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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 computationFri, 16 Dec 2016 15:47:58 +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/16/t14818997540hq1qqfeflrcob6.htm/, Retrieved Thu, 02 May 2024 18:43:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300330, Retrieved Thu, 02 May 2024 18:43:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
-    D  [ARIMA Backward Selection] [] [2016-12-16 14:17:56] [683f400e1b95307fc738e729f07c4fce]
- RM D      [Exponential Smoothing] [] [2016-12-16 14:47:58] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataseries X:
5100
5100
5050
5150
5150
5050
4800
4750
4900
4950
5050
4900
4950
4850
5100
5200
5450
5150
5150
5000
5200
5350
5600
5600
5650
5550
5700
5750
5850
5750
5700
5500
5750
5750
5750
5500
5750
5750
5900
6000
6150
5950
5900
5750
5750
5800
5800
5450
5400
5600
5600
5800
5650
5700
5550
5350
5800
5700
5950
5450
5400
5400
5450
5700
5850
5850
5700
5450
5800
5600
5700
5800
5750
5850
6250
6450
6550
6500
6150
6100
6300
6350
6250
6200
6250
6450
6050
6500
6600
6450




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=300330&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=300330&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300330&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
alpha0.613074904643624
beta0
gamma0.497745885752945

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.613074904643624 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.497745885752945 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300330&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]0.613074904643624[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.497745885752945[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300330&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300330&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
alpha0.613074904643624
beta0
gamma0.497745885752945







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1349504897.3424145299252.6575854700823
1448504822.9748176951127.0251823048893
1551005084.9759710673515.0240289326512
1652005183.3695184802916.63048151971
1754505422.3312749931927.6687250068117
1851505105.5603015793744.439698420626
1951504999.07119109202150.928808907984
2050005076.61788186228-76.6178818622802
2152005206.32807355326-6.32807355325713
2253505266.6311827707183.3688172292914
2356005421.50853808483178.491461915167
2456005382.61986638587217.380133614134
2556505575.6308741429874.3691258570225
2655505509.6375237405640.3624762594436
2757005777.5041307121-77.5041307120982
2857505819.48037277903-69.480372779035
2958506007.77558494884-157.775584948836
3057505580.54328693954169.45671306046
3157005571.20774842984128.792251570164
3255005591.35976907304-91.3597690730394
3357505725.569220160324.4307798397003
3457505822.00456825868-72.0045682586788
3557505899.94610582585-149.946105825848
3655005667.19018744153-167.190187441527
3757505596.88823877454153.111761225463
3857505572.62066866704177.379331332956
3959005901.78889704226-1.78889704226094
4060005991.729547315098.2704526849102
4161506210.68703143076-60.6870314307571
4259505905.9990798708944.0009201291114
4359005811.9181592133588.08184078665
4457505764.71248858707-14.7124885870662
4557505968.21260900591-218.212609005915
4658005897.31686483855-97.3168648385536
