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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 14 Dec 2016 13:35:38 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/14/t1481719157r13x261aujqoyxp.htm/, Retrieved Fri, 03 May 2024 19:58:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299367, Retrieved Fri, 03 May 2024 19:58:19 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-14 12:35:38] [349958aef20b862f8399a5ba04d6f6e3] [Current]
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Dataseries X:
6830
6827
6841
6754
6869
6809
6836
6766
6759
6719
6702
6627
6630
6606
6512
6550
6578
6499
6371
6332
6291
6307
6252
6250
6164
6213
6174
6154
6091
6096
6046
6001
5979
5921
5863
5818
5758
5786
5734
5678
5610
5578
5589
5553
5533
5521
5464
5419
5346
5296
5255
5235
5164
5164
5172
5093
5070
5108
5051
5021
5001
4918
4886




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299367&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299367&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299367&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.62012189933983
beta0.0110029565538354
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.62012189933983 \tabularnewline
beta & 0.0110029565538354 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299367&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]0.62012189933983[/C][/ROW]
[ROW][C]beta[/C][C]0.0110029565538354[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299367&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299367&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
alpha0.62012189933983
beta0.0110029565538354
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1366306771.3234508547-141.323450854703
1466066666.28128717161-60.2812871716069
1565126541.20883422789-29.2088342278894
1665506566.28912618659-16.2891261865898
1765786588.52006848734-10.5200684873435
1864996505.79841621151-6.7984162115099
1963716484.1715885681-113.171588568095
2063326329.058237767632.94176223236536
2162916314.34439076078-23.3443907607762
2263076249.4623084526657.5376915473353
2362526256.54623301389-4.5462330138871
2462506171.5162032840678.4837967159383
2561646170.07473782913-6.07473782912894
2662136178.79371830134.2062816990037
2761746123.8678377265350.1321622734658
2861546203.34750802265-49.3475080226544
2960916207.3345741093-116.334574109297
3060966059.7516246480436.2483753519573
3160466024.0467530567521.9532469432525
3260015997.394707955433.60529204456998
3359795973.669840713365.33015928664281
3459215958.0535023715-37.0535023715038
3558635883.00831627368-20.0083162736837
3658185819.93898312576-1.93898312576312
3757585735.9626995709422.0373004290641
3857865777.067305513548.93269448646333
3957345711.9970249272622.0029750727363
4056785735.52950330513-57.5295033051334
4156105708.2264696049-98.226469604896
4255785629.18988219227-51.1898821922696
4355895532.5898284113856.4101715886191
4455535519.327998594233.6720014057955
4555335514.1012539445718.8987460554254
4655215490.0889077288230.9110922711807
4754645463.419321562920.580678437076131
4854195419.87647467088-0.87647467088118
4953465345.569046409170.430953590825993
5052965368.05141230077-72.0514123007724
5152555256.92813988749-1.9281398874864
5252355234.446389732980.553610267022123
5351645227.1370184459-63.1370184458965
5451645187.40269702836-23.4026970283594
5551725148.7729455657123.2270544342891
5650935105.9333472344-12.9333472344006
5750705065.513114688864.48688531114021
5851085036.3480962474871.651903752524
5950515022.9201121042628.0798878957403
6050214995.5634111825125.4365888174916
6150014937.9363163379163.0636836620879
6249184972.01786345553-54.017863455525
6348864899.13264836738-13.132648367382

