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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 15:33:21 +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/t1481898818jhebux1va30vebb.htm/, Retrieved Fri, 03 May 2024 00:54:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300313, Retrieved Fri, 03 May 2024 00:54:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
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 14:33:21] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataseries X:
5495
5365
5315
5335
5330
5365
5435
5535
5585
5615
5610
5585
5820
5645
5650
5725
5825
5870
5860
5835
5840
5805
5770
5680
5675
5690
5610
5610
5630
5615
5585
5555
5585
5530
5425
5630
5560
5435
5320
5150
5125
5025
5020
4935
4880
4870
4920
4935
5000
4955
4970
4990
4920
4930
4955
5000
5025
5075
5075
5105
5050
5055
5095
5025
5050
5035
4985
5005
4910
4910
4870
4850
4810
4810
4730
4850
4895
4845
4805
4825
4830
4720
4785
4705
4840
4820
4795
4810
4840
4810
4835
4860
4845
4935
4870
4830
4895
4920
4925
4860
4820
4790
4775
4735
4755
4745
4705
4665
4650
4590
4625
4685
4665
4675
4690
4600




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=300313&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=300313&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300313&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
alpha0.820831438265627
beta0.331692482058871
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.820831438265627 \tabularnewline
beta & 0.331692482058871 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300313&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]0.820831438265627[/C][/ROW]
[ROW][C]beta[/C][C]0.331692482058871[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300313&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300313&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
alpha0.820831438265627
beta0.331692482058871
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
35315523580
453355192.44760443007142.552395569928
553305240.0520125283789.9479874716271
653655268.9666330890596.0333669109514
754355329.02271624575105.977283754249
855355426.09483757339108.905162426614
955855555.2211672069829.778832793023
1056155627.5058106123-12.5058106122988
1156105661.67701212248-51.677012122479
1255855649.62548971655-64.6254897165491
1358205609.35028023598210.649719764022
1456455852.38187151843-207.381871518434
1556505695.81745202534-45.8174520253351
1657255659.3957621421165.6042378578868
1758255732.2941453166792.7058546833268
1858705852.6788189327717.3211810672337
1958605915.90130989136-55.9013098913638
2058355903.8005854508-68.8005854507983
2158405862.37983384606-22.3798338460583
2258055852.96948003315-47.9694800331536
2357705809.49399599106-39.4939959910616
2456805762.22267750257-82.222677502572
2556755657.4920703284517.5079296715476
2656905639.3902531406650.6097468593407
2756105662.23864090529-52.238640905287
2856105586.4431572919823.5568427080234
2956305579.276660710450.7233392895969
3056155608.219398417426.78060158258177
3155855602.93866664411-17.9386666441114
3255555572.48353611275-17.4835361127534
3355855537.6418602481147.3581397518883
3455305568.91816887146-38.9181688714607
3554255518.780169571-93.7801695710041
3656305398.07678714959231.923212850405
3755605607.86523339162-47.8652333916198
3854355574.96256531767-139.962565317667
3953205428.35679752501-108.356797525009
4051505278.19242393444-128.192423934443
4151255076.844211562848.1557884372032
4250255033.35922513245-8.35922513245077
4350204941.2090259593278.7909740406758
4449354942.04636570657-7.04636570656658
4548804870.507249397439.49275060256605
4648704815.1284903313554.8715096686501
4749204811.93755903488108.062440965123
4849354881.8288874281153.171112571893
4950004921.1402472226178.8597527773882
5049555003.00829203968-48.0082920396753
5149704967.668145917592.33185408240752
5249904974.2836533664515.7163466335496