4758005944.72927869949-144.729278699487
4854505711.85062197524-261.850621975237
4954005645.20180861839-245.201808618391
5056005381.41188507117218.588114928832
5156005701.33810835299-101.338108352987
5258005732.184969323467.8150306766029
5356505974.36719223618-324.367192236178
5457005528.18544301059171.814556989415
5555505520.9534165926229.0465834073821
5653505417.75751280708-67.7575128070839
5758005549.5448956972250.455104302804
5857005789.26092179758-89.2609217975842
5959505832.48105763784117.51894236216
6054505737.82376069296-287.823760692964
6154005658.45786898963-258.457868989633
6254005475.86246247069-75.8624624706936
6354505553.65371499818-103.653714998183
6457005615.6582020065184.3417979934866
6558505792.4420501083757.557949891635
6658505675.96884978204174.03115021796
6757005642.6000235749157.3999764250912
6854505538.14333638552-88.1433363855185
6958005718.7173694679981.2826305320141
7056005789.29196071785-189.291960717853
7157005811.00938834859-111.009388348588
7258005498.18200394037301.817996059632
7357505785.96626410707-35.9662641070727
7458505774.9409947239675.0590052760435
7562505939.90608397219310.09391602781
7664506291.77498663363158.225013366366
7765506508.6964686236341.3035313763721
7865006404.6897094637495.3102905362584
7961506300.59705829701-150.597058297015
8061006040.5923677869659.4076322130377
8163006344.25600725924-44.2560072592405
8263506285.7559483090464.2440516909564
8362506477.98641248544-227.986412485439
8462006172.9499306468827.0500693531203
8562506227.2268732479422.7731267520612
8664506273.59564850277176.404351497225
8760506545.95848765881-495.958487658811
8865006374.40840098297125.591599017027
8966006548.8052036014351.1947963985731
9064506461.26371276361-11.2637127636062

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4950 & 4897.34241452992 & 52.6575854700823 \tabularnewline
14 & 4850 & 4822.97481769511 & 27.0251823048893 \tabularnewline
15 & 5100 & 5084.97597106735 & 15.0240289326512 \tabularnewline
16 & 5200 & 5183.36951848029 & 16.63048151971 \tabularnewline
17 & 5450 & 5422.33127499319 & 27.6687250068117 \tabularnewline
18 & 5150 & 5105.56030157937 & 44.439698420626 \tabularnewline
19 & 5150 & 4999.07119109202 & 150.928808907984 \tabularnewline
20 & 5000 & 5076.61788186228 & -76.6178818622802 \tabularnewline
21 & 5200 & 5206.32807355326 & -6.32807355325713 \tabularnewline
22 & 5350 & 5266.63118277071 & 83.3688172292914 \tabularnewline
23 & 5600 & 5421.50853808483 & 178.491461915167 \tabularnewline
24 & 5600 & 5382.61986638587 & 217.380133614134 \tabularnewline
25 & 5650 & 5575.63087414298 & 74.3691258570225 \tabularnewline
26 & 5550 & 5509.63752374056 & 40.3624762594436 \tabularnewline
27 & 5700 & 5777.5041307121 & -77.5041307120982 \tabularnewline
28 & 5750 & 5819.48037277903 & -69.480372779035 \tabularnewline
29 & 5850 & 6007.77558494884 & -157.775584948836 \tabularnewline
30 & 5750 & 5580.54328693954 & 169.45671306046 \tabularnewline
31 & 5700 & 5571.20774842984 & 128.792251570164 \tabularnewline
32 & 5500 & 5591.35976907304 & -91.3597690730394 \tabularnewline
33 & 5750 & 5725.5692201603 & 24.4307798397003 \tabularnewline
34 & 5750 & 5822.00456825868 & -72.0045682586788 \tabularnewline
35 & 5750 & 5899.94610582585 & -149.946105825848 \tabularnewline
36 & 5500 & 5667.19018744153 & -167.190187441527 \tabularnewline
