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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 computationThu, 22 Dec 2016 20:56:11 +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/22/t1482436592rue37p09tdlqd3x.htm/, Retrieved Mon, 29 Apr 2024 05:56:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302662, Retrieved Mon, 29 Apr 2024 05:56:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-22 19:56:11] [037fdaa34a77b5f63489b3bcd360a80c] [Current]
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Dataseries X:
3455
3585
3675
3680
3735
3860
3765
3905
4110
4170
4110
4025
4145
4285
4370
4355
4385
4525
4375
4525
4610
4595
4500
4370
4390
4530
4590
4580
4595
4685
4490
4635
4710
4655
4665
4550
4590
4675
4645
4665
4635
4720
4565
4720
4830
4830
4765
4705
4675
4900
4945
4905
4955
5120
4860
5040
5140
5240
5145
5070
5085
5215
5255
5275
5315
5450
5205
5370
5500
5490
5440
5360
5380
5460
5450
5520
5475
5600
5250
5465
5515
5425
5325
5275
5160
5360
5435
5285
5415
5575
5265
5480
5565
5500
5280
5135
5050
5100
5070
5115
5140
5330
5080
5285
5405
5385
5255
5100
5040
5235
5310
5265
5380
5465
5225
5445




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=302662&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=302662&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302662&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
alpha0.686885392408528
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.686885392408528 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302662&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]0.686885392408528[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302662&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302662&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
alpha0.686885392408528
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
235853455130
336753544.29510101311130.704898986891
436803634.0743868434445.9256131565635
537353665.6200196580869.3799803419151
638603713.27611468054146.723885319463
737653814.0586082239-49.0586082239006
839053780.36096686301124.639033136989
941103865.97369804873244.026301951269
1041704033.59180022253136.40819977747
1141104127.28860005442-17.2886000544186
1240254115.41331322184-90.4133132218449
1341454053.309729090591.690270909497
1442854116.29043680422168.709563195784
1543704232.17457132302137.825428676977
1643554326.8448449836828.1551550163185
1743854346.1842096853938.8157903146121
1845254372.84620904729152.153790952712
1943754477.35842545229-102.358425452287
2045254407.04991821917117.950081780826
2146104488.06810642782121.931893572185
2245954571.8213429912623.1786570087397
2345004587.74242390621-87.7424239062111
2443704527.47343463052-157.473434630518
2543904419.30723269042-29.3072326904157
2645304399.17652266345130.823477336548
2745904489.03725823002100.962741769985
2845804558.3870907293321.6129092706678
2945954573.232682394821.7673176051958
3046854588.1843348897396.8156651102699
3144904654.68560101029-164.68560101029
3246354541.565467336393.4345326636976
3347104605.74428296951104.255717030486
3446554677.35601207283-22.3560120728316
3546654661.999993947493.00000605250534
3645504664.0606542821-114.060654282098
3745904585.714057007174.28594299283395
3846754588.6580086416486.3419913583602
3946454647.96506125716-2.96506125716041
4046654645.9284039920219.0715960079797
4146354659.02840469982-24.0284046998186
4247204642.5236445086377.476355491367
4345654695.7410213527-130.741021352704
4447204605.93692359696114.06307640304
4548304684.28518459139145.714815408614
4648304784.3745627530745.6254372469321
4747654815.71400912024-50.7140091202373
4847054780.87929706507-75.8792970650738
4946754728.75891632485-53.7589163248467
5049004691.8327019896208.167298010403
5149454834.8197781701110.180221829904
5249054910.50096307739-5.50096307738841
5349554906.7224318953548.2775681046478
5451204939.88358820744180.116411792557
