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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, 09 Dec 2016 17:00:59 +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/09/t1481299274rg9c4w4dxhk7sox.htm/, Retrieved Tue, 21 May 2024 02:13:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298583, Retrieved Tue, 21 May 2024 02:13:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Autocorr eerste] [2016-12-07 13:39:31] [5f979cb1c6fa86b57093c7542788c28c]
- RM D    [Exponential Smoothing] [Double] [2016-12-09 16:00:59] [4c05fa0998bf98e29c2e453b139976f4] [Current]
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Dataseries X:
5345
5245
5100
5070
5035
5050
5065
5255
5335
5440
5490
5445
5675
5615
5545
5510
5570
5610
5555
5630
5685
5545
5625
5570
5555
5635
5535
5430
5400
5410
5255
5350
5405
5420
5430
5580
5595
5485
5295
5055
4975
4895
4795
4855
4785
4875
5010
4970
4995
5020
4950
4880
4850
4885
4785
5025
5030
5160
5240
5175
5130
5140
5140
5055
5015
5015
4920
5095
5010
5100
5115
5060
5035
5005
4960
5035
4980
4940
4810
5025
5035
5060
5140
4955
5135
5135
5070
5070
5005
5045
4975
5080
5125
5225
5240
5090
5105
5200
5115
4990
4905
4980
4840
4960
4970
5035
5030
4965
4925
4920
4895
4890
4895
4850
4830
4870




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=298583&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=298583&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298583&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
alpha0.970983134168638
beta0.115205603321906
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.970983134168638 \tabularnewline
beta & 0.115205603321906 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298583&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]0.970983134168638[/C][/ROW]
[ROW][C]beta[/C][C]0.115205603321906[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298583&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298583&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
alpha0.970983134168638
beta0.115205603321906
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
351005145-45
450704996.2719375619873.7280624380164
550354971.0742412707563.9257587292514
650504943.50958123186106.490418768142
750654969.1867937342595.8132062657451
852554995.21453671343259.785463286574
953355209.51687850054125.483121499456
1054405307.45079203072132.549207969281
1154905427.0730683406862.9269316593163
1254455486.13246493013-41.1324649301314
1356755439.55075398574235.449246014265
1456155687.86320743899-72.8632074389934
1555455628.65879358142-83.6587935814223
1655105549.61374931244-39.6137493124406
1755705508.9043993047961.0956006952083
1856105572.8164483243637.1835516756428
1955555617.66975344626-62.669753446261
2056305558.5567757136471.4432242863622
2156855637.6570692398247.3429307601773
2255455698.65229217956-153.652292179559
2356255547.2965836719477.7034163280623
2455705629.2754798966-59.2754798965998
2555555571.61946305621-16.6194630562077
2656355553.5226211654181.4773788345938
2755355639.79043767086-104.790437670856
2854305533.47320485092-103.473204850921
2954005416.8601910396-16.8601910395955
3054105382.4609263836827.5390736163154
3152555394.25319394744-139.253193947437
3253505228.51574484659121.484255153414
3354055329.5395177889675.4604822110441
3454205394.3161965499325.6838034500652
3554305413.6336193024416.3663806975646
3655805425.73476920618154.265230793818
3755955588.989901666026.01009833398439
3854855608.96410676702-123.96410676702
3952955488.86859142622-193.868591426222
4050555279.21033682543-224.21033682543
4149755015.00998603168-40.0099860316777
4248954925.18944419067-30.1894441906716
4347954841.52741017381-46.5274101738114
4448554736.7968051176118.203194882397
4547854805.23936751899-20.2393675189896
4648754736.99250652536138.007493474643
4750104837.83856912661172.161430873393
4849704991.10597101991-21.1059710199133
4949954954.3530144325240.6469855674795