37 & 5750 & 5596.88823877454 & 153.111761225463 \tabularnewline
38 & 5750 & 5572.62066866704 & 177.379331332956 \tabularnewline
39 & 5900 & 5901.78889704226 & -1.78889704226094 \tabularnewline
40 & 6000 & 5991.72954731509 & 8.2704526849102 \tabularnewline
41 & 6150 & 6210.68703143076 & -60.6870314307571 \tabularnewline
42 & 5950 & 5905.99907987089 & 44.0009201291114 \tabularnewline
43 & 5900 & 5811.91815921335 & 88.08184078665 \tabularnewline
44 & 5750 & 5764.71248858707 & -14.7124885870662 \tabularnewline
45 & 5750 & 5968.21260900591 & -218.212609005915 \tabularnewline
46 & 5800 & 5897.31686483855 & -97.3168648385536 \tabularnewline
47 & 5800 & 5944.72927869949 & -144.729278699487 \tabularnewline
48 & 5450 & 5711.85062197524 & -261.850621975237 \tabularnewline
49 & 5400 & 5645.20180861839 & -245.201808618391 \tabularnewline
50 & 5600 & 5381.41188507117 & 218.588114928832 \tabularnewline
51 & 5600 & 5701.33810835299 & -101.338108352987 \tabularnewline
52 & 5800 & 5732.1849693234 & 67.8150306766029 \tabularnewline
53 & 5650 & 5974.36719223618 & -324.367192236178 \tabularnewline
54 & 5700 & 5528.18544301059 & 171.814556989415 \tabularnewline
55 & 5550 & 5520.95341659262 & 29.0465834073821 \tabularnewline
56 & 5350 & 5417.75751280708 & -67.7575128070839 \tabularnewline
57 & 5800 & 5549.5448956972 & 250.455104302804 \tabularnewline
58 & 5700 & 5789.26092179758 & -89.2609217975842 \tabularnewline
59 & 5950 & 5832.48105763784 & 117.51894236216 \tabularnewline
60 & 5450 & 5737.82376069296 & -287.823760692964 \tabularnewline
61 & 5400 & 5658.45786898963 & -258.457868989633 \tabularnewline
62 & 5400 & 5475.86246247069 & -75.8624624706936 \tabularnewline
63 & 5450 & 5553.65371499818 & -103.653714998183 \tabularnewline
64 & 5700 & 5615.65820200651 & 84.3417979934866 \tabularnewline
65 & 5850 & 5792.44205010837 & 57.557949891635 \tabularnewline
66 & 5850 & 5675.96884978204 & 174.03115021796 \tabularnewline
67 & 5700 & 5642.60002357491 & 57.3999764250912 \tabularnewline
68 & 5450 & 5538.14333638552 & -88.1433363855185 \tabularnewline
69 & 5800 & 5718.71736946799 & 81.2826305320141 \tabularnewline
70 & 5600 & 5789.29196071785 & -189.291960717853 \tabularnewline
71 & 5700 & 5811.00938834859 & -111.009388348588 \tabularnewline
72 & 5800 & 5498.18200394037 & 301.817996059632 \tabularnewline
73 & 5750 & 5785.96626410707 & -35.9662641070727 \tabularnewline
74 & 5850 & 5774.94099472396 & 75.0590052760435 \tabularnewline
75 & 6250 & 5939.90608397219 & 310.09391602781 \tabularnewline
76 & 6450 & 6291.77498663363 & 158.225013366366 \tabularnewline
77 & 6550 & 6508.69646862363 & 41.3035313763721 \tabularnewline
78 & 6500 & 6404.68970946374 & 95.3102905362584 \tabularnewline
79 & 6150 & 6300.59705829701 & -150.597058297015 \tabularnewline
80 & 6100 & 6040.59236778696 & 59.4076322130377 \tabularnewline
81 & 6300 & 6344.25600725924 & -44.2560072592405 \tabularnewline
82 & 6350 & 6285.75594830904 & 64.2440516909564 \tabularnewline
83 & 6250 & 6477.98641248544 & -227.986412485439 \tabularnewline
84 & 6200 & 6172.94993064688 & 27.0500693531203 \tabularnewline
85 & 6250 & 6227.22687324794 & 22.7731267520612 \tabularnewline
86 & 6450 & 6273.59564850277 & 176.404351497225 \tabularnewline
87 & 6050 & 6545.95848765881 & -495.958487658811 \tabularnewline