5349204996.16456246873-76.1645624687271
5449304921.889893530078.11010646992872
5549554918.9986092283436.0013907716557
5650004948.8032368075751.196763192429
5750255005.0197197170319.9802802829681
5850755041.0526354430433.9473645569569
5950755097.79280530769-22.7928053076885
6051055101.753208317743.24679168226066
6150505127.97171442432-77.9717144243241
6250555066.2946563482-11.2946563481992
6350955056.2730997606438.7269002393587
6450255097.85473534977-72.8547353497706
6550505028.010962744321.9890372556965
6650355042.00475523713-7.00475523712794
6749855030.29239133946-45.2923913394607
6850054974.8208617384730.1791382615311
6949104989.51541767232-79.5154176723208
7049104892.5200782575817.4799217424197
7148704879.9007095201-9.90070952009955
7248504842.110854856887.88914514311637
7348104821.07139937598-11.0713993759846
7448104781.4541936265928.5458063734059
7547304782.1280203491-52.1280203490951
7648504702.38967047953147.610329520469
7748954826.7917598482968.2082401517127
7848454904.58874017962-59.5887401796226
7948054861.26209539924-56.2620953992364
8048254805.3479436389319.6520563610675
8148304817.0970542012712.9029457987263
8247204826.81928532825-106.819285328253
8347854709.186740286375.813259713701
8447054762.10592217982-57.1059221798178
8548404690.37299589549149.627004104506
8648204829.07094418486-9.07094418486122
8747954835.03493925569-40.0349392556873
8848104804.682656345535.31734365446664
8948404813.0046722619326.9953277380655
9048104846.47050460742-36.4705046074187
9148354817.9119950057817.0880049942189
9248604837.9684359207422.031564079256
9348454868.08109887644-23.0810988764433
9449354854.8797263472480.1202736527557
9548704948.20312037074-78.2031203707393
9648304890.27783074538-60.2778307453837
9748954830.6547221542464.3452778457622
9849204890.8450571193529.1549428806511
9949254930.08788902733-5.08788902732886
10048604939.83788089996-79.837880899956
10148204866.49377919719-46.4937791971897
10247904807.86099995543-17.8609999554274
10347754767.868005627157.13199437284857
10447354750.33182936508-15.3318293650809
10547554710.1823410354144.8176589645936
10647454731.6076616624313.3923383375659
10747054730.88433763857-25.8843376385712
10846654690.87411979094-25.8741197909412
10946504643.827707630056.17229236994899
11045904624.76648870094-34.7664887009414
11146254562.6357812566362.3642187433697
11246854597.2125198769287.7874801230828
11346654676.55880757622-11.5588075762234
11446754671.211496296773.78850370322652
11546904679.4932123300210.5067876699786
11646004696.15012306961-96.150123069614

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5315 & 5235 & 80 \tabularnewline
4 & 5335 & 5192.44760443007 & 142.552395569928 \tabularnewline
5 & 5330 & 5240.05201252837 & 89.9479874716271 \tabularnewline
6 & 5365 & 5268.96663308905 & 96.0333669109514 \tabularnewline
7 & 5435 & 5329.02271624575 & 105.977283754249 \tabularnewline
8 & 5535 & 5426.09483757339 & 108.905162426614 \tabularnewline
9 & 5585 & 5555.22116720698 & 29.778832793023 \tabularnewline
10 & 5615 & 5627.5058106123 & -12.5058106122988 \tabularnewline
11 & 5610 & 5661.67701212248 & -51.677012122479 \tabularnewline
12 & 5585 & 5649.62548971655 & -64.6254897165491 \tabularnewline
13 & 5820 & 5609.35028023598 & 210.649719764022 \tabularnewline
14 & 5645 & 5852.38187151843 & -207.381871518434 \tabularnewline
15 & 5650 & 5695.81745202534 & -45.8174520253351 \tabularnewline
16 & 5725 & 5659.39576214211 & 65.6042378578868 \tabularnewline
17 & 5825 & 5732.29414531667 & 92.7058546833268 \tabularnewline
18 & 5870 & 5852.67881893277 & 17.3211810672337 \tabularnewline
19 & 5860 & 5915.90130989136 & -55.9013098913638 \tabularnewline
20 & 5835 & 5903.8005854508 & -68.8005854507983 \tabularnewline
21 & 5840 & 5862.37983384606 & -22.3798338460583 \tabularnewline
22 & 5805 & 5852.96948003315 & -47.9694800331536 \tabularnewline
23 & 5770 & 5809.49399599106 & -39.4939959910616 \tabularnewline
