Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 10 Aug 2015 15:25:42 +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/2015/Aug/10/t1439216772dq5ebj00pp7mjj7.htm/, Retrieved Wed, 22 May 2024 10:18:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279998, Retrieved Wed, 22 May 2024 10:18:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2015-08-10 14:25:42] [d3245c242fac7b2d7caab09de558415e] [Current]
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Dataseries X:
6195800
6172725
6149325
6100900
6579950
6554600
6195800
5957250
5980325
5980325
6006000
6052150
6123975
6123975
6077825
5957250
6579950
6674850
6531525
6195800
6339450
6123975
6221150
6267625
6316050
6195800
6221150
6052150
6579950
6746675
6603350
6339450
6626425
6316050
6603350
6579950
6651775
6387875
6674850
6651775
7082400
6985225
6603350
6410950
6674850
6316050
6579950
6626425
6723600
6508450
6626425
6698250
6962150
6746675
6459700
6149325
6436625
5646875
6029075
6244225
6459700
6149325
6149325
6149325
6316050
6077825
5765175
5503550
5693350
4952350
5406375
5670275
5718700
5454800
5477875
5406375
5646875
5477875
5144750
4903925
5311150
4426825
5001100
5262725
5262725
4952350
4665375
4642300
4903925
4665375
4211675
3899025
4234750
3445325
4162925
4544800
4665375
4401475
4068025
4306575
4401475
4329650
3611725
3278600
3516825
2799225
3540225
3804125
4019275
3660475
3324750
3516825
3611725
3421925
2704325
2391675
2678650
1889225
2750475
3278600




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279998&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279998&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405343002238898
beta0.0645195510985462
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238898 \tabularnewline
beta & 0.0645195510985462 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279998&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]0.405343002238898[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510985462[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279998&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
alpha0.405343002238898
beta0.0645195510985462
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1361239756123708.68055556266.319444443099
1461239756110268.3878775913706.6121224128
1560778256055509.486623622315.5133763989
1659572505934352.9174634422897.0825365577
1765799506563304.8586885916645.1413114108
1866748506659365.2238205715484.7761794291
1965315256301050.83442701230474.165572989
2061958006179734.4180500116065.5819499856
2163394506233540.59692667105909.403073328
2261239756307413.30746203-183438.307462034
2362211506281899.40241039-60749.4024103899
2462676256314007.00144481-46382.0014448082
2563160506362570.14543118-46520.1454311786
2661958006340940.50206261-145140.502062611
2762211506225541.9725099-4391.97250990011
2860521506091835.67067624-39685.6706762398
2965799506687995.79740224-108045.797402243
3067466756725855.9851861120819.0148138925
3166033506490720.68222516112629.31777484
3263394506184227.11899154155222.881008461
3366264256341595.31238741284829.687612592
3463160506314338.008989311711.99101068638
3566033506440081.99151761163268.008482393
3665799506580646.47596927-696.47596926894
3766517756657949.89265374-6174.89265373908
3863878756605387.8740925-217512.874092504
3966748506553817.33014531121032.66985469