88 & 6500 & 6374.40840098297 & 125.591599017027 \tabularnewline
89 & 6600 & 6548.80520360143 & 51.1947963985731 \tabularnewline
90 & 6450 & 6461.26371276361 & -11.2637127636062 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300330&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]4950[/C][C]4897.34241452992[/C][C]52.6575854700823[/C][/ROW]
[ROW][C]14[/C][C]4850[/C][C]4822.97481769511[/C][C]27.0251823048893[/C][/ROW]
[ROW][C]15[/C][C]5100[/C][C]5084.97597106735[/C][C]15.0240289326512[/C][/ROW]
[ROW][C]16[/C][C]5200[/C][C]5183.36951848029[/C][C]16.63048151971[/C][/ROW]
[ROW][C]17[/C][C]5450[/C][C]5422.33127499319[/C][C]27.6687250068117[/C][/ROW]
[ROW][C]18[/C][C]5150[/C][C]5105.56030157937[/C][C]44.439698420626[/C][/ROW]
[ROW][C]19[/C][C]5150[/C][C]4999.07119109202[/C][C]150.928808907984[/C][/ROW]
[ROW][C]20[/C][C]5000[/C][C]5076.61788186228[/C][C]-76.6178818622802[/C][/ROW]
[ROW][C]21[/C][C]5200[/C][C]5206.32807355326[/C][C]-6.32807355325713[/C][/ROW]
[ROW][C]22[/C][C]5350[/C][C]5266.63118277071[/C][C]83.3688172292914[/C][/ROW]
[ROW][C]23[/C][C]5600[/C][C]5421.50853808483[/C][C]178.491461915167[/C][/ROW]
[ROW][C]24[/C][C]5600[/C][C]5382.61986638587[/C][C]217.380133614134[/C][/ROW]
[ROW][C]25[/C][C]5650[/C][C]5575.63087414298[/C][C]74.3691258570225[/C][/ROW]
[ROW][C]26[/C][C]5550[/C][C]5509.63752374056[/C][C]40.3624762594436[/C][/ROW]
[ROW][C]27[/C][C]5700[/C][C]5777.5041307121[/C][C]-77.5041307120982[/C][/ROW]
[ROW][C]28[/C][C]5750[/C][C]5819.48037277903[/C][C]-69.480372779035[/C][/ROW]
[ROW][C]29[/C][C]5850[/C][C]6007.77558494884[/C][C]-157.775584948836[/C][/ROW]
[ROW][C]30[/C][C]5750[/C][C]5580.54328693954[/C][C]169.45671306046[/C][/ROW]
[ROW][C]31[/C][C]5700[/C][C]5571.20774842984[/C][C]128.792251570164[/C][/ROW]
[ROW][C]32[/C][C]5500[/C][C]5591.35976907304[/C][C]-91.3597690730394[/C][/ROW]
[ROW][C]33[/C][C]5750[/C][C]5725.5692201603[/C][C]24.4307798397003[/C][/ROW]
[ROW][C]34[/C][C]5750[/C][C]5822.00456825868[/C][C]-72.0045682586788[/C][/ROW]
[ROW][C]35[/C][C]5750[/C][C]5899.94610582585[/C][C]-149.946105825848[/C][/ROW]
[ROW][C]36[/C][C]5500[/C][C]5667.19018744153[/C][C]-167.190187441527[/C][/ROW]
[ROW][C]37[/C][C]5750[/C][C]5596.88823877454[/C][C]153.111761225463[/C][/ROW]
[ROW][C]38[/C][C]5750[/C][C]5572.62066866704[/C][C]177.379331332956[/C][/ROW]
[ROW][C]39[/C][C]5900[/C][C]5901.78889704226[/C][C]-1.78889704226094[/C][/ROW]
[ROW][C]40[/C][C]6000[/C][C]5991.72954731509[/C][C]8.2704526849102[/C][/ROW]
[ROW][C]41[/C][C]6150[/C][C]6210.68703143076[/C][C]-60.6870314307571[/C][/ROW]
[ROW][C]42[/C][C]5950[/C][C]5905.99907987089[/C][C]44.0009201291114[/C][/ROW]
[ROW][C]43[/C][C]5900[/C][C]5811.91815921335[/C][C]88.08184078665[/C][/ROW]
[ROW][C]44[/C][C]5750[/C][C]5764.71248858707[/C][C]-14.7124885870662[/C][/ROW]
[ROW][C]45[/C][C]5750[/C][C]5968.21260900591[/C][C]-218.212609005915[/C][/ROW]
[ROW][C]46[/C][C]5800[/C][C]5897.31686483855[/C][C]-97.3168648385536[/C][/ROW]
[ROW][C]47[/C][C]5800[/C][C]5944.72927869949[/C][C]-144.729278699487[/C][/ROW]
[ROW][C]48[/C][C]5450[/C][C]5711.85062197524[/C][C]-261.850621975237[/C][/ROW]
[ROW][C]49[/C][C]5400[/C][C]5645.20180861839[/C][C]-245.201808618391[/C][/ROW]
[ROW][C]50[/C][C]5600[/C][C]5381.41188507117[/C][C]218.588114928832[/C][/ROW]
[ROW][C]51[/C][C]5600[/C][C]5701.33810835299[/C][C]-101.338108352987[/C][/ROW]