24 & 5680 & 5762.22267750257 & -82.222677502572 \tabularnewline
25 & 5675 & 5657.49207032845 & 17.5079296715476 \tabularnewline
26 & 5690 & 5639.39025314066 & 50.6097468593407 \tabularnewline
27 & 5610 & 5662.23864090529 & -52.238640905287 \tabularnewline
28 & 5610 & 5586.44315729198 & 23.5568427080234 \tabularnewline
29 & 5630 & 5579.2766607104 & 50.7233392895969 \tabularnewline
30 & 5615 & 5608.21939841742 & 6.78060158258177 \tabularnewline
31 & 5585 & 5602.93866664411 & -17.9386666441114 \tabularnewline
32 & 5555 & 5572.48353611275 & -17.4835361127534 \tabularnewline
33 & 5585 & 5537.64186024811 & 47.3581397518883 \tabularnewline
34 & 5530 & 5568.91816887146 & -38.9181688714607 \tabularnewline
35 & 5425 & 5518.780169571 & -93.7801695710041 \tabularnewline
36 & 5630 & 5398.07678714959 & 231.923212850405 \tabularnewline
37 & 5560 & 5607.86523339162 & -47.8652333916198 \tabularnewline
38 & 5435 & 5574.96256531767 & -139.962565317667 \tabularnewline
39 & 5320 & 5428.35679752501 & -108.356797525009 \tabularnewline
40 & 5150 & 5278.19242393444 & -128.192423934443 \tabularnewline
41 & 5125 & 5076.8442115628 & 48.1557884372032 \tabularnewline
42 & 5025 & 5033.35922513245 & -8.35922513245077 \tabularnewline
43 & 5020 & 4941.20902595932 & 78.7909740406758 \tabularnewline
44 & 4935 & 4942.04636570657 & -7.04636570656658 \tabularnewline
45 & 4880 & 4870.50724939743 & 9.49275060256605 \tabularnewline
46 & 4870 & 4815.12849033135 & 54.8715096686501 \tabularnewline
47 & 4920 & 4811.93755903488 & 108.062440965123 \tabularnewline
48 & 4935 & 4881.82888742811 & 53.171112571893 \tabularnewline
49 & 5000 & 4921.14024722261 & 78.8597527773882 \tabularnewline
50 & 4955 & 5003.00829203968 & -48.0082920396753 \tabularnewline
51 & 4970 & 4967.66814591759 & 2.33185408240752 \tabularnewline
52 & 4990 & 4974.28365336645 & 15.7163466335496 \tabularnewline
53 & 4920 & 4996.16456246873 & -76.1645624687271 \tabularnewline
54 & 4930 & 4921.88989353007 & 8.11010646992872 \tabularnewline
55 & 4955 & 4918.99860922834 & 36.0013907716557 \tabularnewline
56 & 5000 & 4948.80323680757 & 51.196763192429 \tabularnewline
57 & 5025 & 5005.01971971703 & 19.9802802829681 \tabularnewline
58 & 5075 & 5041.05263544304 & 33.9473645569569 \tabularnewline
59 & 5075 & 5097.79280530769 & -22.7928053076885 \tabularnewline
60 & 5105 & 5101.75320831774 & 3.24679168226066 \tabularnewline
61 & 5050 & 5127.97171442432 & -77.9717144243241 \tabularnewline
62 & 5055 & 5066.2946563482 & -11.2946563481992 \tabularnewline
63 & 5095 & 5056.27309976064 & 38.7269002393587 \tabularnewline
64 & 5025 & 5097.85473534977 & -72.8547353497706 \tabularnewline
65 & 5050 & 5028.0109627443 & 21.9890372556965 \tabularnewline
66 & 5035 & 5042.00475523713 & -7.00475523712794 \tabularnewline
67 & 4985 & 5030.29239133946 & -45.2923913394607 \tabularnewline
68 & 5005 & 4974.82086173847 & 30.1791382615311 \tabularnewline
69 & 4910 & 4989.51541767232 & -79.5154176723208 \tabularnewline
70 & 4910 & 4892.52007825758 & 17.4799217424197 \tabularnewline
71 & 4870 & 4879.9007095201 & -9.90070952009955 \tabularnewline
72 & 4850 & 4842.11085485688 & 7.88914514311637 \tabularnewline
73 & 4810 & 4821.07139937598 & -11.0713993759846 \tabularnewline
74 & 4810 & 4781.45419362659 & 28.5458063734059 \tabularnewline
75 & 4730 & 4782.1280203491 & -52.1280203490951 \tabularnewline
76 & 4850 & 4702.38967047953 & 147.610329520469 \tabularnewline
77 & 4895 & 4826.79175984829 & 68.2082401517127 \tabularnewline
78 & 4845 & 4904.58874017962 & -59.5887401796226 \tabularnewline
79 & 4805 & 4861.26209539924 & -56.2620953992364 \tabularnewline
80 & 4825 & 4805.34794363893 & 19.6520563610675 \tabularnewline
81 & 4830 & 4817.09705420127 & 12.9029457987263 \tabularnewline
82 & 4720 & 4826.81928532825 & -106.819285328253 \tabularnewline
83 & 4785 & 4709.1867402863 & 75.813259713701 \tabularnewline
84 & 4705 & 4762.10592217982 & -57.1059221798178 \tabularnewline