4066517756462710.08099936189064.919000644
4170824007129670.93787315-47270.9378731493
4269852257289114.67658255-303889.676582552
4366033506988783.18165922-385433.181659215
4464109506504532.99108277-93582.9910827652
4566748506630415.1132108144434.8867891897
4663160506323364.6567471-7314.65674709901
4765799506527291.2139464752658.7860535327
4866264256508396.7298343118028.270165703
4967236006616549.90122019107050.098779807
5065084506473153.6416259535296.3583740471
5166264256720932.04402042-94507.0440204199
5266982506572832.23663903125417.763360973
5369621507061709.9613827-99559.9613827011
5467466757034245.6584954-287570.658495402
5564597006679352.40826101-219652.408261008
5661493256427500.50275537-278175.502755372
5764366256547454.52482519-110829.524825186
5856468756129456.8232812-482581.823281201
5960290756146732.66598762-117657.665987621
6062442256063551.689976180673.310024
6164597006158085.33983647301614.660163535
6261493256023489.95535205125835.044647945
6361493256205751.25199757-56426.2519975677
6461493256179835.13554007-30510.1355400737
6563160506443614.16997272-127564.16997272
6660778256264154.4697051-186329.469705104
6757651755964492.19406431-199317.194064305
6855035505660419.17973861-156869.179738613
6956933505906567.11937351-213217.119373509
7049523505200834.31219532-248484.312195321
7154063755510958.98821435-104583.98821435
7256702755591778.190094278496.8099058019
7357187005695438.0064964423261.9935035622
7454548005314830.182048139969.817951996
7554778755366152.05906553111722.940934474
7654063755399916.875628666458.12437133584
7756468755598045.3233242748829.6766757295
7854778755436832.0348990441042.9651009627
7951447505209248.30924968-64498.3092496786
8049039254976229.01845901-72304.0184590071
8153111505216522.5755700294627.4244299792
8244268254616026.85410491-189201.854104912
8350011005038729.31877267-37629.3187726736
8452627255260286.164849562438.8351504365
8552627255303009.29316336-40284.293163362
8649523504967121.30308777-14771.3030877728
8746653754935952.62425971-270577.624259709
8846423004739189.86590178-96889.865901784
8949039254904952.39941553-1027.39941553213
9046653754701924.51234132-36549.5123413187
9142116754361124.16134024-149449.161340239
9238990254067803.03598446-168778.035984464
9342347504344509.5528951-109759.552895103
9434453253463291.77046686-17966.7704668613
9541629254020920.91736093142004.082639067
9645448004319199.65556911225600.34443089
9746653754412892.31680861252482.683191394
9844014754204421.63651676197053.363483237
9940680254106112.12645349-38087.1264534853
10043065754112067.1658566194507.834143396
10144014754465766.55742258-64291.5574225849
10243296504227132.54756936102517.452430643
10336117253890363.44079473-278638.440794731
10432786003544601.6551148-266001.655114796
10535168253825871.72753892-309046.727538923
10627992252922124.35155239-122899.351552392
10735402253533268.191517636956.80848237127
10838041253823906.32712662-19781.327126618
10940192753825092.42259565194182.577404354
11036604753549475.48001378110999.519986217
11133247503263652.8920219461097.1079780567
11235168253437915.8913996878909.1086003152
11336117253577628.1816589434096.8183410624
11434219253467409.36556636-45484.3655663598
11527043252829461.12281807-125136.122818071
11623916752542918.84182833-151243.84182833
11726786502837593.20780428-158943.207804284
11818892252101793.74300563-212568.74300563