[ROW][C]52[/C][C]5800[/C][C]5732.1849693234[/C][C]67.8150306766029[/C][/ROW]
[ROW][C]53[/C][C]5650[/C][C]5974.36719223618[/C][C]-324.367192236178[/C][/ROW]
[ROW][C]54[/C][C]5700[/C][C]5528.18544301059[/C][C]171.814556989415[/C][/ROW]
[ROW][C]55[/C][C]5550[/C][C]5520.95341659262[/C][C]29.0465834073821[/C][/ROW]
[ROW][C]56[/C][C]5350[/C][C]5417.75751280708[/C][C]-67.7575128070839[/C][/ROW]
[ROW][C]57[/C][C]5800[/C][C]5549.5448956972[/C][C]250.455104302804[/C][/ROW]
[ROW][C]58[/C][C]5700[/C][C]5789.26092179758[/C][C]-89.2609217975842[/C][/ROW]
[ROW][C]59[/C][C]5950[/C][C]5832.48105763784[/C][C]117.51894236216[/C][/ROW]
[ROW][C]60[/C][C]5450[/C][C]5737.82376069296[/C][C]-287.823760692964[/C][/ROW]
[ROW][C]61[/C][C]5400[/C][C]5658.45786898963[/C][C]-258.457868989633[/C][/ROW]
[ROW][C]62[/C][C]5400[/C][C]5475.86246247069[/C][C]-75.8624624706936[/C][/ROW]
[ROW][C]63[/C][C]5450[/C][C]5553.65371499818[/C][C]-103.653714998183[/C][/ROW]
[ROW][C]64[/C][C]5700[/C][C]5615.65820200651[/C][C]84.3417979934866[/C][/ROW]
[ROW][C]65[/C][C]5850[/C][C]5792.44205010837[/C][C]57.557949891635[/C][/ROW]
[ROW][C]66[/C][C]5850[/C][C]5675.96884978204[/C][C]174.03115021796[/C][/ROW]
[ROW][C]67[/C][C]5700[/C][C]5642.60002357491[/C][C]57.3999764250912[/C][/ROW]
[ROW][C]68[/C][C]5450[/C][C]5538.14333638552[/C][C]-88.1433363855185[/C][/ROW]
[ROW][C]69[/C][C]5800[/C][C]5718.71736946799[/C][C]81.2826305320141[/C][/ROW]
[ROW][C]70[/C][C]5600[/C][C]5789.29196071785[/C][C]-189.291960717853[/C][/ROW]
[ROW][C]71[/C][C]5700[/C][C]5811.00938834859[/C][C]-111.009388348588[/C][/ROW]
[ROW][C]72[/C][C]5800[/C][C]5498.18200394037[/C][C]301.817996059632[/C][/ROW]
[ROW][C]73[/C][C]5750[/C][C]5785.96626410707[/C][C]-35.9662641070727[/C][/ROW]
[ROW][C]74[/C][C]5850[/C][C]5774.94099472396[/C][C]75.0590052760435[/C][/ROW]
[ROW][C]75[/C][C]6250[/C][C]5939.90608397219[/C][C]310.09391602781[/C][/ROW]
[ROW][C]76[/C][C]6450[/C][C]6291.77498663363[/C][C]158.225013366366[/C][/ROW]
[ROW][C]77[/C][C]6550[/C][C]6508.69646862363[/C][C]41.3035313763721[/C][/ROW]
[ROW][C]78[/C][C]6500[/C][C]6404.68970946374[/C][C]95.3102905362584[/C][/ROW]
[ROW][C]79[/C][C]6150[/C][C]6300.59705829701[/C][C]-150.597058297015[/C][/ROW]
[ROW][C]80[/C][C]6100[/C][C]6040.59236778696[/C][C]59.4076322130377[/C][/ROW]
[ROW][C]81[/C][C]6300[/C][C]6344.25600725924[/C][C]-44.2560072592405[/C][/ROW]
[ROW][C]82[/C][C]6350[/C][C]6285.75594830904[/C][C]64.2440516909564[/C][/ROW]
[ROW][C]83[/C][C]6250[/C][C]6477.98641248544[/C][C]-227.986412485439[/C][/ROW]
[ROW][C]84[/C][C]6200[/C][C]6172.94993064688[/C][C]27.0500693531203[/C][/ROW]
[ROW][C]85[/C][C]6250[/C][C]6227.22687324794[/C][C]22.7731267520612[/C][/ROW]
[ROW][C]86[/C][C]6450[/C][C]6273.59564850277[/C][C]176.404351497225[/C][/ROW]
[ROW][C]87[/C][C]6050[/C][C]6545.95848765881[/C][C]-495.958487658811[/C][/ROW]
[ROW][C]88[/C][C]6500[/C][C]6374.40840098297[/C][C]125.591599017027[/C][/ROW]
[ROW][C]89[/C][C]6600[/C][C]6548.80520360143[/C][C]51.1947963985731[/C][/ROW]
[ROW][C]90[/C][C]6450[/C][C]6461.26371276361[/C][C]-11.2637127636062[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300330&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300330&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
1349504897.3424145299252.6575854700823
1448504822.9748176951127.0251823048893
1551005084.9759710673515.0240289326512