5050204982.1080186390337.8919813609673
5149505011.426659486-61.4266594860019
5248804937.43722331585-57.4372233158456
5348504860.89637962823-10.8963796282314
5448854828.3270117899456.672988210059
5547854867.70595386191-82.7059538619114
5650254762.49858280167262.501417198334
5750305021.845863532418.15413646759134
5851605035.13836815534124.861631844665
5952405175.7192414087364.2807585912688
6051755264.6677275517-89.667727551705
6151305194.10435621067-64.104356210667
6251405141.19170106862-1.19170106862475
6351405149.23286609878-9.23286609878051
6450555148.43338219547-93.4333821954706
6550155055.4249070782-40.4249070782034
6650155009.364728104235.6352718957678
6749205008.6585827878-88.6585827878016
6850954906.47710666523188.522893334766
6950105094.52284840474-84.5228484047402
7051005007.990826211492.0091737885996
7151155103.1608146096511.8391853903504
7250605121.81145962407-61.8114596240712
7350355062.03417388113-27.0341738811294
7450055033.00093042395-28.0009304239538
7549604999.89672305107-39.8967230510707
7650354950.7789465963384.2210534036749
7749805031.59863197387-51.5986319738731
7849404974.767731387-34.7677313869999
7948104930.39013917395-120.390139173955
8050254789.40746733788235.592532662119
8150355020.4319821930514.5680178069506
8250605038.4750386593421.5249613406568
8351405065.6810102075674.3189897924376
8449555152.46261566229-197.462615662288
8551354953.26016514308181.739834856919
8651355142.58680673595-7.58680673595427
8750705147.23179182428-77.2317918242825
8850705075.61331442401-5.6133144240066
8950055072.90725017924-67.9072501792389
9050455002.1185367507942.8814632492104
9149755043.70063168173-68.7006316817306
9250804969.25335635991110.746643640085
9351255081.4347771765743.5652228234339
9452255133.257494805591.7425051945038
9552405242.12210519964-2.1221051996381
9650905259.60837759314-169.608377593137
9751055095.495453602889.50454639712007
9852005106.3613621200293.6386378799816
9951155209.394725126-94.3947251259988
10049905119.29161538268-129.291615382679
10149054980.84130486721-75.8413048672055
10249804885.8065314121894.1934685878223
10348404966.40939071435-126.409390714345
10449604818.67009881378141.329901186225
10549704946.7106877276223.2893122723844
10650354962.7410609591872.2589390408166
10750305034.40319572979-4.40319572978569
10849655031.13513725555-66.13513725555
10949254960.52834984838-35.528349848375
11049204915.665939742684.33406025731892
11148954909.99407720969-14.9940772096852
11248904883.877641253836.1223587461709
11348954878.9497720310316.0502279689699
11448504885.45711818251-35.4571181825104
11548304837.98537103946-7.9853710394591
11648704816.2949618911553.7050381088502

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5100 & 5145 & -45 \tabularnewline
4 & 5070 & 4996.27193756198 & 73.7280624380164 \tabularnewline
5 & 5035 & 4971.07424127075 & 63.9257587292514 \tabularnewline
6 & 5050 & 4943.50958123186 & 106.490418768142 \tabularnewline
7 & 5065 & 4969.18679373425 & 95.8132062657451 \tabularnewline
8 & 5255 & 4995.21453671343 & 259.785463286574 \tabularnewline
9 & 5335 & 5209.51687850054 & 125.483121499456 \tabularnewline
10 & 5440 & 5307.45079203072 & 132.549207969281 \tabularnewline
11 & 5490 & 5427.07306834068 & 62.9269316593163 \tabularnewline
12 & 5445 & 5486.13246493013 & -41.1324649301314 \tabularnewline
13 & 5675 & 5439.55075398574 & 235.449246014265 \tabularnewline
14 & 5615 & 5687.86320743899 & -72.8632074389934 \tabularnewline
15 & 5545 & 5628.65879358142 & -83.6587935814223 \tabularnewline
16 & 5510 & 5549.61374931244 & -39.6137493124406 \tabularnewline
17 & 5570 & 5508.90439930479 & 61.0956006952083 \tabularnewline
18 & 5610 & 5572.81644832436 & 37.1835516756428 \tabularnewline
19 & 5555 & 5617.66975344626 & -62.669753446261 \tabularnewline
20 & 5630 & 5558.55677571364 & 71.4432242863622 \tabularnewline
21 & 5685 & 5637.65706923982 & 47.3429307601773 \tabularnewline