11927504752747876.173891072598.8261089283
12032786003014799.41704229263800.582957708

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6123975 & 6123708.68055556 & 266.319444443099 \tabularnewline
14 & 6123975 & 6110268.38787759 & 13706.6121224128 \tabularnewline
15 & 6077825 & 6055509.4866236 & 22315.5133763989 \tabularnewline
16 & 5957250 & 5934352.91746344 & 22897.0825365577 \tabularnewline
17 & 6579950 & 6563304.85868859 & 16645.1413114108 \tabularnewline
18 & 6674850 & 6659365.22382057 & 15484.7761794291 \tabularnewline
19 & 6531525 & 6301050.83442701 & 230474.165572989 \tabularnewline
20 & 6195800 & 6179734.41805001 & 16065.5819499856 \tabularnewline
21 & 6339450 & 6233540.59692667 & 105909.403073328 \tabularnewline
22 & 6123975 & 6307413.30746203 & -183438.307462034 \tabularnewline
23 & 6221150 & 6281899.40241039 & -60749.4024103899 \tabularnewline
24 & 6267625 & 6314007.00144481 & -46382.0014448082 \tabularnewline
25 & 6316050 & 6362570.14543118 & -46520.1454311786 \tabularnewline
26 & 6195800 & 6340940.50206261 & -145140.502062611 \tabularnewline
27 & 6221150 & 6225541.9725099 & -4391.97250990011 \tabularnewline
28 & 6052150 & 6091835.67067624 & -39685.6706762398 \tabularnewline
29 & 6579950 & 6687995.79740224 & -108045.797402243 \tabularnewline
30 & 6746675 & 6725855.98518611 & 20819.0148138925 \tabularnewline
31 & 6603350 & 6490720.68222516 & 112629.31777484 \tabularnewline
32 & 6339450 & 6184227.11899154 & 155222.881008461 \tabularnewline
33 & 6626425 & 6341595.31238741 & 284829.687612592 \tabularnewline
34 & 6316050 & 6314338.00898931 & 1711.99101068638 \tabularnewline
35 & 6603350 & 6440081.99151761 & 163268.008482393 \tabularnewline
36 & 6579950 & 6580646.47596927 & -696.47596926894 \tabularnewline
37 & 6651775 & 6657949.89265374 & -6174.89265373908 \tabularnewline
38 & 6387875 & 6605387.8740925 & -217512.874092504 \tabularnewline
39 & 6674850 & 6553817.33014531 & 121032.66985469 \tabularnewline
40 & 6651775 & 6462710.08099936 & 189064.919000644 \tabularnewline
41 & 7082400 & 7129670.93787315 & -47270.9378731493 \tabularnewline
42 & 6985225 & 7289114.67658255 & -303889.676582552 \tabularnewline
43 & 6603350 & 6988783.18165922 & -385433.181659215 \tabularnewline
44 & 6410950 & 6504532.99108277 & -93582.9910827652 \tabularnewline
45 & 6674850 & 6630415.11321081 & 44434.8867891897 \tabularnewline
46 & 6316050 & 6323364.6567471 & -7314.65674709901 \tabularnewline
47 & 6579950 & 6527291.21394647 & 52658.7860535327 \tabularnewline
48 & 6626425 & 6508396.7298343 & 118028.270165703 \tabularnewline
49 & 6723600 & 6616549.90122019 & 107050.098779807 \tabularnewline
50 & 6508450 & 6473153.64162595 & 35296.3583740471 \tabularnewline
51 & 6626425 & 6720932.04402042 & -94507.0440204199 \tabularnewline
52 & 6698250 & 6572832.23663903 & 125417.763360973 \tabularnewline
53 & 6962150 & 7061709.9613827 & -99559.9613827011 \tabularnewline
54 & 6746675 & 7034245.6584954 & -287570.658495402 \tabularnewline
55 & 6459700 & 6679352.40826101 & -219652.408261008 \tabularnewline
56 & 6149325 & 6427500.50275537 & -278175.502755372 \tabularnewline
57 & 6436625 & 6547454.52482519 & -110829.524825186 \tabularnewline
58 & 5646875 & 6129456.8232812 & -482581.823281201 \tabularnewline
59 & 6029075 & 6146732.66598762 & -117657.665987621 \tabularnewline