5548605063.60292040079-203.60292040079
5650404923.75104852577116.248951474228
5751405003.60075517623136.399244823773
5852405097.29140398123142.708596018769
5951455195.31585395765-50.3158539576534
6050705160.75462886758-90.7546288675803
6150855098.41660000498-13.4166000049827
6252155089.20093344577125.799066554227
6352555175.610474640579.3895253595001
6452755230.1419799201944.8580200798133
6553155260.9542986453854.0457013546211
6654505298.07750142834151.922498571658
6752055402.43084647542-197.430846475419
6853705266.8184820206103.181517979397
6955005337.69235948719162.307640512811
7054905449.1791068317340.8208931682666
7154405477.21838205408-37.2183820540849
7253605451.65361909205-91.6536190920542
7353805388.69808697635-8.69808697634653
7454605382.7234980903977.276501909605
7554505435.8035984285314.1964015714675
7655205445.5548992927474.4451007072612
7754755496.69015150494-21.6901515049385
7856005481.79150327707118.208496722931
7952505562.98719293462-312.987192934622
8054655348.00086209688116.99913790312
8155155428.3658608469286.6341391530759
8254255487.87358551506-62.8735855150599
8353255444.68663805642-119.686638056417
8452755362.47563470898-87.4756347089779
8551605302.38989903572-142.389899035717
8653605204.58435736156155.415642638442
8754355311.33709204169123.662907958313
8852855396.27933710101-111.279337101012
8954155319.8431859694295.1568140305772
9055755385.20501151516189.794988484839
9152655515.57241665774-250.572416657742
9254805343.45788391504136.542116084964
9355655437.24666890235127.753331097652
9455005524.99856586485-24.9985658648548
9552805507.82741614112-227.827416141124
9651355351.33609200361-216.336092003607
9750505202.73799055558-152.737990555582
9851005097.824495977122.17550402287907
9950705099.31881791156-29.3188179115623
10051155079.1801501654235.8198498345755
10151405103.7842817750636.2157182249384
10253305128.66032959936201.339670400645
10350805266.95760810991-186.957608109906
10452855138.53915809957146.460841900427
10554055239.14097096083165.859029039169
10653855353.067115206931.9328847931019
10752555375.00134730874-120.001347308744
10851005292.57417477303-192.574174773025
10950405160.29778716631-120.297787166307
11052355077.6669944227157.333005577299
11153105185.73673769748124.263262302523
11252655271.09135738611-6.09135738610894
11353805266.90729297765113.092707022349
11454655344.58902141924120.41097858076
11552255427.29756369198-202.29756369198
11654455288.34232227212156.657677727875

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3585 & 3455 & 130 \tabularnewline
3 & 3675 & 3544.29510101311 & 130.704898986891 \tabularnewline
4 & 3680 & 3634.07438684344 & 45.9256131565635 \tabularnewline
5 & 3735 & 3665.62001965808 & 69.3799803419151 \tabularnewline
6 & 3860 & 3713.27611468054 & 146.723885319463 \tabularnewline
7 & 3765 & 3814.0586082239 & -49.0586082239006 \tabularnewline
8 & 3905 & 3780.36096686301 & 124.639033136989 \tabularnewline
9 & 4110 & 3865.97369804873 & 244.026301951269 \tabularnewline
10 & 4170 & 4033.59180022253 & 136.40819977747 \tabularnewline
11 & 4110 & 4127.28860005442 & -17.2886000544186 \tabularnewline
12 & 4025 & 4115.41331322184 & -90.4133132218449 \tabularnewline
13 & 4145 & 4053.3097290905 & 91.690270909497 \tabularnewline
14 & 4285 & 4116.29043680422 & 168.709563195784 \tabularnewline
15 & 4370 & 4232.17457132302 & 137.825428676977 \tabularnewline
16 & 4355 & 4326.84484498368 & 28.1551550163185 \tabularnewline
17 & 4385 & 4346.18420968539 & 38.8157903146121 \tabularnewline
18 & 4525 & 4372.84620904729 & 152.153790952712 \tabularnewline
19 & 4375 & 4477.35842545229 & -102.358425452287 \tabularnewline
20 & 4525 & 4407.04991821917 & 117.950081780826 \tabularnewline
21 & 4610 & 4488.06810642782 & 121.931893572185 \tabularnewline
22 & 4595 & 4571.82134299126 & 23.1786570087397 \tabularnewline
23 & 4500 & 4587.74242390621 & -87.7424239062111 \tabularnewline