22 & 5545 & 5698.65229217956 & -153.652292179559 \tabularnewline
23 & 5625 & 5547.29658367194 & 77.7034163280623 \tabularnewline
24 & 5570 & 5629.2754798966 & -59.2754798965998 \tabularnewline
25 & 5555 & 5571.61946305621 & -16.6194630562077 \tabularnewline
26 & 5635 & 5553.52262116541 & 81.4773788345938 \tabularnewline
27 & 5535 & 5639.79043767086 & -104.790437670856 \tabularnewline
28 & 5430 & 5533.47320485092 & -103.473204850921 \tabularnewline
29 & 5400 & 5416.8601910396 & -16.8601910395955 \tabularnewline
30 & 5410 & 5382.46092638368 & 27.5390736163154 \tabularnewline
31 & 5255 & 5394.25319394744 & -139.253193947437 \tabularnewline
32 & 5350 & 5228.51574484659 & 121.484255153414 \tabularnewline
33 & 5405 & 5329.53951778896 & 75.4604822110441 \tabularnewline
34 & 5420 & 5394.31619654993 & 25.6838034500652 \tabularnewline
35 & 5430 & 5413.63361930244 & 16.3663806975646 \tabularnewline
36 & 5580 & 5425.73476920618 & 154.265230793818 \tabularnewline
37 & 5595 & 5588.98990166602 & 6.01009833398439 \tabularnewline
38 & 5485 & 5608.96410676702 & -123.96410676702 \tabularnewline
39 & 5295 & 5488.86859142622 & -193.868591426222 \tabularnewline
40 & 5055 & 5279.21033682543 & -224.21033682543 \tabularnewline
41 & 4975 & 5015.00998603168 & -40.0099860316777 \tabularnewline
42 & 4895 & 4925.18944419067 & -30.1894441906716 \tabularnewline
43 & 4795 & 4841.52741017381 & -46.5274101738114 \tabularnewline
44 & 4855 & 4736.7968051176 & 118.203194882397 \tabularnewline
45 & 4785 & 4805.23936751899 & -20.2393675189896 \tabularnewline
46 & 4875 & 4736.99250652536 & 138.007493474643 \tabularnewline
47 & 5010 & 4837.83856912661 & 172.161430873393 \tabularnewline
48 & 4970 & 4991.10597101991 & -21.1059710199133 \tabularnewline
49 & 4995 & 4954.35301443252 & 40.6469855674795 \tabularnewline
50 & 5020 & 4982.10801863903 & 37.8919813609673 \tabularnewline
51 & 4950 & 5011.426659486 & -61.4266594860019 \tabularnewline
52 & 4880 & 4937.43722331585 & -57.4372233158456 \tabularnewline
53 & 4850 & 4860.89637962823 & -10.8963796282314 \tabularnewline
54 & 4885 & 4828.32701178994 & 56.672988210059 \tabularnewline
55 & 4785 & 4867.70595386191 & -82.7059538619114 \tabularnewline
56 & 5025 & 4762.49858280167 & 262.501417198334 \tabularnewline
57 & 5030 & 5021.84586353241 & 8.15413646759134 \tabularnewline
58 & 5160 & 5035.13836815534 & 124.861631844665 \tabularnewline
59 & 5240 & 5175.71924140873 & 64.2807585912688 \tabularnewline
60 & 5175 & 5264.6677275517 & -89.667727551705 \tabularnewline
61 & 5130 & 5194.10435621067 & -64.104356210667 \tabularnewline
62 & 5140 & 5141.19170106862 & -1.19170106862475 \tabularnewline
63 & 5140 & 5149.23286609878 & -9.23286609878051 \tabularnewline
64 & 5055 & 5148.43338219547 & -93.4333821954706 \tabularnewline
65 & 5015 & 5055.4249070782 & -40.4249070782034 \tabularnewline
66 & 5015 & 5009.36472810423 & 5.6352718957678 \tabularnewline
67 & 4920 & 5008.6585827878 & -88.6585827878016 \tabularnewline
68 & 5095 & 4906.47710666523 & 188.522893334766 \tabularnewline
69 & 5010 & 5094.52284840474 & -84.5228484047402 \tabularnewline
70 & 5100 & 5007.9908262114 & 92.0091737885996 \tabularnewline
71 & 5115 & 5103.16081460965 & 11.8391853903504 \tabularnewline
72 & 5060 & 5121.81145962407 & -61.8114596240712 \tabularnewline
73 & 5035 & 5062.03417388113 & -27.0341738811294 \tabularnewline
74 & 5005 & 5033.00093042395 & -28.0009304239538 \tabularnewline
75 & 4960 & 4999.89672305107 & -39.8967230510707 \tabularnewline
76 & 5035 & 4950.77894659633 & 84.2210534036749 \tabularnewline
77 & 4980 & 5031.59863197387 & -51.5986319738731 \tabularnewline
78 & 4940 & 4974.767731387 & -34.7677313869999 \tabularnewline
79 & 4810 & 4930.39013917395 & -120.390139173955 \tabularnewline
80 & 5025 & 4789.40746733788 & 235.592532662119 \tabularnewline
81 & 5035 & 5020.43198219305 & 14.5680178069506 \tabularnewline
82 & 5060 & 5038.47503865934 & 21.5249613406568 \tabularnewline