60 & 6244225 & 6063551.689976 & 180673.310024 \tabularnewline
61 & 6459700 & 6158085.33983647 & 301614.660163535 \tabularnewline
62 & 6149325 & 6023489.95535205 & 125835.044647945 \tabularnewline
63 & 6149325 & 6205751.25199757 & -56426.2519975677 \tabularnewline
64 & 6149325 & 6179835.13554007 & -30510.1355400737 \tabularnewline
65 & 6316050 & 6443614.16997272 & -127564.16997272 \tabularnewline
66 & 6077825 & 6264154.4697051 & -186329.469705104 \tabularnewline
67 & 5765175 & 5964492.19406431 & -199317.194064305 \tabularnewline
68 & 5503550 & 5660419.17973861 & -156869.179738613 \tabularnewline
69 & 5693350 & 5906567.11937351 & -213217.119373509 \tabularnewline
70 & 4952350 & 5200834.31219532 & -248484.312195321 \tabularnewline
71 & 5406375 & 5510958.98821435 & -104583.98821435 \tabularnewline
72 & 5670275 & 5591778.1900942 & 78496.8099058019 \tabularnewline
73 & 5718700 & 5695438.00649644 & 23261.9935035622 \tabularnewline
74 & 5454800 & 5314830.182048 & 139969.817951996 \tabularnewline
75 & 5477875 & 5366152.05906553 & 111722.940934474 \tabularnewline
76 & 5406375 & 5399916.87562866 & 6458.12437133584 \tabularnewline
77 & 5646875 & 5598045.32332427 & 48829.6766757295 \tabularnewline
78 & 5477875 & 5436832.03489904 & 41042.9651009627 \tabularnewline
79 & 5144750 & 5209248.30924968 & -64498.3092496786 \tabularnewline
80 & 4903925 & 4976229.01845901 & -72304.0184590071 \tabularnewline
81 & 5311150 & 5216522.57557002 & 94627.4244299792 \tabularnewline
82 & 4426825 & 4616026.85410491 & -189201.854104912 \tabularnewline
83 & 5001100 & 5038729.31877267 & -37629.3187726736 \tabularnewline
84 & 5262725 & 5260286.16484956 & 2438.8351504365 \tabularnewline
85 & 5262725 & 5303009.29316336 & -40284.293163362 \tabularnewline
86 & 4952350 & 4967121.30308777 & -14771.3030877728 \tabularnewline
87 & 4665375 & 4935952.62425971 & -270577.624259709 \tabularnewline
88 & 4642300 & 4739189.86590178 & -96889.865901784 \tabularnewline
89 & 4903925 & 4904952.39941553 & -1027.39941553213 \tabularnewline
90 & 4665375 & 4701924.51234132 & -36549.5123413187 \tabularnewline
91 & 4211675 & 4361124.16134024 & -149449.161340239 \tabularnewline
92 & 3899025 & 4067803.03598446 & -168778.035984464 \tabularnewline
93 & 4234750 & 4344509.5528951 & -109759.552895103 \tabularnewline
94 & 3445325 & 3463291.77046686 & -17966.7704668613 \tabularnewline
95 & 4162925 & 4020920.91736093 & 142004.082639067 \tabularnewline
96 & 4544800 & 4319199.65556911 & 225600.34443089 \tabularnewline
97 & 4665375 & 4412892.31680861 & 252482.683191394 \tabularnewline
98 & 4401475 & 4204421.63651676 & 197053.363483237 \tabularnewline
99 & 4068025 & 4106112.12645349 & -38087.1264534853 \tabularnewline
100 & 4306575 & 4112067.1658566 & 194507.834143396 \tabularnewline
101 & 4401475 & 4465766.55742258 & -64291.5574225849 \tabularnewline
102 & 4329650 & 4227132.54756936 & 102517.452430643 \tabularnewline
103 & 3611725 & 3890363.44079473 & -278638.440794731 \tabularnewline
104 & 3278600 & 3544601.6551148 & -266001.655114796 \tabularnewline
105 & 3516825 & 3825871.72753892 & -309046.727538923 \tabularnewline
106 & 2799225 & 2922124.35155239 & -122899.351552392 \tabularnewline
107 & 3540225 & 3533268.19151763 & 6956.80848237127 \tabularnewline
108 & 3804125 & 3823906.32712662 & -19781.327126618 \tabularnewline
109 & 4019275 & 3825092.42259565 & 194182.577404354 \tabularnewline