24 & 4370 & 4527.47343463052 & -157.473434630518 \tabularnewline
25 & 4390 & 4419.30723269042 & -29.3072326904157 \tabularnewline
26 & 4530 & 4399.17652266345 & 130.823477336548 \tabularnewline
27 & 4590 & 4489.03725823002 & 100.962741769985 \tabularnewline
28 & 4580 & 4558.38709072933 & 21.6129092706678 \tabularnewline
29 & 4595 & 4573.2326823948 & 21.7673176051958 \tabularnewline
30 & 4685 & 4588.18433488973 & 96.8156651102699 \tabularnewline
31 & 4490 & 4654.68560101029 & -164.68560101029 \tabularnewline
32 & 4635 & 4541.5654673363 & 93.4345326636976 \tabularnewline
33 & 4710 & 4605.74428296951 & 104.255717030486 \tabularnewline
34 & 4655 & 4677.35601207283 & -22.3560120728316 \tabularnewline
35 & 4665 & 4661.99999394749 & 3.00000605250534 \tabularnewline
36 & 4550 & 4664.0606542821 & -114.060654282098 \tabularnewline
37 & 4590 & 4585.71405700717 & 4.28594299283395 \tabularnewline
38 & 4675 & 4588.65800864164 & 86.3419913583602 \tabularnewline
39 & 4645 & 4647.96506125716 & -2.96506125716041 \tabularnewline
40 & 4665 & 4645.92840399202 & 19.0715960079797 \tabularnewline
41 & 4635 & 4659.02840469982 & -24.0284046998186 \tabularnewline
42 & 4720 & 4642.52364450863 & 77.476355491367 \tabularnewline
43 & 4565 & 4695.7410213527 & -130.741021352704 \tabularnewline
44 & 4720 & 4605.93692359696 & 114.06307640304 \tabularnewline
45 & 4830 & 4684.28518459139 & 145.714815408614 \tabularnewline
46 & 4830 & 4784.37456275307 & 45.6254372469321 \tabularnewline
47 & 4765 & 4815.71400912024 & -50.7140091202373 \tabularnewline
48 & 4705 & 4780.87929706507 & -75.8792970650738 \tabularnewline
49 & 4675 & 4728.75891632485 & -53.7589163248467 \tabularnewline
50 & 4900 & 4691.8327019896 & 208.167298010403 \tabularnewline
51 & 4945 & 4834.8197781701 & 110.180221829904 \tabularnewline
52 & 4905 & 4910.50096307739 & -5.50096307738841 \tabularnewline
53 & 4955 & 4906.72243189535 & 48.2775681046478 \tabularnewline
54 & 5120 & 4939.88358820744 & 180.116411792557 \tabularnewline
55 & 4860 & 5063.60292040079 & -203.60292040079 \tabularnewline
56 & 5040 & 4923.75104852577 & 116.248951474228 \tabularnewline
57 & 5140 & 5003.60075517623 & 136.399244823773 \tabularnewline
58 & 5240 & 5097.29140398123 & 142.708596018769 \tabularnewline
59 & 5145 & 5195.31585395765 & -50.3158539576534 \tabularnewline
60 & 5070 & 5160.75462886758 & -90.7546288675803 \tabularnewline
61 & 5085 & 5098.41660000498 & -13.4166000049827 \tabularnewline
62 & 5215 & 5089.20093344577 & 125.799066554227 \tabularnewline
63 & 5255 & 5175.6104746405 & 79.3895253595001 \tabularnewline
64 & 5275 & 5230.14197992019 & 44.8580200798133 \tabularnewline
65 & 5315 & 5260.95429864538 & 54.0457013546211 \tabularnewline
66 & 5450 & 5298.07750142834 & 151.922498571658 \tabularnewline
67 & 5205 & 5402.43084647542 & -197.430846475419 \tabularnewline
68 & 5370 & 5266.8184820206 & 103.181517979397 \tabularnewline
69 & 5500 & 5337.69235948719 & 162.307640512811 \tabularnewline
70 & 5490 & 5449.17910683173 & 40.8208931682666 \tabularnewline
71 & 5440 & 5477.21838205408 & -37.2183820540849 \tabularnewline
72 & 5360 & 5451.65361909205 & -91.6536190920542 \tabularnewline
73 & 5380 & 5388.69808697635 & -8.69808697634653 \tabularnewline
74 & 5460 & 5382.72349809039 & 77.276501909605 \tabularnewline
75 & 5450 & 5435.80359842853 & 14.1964015714675 \tabularnewline
76 & 5520 & 5445.55489929274 & 74.4451007072612 \tabularnewline
77 & 5475 & 5496.69015150494 & -21.6901515049385 \tabularnewline
78 & 5600 & 5481.79150327707 & 118.208496722931 \tabularnewline
79 & 5250 & 5562.98719293462 & -312.987192934622 \tabularnewline
80 & 5465 & 5348.00086209688 & 116.99913790312 \tabularnewline
81 & 5515 & 5428.36586084692 & 86.6341391530759 \tabularnewline
82 & 5425 & 5487.87358551506 & -62.8735855150599 \tabularnewline
83 & 5325 & 5444.68663805642 & -119.686638056417 \tabularnewline
84 & 5275 & 5362.47563470898 & -87.4756347089779 \tabularnewline