85 & 4840 & 4690.37299589549 & 149.627004104506 \tabularnewline
86 & 4820 & 4829.07094418486 & -9.07094418486122 \tabularnewline
87 & 4795 & 4835.03493925569 & -40.0349392556873 \tabularnewline
88 & 4810 & 4804.68265634553 & 5.31734365446664 \tabularnewline
89 & 4840 & 4813.00467226193 & 26.9953277380655 \tabularnewline
90 & 4810 & 4846.47050460742 & -36.4705046074187 \tabularnewline
91 & 4835 & 4817.91199500578 & 17.0880049942189 \tabularnewline
92 & 4860 & 4837.96843592074 & 22.031564079256 \tabularnewline
93 & 4845 & 4868.08109887644 & -23.0810988764433 \tabularnewline
94 & 4935 & 4854.87972634724 & 80.1202736527557 \tabularnewline
95 & 4870 & 4948.20312037074 & -78.2031203707393 \tabularnewline
96 & 4830 & 4890.27783074538 & -60.2778307453837 \tabularnewline
97 & 4895 & 4830.65472215424 & 64.3452778457622 \tabularnewline
98 & 4920 & 4890.84505711935 & 29.1549428806511 \tabularnewline
99 & 4925 & 4930.08788902733 & -5.08788902732886 \tabularnewline
100 & 4860 & 4939.83788089996 & -79.837880899956 \tabularnewline
101 & 4820 & 4866.49377919719 & -46.4937791971897 \tabularnewline
102 & 4790 & 4807.86099995543 & -17.8609999554274 \tabularnewline
103 & 4775 & 4767.86800562715 & 7.13199437284857 \tabularnewline
104 & 4735 & 4750.33182936508 & -15.3318293650809 \tabularnewline
105 & 4755 & 4710.18234103541 & 44.8176589645936 \tabularnewline
106 & 4745 & 4731.60766166243 & 13.3923383375659 \tabularnewline
107 & 4705 & 4730.88433763857 & -25.8843376385712 \tabularnewline
108 & 4665 & 4690.87411979094 & -25.8741197909412 \tabularnewline
109 & 4650 & 4643.82770763005 & 6.17229236994899 \tabularnewline
110 & 4590 & 4624.76648870094 & -34.7664887009414 \tabularnewline
111 & 4625 & 4562.63578125663 & 62.3642187433697 \tabularnewline
112 & 4685 & 4597.21251987692 & 87.7874801230828 \tabularnewline
113 & 4665 & 4676.55880757622 & -11.5588075762234 \tabularnewline
114 & 4675 & 4671.21149629677 & 3.78850370322652 \tabularnewline
115 & 4690 & 4679.49321233002 & 10.5067876699786 \tabularnewline
116 & 4600 & 4696.15012306961 & -96.150123069614 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300313&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]5315[/C][C]5235[/C][C]80[/C][/ROW]
[ROW][C]4[/C][C]5335[/C][C]5192.44760443007[/C][C]142.552395569928[/C][/ROW]
[ROW][C]5[/C][C]5330[/C][C]5240.05201252837[/C][C]89.9479874716271[/C][/ROW]
[ROW][C]6[/C][C]5365[/C][C]5268.96663308905[/C][C]96.0333669109514[/C][/ROW]
[ROW][C]7[/C][C]5435[/C][C]5329.02271624575[/C][C]105.977283754249[/C][/ROW]
[ROW][C]8[/C][C]5535[/C][C]5426.09483757339[/C][C]108.905162426614[/C][/ROW]
[ROW][C]9[/C][C]5585[/C][C]5555.22116720698[/C][C]29.778832793023[/C][/ROW]
[ROW][C]10[/C][C]5615[/C][C]5627.5058106123[/C][C]-12.5058106122988[/C][/ROW]
[ROW][C]11[/C][C]5610[/C][C]5661.67701212248[/C][C]-51.677012122479[/C][/ROW]
[ROW][C]12[/C][C]5585[/C][C]5649.62548971655[/C][C]-64.6254897165491[/C][/ROW]
[ROW][C]13[/C][C]5820[/C][C]5609.35028023598[/C][C]210.649719764022[/C][/ROW]
[ROW][C]14[/C][C]5645[/C][C]5852.38187151843[/C][C]-207.381871518434[/C][/ROW]
[ROW][C]15[/C][C]5650[/C][C]5695.81745202534[/C][C]-45.8174520253351[/C][/ROW]
[ROW][C]16[/C][C]5725[/C][C]5659.39576214211[/C][C]65.6042378578868[/C][/ROW]
[ROW][C]17[/C][C]5825[/C][C]5732.29414531667[/C][C]92.7058546833268[/C][/ROW]
[ROW][C]18[/C][C]5870[/C][C]5852.67881893277[/C][C]17.3211810672337[/C][/ROW]
[ROW][C]19[/C][C]5860[/C][C]5915.90130989136[/C][C]-55.9013098913638[/C][/ROW]
[ROW][C]20[/C][C]5835[/C][C]5903.8005854508[/C][C]-68.8005854507983[/C][/ROW]
[ROW][C]21[/C][C]5840[/C][C]5862.37983384606[/C][C]-22.3798338460583[/C][/ROW]
[ROW][C]22[/C][C]5805[/C][C]5852.96948003315[/C][C]-47.9694800331536[/C][/ROW]
[ROW][C]23[/C][C]5770[/C][C]5809.49399599106[/C][C]-39.4939959910616[/C][/ROW]
[ROW][C]24[/C][C]5680[/C][C]5762.22267750257[/C][C]-82.222677502572[/C][/ROW]
