 & 2029.60095674754 & 41.2290432524567 \tabularnewline
56 & 2293.41 & 2070.82823996966 & 222.581760030335 \tabularnewline
57 & 2443.27 & 2293.40049818723 & 149.869501812773 \tabularnewline
58 & 2513.17 & 2443.26360220736 & 69.9063977926421 \tabularnewline
59 & 2466.92 & 2513.1670157595 & -46.2470157594971 \tabularnewline
60 & 2502.66 & 2466.92197424302 & 35.7380257569844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117409&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]3080.58[/C][C]2981.85[/C][C]98.73[/C][/ROW]
[ROW][C]3[/C][C]3106.22[/C][C]3080.57578530615[/C][C]25.6442146938498[/C][/ROW]
[ROW][C]4[/C][C]3119.31[/C][C]3106.21890527181[/C][C]13.0910947281877[/C][/ROW]
[ROW][C]5[/C][C]3061.26[/C][C]3119.30944115308[/C][C]-58.0494411530794[/C][/ROW]
[ROW][C]6[/C][C]3097.31[/C][C]3061.26247807781[/C][C]36.0475219221853[/C][/ROW]
[ROW][C]7[/C][C]3161.69[/C][C]3097.30846116409[/C][C]64.3815388359058[/C][/ROW]
[ROW][C]8[/C][C]3257.16[/C][C]3161.6872516107[/C][C]95.4727483893016[/C][/ROW]
[ROW][C]9[/C][C]3277.01[/C][C]3257.15592435526[/C][C]19.8540756447433[/C][/ROW]
[ROW][C]10[/C][C]3295.32[/C][C]3277.00915244758[/C][C]18.3108475524209[/C][/ROW]
[ROW][C]11[/C][C]3363.99[/C][C]3295.31921832658[/C][C]68.6707816734179[/C][/ROW]
[ROW][C]12[/C][C]3494.17[/C][C]3363.98706850682[/C][C]130.182931493176[/C][/ROW]
[ROW][C]13[/C][C]3667.03[/C][C]3494.16444260913[/C][C]172.865557390871[/C][/ROW]
[ROW][C]14[/C][C]3813.06[/C][C]3667.02262052667[/C][C]146.037379473327[/C][/ROW]
[ROW][C]15[/C][C]3917.96[/C][C]3813.05376579717[/C][C]104.906234202827[/C][/ROW]
[ROW][C]16[/C][C]3895.51[/C][C]3917.95552164833[/C][C]-22.4455216483325[/C][/ROW]
[ROW][C]17[/C][C]3801.06[/C][C]3895.51095817889[/C][C]-94.4509581788925[/C][/ROW]
[ROW][C]18[/C][C]3570.12[/C][C]3801.06403202545[/C][C]-230.944032025448[/C][/ROW]
[ROW][C]19[/C][C]3701.61[/C][C]3570.12985879055[/C][C]131.480141209446[/C][/ROW]
[ROW][C]20[/C][C]3862.27[/C][C]3701.60438723243[/C][C]160.665612767573[/C][/ROW]
[ROW][C]21[/C][C]3970.1[/C][C]3862.26314133121[/C][C]107.836858668793[/C][/ROW]
[ROW][C]22[/C][C]4138.52[/C][C]3970.09539654264[/C][C]168.424603457359[/C][/ROW]
[ROW][C]23[/C][C]4199.75[/C][C]4138.51281010695[/C][C]61.2371898930451[/C][/ROW]
[ROW][C]24[/C][C]4290.89[/C][C]4199.74738584009[/C][C]91.1426141599077[/C][/ROW]
[ROW][C]25[/C][C]4443.91[/C][C]4290.88610920475[/C][C]153.023890795253[/C][/ROW]
[ROW][C]26[/C][C]4502.64[/C][C]4443.90346754936[/C][C]58.7365324506372[/C][/ROW]
[ROW][C]27[/C][C]4356.98[/C][C]4502.63749259088[/C][C]-145.657492590884[/C][/ROW]
[ROW][C]28[/C][C]4591.27[/C][C]4356.9862179858[/C][C]234.283782014199[/C][/ROW]
[ROW][C]29[/C][C]4696.96[/C][C]4591.25999863856[/C][C]105.700001361442[/C][/ROW]
[ROW][C]30[/C][C]4621.4[/C][C]4696.95548776314[/C][C]-75.5554877631357[/C][/ROW]
[ROW][C]31[/C][C]4562.84[/C][C]4621.40322539501[/C][C]-58.5632253950125[/C][/ROW]
[ROW][C]32[/C][C]4202.52[/C][C]4562.8425000108[/C][C]-360.322500010796[/C][/ROW]
[ROW][C]33[/C][C]4296.49[/C][C]4202.53538183961[/C][C]93.9546181603891[/C][/ROW]
[ROW][C]34[/C][C]4435.23[/C][C]4296.48598916285[/C][C]138.744010837145[/C][/ROW]
[ROW][C]35[/C][C]4105.18[/C][C]4435.22407714444[/C][C]-330.044077144442[/C][/ROW]
[ROW][C]36[/C][C]4116.68[/C][C]4105.19408928129[/C][C]11.4859107187067[/C][/ROW]
[ROW][C]37[/C][C]3844.49[/C][C]4116.67950967692[/C][C]-272.189509676925[/C][/ROW]
[ROW][C]38[/C][C]3720.98[/C][C]3844.50161952246[/C][C]-123.521619522459[/C][/ROW]
[ROW][C]39[/C][C]3674.4[/C][C]3720.98527302553[/C][C]-46.5852730255251[/C][/ROW]
[ROW][C]40[/C][C]3857.62[/C][C]3674.40198868291[/C][C]183.21801131709[/C][/ROW]
[ROW][C]41[/C][C]3801.06[/C][C]3857.61217858984[/C][C]-56.5521785898363[/C][/ROW]
[ROW][C]42[/C][C]3504.37[/C][C]3801.06241416104[/C][C]-296.692414161038[/C][/ROW]