83 & 5140 & 5065.68101020756 & 74.3189897924376 \tabularnewline
84 & 4955 & 5152.46261566229 & -197.462615662288 \tabularnewline
85 & 5135 & 4953.26016514308 & 181.739834856919 \tabularnewline
86 & 5135 & 5142.58680673595 & -7.58680673595427 \tabularnewline
87 & 5070 & 5147.23179182428 & -77.2317918242825 \tabularnewline
88 & 5070 & 5075.61331442401 & -5.6133144240066 \tabularnewline
89 & 5005 & 5072.90725017924 & -67.9072501792389 \tabularnewline
90 & 5045 & 5002.11853675079 & 42.8814632492104 \tabularnewline
91 & 4975 & 5043.70063168173 & -68.7006316817306 \tabularnewline
92 & 5080 & 4969.25335635991 & 110.746643640085 \tabularnewline
93 & 5125 & 5081.43477717657 & 43.5652228234339 \tabularnewline
94 & 5225 & 5133.2574948055 & 91.7425051945038 \tabularnewline
95 & 5240 & 5242.12210519964 & -2.1221051996381 \tabularnewline
96 & 5090 & 5259.60837759314 & -169.608377593137 \tabularnewline
97 & 5105 & 5095.49545360288 & 9.50454639712007 \tabularnewline
98 & 5200 & 5106.36136212002 & 93.6386378799816 \tabularnewline
99 & 5115 & 5209.394725126 & -94.3947251259988 \tabularnewline
100 & 4990 & 5119.29161538268 & -129.291615382679 \tabularnewline
101 & 4905 & 4980.84130486721 & -75.8413048672055 \tabularnewline
102 & 4980 & 4885.80653141218 & 94.1934685878223 \tabularnewline
103 & 4840 & 4966.40939071435 & -126.409390714345 \tabularnewline
104 & 4960 & 4818.67009881378 & 141.329901186225 \tabularnewline
105 & 4970 & 4946.71068772762 & 23.2893122723844 \tabularnewline
106 & 5035 & 4962.74106095918 & 72.2589390408166 \tabularnewline
107 & 5030 & 5034.40319572979 & -4.40319572978569 \tabularnewline
108 & 4965 & 5031.13513725555 & -66.13513725555 \tabularnewline
109 & 4925 & 4960.52834984838 & -35.528349848375 \tabularnewline
110 & 4920 & 4915.66593974268 & 4.33406025731892 \tabularnewline
111 & 4895 & 4909.99407720969 & -14.9940772096852 \tabularnewline
112 & 4890 & 4883.87764125383 & 6.1223587461709 \tabularnewline
113 & 4895 & 4878.94977203103 & 16.0502279689699 \tabularnewline
114 & 4850 & 4885.45711818251 & -35.4571181825104 \tabularnewline
115 & 4830 & 4837.98537103946 & -7.9853710394591 \tabularnewline
116 & 4870 & 4816.29496189115 & 53.7050381088502 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298583&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]5100[/C][C]5145[/C][C]-45[/C][/ROW]
[ROW][C]4[/C][C]5070[/C][C]4996.27193756198[/C][C]73.7280624380164[/C][/ROW]
[ROW][C]5[/C][C]5035[/C][C]4971.07424127075[/C][C]63.9257587292514[/C][/ROW]
[ROW][C]6[/C][C]5050[/C][C]4943.50958123186[/C][C]106.490418768142[/C][/ROW]
[ROW][C]7[/C][C]5065[/C][C]4969.18679373425[/C][C]95.8132062657451[/C][/ROW]
[ROW][C]8[/C][C]5255[/C][C]4995.21453671343[/C][C]259.785463286574[/C][/ROW]
[ROW][C]9[/C][C]5335[/C][C]5209.51687850054[/C][C]125.483121499456[/C][/ROW]
[ROW][C]10[/C][C]5440[/C][C]5307.45079203072[/C][C]132.549207969281[/C][/ROW]
[ROW][C]11[/C][C]5490[/C][C]5427.07306834068[/C][C]62.9269316593163[/C][/ROW]
[ROW][C]12[/C][C]5445[/C][C]5486.13246493013[/C][C]-41.1324649301314[/C][/ROW]
[ROW][C]13[/C][C]5675[/C][C]5439.55075398574[/C][C]235.449246014265[/C][/ROW]
[ROW][C]14[/C][C]5615[/C][C]5687.86320743899[/C][C]-72.8632074389934[/C][/ROW]
[ROW][C]15[/C][C]5545[/C][C]5628.65879358142[/C][C]-83.6587935814223[/C][/ROW]
[ROW][C]16[/C][C]5510[/C][C]5549.61374931244[/C][C]-39.6137493124406[/C][/ROW]
[ROW][C]17[/C][C]5570[/C][C]5508.90439930479[/C][C]61.0956006952083[/C][/ROW]
[ROW][C]18[/C][C]5610[/C][C]5572.81644832436[/C][C]37.1835516756428[/C][/ROW]
[ROW][C]19[/C][C]5555[/C][C]5617.66975344626[/C][C]-62.669753446261[/C][/ROW]
[ROW][C]20[/C][C]5630[/C][C]5558.55677571364[/C][C]71.4432242863622[/C][/ROW]
[ROW][C]21[/C][C]5685[/C][C]5637.65706923982[/C][C]47.3429307601773[/C][/ROW]
[ROW][C]22[/C][C]5545[/C][C]5698.65229217956[/C][C]-153.652292179559[/C][/ROW]
[ROW][C]23[/C][C]5625[/C][C]5547.29658367194[/C][C]77.7034163280623[/C][/ROW]