85 & 5160 & 5302.38989903572 & -142.389899035717 \tabularnewline
86 & 5360 & 5204.58435736156 & 155.415642638442 \tabularnewline
87 & 5435 & 5311.33709204169 & 123.662907958313 \tabularnewline
88 & 5285 & 5396.27933710101 & -111.279337101012 \tabularnewline
89 & 5415 & 5319.84318596942 & 95.1568140305772 \tabularnewline
90 & 5575 & 5385.20501151516 & 189.794988484839 \tabularnewline
91 & 5265 & 5515.57241665774 & -250.572416657742 \tabularnewline
92 & 5480 & 5343.45788391504 & 136.542116084964 \tabularnewline
93 & 5565 & 5437.24666890235 & 127.753331097652 \tabularnewline
94 & 5500 & 5524.99856586485 & -24.9985658648548 \tabularnewline
95 & 5280 & 5507.82741614112 & -227.827416141124 \tabularnewline
96 & 5135 & 5351.33609200361 & -216.336092003607 \tabularnewline
97 & 5050 & 5202.73799055558 & -152.737990555582 \tabularnewline
98 & 5100 & 5097.82449597712 & 2.17550402287907 \tabularnewline
99 & 5070 & 5099.31881791156 & -29.3188179115623 \tabularnewline
100 & 5115 & 5079.18015016542 & 35.8198498345755 \tabularnewline
101 & 5140 & 5103.78428177506 & 36.2157182249384 \tabularnewline
102 & 5330 & 5128.66032959936 & 201.339670400645 \tabularnewline
103 & 5080 & 5266.95760810991 & -186.957608109906 \tabularnewline
104 & 5285 & 5138.53915809957 & 146.460841900427 \tabularnewline
105 & 5405 & 5239.14097096083 & 165.859029039169 \tabularnewline
106 & 5385 & 5353.0671152069 & 31.9328847931019 \tabularnewline
107 & 5255 & 5375.00134730874 & -120.001347308744 \tabularnewline
108 & 5100 & 5292.57417477303 & -192.574174773025 \tabularnewline
109 & 5040 & 5160.29778716631 & -120.297787166307 \tabularnewline
110 & 5235 & 5077.6669944227 & 157.333005577299 \tabularnewline
111 & 5310 & 5185.73673769748 & 124.263262302523 \tabularnewline
112 & 5265 & 5271.09135738611 & -6.09135738610894 \tabularnewline
113 & 5380 & 5266.90729297765 & 113.092707022349 \tabularnewline
114 & 5465 & 5344.58902141924 & 120.41097858076 \tabularnewline
115 & 5225 & 5427.29756369198 & -202.29756369198 \tabularnewline
116 & 5445 & 5288.34232227212 & 156.657677727875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302662&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]3585[/C][C]3455[/C][C]130[/C][/ROW]
[ROW][C]3[/C][C]3675[/C][C]3544.29510101311[/C][C]130.704898986891[/C][/ROW]
[ROW][C]4[/C][C]3680[/C][C]3634.07438684344[/C][C]45.9256131565635[/C][/ROW]
[ROW][C]5[/C][C]3735[/C][C]3665.62001965808[/C][C]69.3799803419151[/C][/ROW]
[ROW][C]6[/C][C]3860[/C][C]3713.27611468054[/C][C]146.723885319463[/C][/ROW]
[ROW][C]7[/C][C]3765[/C][C]3814.0586082239[/C][C]-49.0586082239006[/C][/ROW]
[ROW][C]8[/C][C]3905[/C][C]3780.36096686301[/C][C]124.639033136989[/C][/ROW]
[ROW][C]9[/C][C]4110[/C][C]3865.97369804873[/C][C]244.026301951269[/C][/ROW]
[ROW][C]10[/C][C]4170[/C][C]4033.59180022253[/C][C]136.40819977747[/C][/ROW]
[ROW][C]11[/C][C]4110[/C][C]4127.28860005442[/C][C]-17.2886000544186[/C][/ROW]
[ROW][C]12[/C][C]4025[/C][C]4115.41331322184[/C][C]-90.4133132218449[/C][/ROW]
[ROW][C]13[/C][C]4145[/C][C]4053.3097290905[/C][C]91.690270909497[/C][/ROW]
[ROW][C]14[/C][C]4285[/C][C]4116.29043680422[/C][C]168.709563195784[/C][/ROW]
[ROW][C]15[/C][C]4370[/C][C]4232.17457132302[/C][C]137.825428676977[/C][/ROW]
[ROW][C]16[/C][C]4355[/C][C]4326.84484498368[/C][C]28.1551550163185[/C][/ROW]
[ROW][C]17[/C][C]4385[/C][C]4346.18420968539[/C][C]38.8157903146121[/C][/ROW]
[ROW][C]18[/C][C]4525[/C][C]4372.84620904729[/C][C]152.153790952712[/C][/ROW]
[ROW][C]19[/C][C]4375[/C][C]4477.35842545229[/C][C]-102.358425452287[/C][/ROW]
[ROW][C]20[/C][C]4525[/C][C]4407.04991821917[/C][C]117.950081780826[/C][/ROW]
[ROW][C]21[/C][C]4610[/C][C]4488.06810642782[/C][C]121.931893572185[/C][/ROW]
[ROW][C]22[/C][C]4595[/C][C]4571.82134299126[/C][C]23.1786570087397[/C][/ROW]
[ROW][C]23[/C][C]4500[/C][C]4587.74242390621[/C][C]-87.7424239062111[/C][/ROW]
[ROW][C]24[/C][C]4370[/C][C]4527.47343463052[/C][C]-157.473434630518[/C][/ROW]