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6630 & 6771.3234508547 & -141.323450854703 \tabularnewline
14 & 6606 & 6666.28128717161 & -60.2812871716069 \tabularnewline
15 & 6512 & 6541.20883422789 & -29.2088342278894 \tabularnewline
16 & 6550 & 6566.28912618659 & -16.2891261865898 \tabularnewline
17 & 6578 & 6588.52006848734 & -10.5200684873435 \tabularnewline
18 & 6499 & 6505.79841621151 & -6.7984162115099 \tabularnewline
19 & 6371 & 6484.1715885681 & -113.171588568095 \tabularnewline
20 & 6332 & 6329.05823776763 & 2.94176223236536 \tabularnewline
21 & 6291 & 6314.34439076078 & -23.3443907607762 \tabularnewline
22 & 6307 & 6249.46230845266 & 57.5376915473353 \tabularnewline
23 & 6252 & 6256.54623301389 & -4.5462330138871 \tabularnewline
24 & 6250 & 6171.51620328406 & 78.4837967159383 \tabularnewline
25 & 6164 & 6170.07473782913 & -6.07473782912894 \tabularnewline
26 & 6213 & 6178.793718301 & 34.2062816990037 \tabularnewline
27 & 6174 & 6123.86783772653 & 50.1321622734658 \tabularnewline
28 & 6154 & 6203.34750802265 & -49.3475080226544 \tabularnewline
29 & 6091 & 6207.3345741093 & -116.334574109297 \tabularnewline
30 & 6096 & 6059.75162464804 & 36.2483753519573 \tabularnewline
31 & 6046 & 6024.04675305675 & 21.9532469432525 \tabularnewline
32 & 6001 & 5997.39470795543 & 3.60529204456998 \tabularnewline
33 & 5979 & 5973.66984071336 & 5.33015928664281 \tabularnewline
34 & 5921 & 5958.0535023715 & -37.0535023715038 \tabularnewline
35 & 5863 & 5883.00831627368 & -20.0083162736837 \tabularnewline
36 & 5818 & 5819.93898312576 & -1.93898312576312 \tabularnewline
37 & 5758 & 5735.96269957094 & 22.0373004290641 \tabularnewline
38 & 5786 & 5777.06730551354 & 8.93269448646333 \tabularnewline
39 & 5734 & 5711.99702492726 & 22.0029750727363 \tabularnewline
40 & 5678 & 5735.52950330513 & -57.5295033051334 \tabularnewline
41 & 5610 & 5708.2264696049 & -98.226469604896 \tabularnewline
42 & 5578 & 5629.18988219227 & -51.1898821922696 \tabularnewline
43 & 5589 & 5532.58982841138 & 56.4101715886191 \tabularnewline
44 & 5553 & 5519.3279985942 & 33.6720014057955 \tabularnewline
45 & 5533 & 5514.10125394457 & 18.8987460554254 \tabularnewline
46 & 5521 & 5490.08890772882 & 30.9110922711807 \tabularnewline
47 & 5464 & 5463.41932156292 & 0.580678437076131 \tabularnewline
48 & 5419 & 5419.87647467088 & -0.87647467088118 \tabularnewline
49 & 5346 & 5345.56904640917 & 0.430953590825993 \tabularnewline
50 & 5296 & 5368.05141230077 & -72.0514123007724 \tabularnewline
51 & 5255 & 5256.92813988749 & -1.9281398874864 \tabularnewline
52 & 5235 & 5234.44638973298 & 0.553610267022123 \tabularnewline
53 & 5164 & 5227.1370184459 & -63.1370184458965 \tabularnewline
54 & 5164 & 5187.40269702836 & -23.4026970283594 \tabularnewline
55 & 5172 & 5148.77294556571 & 23.2270544342891 \tabularnewline
56 & 5093 & 5105.9333472344 & -12.9333472344006 \tabularnewline
57 & 5070 & 5065.51311468886 & 4.48688531114021 \tabularnewline
58 & 5108 & 5036.34809624748 & 71.651903752524 \tabularnewline
59 & 5051 & 5022.92011210426 & 28.0798878957403 \tabularnewline
60 & 5021 & 4995.56341118251 & 25.4365888174916 \tabularnewline
61 & 5001 & 4937.93631633791 & 63.0636836620879 \tabularnewline
62 & 4918 & 4972.01786345553 & -54.017863455525 \tabularnewline
63 & 4886 & 4899.13264836738 & -13.132648367382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299367&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]6630[/C][C]6771.3234508547[/C][C]-141.323450854703[/C][/ROW]
[ROW][C]14[/C][C]6606[/C][C]6666.28128717161[/C][C]-60.2812871716069[/C][/ROW]
[ROW][C]15[/C][C]6512[/C][C]6541.20883422789[/C][C]-29.2088342278894[/C][/ROW]
[ROW][C]16[/C][C]6550[/C][C]6566.28912618659[/C][C]-16.2891261865898[/C][/ROW]