[ROW][C]24[/C][C]5570[/C][C]5629.2754798966[/C][C]-59.2754798965998[/C][/ROW]
[ROW][C]25[/C][C]5555[/C][C]5571.61946305621[/C][C]-16.6194630562077[/C][/ROW]
[ROW][C]26[/C][C]5635[/C][C]5553.52262116541[/C][C]81.4773788345938[/C][/ROW]
[ROW][C]27[/C][C]5535[/C][C]5639.79043767086[/C][C]-104.790437670856[/C][/ROW]
[ROW][C]28[/C][C]5430[/C][C]5533.47320485092[/C][C]-103.473204850921[/C][/ROW]
[ROW][C]29[/C][C]5400[/C][C]5416.8601910396[/C][C]-16.8601910395955[/C][/ROW]
[ROW][C]30[/C][C]5410[/C][C]5382.46092638368[/C][C]27.5390736163154[/C][/ROW]
[ROW][C]31[/C][C]5255[/C][C]5394.25319394744[/C][C]-139.253193947437[/C][/ROW]
[ROW][C]32[/C][C]5350[/C][C]5228.51574484659[/C][C]121.484255153414[/C][/ROW]
[ROW][C]33[/C][C]5405[/C][C]5329.53951778896[/C][C]75.4604822110441[/C][/ROW]
[ROW][C]34[/C][C]5420[/C][C]5394.31619654993[/C][C]25.6838034500652[/C][/ROW]
[ROW][C]35[/C][C]5430[/C][C]5413.63361930244[/C][C]16.3663806975646[/C][/ROW]
[ROW][C]36[/C][C]5580[/C][C]5425.73476920618[/C][C]154.265230793818[/C][/ROW]
[ROW][C]37[/C][C]5595[/C][C]5588.98990166602[/C][C]6.01009833398439[/C][/ROW]
[ROW][C]38[/C][C]5485[/C][C]5608.96410676702[/C][C]-123.96410676702[/C][/ROW]
[ROW][C]39[/C][C]5295[/C][C]5488.86859142622[/C][C]-193.868591426222[/C][/ROW]
[ROW][C]40[/C][C]5055[/C][C]5279.21033682543[/C][C]-224.21033682543[/C][/ROW]
[ROW][C]41[/C][C]4975[/C][C]5015.00998603168[/C][C]-40.0099860316777[/C][/ROW]
[ROW][C]42[/C][C]4895[/C][C]4925.18944419067[/C][C]-30.1894441906716[/C][/ROW]
[ROW][C]43[/C][C]4795[/C][C]4841.52741017381[/C][C]-46.5274101738114[/C][/ROW]
[ROW][C]44[/C][C]4855[/C][C]4736.7968051176[/C][C]118.203194882397[/C][/ROW]
[ROW][C]45[/C][C]4785[/C][C]4805.23936751899[/C][C]-20.2393675189896[/C][/ROW]
[ROW][C]46[/C][C]4875[/C][C]4736.99250652536[/C][C]138.007493474643[/C][/ROW]
[ROW][C]47[/C][C]5010[/C][C]4837.83856912661[/C][C]172.161430873393[/C][/ROW]
[ROW][C]48[/C][C]4970[/C][C]4991.10597101991[/C][C]-21.1059710199133[/C][/ROW]
[ROW][C]49[/C][C]4995[/C][C]4954.35301443252[/C][C]40.6469855674795[/C][/ROW]
[ROW][C]50[/C][C]5020[/C][C]4982.10801863903[/C][C]37.8919813609673[/C][/ROW]
[ROW][C]51[/C][C]4950[/C][C]5011.426659486[/C][C]-61.4266594860019[/C][/ROW]
[ROW][C]52[/C][C]4880[/C][C]4937.43722331585[/C][C]-57.4372233158456[/C][/ROW]
[ROW][C]53[/C][C]4850[/C][C]4860.89637962823[/C][C]-10.8963796282314[/C][/ROW]
[ROW][C]54[/C][C]4885[/C][C]4828.32701178994[/C][C]56.672988210059[/C][/ROW]
[ROW][C]55[/C][C]4785[/C][C]4867.70595386191[/C][C]-82.7059538619114[/C][/ROW]
[ROW][C]56[/C][C]5025[/C][C]4762.49858280167[/C][C]262.501417198334[/C][/ROW]
[ROW][C]57[/C][C]5030[/C][C]5021.84586353241[/C][C]8.15413646759134[/C][/ROW]
[ROW][C]58[/C][C]5160[/C][C]5035.13836815534[/C][C]124.861631844665[/C][/ROW]
[ROW][C]59[/C][C]5240[/C][C]5175.71924140873[/C][C]64.2807585912688[/C][/ROW]
[ROW][C]60[/C][C]5175[/C][C]5264.6677275517[/C][C]-89.667727551705[/C][/ROW]
[ROW][C]61[/C][C]5130[/C][C]5194.10435621067[/C][C]-64.104356210667[/C][/ROW]
[ROW][C]62[/C][C]5140[/C][C]5141.19170106862[/C][C]-1.19170106862475[/C][/ROW]
[ROW][C]63[/C][C]5140[/C][C]5149.23286609878[/C][C]-9.23286609878051[/C][/ROW]
[ROW][C]64[/C][C]5055[/C][C]5148.43338219547[/C][C]-93.4333821954706[/C][/ROW]
[ROW][C]65[/C][C]5015[/C][C]5055.4249070782[/C][C]-40.4249070782034[/C][/ROW]
[ROW][C]66[/C][C]5015[/C][C]5009.36472810423[/C][C]5.6352718957678[/C][/ROW]
[ROW][C]67[/C][C]4920[/C][C]5008.6585827878[/C][C]-88.6585827878016[/C][/ROW]
[ROW][C]68[/C][C]5095[/C][C]4906.47710666523[/C][C]188.522893334766[/C][/ROW]
[ROW][C]69[/C][C]5010[/C][C]5094.52284840474[/C][C]-84.5228484047402[/C][/ROW]
[ROW][C]70[/C][C]5100[/C][C]5007.9908262114[/C][C]92.0091737885996[/C][/ROW]
[ROW][C]71[/C][C]5115[/C][C]5103.16081460965[/C][C]11.8391853903504[/C][/ROW]
[ROW][C]72[/C][C]5060[/C][C]5121.81145962407[/C][C]-61.8114596240712[/C][/ROW]
[ROW][C]73[/C][C]5035[/C][C]5062.03417388113[/C][C]-27.0341738811294[/C][/ROW]