[ROW][C]25[/C][C]4390[/C][C]4419.30723269042[/C][C]-29.3072326904157[/C][/ROW]
[ROW][C]26[/C][C]4530[/C][C]4399.17652266345[/C][C]130.823477336548[/C][/ROW]
[ROW][C]27[/C][C]4590[/C][C]4489.03725823002[/C][C]100.962741769985[/C][/ROW]
[ROW][C]28[/C][C]4580[/C][C]4558.38709072933[/C][C]21.6129092706678[/C][/ROW]
[ROW][C]29[/C][C]4595[/C][C]4573.2326823948[/C][C]21.7673176051958[/C][/ROW]
[ROW][C]30[/C][C]4685[/C][C]4588.18433488973[/C][C]96.8156651102699[/C][/ROW]
[ROW][C]31[/C][C]4490[/C][C]4654.68560101029[/C][C]-164.68560101029[/C][/ROW]
[ROW][C]32[/C][C]4635[/C][C]4541.5654673363[/C][C]93.4345326636976[/C][/ROW]
[ROW][C]33[/C][C]4710[/C][C]4605.74428296951[/C][C]104.255717030486[/C][/ROW]
[ROW][C]34[/C][C]4655[/C][C]4677.35601207283[/C][C]-22.3560120728316[/C][/ROW]
[ROW][C]35[/C][C]4665[/C][C]4661.99999394749[/C][C]3.00000605250534[/C][/ROW]
[ROW][C]36[/C][C]4550[/C][C]4664.0606542821[/C][C]-114.060654282098[/C][/ROW]
[ROW][C]37[/C][C]4590[/C][C]4585.71405700717[/C][C]4.28594299283395[/C][/ROW]
[ROW][C]38[/C][C]4675[/C][C]4588.65800864164[/C][C]86.3419913583602[/C][/ROW]
[ROW][C]39[/C][C]4645[/C][C]4647.96506125716[/C][C]-2.96506125716041[/C][/ROW]
[ROW][C]40[/C][C]4665[/C][C]4645.92840399202[/C][C]19.0715960079797[/C][/ROW]
[ROW][C]41[/C][C]4635[/C][C]4659.02840469982[/C][C]-24.0284046998186[/C][/ROW]
[ROW][C]42[/C][C]4720[/C][C]4642.52364450863[/C][C]77.476355491367[/C][/ROW]
[ROW][C]43[/C][C]4565[/C][C]4695.7410213527[/C][C]-130.741021352704[/C][/ROW]
[ROW][C]44[/C][C]4720[/C][C]4605.93692359696[/C][C]114.06307640304[/C][/ROW]
[ROW][C]45[/C][C]4830[/C][C]4684.28518459139[/C][C]145.714815408614[/C][/ROW]
[ROW][C]46[/C][C]4830[/C][C]4784.37456275307[/C][C]45.6254372469321[/C][/ROW]
[ROW][C]47[/C][C]4765[/C][C]4815.71400912024[/C][C]-50.7140091202373[/C][/ROW]
[ROW][C]48[/C][C]4705[/C][C]4780.87929706507[/C][C]-75.8792970650738[/C][/ROW]
[ROW][C]49[/C][C]4675[/C][C]4728.75891632485[/C][C]-53.7589163248467[/C][/ROW]
[ROW][C]50[/C][C]4900[/C][C]4691.8327019896[/C][C]208.167298010403[/C][/ROW]
[ROW][C]51[/C][C]4945[/C][C]4834.8197781701[/C][C]110.180221829904[/C][/ROW]
[ROW][C]52[/C][C]4905[/C][C]4910.50096307739[/C][C]-5.50096307738841[/C][/ROW]
[ROW][C]53[/C][C]4955[/C][C]4906.72243189535[/C][C]48.2775681046478[/C][/ROW]
[ROW][C]54[/C][C]5120[/C][C]4939.88358820744[/C][C]180.116411792557[/C][/ROW]
[ROW][C]55[/C][C]4860[/C][C]5063.60292040079[/C][C]-203.60292040079[/C][/ROW]
[ROW][C]56[/C][C]5040[/C][C]4923.75104852577[/C][C]116.248951474228[/C][/ROW]
[ROW][C]57[/C][C]5140[/C][C]5003.60075517623[/C][C]136.399244823773[/C][/ROW]
[ROW][C]58[/C][C]5240[/C][C]5097.29140398123[/C][C]142.708596018769[/C][/ROW]
[ROW][C]59[/C][C]5145[/C][C]5195.31585395765[/C][C]-50.3158539576534[/C][/ROW]
[ROW][C]60[/C][C]5070[/C][C]5160.75462886758[/C][C]-90.7546288675803[/C][/ROW]
[ROW][C]61[/C][C]5085[/C][C]5098.41660000498[/C][C]-13.4166000049827[/C][/ROW]
[ROW][C]62[/C][C]5215[/C][C]5089.20093344577[/C][C]125.799066554227[/C][/ROW]
[ROW][C]63[/C][C]5255[/C][C]5175.6104746405[/C][C]79.3895253595001[/C][/ROW]
[ROW][C]64[/C][C]5275[/C][C]5230.14197992019[/C][C]44.8580200798133[/C][/ROW]
[ROW][C]65[/C][C]5315[/C][C]5260.95429864538[/C][C]54.0457013546211[/C][/ROW]
[ROW][C]66[/C][C]5450[/C][C]5298.07750142834[/C][C]151.922498571658[/C][/ROW]
[ROW][C]67[/C][C]5205[/C][C]5402.43084647542[/C][C]-197.430846475419[/C][/ROW]
[ROW][C]68[/C][C]5370[/C][C]5266.8184820206[/C][C]103.181517979397[/C][/ROW]
[ROW][C]69[/C][C]5500[/C][C]5337.69235948719[/C][C]162.307640512811[/C][/ROW]
[ROW][C]70[/C][C]5490[/C][C]5449.17910683173[/C][C]40.8208931682666[/C][/ROW]
[ROW][C]71[/C][C]5440[/C][C]5477.21838205408[/C][C]-37.2183820540849[/C][/ROW]
[ROW][C]72[/C][C]5360[/C][C]5451.65361909205[/C][C]-91.6536190920542[/C][/ROW]
[ROW][C]73[/C][C]5380[/C][C]5388.69808697635[/C][C]-8.69808697634653[/C][/ROW]