[ROW][C]25[/C][C]5675[/C][C]5657.49207032845[/C][C]17.5079296715476[/C][/ROW]
[ROW][C]26[/C][C]5690[/C][C]5639.39025314066[/C][C]50.6097468593407[/C][/ROW]
[ROW][C]27[/C][C]5610[/C][C]5662.23864090529[/C][C]-52.238640905287[/C][/ROW]
[ROW][C]28[/C][C]5610[/C][C]5586.44315729198[/C][C]23.5568427080234[/C][/ROW]
[ROW][C]29[/C][C]5630[/C][C]5579.2766607104[/C][C]50.7233392895969[/C][/ROW]
[ROW][C]30[/C][C]5615[/C][C]5608.21939841742[/C][C]6.78060158258177[/C][/ROW]
[ROW][C]31[/C][C]5585[/C][C]5602.93866664411[/C][C]-17.9386666441114[/C][/ROW]
[ROW][C]32[/C][C]5555[/C][C]5572.48353611275[/C][C]-17.4835361127534[/C][/ROW]
[ROW][C]33[/C][C]5585[/C][C]5537.64186024811[/C][C]47.3581397518883[/C][/ROW]
[ROW][C]34[/C][C]5530[/C][C]5568.91816887146[/C][C]-38.9181688714607[/C][/ROW]
[ROW][C]35[/C][C]5425[/C][C]5518.780169571[/C][C]-93.7801695710041[/C][/ROW]
[ROW][C]36[/C][C]5630[/C][C]5398.07678714959[/C][C]231.923212850405[/C][/ROW]
[ROW][C]37[/C][C]5560[/C][C]5607.86523339162[/C][C]-47.8652333916198[/C][/ROW]
[ROW][C]38[/C][C]5435[/C][C]5574.96256531767[/C][C]-139.962565317667[/C][/ROW]
[ROW][C]39[/C][C]5320[/C][C]5428.35679752501[/C][C]-108.356797525009[/C][/ROW]
[ROW][C]40[/C][C]5150[/C][C]5278.19242393444[/C][C]-128.192423934443[/C][/ROW]
[ROW][C]41[/C][C]5125[/C][C]5076.8442115628[/C][C]48.1557884372032[/C][/ROW]
[ROW][C]42[/C][C]5025[/C][C]5033.35922513245[/C][C]-8.35922513245077[/C][/ROW]
[ROW][C]43[/C][C]5020[/C][C]4941.20902595932[/C][C]78.7909740406758[/C][/ROW]
[ROW][C]44[/C][C]4935[/C][C]4942.04636570657[/C][C]-7.04636570656658[/C][/ROW]
[ROW][C]45[/C][C]4880[/C][C]4870.50724939743[/C][C]9.49275060256605[/C][/ROW]
[ROW][C]46[/C][C]4870[/C][C]4815.12849033135[/C][C]54.8715096686501[/C][/ROW]
[ROW][C]47[/C][C]4920[/C][C]4811.93755903488[/C][C]108.062440965123[/C][/ROW]
[ROW][C]48[/C][C]4935[/C][C]4881.82888742811[/C][C]53.171112571893[/C][/ROW]
[ROW][C]49[/C][C]5000[/C][C]4921.14024722261[/C][C]78.8597527773882[/C][/ROW]
[ROW][C]50[/C][C]4955[/C][C]5003.00829203968[/C][C]-48.0082920396753[/C][/ROW]
[ROW][C]51[/C][C]4970[/C][C]4967.66814591759[/C][C]2.33185408240752[/C][/ROW]
[ROW][C]52[/C][C]4990[/C][C]4974.28365336645[/C][C]15.7163466335496[/C][/ROW]
[ROW][C]53[/C][C]4920[/C][C]4996.16456246873[/C][C]-76.1645624687271[/C][/ROW]
[ROW][C]54[/C][C]4930[/C][C]4921.88989353007[/C][C]8.11010646992872[/C][/ROW]
[ROW][C]55[/C][C]4955[/C][C]4918.99860922834[/C][C]36.0013907716557[/C][/ROW]
[ROW][C]56[/C][C]5000[/C][C]4948.80323680757[/C][C]51.196763192429[/C][/ROW]
[ROW][C]57[/C][C]5025[/C][C]5005.01971971703[/C][C]19.9802802829681[/C][/ROW]
[ROW][C]58[/C][C]5075[/C][C]5041.05263544304[/C][C]33.9473645569569[/C][/ROW]
[ROW][C]59[/C][C]5075[/C][C]5097.79280530769[/C][C]-22.7928053076885[/C][/ROW]
[ROW][C]60[/C][C]5105[/C][C]5101.75320831774[/C][C]3.24679168226066[/C][/ROW]
[ROW][C]61[/C][C]5050[/C][C]5127.97171442432[/C][C]-77.9717144243241[/C][/ROW]
[ROW][C]62[/C][C]5055[/C][C]5066.2946563482[/C][C]-11.2946563481992[/C][/ROW]
[ROW][C]63[/C][C]5095[/C][C]5056.27309976064[/C][C]38.7269002393587[/C][/ROW]
[ROW][C]64[/C][C]5025[/C][C]5097.85473534977[/C][C]-72.8547353497706[/C][/ROW]
[ROW][C]65[/C][C]5050[/C][C]5028.0109627443[/C][C]21.9890372556965[/C][/ROW]
[ROW][C]66[/C][C]5035[/C][C]5042.00475523713[/C][C]-7.00475523712794[/C][/ROW]
[ROW][C]67[/C][C]4985[/C][C]5030.29239133946[/C][C]-45.2923913394607[/C][/ROW]
[ROW][C]68[/C][C]5005[/C][C]4974.82086173847[/C][C]30.1791382615311[/C][/ROW]
[ROW][C]69[/C][C]4910[/C][C]4989.51541767232[/C][C]-79.5154176723208[/C][/ROW]
[ROW][C]70[/C][C]4910[/C][C]4892.52007825758[/C][C]17.4799217424197[/C][/ROW]
[ROW][C]71[/C][C]4870[/C][C]4879.9007095201[/C][C]-9.90070952009955[/C][/ROW]
[ROW][C]72[/C][C]4850[/C][C]4842.11085485688[/C][C]7.88914514311637[/C][/ROW]
[ROW][C]73[/C][C]4810[/C][C]4821.07139937598[/C][C]-11.0713993759846[/C][/ROW]
[ROW][C]74[/C][C]4810[/C][C]4781.45419362659[/C][C]28.5458063734059[/C][/ROW]