[ROW][C]74[/C][C]5005[/C][C]5033.00093042395[/C][C]-28.0009304239538[/C][/ROW]
[ROW][C]75[/C][C]4960[/C][C]4999.89672305107[/C][C]-39.8967230510707[/C][/ROW]
[ROW][C]76[/C][C]5035[/C][C]4950.77894659633[/C][C]84.2210534036749[/C][/ROW]
[ROW][C]77[/C][C]4980[/C][C]5031.59863197387[/C][C]-51.5986319738731[/C][/ROW]
[ROW][C]78[/C][C]4940[/C][C]4974.767731387[/C][C]-34.7677313869999[/C][/ROW]
[ROW][C]79[/C][C]4810[/C][C]4930.39013917395[/C][C]-120.390139173955[/C][/ROW]
[ROW][C]80[/C][C]5025[/C][C]4789.40746733788[/C][C]235.592532662119[/C][/ROW]
[ROW][C]81[/C][C]5035[/C][C]5020.43198219305[/C][C]14.5680178069506[/C][/ROW]
[ROW][C]82[/C][C]5060[/C][C]5038.47503865934[/C][C]21.5249613406568[/C][/ROW]
[ROW][C]83[/C][C]5140[/C][C]5065.68101020756[/C][C]74.3189897924376[/C][/ROW]
[ROW][C]84[/C][C]4955[/C][C]5152.46261566229[/C][C]-197.462615662288[/C][/ROW]
[ROW][C]85[/C][C]5135[/C][C]4953.26016514308[/C][C]181.739834856919[/C][/ROW]
[ROW][C]86[/C][C]5135[/C][C]5142.58680673595[/C][C]-7.58680673595427[/C][/ROW]
[ROW][C]87[/C][C]5070[/C][C]5147.23179182428[/C][C]-77.2317918242825[/C][/ROW]
[ROW][C]88[/C][C]5070[/C][C]5075.61331442401[/C][C]-5.6133144240066[/C][/ROW]
[ROW][C]89[/C][C]5005[/C][C]5072.90725017924[/C][C]-67.9072501792389[/C][/ROW]
[ROW][C]90[/C][C]5045[/C][C]5002.11853675079[/C][C]42.8814632492104[/C][/ROW]
[ROW][C]91[/C][C]4975[/C][C]5043.70063168173[/C][C]-68.7006316817306[/C][/ROW]
[ROW][C]92[/C][C]5080[/C][C]4969.25335635991[/C][C]110.746643640085[/C][/ROW]
[ROW][C]93[/C][C]5125[/C][C]5081.43477717657[/C][C]43.5652228234339[/C][/ROW]
[ROW][C]94[/C][C]5225[/C][C]5133.2574948055[/C][C]91.7425051945038[/C][/ROW]
[ROW][C]95[/C][C]5240[/C][C]5242.12210519964[/C][C]-2.1221051996381[/C][/ROW]
[ROW][C]96[/C][C]5090[/C][C]5259.60837759314[/C][C]-169.608377593137[/C][/ROW]
[ROW][C]97[/C][C]5105[/C][C]5095.49545360288[/C][C]9.50454639712007[/C][/ROW]
[ROW][C]98[/C][C]5200[/C][C]5106.36136212002[/C][C]93.6386378799816[/C][/ROW]
[ROW][C]99[/C][C]5115[/C][C]5209.394725126[/C][C]-94.3947251259988[/C][/ROW]
[ROW][C]100[/C][C]4990[/C][C]5119.29161538268[/C][C]-129.291615382679[/C][/ROW]
[ROW][C]101[/C][C]4905[/C][C]4980.84130486721[/C][C]-75.8413048672055[/C][/ROW]
[ROW][C]102[/C][C]4980[/C][C]4885.80653141218[/C][C]94.1934685878223[/C][/ROW]
[ROW][C]103[/C][C]4840[/C][C]4966.40939071435[/C][C]-126.409390714345[/C][/ROW]
[ROW][C]104[/C][C]4960[/C][C]4818.67009881378[/C][C]141.329901186225[/C][/ROW]
[ROW][C]105[/C][C]4970[/C][C]4946.71068772762[/C][C]23.2893122723844[/C][/ROW]
[ROW][C]106[/C][C]5035[/C][C]4962.74106095918[/C][C]72.2589390408166[/C][/ROW]
[ROW][C]107[/C][C]5030[/C][C]5034.40319572979[/C][C]-4.40319572978569[/C][/ROW]
[ROW][C]108[/C][C]4965[/C][C]5031.13513725555[/C][C]-66.13513725555[/C][/ROW]
[ROW][C]109[/C][C]4925[/C][C]4960.52834984838[/C][C]-35.528349848375[/C][/ROW]
[ROW][C]110[/C][C]4920[/C][C]4915.66593974268[/C][C]4.33406025731892[/C][/ROW]
[ROW][C]111[/C][C]4895[/C][C]4909.99407720969[/C][C]-14.9940772096852[/C][/ROW]
[ROW][C]112[/C][C]4890[/C][C]4883.87764125383[/C][C]6.1223587461709[/C][/ROW]
[ROW][C]113[/C][C]4895[/C][C]4878.94977203103[/C][C]16.0502279689699[/C][/ROW]
[ROW][C]114[/C][C]4850[/C][C]4885.45711818251[/C][C]-35.4571181825104[/C][/ROW]
[ROW][C]115[/C][C]4830[/C][C]4837.98537103946[/C][C]-7.9853710394591[/C][/ROW]
[ROW][C]116[/C][C]4870[/C][C]4816.29496189115[/C][C]53.7050381088502[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298583&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298583&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
351005145-45
450704996.2719375619873.7280624380164
550354971.0742412707563.9257587292514
650504943.50958123186106.490418768142
750654969.1867937342595.8132062657451
852554995.21453671343259.785463286574
953355209.51687850054125.483121499456
1054405307.45079203072132.549207969281
1154905427.0730683406862.9269316593163
1254455486.13246493013-41.1324649301314