[ROW][C]43[/C][C]3032.6[/C][C]3504.38266552915[/C][C]-471.782665529153[/C][/ROW]
[ROW][C]44[/C][C]3047.03[/C][C]3032.62013997264[/C][C]14.4098600273592[/C][/ROW]
[ROW][C]45[/C][C]2962.34[/C][C]3047.02938485619[/C][C]-84.6893848561895[/C][/ROW]
[ROW][C]46[/C][C]2197.82[/C][C]2962.34361531277[/C][C]-764.523615312767[/C][/ROW]
[ROW][C]47[/C][C]2014.45[/C][C]2197.85263681738[/C][C]-183.402636817376[/C][/ROW]
[ROW][C]48[/C][C]1862.83[/C][C]2014.45782929166[/C][C]-151.627829291658[/C][/ROW]
[ROW][C]49[/C][C]1905.41[/C][C]1862.83647285404[/C][C]42.5735271459582[/C][/ROW]
[ROW][C]50[/C][C]1810.99[/C][C]1905.40818257487[/C][C]-94.4181825748706[/C][/ROW]
[ROW][C]51[/C][C]1670.07[/C][C]1810.99403062629[/C][C]-140.924030626288[/C][/ROW]
[ROW][C]52[/C][C]1864.44[/C][C]1670.07601591862[/C][C]194.363984081382[/C][/ROW]
[ROW][C]53[/C][C]2052.02[/C][C]1864.4317027784[/C][C]187.588297221597[/C][/ROW]
[ROW][C]54[/C][C]2029.6[/C][C]2052.01199202631[/C][C]-22.4119920263083[/C][/ROW]
[ROW][C]55[/C][C]2070.83[/C][C]2029.60095674754[/C][C]41.2290432524567[/C][/ROW]
[ROW][C]56[/C][C]2293.41[/C][C]2070.82823996966[/C][C]222.581760030335[/C][/ROW]
[ROW][C]57[/C][C]2443.27[/C][C]2293.40049818723[/C][C]149.869501812773[/C][/ROW]
[ROW][C]58[/C][C]2513.17[/C][C]2443.26360220736[/C][C]69.9063977926421[/C][/ROW]
[ROW][C]59[/C][C]2466.92[/C][C]2513.1670157595[/C][C]-46.2470157594971[/C][/ROW]
[ROW][C]60[/C][C]2502.66[/C][C]2466.92197424302[/C][C]35.7380257569844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117409&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117409&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
23080.582981.8598.73
33106.223080.5757853061525.6442146938498
43119.313106.2189052718113.0910947281877
53061.263119.30944115308-58.0494411530794
63097.313061.2624780778136.0475219221853
73161.693097.3084611640964.3815388359058
83257.163161.687251610795.4727483893016
93277.013257.1559243552619.8540756447433
103295.323277.0091524475818.3108475524209
113363.993295.3192183265868.6707816734179
123494.173363.98706850682130.182931493176
133667.033494.16444260913172.865557390871
143813.063667.02262052667146.037379473327
153917.963813.05376579717104.906234202827
163895.513917.95552164833-22.4455216483325
173801.063895.51095817889-94.4509581788925
183570.123801.06403202545-230.944032025448
193701.613570.12985879055131.480141209446
203862.273701.60438723243160.665612767573
213970.13862.26314133121107.836858668793
224138.523970.09539654264168.424603457359
234199.754138.5128101069561.2371898930451
244290.894199.7473858400991.1426141599077
254443.914290.88610920475153.023890795253
264502.644443.9034675493658.7365324506372
274356.984502.63749259088-145.657492590884
284591.274356.9862179858234.283782014199
294696.964591.25999863856105.700001361442
304621.44696.95548776314-75.5554877631357
314562.844621.40322539501-58.5632253950125
324202.524562.8425000108-360.322500010796
334296.494202.5353818396193.9546181603891
344435.234296.48598916285138.744010837145
354105.184435.22407714444-330.044077144442
364116.684105.1940892812911.4859107187067
373844.494116.67950967692-272.189509676925
383720.983844.50161952246-123.521619522459
393674.43720.98527302553-46.5852730255251
403857.623674.40198868291183.21801131709
413801.063857.61217858984-56.5521785898363
423504.373801.06241416104-296.692414161038
433032.63504.38266552915-471.782665529153
443047.033032.6201399726414.4098600273592
452962.343047.02938485619-84.6893848561895
462197.822962.34361531277-764.523615312767
472014.452197.85263681738-183.402636817376
481862.832014.45782929166-151.627829291658
491905.411862.8364728540442.5735271459582
501810.991905.40818257487-94.4181825748706
511670.071810.99403062629-140.924030626288
521864.441670.07601591862194.363984081382
532052.021864.4317027784187.588297221597
542029.62052.01199202631-22.4119920263083