1652005183.3695184802916.63048151971
1754505422.3312749931927.6687250068117
1851505105.5603015793744.439698420626
1951504999.07119109202150.928808907984
2050005076.61788186228-76.6178818622802
2152005206.32807355326-6.32807355325713
2253505266.6311827707183.3688172292914
2356005421.50853808483178.491461915167
2456005382.61986638587217.380133614134
2556505575.6308741429874.3691258570225
2655505509.6375237405640.3624762594436
2757005777.5041307121-77.5041307120982
2857505819.48037277903-69.480372779035
2958506007.77558494884-157.775584948836
3057505580.54328693954169.45671306046
3157005571.20774842984128.792251570164
3255005591.35976907304-91.3597690730394
3357505725.569220160324.4307798397003
3457505822.00456825868-72.0045682586788
3557505899.94610582585-149.946105825848
3655005667.19018744153-167.190187441527
3757505596.88823877454153.111761225463
3857505572.62066866704177.379331332956
3959005901.78889704226-1.78889704226094
4060005991.729547315098.2704526849102
4161506210.68703143076-60.6870314307571
4259505905.9990798708944.0009201291114
4359005811.9181592133588.08184078665
4457505764.71248858707-14.7124885870662
4557505968.21260900591-218.212609005915
4658005897.31686483855-97.3168648385536
4758005944.72927869949-144.729278699487
4854505711.85062197524-261.850621975237
4954005645.20180861839-245.201808618391
5056005381.41188507117218.588114928832
5156005701.33810835299-101.338108352987
5258005732.184969323467.8150306766029
5356505974.36719223618-324.367192236178
5457005528.18544301059171.814556989415
5555505520.9534165926229.0465834073821
5653505417.75751280708-67.7575128070839
5758005549.5448956972250.455104302804
5857005789.26092179758-89.2609217975842
5959505832.48105763784117.51894236216
6054505737.82376069296-287.823760692964
6154005658.45786898963-258.457868989633
6254005475.86246247069-75.8624624706936
6354505553.65371499818-103.653714998183
6457005615.6582020065184.3417979934866
6558505792.4420501083757.557949891635
6658505675.96884978204174.03115021796
6757005642.6000235749157.3999764250912
6854505538.14333638552-88.1433363855185
6958005718.7173694679981.2826305320141
7056005789.29196071785-189.291960717853
7157005811.00938834859-111.009388348588
7258005498.18200394037301.817996059632
7357505785.96626410707-35.9662641070727
7458505774.9409947239675.0590052760435
7562505939.90608397219310.09391602781
7664506291.77498663363158.225013366366
7765506508.6964686236341.3035313763721
7865006404.6897094637495.3102905362584
7961506300.59705829701-150.597058297015
8061006040.5923677869659.4076322130377
8163006344.25600725924-44.2560072592405
8263506285.7559483090464.2440516909564
8362506477.98641248544-227.986412485439
8462006172.9499306468827.0500693531203
8562506227.2268732479422.7731267520612
8664506273.59564850277176.404351497225
8760506545.95848765881-495.958487658811
8865006374.40840098297125.591599017027
8966006548.8052036014351.1947963985731
9064506461.26371276361-11.2637127636062







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
916244.473826329395951.483748777866537.46390388091
926117.24129492625773.572446673866460.91014317854
936364.518986816255976.738934499826752.29903913267
946354.04724226215926.685029742126781.40945478208
956450.610516094155987.033605101586914.18742708672
966334.464353849685837.303772024396831.62493567496