1356755439.55075398574235.449246014265
1456155687.86320743899-72.8632074389934
1555455628.65879358142-83.6587935814223
1655105549.61374931244-39.6137493124406
1755705508.9043993047961.0956006952083
1856105572.8164483243637.1835516756428
1955555617.66975344626-62.669753446261
2056305558.5567757136471.4432242863622
2156855637.6570692398247.3429307601773
2255455698.65229217956-153.652292179559
2356255547.2965836719477.7034163280623
2455705629.2754798966-59.2754798965998
2555555571.61946305621-16.6194630562077
2656355553.5226211654181.4773788345938
2755355639.79043767086-104.790437670856
2854305533.47320485092-103.473204850921
2954005416.8601910396-16.8601910395955
3054105382.4609263836827.5390736163154
3152555394.25319394744-139.253193947437
3253505228.51574484659121.484255153414
3354055329.5395177889675.4604822110441
3454205394.3161965499325.6838034500652
3554305413.6336193024416.3663806975646
3655805425.73476920618154.265230793818
3755955588.989901666026.01009833398439
3854855608.96410676702-123.96410676702
3952955488.86859142622-193.868591426222
4050555279.21033682543-224.21033682543
4149755015.00998603168-40.0099860316777
4248954925.18944419067-30.1894441906716
4347954841.52741017381-46.5274101738114
4448554736.7968051176118.203194882397
4547854805.23936751899-20.2393675189896
4648754736.99250652536138.007493474643
4750104837.83856912661172.161430873393
4849704991.10597101991-21.1059710199133
4949954954.3530144325240.6469855674795
5050204982.1080186390337.8919813609673
5149505011.426659486-61.4266594860019
5248804937.43722331585-57.4372233158456
5348504860.89637962823-10.8963796282314
5448854828.3270117899456.672988210059
5547854867.70595386191-82.7059538619114
5650254762.49858280167262.501417198334
5750305021.845863532418.15413646759134
5851605035.13836815534124.861631844665
5952405175.7192414087364.2807585912688
6051755264.6677275517-89.667727551705
6151305194.10435621067-64.104356210667
6251405141.19170106862-1.19170106862475
6351405149.23286609878-9.23286609878051
6450555148.43338219547-93.4333821954706
6550155055.4249070782-40.4249070782034
6650155009.364728104235.6352718957678
6749205008.6585827878-88.6585827878016
6850954906.47710666523188.522893334766
6950105094.52284840474-84.5228484047402
7051005007.990826211492.0091737885996
7151155103.1608146096511.8391853903504
7250605121.81145962407-61.8114596240712
7350355062.03417388113-27.0341738811294
7450055033.00093042395-28.0009304239538
7549604999.89672305107-39.8967230510707
7650354950.7789465963384.2210534036749
7749805031.59863197387-51.5986319738731
7849404974.767731387-34.7677313869999
7948104930.39013917395-120.390139173955
8050254789.40746733788235.592532662119
8150355020.4319821930514.5680178069506
8250605038.4750386593421.5249613406568
8351405065.6810102075674.3189897924376
8449555152.46261566229-197.462615662288
8551354953.26016514308181.739834856919
8651355142.58680673595-7.58680673595427
8750705147.23179182428-77.2317918242825
8850705075.61331442401-5.6133144240066
8950055072.90725017924-67.9072501792389
9050455002.1185367507942.8814632492104
9149755043.70063168173-68.7006316817306
9250804969.25335635991110.746643640085
9351255081.4347771765743.5652228234339
9452255133.257494805591.7425051945038
9552405242.12210519964-2.1221051996381
9650905259.60837759314-169.608377593137
9751055095.495453602889.50454639712007
9852005106.3613621200293.6386378799816
9951155209.394725126-94.3947251259988
10049905119.29161538268-129.291615382679
10149054980.84130486721-75.8413048672055
10249804885.8065314121894.1934685878223
10348404966.40939071435-126.409390714345
10449604818.67009881378141.329901186225
10549704946.7106877276223.2893122723844
10650354962.7410609591872.2589390408166
10750305034.40319572979-4.40319572978569
10849655031.13513725555-66.13513725555
10949254960.52834984838-35.528349848375
11049204915.665939742684.33406025731892
11148954909.99407720969-14.9940772096852