[ROW][C]17[/C][C]6578[/C][C]6588.52006848734[/C][C]-10.5200684873435[/C][/ROW]
[ROW][C]18[/C][C]6499[/C][C]6505.79841621151[/C][C]-6.7984162115099[/C][/ROW]
[ROW][C]19[/C][C]6371[/C][C]6484.1715885681[/C][C]-113.171588568095[/C][/ROW]
[ROW][C]20[/C][C]6332[/C][C]6329.05823776763[/C][C]2.94176223236536[/C][/ROW]
[ROW][C]21[/C][C]6291[/C][C]6314.34439076078[/C][C]-23.3443907607762[/C][/ROW]
[ROW][C]22[/C][C]6307[/C][C]6249.46230845266[/C][C]57.5376915473353[/C][/ROW]
[ROW][C]23[/C][C]6252[/C][C]6256.54623301389[/C][C]-4.5462330138871[/C][/ROW]
[ROW][C]24[/C][C]6250[/C][C]6171.51620328406[/C][C]78.4837967159383[/C][/ROW]
[ROW][C]25[/C][C]6164[/C][C]6170.07473782913[/C][C]-6.07473782912894[/C][/ROW]
[ROW][C]26[/C][C]6213[/C][C]6178.793718301[/C][C]34.2062816990037[/C][/ROW]
[ROW][C]27[/C][C]6174[/C][C]6123.86783772653[/C][C]50.1321622734658[/C][/ROW]
[ROW][C]28[/C][C]6154[/C][C]6203.34750802265[/C][C]-49.3475080226544[/C][/ROW]
[ROW][C]29[/C][C]6091[/C][C]6207.3345741093[/C][C]-116.334574109297[/C][/ROW]
[ROW][C]30[/C][C]6096[/C][C]6059.75162464804[/C][C]36.2483753519573[/C][/ROW]
[ROW][C]31[/C][C]6046[/C][C]6024.04675305675[/C][C]21.9532469432525[/C][/ROW]
[ROW][C]32[/C][C]6001[/C][C]5997.39470795543[/C][C]3.60529204456998[/C][/ROW]
[ROW][C]33[/C][C]5979[/C][C]5973.66984071336[/C][C]5.33015928664281[/C][/ROW]
[ROW][C]34[/C][C]5921[/C][C]5958.0535023715[/C][C]-37.0535023715038[/C][/ROW]
[ROW][C]35[/C][C]5863[/C][C]5883.00831627368[/C][C]-20.0083162736837[/C][/ROW]
[ROW][C]36[/C][C]5818[/C][C]5819.93898312576[/C][C]-1.93898312576312[/C][/ROW]
[ROW][C]37[/C][C]5758[/C][C]5735.96269957094[/C][C]22.0373004290641[/C][/ROW]
[ROW][C]38[/C][C]5786[/C][C]5777.06730551354[/C][C]8.93269448646333[/C][/ROW]
[ROW][C]39[/C][C]5734[/C][C]5711.99702492726[/C][C]22.0029750727363[/C][/ROW]
[ROW][C]40[/C][C]5678[/C][C]5735.52950330513[/C][C]-57.5295033051334[/C][/ROW]
[ROW][C]41[/C][C]5610[/C][C]5708.2264696049[/C][C]-98.226469604896[/C][/ROW]
[ROW][C]42[/C][C]5578[/C][C]5629.18988219227[/C][C]-51.1898821922696[/C][/ROW]
[ROW][C]43[/C][C]5589[/C][C]5532.58982841138[/C][C]56.4101715886191[/C][/ROW]
[ROW][C]44[/C][C]5553[/C][C]5519.3279985942[/C][C]33.6720014057955[/C][/ROW]
[ROW][C]45[/C][C]5533[/C][C]5514.10125394457[/C][C]18.8987460554254[/C][/ROW]
[ROW][C]46[/C][C]5521[/C][C]5490.08890772882[/C][C]30.9110922711807[/C][/ROW]
[ROW][C]47[/C][C]5464[/C][C]5463.41932156292[/C][C]0.580678437076131[/C][/ROW]
[ROW][C]48[/C][C]5419[/C][C]5419.87647467088[/C][C]-0.87647467088118[/C][/ROW]
[ROW][C]49[/C][C]5346[/C][C]5345.56904640917[/C][C]0.430953590825993[/C][/ROW]
[ROW][C]50[/C][C]5296[/C][C]5368.05141230077[/C][C]-72.0514123007724[/C][/ROW]
[ROW][C]51[/C][C]5255[/C][C]5256.92813988749[/C][C]-1.9281398874864[/C][/ROW]
[ROW][C]52[/C][C]5235[/C][C]5234.44638973298[/C][C]0.553610267022123[/C][/ROW]
[ROW][C]53[/C][C]5164[/C][C]5227.1370184459[/C][C]-63.1370184458965[/C][/ROW]
[ROW][C]54[/C][C]5164[/C][C]5187.40269702836[/C][C]-23.4026970283594[/C][/ROW]
[ROW][C]55[/C][C]5172[/C][C]5148.77294556571[/C][C]23.2270544342891[/C][/ROW]
[ROW][C]56[/C][C]5093[/C][C]5105.9333472344[/C][C]-12.9333472344006[/C][/ROW]
[ROW][C]57[/C][C]5070[/C][C]5065.51311468886[/C][C]4.48688531114021[/C][/ROW]
[ROW][C]58[/C][C]5108[/C][C]5036.34809624748[/C][C]71.651903752524[/C][/ROW]
[ROW][C]59[/C][C]5051[/C][C]5022.92011210426[/C][C]28.0798878957403[/C][/ROW]
[ROW][C]60[/C][C]5021[/C][C]4995.56341118251[/C][C]25.4365888174916[/C][/ROW]
[ROW][C]61[/C][C]5001[/C][C]4937.93631633791[/C][C]63.0636836620879[/C][/ROW]
[ROW][C]62[/C][C]4918[/C][C]4972.01786345553[/C][C]-54.017863455525[/C][/ROW]
[ROW][C]63[/C][C]4886[/C][C]4899.13264836738[/C][C]-13.132648367382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299367&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299367&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