[ROW][C]74[/C][C]5460[/C][C]5382.72349809039[/C][C]77.276501909605[/C][/ROW]
[ROW][C]75[/C][C]5450[/C][C]5435.80359842853[/C][C]14.1964015714675[/C][/ROW]
[ROW][C]76[/C][C]5520[/C][C]5445.55489929274[/C][C]74.4451007072612[/C][/ROW]
[ROW][C]77[/C][C]5475[/C][C]5496.69015150494[/C][C]-21.6901515049385[/C][/ROW]
[ROW][C]78[/C][C]5600[/C][C]5481.79150327707[/C][C]118.208496722931[/C][/ROW]
[ROW][C]79[/C][C]5250[/C][C]5562.98719293462[/C][C]-312.987192934622[/C][/ROW]
[ROW][C]80[/C][C]5465[/C][C]5348.00086209688[/C][C]116.99913790312[/C][/ROW]
[ROW][C]81[/C][C]5515[/C][C]5428.36586084692[/C][C]86.6341391530759[/C][/ROW]
[ROW][C]82[/C][C]5425[/C][C]5487.87358551506[/C][C]-62.8735855150599[/C][/ROW]
[ROW][C]83[/C][C]5325[/C][C]5444.68663805642[/C][C]-119.686638056417[/C][/ROW]
[ROW][C]84[/C][C]5275[/C][C]5362.47563470898[/C][C]-87.4756347089779[/C][/ROW]
[ROW][C]85[/C][C]5160[/C][C]5302.38989903572[/C][C]-142.389899035717[/C][/ROW]
[ROW][C]86[/C][C]5360[/C][C]5204.58435736156[/C][C]155.415642638442[/C][/ROW]
[ROW][C]87[/C][C]5435[/C][C]5311.33709204169[/C][C]123.662907958313[/C][/ROW]
[ROW][C]88[/C][C]5285[/C][C]5396.27933710101[/C][C]-111.279337101012[/C][/ROW]
[ROW][C]89[/C][C]5415[/C][C]5319.84318596942[/C][C]95.1568140305772[/C][/ROW]
[ROW][C]90[/C][C]5575[/C][C]5385.20501151516[/C][C]189.794988484839[/C][/ROW]
[ROW][C]91[/C][C]5265[/C][C]5515.57241665774[/C][C]-250.572416657742[/C][/ROW]
[ROW][C]92[/C][C]5480[/C][C]5343.45788391504[/C][C]136.542116084964[/C][/ROW]
[ROW][C]93[/C][C]5565[/C][C]5437.24666890235[/C][C]127.753331097652[/C][/ROW]
[ROW][C]94[/C][C]5500[/C][C]5524.99856586485[/C][C]-24.9985658648548[/C][/ROW]
[ROW][C]95[/C][C]5280[/C][C]5507.82741614112[/C][C]-227.827416141124[/C][/ROW]
[ROW][C]96[/C][C]5135[/C][C]5351.33609200361[/C][C]-216.336092003607[/C][/ROW]
[ROW][C]97[/C][C]5050[/C][C]5202.73799055558[/C][C]-152.737990555582[/C][/ROW]
[ROW][C]98[/C][C]5100[/C][C]5097.82449597712[/C][C]2.17550402287907[/C][/ROW]
[ROW][C]99[/C][C]5070[/C][C]5099.31881791156[/C][C]-29.3188179115623[/C][/ROW]
[ROW][C]100[/C][C]5115[/C][C]5079.18015016542[/C][C]35.8198498345755[/C][/ROW]
[ROW][C]101[/C][C]5140[/C][C]5103.78428177506[/C][C]36.2157182249384[/C][/ROW]
[ROW][C]102[/C][C]5330[/C][C]5128.66032959936[/C][C]201.339670400645[/C][/ROW]
[ROW][C]103[/C][C]5080[/C][C]5266.95760810991[/C][C]-186.957608109906[/C][/ROW]
[ROW][C]104[/C][C]5285[/C][C]5138.53915809957[/C][C]146.460841900427[/C][/ROW]
[ROW][C]105[/C][C]5405[/C][C]5239.14097096083[/C][C]165.859029039169[/C][/ROW]
[ROW][C]106[/C][C]5385[/C][C]5353.0671152069[/C][C]31.9328847931019[/C][/ROW]
[ROW][C]107[/C][C]5255[/C][C]5375.00134730874[/C][C]-120.001347308744[/C][/ROW]
[ROW][C]108[/C][C]5100[/C][C]5292.57417477303[/C][C]-192.574174773025[/C][/ROW]
[ROW][C]109[/C][C]5040[/C][C]5160.29778716631[/C][C]-120.297787166307[/C][/ROW]
[ROW][C]110[/C][C]5235[/C][C]5077.6669944227[/C][C]157.333005577299[/C][/ROW]
[ROW][C]111[/C][C]5310[/C][C]5185.73673769748[/C][C]124.263262302523[/C][/ROW]
[ROW][C]112[/C][C]5265[/C][C]5271.09135738611[/C][C]-6.09135738610894[/C][/ROW]
[ROW][C]113[/C][C]5380[/C][C]5266.90729297765[/C][C]113.092707022349[/C][/ROW]
[ROW][C]114[/C][C]5465[/C][C]5344.58902141924[/C][C]120.41097858076[/C][/ROW]
[ROW][C]115[/C][C]5225[/C][C]5427.29756369198[/C][C]-202.29756369198[/C][/ROW]
[ROW][C]116[/C][C]5445[/C][C]5288.34232227212[/C][C]156.657677727875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302662&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302662&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
235853455130
336753544.29510101311130.704898986891
436803634.0743868434445.9256131565635
537353665.6200196580869.3799803419151
638603713.27611468054146.723885319463
737653814.0586082239-49.0586082239006
839053780.36096686301124.639033136989
941103865.97369804873244.026301951269
1041704033.59180022253136.40819977747
1141104127.28860005442-17.2886000544186
1240254115.41331322184-90.4133132218449