[ROW][C]75[/C][C]4730[/C][C]4782.1280203491[/C][C]-52.1280203490951[/C][/ROW]
[ROW][C]76[/C][C]4850[/C][C]4702.38967047953[/C][C]147.610329520469[/C][/ROW]
[ROW][C]77[/C][C]4895[/C][C]4826.79175984829[/C][C]68.2082401517127[/C][/ROW]
[ROW][C]78[/C][C]4845[/C][C]4904.58874017962[/C][C]-59.5887401796226[/C][/ROW]
[ROW][C]79[/C][C]4805[/C][C]4861.26209539924[/C][C]-56.2620953992364[/C][/ROW]
[ROW][C]80[/C][C]4825[/C][C]4805.34794363893[/C][C]19.6520563610675[/C][/ROW]
[ROW][C]81[/C][C]4830[/C][C]4817.09705420127[/C][C]12.9029457987263[/C][/ROW]
[ROW][C]82[/C][C]4720[/C][C]4826.81928532825[/C][C]-106.819285328253[/C][/ROW]
[ROW][C]83[/C][C]4785[/C][C]4709.1867402863[/C][C]75.813259713701[/C][/ROW]
[ROW][C]84[/C][C]4705[/C][C]4762.10592217982[/C][C]-57.1059221798178[/C][/ROW]
[ROW][C]85[/C][C]4840[/C][C]4690.37299589549[/C][C]149.627004104506[/C][/ROW]
[ROW][C]86[/C][C]4820[/C][C]4829.07094418486[/C][C]-9.07094418486122[/C][/ROW]
[ROW][C]87[/C][C]4795[/C][C]4835.03493925569[/C][C]-40.0349392556873[/C][/ROW]
[ROW][C]88[/C][C]4810[/C][C]4804.68265634553[/C][C]5.31734365446664[/C][/ROW]
[ROW][C]89[/C][C]4840[/C][C]4813.00467226193[/C][C]26.9953277380655[/C][/ROW]
[ROW][C]90[/C][C]4810[/C][C]4846.47050460742[/C][C]-36.4705046074187[/C][/ROW]
[ROW][C]91[/C][C]4835[/C][C]4817.91199500578[/C][C]17.0880049942189[/C][/ROW]
[ROW][C]92[/C][C]4860[/C][C]4837.96843592074[/C][C]22.031564079256[/C][/ROW]
[ROW][C]93[/C][C]4845[/C][C]4868.08109887644[/C][C]-23.0810988764433[/C][/ROW]
[ROW][C]94[/C][C]4935[/C][C]4854.87972634724[/C][C]80.1202736527557[/C][/ROW]
[ROW][C]95[/C][C]4870[/C][C]4948.20312037074[/C][C]-78.2031203707393[/C][/ROW]
[ROW][C]96[/C][C]4830[/C][C]4890.27783074538[/C][C]-60.2778307453837[/C][/ROW]
[ROW][C]97[/C][C]4895[/C][C]4830.65472215424[/C][C]64.3452778457622[/C][/ROW]
[ROW][C]98[/C][C]4920[/C][C]4890.84505711935[/C][C]29.1549428806511[/C][/ROW]
[ROW][C]99[/C][C]4925[/C][C]4930.08788902733[/C][C]-5.08788902732886[/C][/ROW]
[ROW][C]100[/C][C]4860[/C][C]4939.83788089996[/C][C]-79.837880899956[/C][/ROW]
[ROW][C]101[/C][C]4820[/C][C]4866.49377919719[/C][C]-46.4937791971897[/C][/ROW]
[ROW][C]102[/C][C]4790[/C][C]4807.86099995543[/C][C]-17.8609999554274[/C][/ROW]
[ROW][C]103[/C][C]4775[/C][C]4767.86800562715[/C][C]7.13199437284857[/C][/ROW]
[ROW][C]104[/C][C]4735[/C][C]4750.33182936508[/C][C]-15.3318293650809[/C][/ROW]
[ROW][C]105[/C][C]4755[/C][C]4710.18234103541[/C][C]44.8176589645936[/C][/ROW]
[ROW][C]106[/C][C]4745[/C][C]4731.60766166243[/C][C]13.3923383375659[/C][/ROW]
[ROW][C]107[/C][C]4705[/C][C]4730.88433763857[/C][C]-25.8843376385712[/C][/ROW]
[ROW][C]108[/C][C]4665[/C][C]4690.87411979094[/C][C]-25.8741197909412[/C][/ROW]
[ROW][C]109[/C][C]4650[/C][C]4643.82770763005[/C][C]6.17229236994899[/C][/ROW]
[ROW][C]110[/C][C]4590[/C][C]4624.76648870094[/C][C]-34.7664887009414[/C][/ROW]
[ROW][C]111[/C][C]4625[/C][C]4562.63578125663[/C][C]62.3642187433697[/C][/ROW]
[ROW][C]112[/C][C]4685[/C][C]4597.21251987692[/C][C]87.7874801230828[/C][/ROW]
[ROW][C]113[/C][C]4665[/C][C]4676.55880757622[/C][C]-11.5588075762234[/C][/ROW]
[ROW][C]114[/C][C]4675[/C][C]4671.21149629677[/C][C]3.78850370322652[/C][/ROW]
[ROW][C]115[/C][C]4690[/C][C]4679.49321233002[/C][C]10.5067876699786[/C][/ROW]
[ROW][C]116[/C][C]4600[/C][C]4696.15012306961[/C][C]-96.150123069614[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300313&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300313&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
35315523580
453355192.44760443007142.552395569928
553305240.0520125283789.9479874716271
653655268.9666330890596.0333669109514
754355329.02271624575105.977283754249
855355426.09483757339108.905162426614
955855555.2211672069829.778832793023
1056155627.5058106123-12.5058106122988
1156105661.67701212248-51.677012122479
1255855649.62548971655-64.6254897165491
1358205609.35028023598210.649719764022
1456455852.38187151843-207.381871518434