976371.333879785045842.718957713886899.94880185619
986433.328917607015875.028973534176991.62886167985
996468.052064926185881.567692357597054.53643749478
1006720.266244623166106.891146512217333.64134273411
1016803.337881586596164.202447818397442.47331535478
1026672.381238170196008.484262417557336.27821392283

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
91 & 6244.47382632939 & 5951.48374877786 & 6537.46390388091 \tabularnewline
92 & 6117.2412949262 & 5773.57244667386 & 6460.91014317854 \tabularnewline
93 & 6364.51898681625 & 5976.73893449982 & 6752.29903913267 \tabularnewline
94 & 6354.0472422621 & 5926.68502974212 & 6781.40945478208 \tabularnewline
95 & 6450.61051609415 & 5987.03360510158 & 6914.18742708672 \tabularnewline
96 & 6334.46435384968 & 5837.30377202439 & 6831.62493567496 \tabularnewline
97 & 6371.33387978504 & 5842.71895771388 & 6899.94880185619 \tabularnewline
98 & 6433.32891760701 & 5875.02897353417 & 6991.62886167985 \tabularnewline
99 & 6468.05206492618 & 5881.56769235759 & 7054.53643749478 \tabularnewline
100 & 6720.26624462316 & 6106.89114651221 & 7333.64134273411 \tabularnewline
101 & 6803.33788158659 & 6164.20244781839 & 7442.47331535478 \tabularnewline
102 & 6672.38123817019 & 6008.48426241755 & 7336.27821392283 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300330&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]91[/C][C]6244.47382632939[/C][C]5951.48374877786[/C][C]6537.46390388091[/C][/ROW]
[ROW][C]92[/C][C]6117.2412949262[/C][C]5773.57244667386[/C][C]6460.91014317854[/C][/ROW]
[ROW][C]93[/C][C]6364.51898681625[/C][C]5976.73893449982[/C][C]6752.29903913267[/C][/ROW]
[ROW][C]94[/C][C]6354.0472422621[/C][C]5926.68502974212[/C][C]6781.40945478208[/C][/ROW]
[ROW][C]95[/C][C]6450.61051609415[/C][C]5987.03360510158[/C][C]6914.18742708672[/C][/ROW]
[ROW][C]96[/C][C]6334.46435384968[/C][C]5837.30377202439[/C][C]6831.62493567496[/C][/ROW]
[ROW][C]97[/C][C]6371.33387978504[/C][C]5842.71895771388[/C][C]6899.94880185619[/C][/ROW]
[ROW][C]98[/C][C]6433.32891760701[/C][C]5875.02897353417[/C][C]6991.62886167985[/C][/ROW]
[ROW][C]99[/C][C]6468.05206492618[/C][C]5881.56769235759[/C][C]7054.53643749478[/C][/ROW]
[ROW][C]100[/C][C]6720.26624462316[/C][C]6106.89114651221[/C][C]7333.64134273411[/C][/ROW]
[ROW][C]101[/C][C]6803.33788158659[/C][C]6164.20244781839[/C][C]7442.47331535478[/C][/ROW]
[ROW][C]102[/C][C]6672.38123817019[/C][C]6008.48426241755[/C][C]7336.27821392283[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300330&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300330&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
916244.473826329395951.483748777866537.46390388091
926117.24129492625773.572446673866460.91014317854
936364.518986816255976.738934499826752.29903913267
946354.04724226215926.685029742126781.40945478208
956450.610516094155987.033605101586914.18742708672
966334.464353849685837.303772024396831.62493567496
976371.333879785045842.718957713886899.94880185619
986433.328917607015875.028973534176991.62886167985
996468.052064926185881.567692357597054.53643749478
1006720.266244623166106.891146512217333.64134273411
1016803.337881586596164.202447818397442.47331535478
1026672.381238170196008.484262417557336.27821392283



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
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')