1341454053.309729090591.690270909497
1442854116.29043680422168.709563195784
1543704232.17457132302137.825428676977
1643554326.8448449836828.1551550163185
1743854346.1842096853938.8157903146121
1845254372.84620904729152.153790952712
1943754477.35842545229-102.358425452287
2045254407.04991821917117.950081780826
2146104488.06810642782121.931893572185
2245954571.8213429912623.1786570087397
2345004587.74242390621-87.7424239062111
2443704527.47343463052-157.473434630518
2543904419.30723269042-29.3072326904157
2645304399.17652266345130.823477336548
2745904489.03725823002100.962741769985
2845804558.3870907293321.6129092706678
2945954573.232682394821.7673176051958
3046854588.1843348897396.8156651102699
3144904654.68560101029-164.68560101029
3246354541.565467336393.4345326636976
3347104605.74428296951104.255717030486
3446554677.35601207283-22.3560120728316
3546654661.999993947493.00000605250534
3645504664.0606542821-114.060654282098
3745904585.714057007174.28594299283395
3846754588.6580086416486.3419913583602
3946454647.96506125716-2.96506125716041
4046654645.9284039920219.0715960079797
4146354659.02840469982-24.0284046998186
4247204642.5236445086377.476355491367
4345654695.7410213527-130.741021352704
4447204605.93692359696114.06307640304
4548304684.28518459139145.714815408614
4648304784.3745627530745.6254372469321
4747654815.71400912024-50.7140091202373
4847054780.87929706507-75.8792970650738
4946754728.75891632485-53.7589163248467
5049004691.8327019896208.167298010403
5149454834.8197781701110.180221829904
5249054910.50096307739-5.50096307738841
5349554906.7224318953548.2775681046478
5451204939.88358820744180.116411792557
5548605063.60292040079-203.60292040079
5650404923.75104852577116.248951474228
5751405003.60075517623136.399244823773
5852405097.29140398123142.708596018769
5951455195.31585395765-50.3158539576534
6050705160.75462886758-90.7546288675803
6150855098.41660000498-13.4166000049827
6252155089.20093344577125.799066554227
6352555175.610474640579.3895253595001
6452755230.1419799201944.8580200798133
6553155260.9542986453854.0457013546211
6654505298.07750142834151.922498571658
6752055402.43084647542-197.430846475419
6853705266.8184820206103.181517979397
6955005337.69235948719162.307640512811
7054905449.1791068317340.8208931682666
7154405477.21838205408-37.2183820540849
7253605451.65361909205-91.6536190920542
7353805388.69808697635-8.69808697634653
7454605382.7234980903977.276501909605
7554505435.8035984285314.1964015714675
7655205445.5548992927474.4451007072612
7754755496.69015150494-21.6901515049385
7856005481.79150327707118.208496722931
7952505562.98719293462-312.987192934622
8054655348.00086209688116.99913790312
8155155428.3658608469286.6341391530759
8254255487.87358551506-62.8735855150599
8353255444.68663805642-119.686638056417
8452755362.47563470898-87.4756347089779
8551605302.38989903572-142.389899035717
8653605204.58435736156155.415642638442
8754355311.33709204169123.662907958313
8852855396.27933710101-111.279337101012
8954155319.8431859694295.1568140305772
9055755385.20501151516189.794988484839
9152655515.57241665774-250.572416657742
9254805343.45788391504136.542116084964
9355655437.24666890235127.753331097652
9455005524.99856586485-24.9985658648548
9552805507.82741614112-227.827416141124
9651355351.33609200361-216.336092003607
9750505202.73799055558-152.737990555582
9851005097.824495977122.17550402287907
9950705099.31881791156-29.3188179115623
10051155079.1801501654235.8198498345755
10151405103.7842817750636.2157182249384
10253305128.66032959936201.339670400645
10350805266.95760810991-186.957608109906
10452855138.53915809957146.460841900427
10554055239.14097096083165.859029039169
10653855353.067115206931.9328847931019
10752555375.00134730874-120.001347308744
10851005292.57417477303-192.574174773025
10950405160.29778716631-120.297787166307
11052355077.6669944227157.333005577299