11248904883.877641253836.1223587461709
11348954878.9497720310316.0502279689699
11448504885.45711818251-35.4571181825104
11548304837.98537103946-7.9853710394591
11648704816.2949618911553.7050381088502







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174860.512490013444672.137645997385048.8873340295
1184852.583331912154574.926537622715130.24012620158
1194844.654173810864487.243817150135202.06453047158
1204836.725015709574402.766776828595270.68325459054
1214828.795857608284319.174298132135338.41741708442
1224820.866699506994235.364031917985406.36936709599
1234812.937541405694150.740032319235475.13505049216
1244805.00838330444064.955206784535545.06155982428
1254797.079225203113977.798485041865616.35996536437
1264789.150067101823889.138794538425689.16133966523
1274781.220909000533798.89466429465763.54715370647
1284773.291750899243707.016607971985839.56689382651

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 4860.51249001344 & 4672.13764599738 & 5048.8873340295 \tabularnewline
118 & 4852.58333191215 & 4574.92653762271 & 5130.24012620158 \tabularnewline
119 & 4844.65417381086 & 4487.24381715013 & 5202.06453047158 \tabularnewline
120 & 4836.72501570957 & 4402.76677682859 & 5270.68325459054 \tabularnewline
121 & 4828.79585760828 & 4319.17429813213 & 5338.41741708442 \tabularnewline
122 & 4820.86669950699 & 4235.36403191798 & 5406.36936709599 \tabularnewline
123 & 4812.93754140569 & 4150.74003231923 & 5475.13505049216 \tabularnewline
124 & 4805.0083833044 & 4064.95520678453 & 5545.06155982428 \tabularnewline
125 & 4797.07922520311 & 3977.79848504186 & 5616.35996536437 \tabularnewline
126 & 4789.15006710182 & 3889.13879453842 & 5689.16133966523 \tabularnewline
127 & 4781.22090900053 & 3798.8946642946 & 5763.54715370647 \tabularnewline
128 & 4773.29175089924 & 3707.01660797198 & 5839.56689382651 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298583&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]4860.51249001344[/C][C]4672.13764599738[/C][C]5048.8873340295[/C][/ROW]
[ROW][C]118[/C][C]4852.58333191215[/C][C]4574.92653762271[/C][C]5130.24012620158[/C][/ROW]
[ROW][C]119[/C][C]4844.65417381086[/C][C]4487.24381715013[/C][C]5202.06453047158[/C][/ROW]
[ROW][C]120[/C][C]4836.72501570957[/C][C]4402.76677682859[/C][C]5270.68325459054[/C][/ROW]
[ROW][C]121[/C][C]4828.79585760828[/C][C]4319.17429813213[/C][C]5338.41741708442[/C][/ROW]
[ROW][C]122[/C][C]4820.86669950699[/C][C]4235.36403191798[/C][C]5406.36936709599[/C][/ROW]
[ROW][C]123[/C][C]4812.93754140569[/C][C]4150.74003231923[/C][C]5475.13505049216[/C][/ROW]
[ROW][C]124[/C][C]4805.0083833044[/C][C]4064.95520678453[/C][C]5545.06155982428[/C][/ROW]
[ROW][C]125[/C][C]4797.07922520311[/C][C]3977.79848504186[/C][C]5616.35996536437[/C][/ROW]
[ROW][C]126[/C][C]4789.15006710182[/C][C]3889.13879453842[/C][C]5689.16133966523[/C][/ROW]
[ROW][C]127[/C][C]4781.22090900053[/C][C]3798.8946642946[/C][C]5763.54715370647[/C][/ROW]
[ROW][C]128[/C][C]4773.29175089924[/C][C]3707.01660797198[/C][C]5839.56689382651[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298583&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298583&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
1174860.512490013444672.137645997385048.8873340295
1184852.583331912154574.926537622715130.24012620158
1194844.654173810864487.243817150135202.06453047158
1204836.725015709574402.766776828595270.68325459054
1214828.795857608284319.174298132135338.41741708442
1224820.866699506994235.364031917985406.36936709599
1234812.937541405694150.740032319235475.13505049216
1244805.00838330444064.955206784535545.06155982428
1254797.079225203113977.798485041865616.35996536437
1264789.150067101823889.138794538425689.16133966523
1274781.220909000533798.89466429465763.54715370647
1284773.291750899243707.016607971985839.56689382651



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;
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')