1366306771.3234508547-141.323450854703
1466066666.28128717161-60.2812871716069
1565126541.20883422789-29.2088342278894
1665506566.28912618659-16.2891261865898
1765786588.52006848734-10.5200684873435
1864996505.79841621151-6.7984162115099
1963716484.1715885681-113.171588568095
2063326329.058237767632.94176223236536
2162916314.34439076078-23.3443907607762
2263076249.4623084526657.5376915473353
2362526256.54623301389-4.5462330138871
2462506171.5162032840678.4837967159383
2561646170.07473782913-6.07473782912894
2662136178.79371830134.2062816990037
2761746123.8678377265350.1321622734658
2861546203.34750802265-49.3475080226544
2960916207.3345741093-116.334574109297
3060966059.7516246480436.2483753519573
3160466024.0467530567521.9532469432525
3260015997.394707955433.60529204456998
3359795973.669840713365.33015928664281
3459215958.0535023715-37.0535023715038
3558635883.00831627368-20.0083162736837
3658185819.93898312576-1.93898312576312
3757585735.9626995709422.0373004290641
3857865777.067305513548.93269448646333
3957345711.9970249272622.0029750727363
4056785735.52950330513-57.5295033051334
4156105708.2264696049-98.226469604896
4255785629.18988219227-51.1898821922696
4355895532.5898284113856.4101715886191
4455535519.327998594233.6720014057955
4555335514.1012539445718.8987460554254
4655215490.0889077288230.9110922711807
4754645463.419321562920.580678437076131
4854195419.87647467088-0.87647467088118
4953465345.569046409170.430953590825993
5052965368.05141230077-72.0514123007724
5152555256.92813988749-1.9281398874864
5252355234.446389732980.553610267022123
5351645227.1370184459-63.1370184458965
5451645187.40269702836-23.4026970283594
5551725148.7729455657123.2270544342891
5650935105.9333472344-12.9333472344006
5750705065.513114688864.48688531114021
5851085036.3480962474871.651903752524
5950515022.9201121042628.0798878957403
6050214995.5634111825125.4365888174916
6150014937.9363163379163.0636836620879
6249184972.01786345553-54.017863455525
6348864899.13264836738-13.132648367382







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
644870.985812580634777.194025967254964.777599194
654839.474995911064728.774455926594950.17553589554
664854.754851257764729.104577147194980.40512536832
674849.278257242994710.002043116224988.55447136976
684779.067037950644627.129399569384931.0046763319
694754.141397447884590.280612383374918.0021825124
704748.534643339454573.335854278314923.73343240058
714674.458957032774488.398102825884860.51981123965
724628.830844401114432.302848144034825.35884065819
734569.695787968274363.033574890724776.35800104582
744519.735268404984303.223117328424736.24741948154
754495.789504904884269.672729424534721.90628038522
764480.77531748554232.934205800164728.61642917084
774449.264500815944192.661606859634705.86739477225
784464.544356162634199.307906277934729.78080604734
794459.067762147874185.312354502234732.82316979351
804388.856542855524106.684944564944671.02814114609
814363.930902352764073.435538467094654.42626623843

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
64 & 4870.98581258063 & 4777.19402596725 & 4964.777599194 \tabularnewline
65 & 4839.47499591106 & 4728.77445592659 & 4950.17553589554 \tabularnewline
66 & 4854.75485125776 & 4729.10457714719 & 4980.40512536832 \tabularnewline
67 & 4849.27825724299 & 4710.00204311622 & 4988.55447136976 \tabularnewline
68 & 4779.06703795064 & 4627.12939956938 & 4931.0046763319 \tabularnewline
69 & 4754.14139744788 & 4590.28061238337 & 4918.0021825124 \tabularnewline
70 & 4748.53464333945 & 4573.33585427831 & 4923.73343240058 \tabularnewline
71 & 4674.45895703277 & 4488.39810282588 & 4860.51981123965 \tabularnewline