11153105185.73673769748124.263262302523
11252655271.09135738611-6.09135738610894
11353805266.90729297765113.092707022349
11454655344.58902141924120.41097858076
11552255427.29756369198-202.29756369198
11654455288.34232227212156.657677727875







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1175395.948192712055163.862335135825628.03405028827
1185395.948192712055114.385714377065677.51067104703
1195395.948192712055072.3882861645719.50809926009
1205395.948192712055035.248044327515756.64834109658
1215395.948192712055001.590257627855790.30612779624
1225395.948192712054970.587445953355821.30893947074
1235395.948192712054941.695676150655850.20070927344
1245395.948192712054914.534718947965877.36166647613
1255395.948192712054888.826396058775903.06998936532
1265395.948192712054864.359911652275927.53647377182
1275395.948192712054840.970999956045950.92538546805
1285395.948192712054818.528701874945973.36768354915

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 5395.94819271205 & 5163.86233513582 & 5628.03405028827 \tabularnewline
118 & 5395.94819271205 & 5114.38571437706 & 5677.51067104703 \tabularnewline
119 & 5395.94819271205 & 5072.388286164 & 5719.50809926009 \tabularnewline
120 & 5395.94819271205 & 5035.24804432751 & 5756.64834109658 \tabularnewline
121 & 5395.94819271205 & 5001.59025762785 & 5790.30612779624 \tabularnewline
122 & 5395.94819271205 & 4970.58744595335 & 5821.30893947074 \tabularnewline
123 & 5395.94819271205 & 4941.69567615065 & 5850.20070927344 \tabularnewline
124 & 5395.94819271205 & 4914.53471894796 & 5877.36166647613 \tabularnewline
125 & 5395.94819271205 & 4888.82639605877 & 5903.06998936532 \tabularnewline
126 & 5395.94819271205 & 4864.35991165227 & 5927.53647377182 \tabularnewline
127 & 5395.94819271205 & 4840.97099995604 & 5950.92538546805 \tabularnewline
128 & 5395.94819271205 & 4818.52870187494 & 5973.36768354915 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302662&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]5395.94819271205[/C][C]5163.86233513582[/C][C]5628.03405028827[/C][/ROW]
[ROW][C]118[/C][C]5395.94819271205[/C][C]5114.38571437706[/C][C]5677.51067104703[/C][/ROW]
[ROW][C]119[/C][C]5395.94819271205[/C][C]5072.388286164[/C][C]5719.50809926009[/C][/ROW]
[ROW][C]120[/C][C]5395.94819271205[/C][C]5035.24804432751[/C][C]5756.64834109658[/C][/ROW]
[ROW][C]121[/C][C]5395.94819271205[/C][C]5001.59025762785[/C][C]5790.30612779624[/C][/ROW]
[ROW][C]122[/C][C]5395.94819271205[/C][C]4970.58744595335[/C][C]5821.30893947074[/C][/ROW]
[ROW][C]123[/C][C]5395.94819271205[/C][C]4941.69567615065[/C][C]5850.20070927344[/C][/ROW]
[ROW][C]124[/C][C]5395.94819271205[/C][C]4914.53471894796[/C][C]5877.36166647613[/C][/ROW]
[ROW][C]125[/C][C]5395.94819271205[/C][C]4888.82639605877[/C][C]5903.06998936532[/C][/ROW]
[ROW][C]126[/C][C]5395.94819271205[/C][C]4864.35991165227[/C][C]5927.53647377182[/C][/ROW]
[ROW][C]127[/C][C]5395.94819271205[/C][C]4840.97099995604[/C][C]5950.92538546805[/C][/ROW]
[ROW][C]128[/C][C]5395.94819271205[/C][C]4818.52870187494[/C][C]5973.36768354915[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302662&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302662&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
1175395.948192712055163.862335135825628.03405028827
1185395.948192712055114.385714377065677.51067104703
1195395.948192712055072.3882861645719.50809926009
1205395.948192712055035.248044327515756.64834109658
1215395.948192712055001.590257627855790.30612779624
1225395.948192712054970.587445953355821.30893947074
1235395.948192712054941.695676150655850.20070927344
1245395.948192712054914.534718947965877.36166647613
1255395.948192712054888.826396058775903.06998936532
1265395.948192712054864.359911652275927.53647377182
1275395.948192712054840.970999956045950.92538546805
1285395.948192712054818.528701874945973.36768354915



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')