552070.832029.6009567475441.2290432524567
562293.412070.82823996966222.581760030335
572443.272293.40049818723149.869501812773
582513.172443.2636022073669.9063977926421
592466.922513.1670157595-46.2470157594971
602502.662466.9219742430235.7380257569844







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
612502.65847437622145.050473722622860.26647502979
622502.65847437621996.935184387483008.38176436492
632502.65847437621883.2808755383122.03607321441
642502.65847437621787.4653718873217.85157686541
652502.65847437621703.049984080053302.26696467236
662502.65847437621626.732506237773378.58444251464
672502.65847437621556.551257637623448.76569111478
682502.65847437621491.228086524243514.08886222817
692502.65847437621429.875181545853575.44176720656
702502.65847437621371.846130403293633.47081834911
712502.65847437621316.652942691353688.66400606106
722502.65847437621263.916497573683741.40045117873

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 2502.6584743762 & 2145.05047372262 & 2860.26647502979 \tabularnewline
62 & 2502.6584743762 & 1996.93518438748 & 3008.38176436492 \tabularnewline
63 & 2502.6584743762 & 1883.280875538 & 3122.03607321441 \tabularnewline
64 & 2502.6584743762 & 1787.465371887 & 3217.85157686541 \tabularnewline
65 & 2502.6584743762 & 1703.04998408005 & 3302.26696467236 \tabularnewline
66 & 2502.6584743762 & 1626.73250623777 & 3378.58444251464 \tabularnewline
67 & 2502.6584743762 & 1556.55125763762 & 3448.76569111478 \tabularnewline
68 & 2502.6584743762 & 1491.22808652424 & 3514.08886222817 \tabularnewline
69 & 2502.6584743762 & 1429.87518154585 & 3575.44176720656 \tabularnewline
70 & 2502.6584743762 & 1371.84613040329 & 3633.47081834911 \tabularnewline
71 & 2502.6584743762 & 1316.65294269135 & 3688.66400606106 \tabularnewline
72 & 2502.6584743762 & 1263.91649757368 & 3741.40045117873 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117409&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]61[/C][C]2502.6584743762[/C][C]2145.05047372262[/C][C]2860.26647502979[/C][/ROW]
[ROW][C]62[/C][C]2502.6584743762[/C][C]1996.93518438748[/C][C]3008.38176436492[/C][/ROW]
[ROW][C]63[/C][C]2502.6584743762[/C][C]1883.280875538[/C][C]3122.03607321441[/C][/ROW]
[ROW][C]64[/C][C]2502.6584743762[/C][C]1787.465371887[/C][C]3217.85157686541[/C][/ROW]
[ROW][C]65[/C][C]2502.6584743762[/C][C]1703.04998408005[/C][C]3302.26696467236[/C][/ROW]
[ROW][C]66[/C][C]2502.6584743762[/C][C]1626.73250623777[/C][C]3378.58444251464[/C][/ROW]
[ROW][C]67[/C][C]2502.6584743762[/C][C]1556.55125763762[/C][C]3448.76569111478[/C][/ROW]
[ROW][C]68[/C][C]2502.6584743762[/C][C]1491.22808652424[/C][C]3514.08886222817[/C][/ROW]
[ROW][C]69[/C][C]2502.6584743762[/C][C]1429.87518154585[/C][C]3575.44176720656[/C][/ROW]
[ROW][C]70[/C][C]2502.6584743762[/C][C]1371.84613040329[/C][C]3633.47081834911[/C][/ROW]
[ROW][C]71[/C][C]2502.6584743762[/C][C]1316.65294269135[/C][C]3688.66400606106[/C][/ROW]
[ROW][C]72[/C][C]2502.6584743762[/C][C]1263.91649757368[/C][C]3741.40045117873[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117409&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117409&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
612502.65847437622145.050473722622860.26647502979
622502.65847437621996.935184387483008.38176436492
632502.65847437621883.2808755383122.03607321441
642502.65847437621787.4653718873217.85157686541
652502.65847437621703.049984080053302.26696467236
662502.65847437621626.732506237773378.58444251464
672502.65847437621556.551257637623448.76569111478
682502.65847437621491.228086524243514.08886222817
692502.65847437621429.875181545853575.44176720656
702502.65847437621371.846130403293633.47081834911
712502.65847437621316.652942691353688.66400606106
722502.65847437621263.916497573683741.40045117873



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')