1556505695.81745202534-45.8174520253351
1657255659.3957621421165.6042378578868
1758255732.2941453166792.7058546833268
1858705852.6788189327717.3211810672337
1958605915.90130989136-55.9013098913638
2058355903.8005854508-68.8005854507983
2158405862.37983384606-22.3798338460583
2258055852.96948003315-47.9694800331536
2357705809.49399599106-39.4939959910616
2456805762.22267750257-82.222677502572
2556755657.4920703284517.5079296715476
2656905639.3902531406650.6097468593407
2756105662.23864090529-52.238640905287
2856105586.4431572919823.5568427080234
2956305579.276660710450.7233392895969
3056155608.219398417426.78060158258177
3155855602.93866664411-17.9386666441114
3255555572.48353611275-17.4835361127534
3355855537.6418602481147.3581397518883
3455305568.91816887146-38.9181688714607
3554255518.780169571-93.7801695710041
3656305398.07678714959231.923212850405
3755605607.86523339162-47.8652333916198
3854355574.96256531767-139.962565317667
3953205428.35679752501-108.356797525009
4051505278.19242393444-128.192423934443
4151255076.844211562848.1557884372032
4250255033.35922513245-8.35922513245077
4350204941.2090259593278.7909740406758
4449354942.04636570657-7.04636570656658
4548804870.507249397439.49275060256605
4648704815.1284903313554.8715096686501
4749204811.93755903488108.062440965123
4849354881.8288874281153.171112571893
4950004921.1402472226178.8597527773882
5049555003.00829203968-48.0082920396753
5149704967.668145917592.33185408240752
5249904974.2836533664515.7163466335496
5349204996.16456246873-76.1645624687271
5449304921.889893530078.11010646992872
5549554918.9986092283436.0013907716557
5650004948.8032368075751.196763192429
5750255005.0197197170319.9802802829681
5850755041.0526354430433.9473645569569
5950755097.79280530769-22.7928053076885
6051055101.753208317743.24679168226066
6150505127.97171442432-77.9717144243241
6250555066.2946563482-11.2946563481992
6350955056.2730997606438.7269002393587
6450255097.85473534977-72.8547353497706
6550505028.010962744321.9890372556965
6650355042.00475523713-7.00475523712794
6749855030.29239133946-45.2923913394607
6850054974.8208617384730.1791382615311
6949104989.51541767232-79.5154176723208
7049104892.5200782575817.4799217424197
7148704879.9007095201-9.90070952009955
7248504842.110854856887.88914514311637
7348104821.07139937598-11.0713993759846
7448104781.4541936265928.5458063734059
7547304782.1280203491-52.1280203490951
7648504702.38967047953147.610329520469
7748954826.7917598482968.2082401517127
7848454904.58874017962-59.5887401796226
7948054861.26209539924-56.2620953992364
8048254805.3479436389319.6520563610675
8148304817.0970542012712.9029457987263
8247204826.81928532825-106.819285328253
8347854709.186740286375.813259713701
8447054762.10592217982-57.1059221798178
8548404690.37299589549149.627004104506
8648204829.07094418486-9.07094418486122
8747954835.03493925569-40.0349392556873
8848104804.682656345535.31734365446664
8948404813.0046722619326.9953277380655
9048104846.47050460742-36.4705046074187
9148354817.9119950057817.0880049942189
9248604837.9684359207422.031564079256
9348454868.08109887644-23.0810988764433
9449354854.8797263472480.1202736527557
9548704948.20312037074-78.2031203707393
9648304890.27783074538-60.2778307453837
9748954830.6547221542464.3452778457622
9849204890.8450571193529.1549428806511
9949254930.08788902733-5.08788902732886
10048604939.83788089996-79.837880899956
10148204866.49377919719-46.4937791971897
10247904807.86099995543-17.8609999554274
10347754767.868005627157.13199437284857
10447354750.33182936508-15.3318293650809
10547554710.1823410354144.8176589645936
10647454731.6076616624313.3923383375659
10747054730.88433763857-25.8843376385712
10846654690.87411979094-25.8741197909412
10946504643.827707630056.17229236994899
11045904624.76648870094-34.7664887009414
11146254562.6357812566362.3642187433697
11246854597.2125198769287.7874801230828