72 & 4628.83084440111 & 4432.30284814403 & 4825.35884065819 \tabularnewline
73 & 4569.69578796827 & 4363.03357489072 & 4776.35800104582 \tabularnewline
74 & 4519.73526840498 & 4303.22311732842 & 4736.24741948154 \tabularnewline
75 & 4495.78950490488 & 4269.67272942453 & 4721.90628038522 \tabularnewline
76 & 4480.7753174855 & 4232.93420580016 & 4728.61642917084 \tabularnewline
77 & 4449.26450081594 & 4192.66160685963 & 4705.86739477225 \tabularnewline
78 & 4464.54435616263 & 4199.30790627793 & 4729.78080604734 \tabularnewline
79 & 4459.06776214787 & 4185.31235450223 & 4732.82316979351 \tabularnewline
80 & 4388.85654285552 & 4106.68494456494 & 4671.02814114609 \tabularnewline
81 & 4363.93090235276 & 4073.43553846709 & 4654.42626623843 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299367&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]64[/C][C]4870.98581258063[/C][C]4777.19402596725[/C][C]4964.777599194[/C][/ROW]
[ROW][C]65[/C][C]4839.47499591106[/C][C]4728.77445592659[/C][C]4950.17553589554[/C][/ROW]
[ROW][C]66[/C][C]4854.75485125776[/C][C]4729.10457714719[/C][C]4980.40512536832[/C][/ROW]
[ROW][C]67[/C][C]4849.27825724299[/C][C]4710.00204311622[/C][C]4988.55447136976[/C][/ROW]
[ROW][C]68[/C][C]4779.06703795064[/C][C]4627.12939956938[/C][C]4931.0046763319[/C][/ROW]
[ROW][C]69[/C][C]4754.14139744788[/C][C]4590.28061238337[/C][C]4918.0021825124[/C][/ROW]
[ROW][C]70[/C][C]4748.53464333945[/C][C]4573.33585427831[/C][C]4923.73343240058[/C][/ROW]
[ROW][C]71[/C][C]4674.45895703277[/C][C]4488.39810282588[/C][C]4860.51981123965[/C][/ROW]
[ROW][C]72[/C][C]4628.83084440111[/C][C]4432.30284814403[/C][C]4825.35884065819[/C][/ROW]
[ROW][C]73[/C][C]4569.69578796827[/C][C]4363.03357489072[/C][C]4776.35800104582[/C][/ROW]
[ROW][C]74[/C][C]4519.73526840498[/C][C]4303.22311732842[/C][C]4736.24741948154[/C][/ROW]
[ROW][C]75[/C][C]4495.78950490488[/C][C]4269.67272942453[/C][C]4721.90628038522[/C][/ROW]
[ROW][C]76[/C][C]4480.7753174855[/C][C]4232.93420580016[/C][C]4728.61642917084[/C][/ROW]
[ROW][C]77[/C][C]4449.26450081594[/C][C]4192.66160685963[/C][C]4705.86739477225[/C][/ROW]
[ROW][C]78[/C][C]4464.54435616263[/C][C]4199.30790627793[/C][C]4729.78080604734[/C][/ROW]
[ROW][C]79[/C][C]4459.06776214787[/C][C]4185.31235450223[/C][C]4732.82316979351[/C][/ROW]
[ROW][C]80[/C][C]4388.85654285552[/C][C]4106.68494456494[/C][C]4671.02814114609[/C][/ROW]
[ROW][C]81[/C][C]4363.93090235276[/C][C]4073.43553846709[/C][C]4654.42626623843[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299367&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299367&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
644870.985812580634777.194025967254964.777599194
654839.474995911064728.774455926594950.17553589554
664854.754851257764729.104577147194980.40512536832
674849.278257242994710.002043116224988.55447136976
684779.067037950644627.129399569384931.0046763319
694754.141397447884590.280612383374918.0021825124
704748.534643339454573.335854278314923.73343240058
714674.458957032774488.398102825884860.51981123965
724628.830844401114432.302848144034825.35884065819
734569.695787968274363.033574890724776.35800104582
744519.735268404984303.223117328424736.24741948154
754495.789504904884269.672729424534721.90628038522
764480.77531748554232.934205800164728.61642917084
774449.264500815944192.661606859634705.86739477225
784464.544356162634199.307906277934729.78080604734
794459.067762147874185.312354502234732.82316979351
804388.856542855524106.684944564944671.02814114609
814363.930902352764073.435538467094654.42626623843



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '18'
par3 <- 'additive'
par2 <- 'Single'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')