11346654676.55880757622-11.5588075762234
11446754671.211496296773.78850370322652
11546904679.4932123300210.5067876699786
11646004696.15012306961-96.150123069614







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174599.081508073334464.519358203864733.6436579428
1184580.935936885694381.58145107524780.29042269617
1194562.790365698054291.686499093184833.89423230292
1204544.644794510414195.278644263844894.01094475697
1214526.499223322774092.788650823884960.20979582166
1224508.353652135133984.592049781255032.11525448901
1234490.208080947493871.010841385135109.40532050985
1244472.062509759853752.32205294515191.8029665746
1254453.916938572213628.766058116015279.06781902841
1264435.771367384573500.553413728085370.98932104106
1274417.625796196933367.870248708925467.38134368494
1284399.480225009293230.882479943245568.07797007534

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 4599.08150807333 & 4464.51935820386 & 4733.6436579428 \tabularnewline
118 & 4580.93593688569 & 4381.5814510752 & 4780.29042269617 \tabularnewline
119 & 4562.79036569805 & 4291.68649909318 & 4833.89423230292 \tabularnewline
120 & 4544.64479451041 & 4195.27864426384 & 4894.01094475697 \tabularnewline
121 & 4526.49922332277 & 4092.78865082388 & 4960.20979582166 \tabularnewline
122 & 4508.35365213513 & 3984.59204978125 & 5032.11525448901 \tabularnewline
123 & 4490.20808094749 & 3871.01084138513 & 5109.40532050985 \tabularnewline
124 & 4472.06250975985 & 3752.3220529451 & 5191.8029665746 \tabularnewline
125 & 4453.91693857221 & 3628.76605811601 & 5279.06781902841 \tabularnewline
126 & 4435.77136738457 & 3500.55341372808 & 5370.98932104106 \tabularnewline
127 & 4417.62579619693 & 3367.87024870892 & 5467.38134368494 \tabularnewline
128 & 4399.48022500929 & 3230.88247994324 & 5568.07797007534 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300313&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]117[/C][C]4599.08150807333[/C][C]4464.51935820386[/C][C]4733.6436579428[/C][/ROW]
[ROW][C]118[/C][C]4580.93593688569[/C][C]4381.5814510752[/C][C]4780.29042269617[/C][/ROW]
[ROW][C]119[/C][C]4562.79036569805[/C][C]4291.68649909318[/C][C]4833.89423230292[/C][/ROW]
[ROW][C]120[/C][C]4544.64479451041[/C][C]4195.27864426384[/C][C]4894.01094475697[/C][/ROW]
[ROW][C]121[/C][C]4526.49922332277[/C][C]4092.78865082388[/C][C]4960.20979582166[/C][/ROW]
[ROW][C]122[/C][C]4508.35365213513[/C][C]3984.59204978125[/C][C]5032.11525448901[/C][/ROW]
[ROW][C]123[/C][C]4490.20808094749[/C][C]3871.01084138513[/C][C]5109.40532050985[/C][/ROW]
[ROW][C]124[/C][C]4472.06250975985[/C][C]3752.3220529451[/C][C]5191.8029665746[/C][/ROW]
[ROW][C]125[/C][C]4453.91693857221[/C][C]3628.76605811601[/C][C]5279.06781902841[/C][/ROW]
[ROW][C]126[/C][C]4435.77136738457[/C][C]3500.55341372808[/C][C]5370.98932104106[/C][/ROW]
[ROW][C]127[/C][C]4417.62579619693[/C][C]3367.87024870892[/C][C]5467.38134368494[/C][/ROW]
[ROW][C]128[/C][C]4399.48022500929[/C][C]3230.88247994324[/C][C]5568.07797007534[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300313&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300313&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
1174599.081508073334464.519358203864733.6436579428
1184580.935936885694381.58145107524780.29042269617
1194562.790365698054291.686499093184833.89423230292
1204544.644794510414195.278644263844894.01094475697
1214526.499223322774092.788650823884960.20979582166
1224508.353652135133984.592049781255032.11525448901
1234490.208080947493871.010841385135109.40532050985
1244472.062509759853752.32205294515191.8029665746
1254453.916938572213628.766058116015279.06781902841
1264435.771367384573500.553413728085370.98932104106
1274417.625796196933367.870248708925467.38134368494
1284399.480225009293230.882479943245568.07797007534



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 = Double ; 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')