110 & 3660475 & 3549475.48001378 & 110999.519986217 \tabularnewline
111 & 3324750 & 3263652.89202194 & 61097.1079780567 \tabularnewline
112 & 3516825 & 3437915.89139968 & 78909.1086003152 \tabularnewline
113 & 3611725 & 3577628.18165894 & 34096.8183410624 \tabularnewline
114 & 3421925 & 3467409.36556636 & -45484.3655663598 \tabularnewline
115 & 2704325 & 2829461.12281807 & -125136.122818071 \tabularnewline
116 & 2391675 & 2542918.84182833 & -151243.84182833 \tabularnewline
117 & 2678650 & 2837593.20780428 & -158943.207804284 \tabularnewline
118 & 1889225 & 2101793.74300563 & -212568.74300563 \tabularnewline
119 & 2750475 & 2747876.17389107 & 2598.8261089283 \tabularnewline
120 & 3278600 & 3014799.41704229 & 263800.582957708 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279998&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]6123975[/C][C]6123708.68055556[/C][C]266.319444443099[/C][/ROW]
[ROW][C]14[/C][C]6123975[/C][C]6110268.38787759[/C][C]13706.6121224128[/C][/ROW]
[ROW][C]15[/C][C]6077825[/C][C]6055509.4866236[/C][C]22315.5133763989[/C][/ROW]
[ROW][C]16[/C][C]5957250[/C][C]5934352.91746344[/C][C]22897.0825365577[/C][/ROW]
[ROW][C]17[/C][C]6579950[/C][C]6563304.85868859[/C][C]16645.1413114108[/C][/ROW]
[ROW][C]18[/C][C]6674850[/C][C]6659365.22382057[/C][C]15484.7761794291[/C][/ROW]
[ROW][C]19[/C][C]6531525[/C][C]6301050.83442701[/C][C]230474.165572989[/C][/ROW]
[ROW][C]20[/C][C]6195800[/C][C]6179734.41805001[/C][C]16065.5819499856[/C][/ROW]
[ROW][C]21[/C][C]6339450[/C][C]6233540.59692667[/C][C]105909.403073328[/C][/ROW]
[ROW][C]22[/C][C]6123975[/C][C]6307413.30746203[/C][C]-183438.307462034[/C][/ROW]
[ROW][C]23[/C][C]6221150[/C][C]6281899.40241039[/C][C]-60749.4024103899[/C][/ROW]
[ROW][C]24[/C][C]6267625[/C][C]6314007.00144481[/C][C]-46382.0014448082[/C][/ROW]
[ROW][C]25[/C][C]6316050[/C][C]6362570.14543118[/C][C]-46520.1454311786[/C][/ROW]
[ROW][C]26[/C][C]6195800[/C][C]6340940.50206261[/C][C]-145140.502062611[/C][/ROW]
[ROW][C]27[/C][C]6221150[/C][C]6225541.9725099[/C][C]-4391.97250990011[/C][/ROW]
[ROW][C]28[/C][C]6052150[/C][C]6091835.67067624[/C][C]-39685.6706762398[/C][/ROW]
[ROW][C]29[/C][C]6579950[/C][C]6687995.79740224[/C][C]-108045.797402243[/C][/ROW]
[ROW][C]30[/C][C]6746675[/C][C]6725855.98518611[/C][C]20819.0148138925[/C][/ROW]
[ROW][C]31[/C][C]6603350[/C][C]6490720.68222516[/C][C]112629.31777484[/C][/ROW]
[ROW][C]32[/C][C]6339450[/C][C]6184227.11899154[/C][C]155222.881008461[/C][/ROW]
[ROW][C]33[/C][C]6626425[/C][C]6341595.31238741[/C][C]284829.687612592[/C][/ROW]
[ROW][C]34[/C][C]6316050[/C][C]6314338.00898931[/C][C]1711.99101068638[/C][/ROW]
[ROW][C]35[/C][C]6603350[/C][C]6440081.99151761[/C][C]163268.008482393[/C][/ROW]
[ROW][C]36[/C][C]6579950[/C][C]6580646.47596927[/C][C]-696.47596926894[/C][/ROW]
[ROW][C]37[/C][C]6651775[/C][C]6657949.89265374[/C][C]-6174.89265373908[/C][/ROW]
[ROW][C]38[/C][C]6387875[/C][C]6605387.8740925[/C][C]-217512.874092504[/C][/ROW]
[ROW][C]39[/C][C]6674850[/C][C]6553817.33014531[/C][C]121032.66985469[/C][/ROW]
[ROW][C]40[/C][C]6651775[/C][C]6462710.08099936[/C][C]189064.919000644[/C][/ROW]
[ROW][C]41[/C][C]7082400[/C][C]7129670.93787315[/C][C]-47270.9378731493[/C][/ROW]
[ROW][C]42[/C][C]6985225[/C][C]7289114.67658255[/C][C]-303889.676582552[/C][/ROW]
[ROW][C]43[/C][C]6603350[/C][C]6988783.18165922[/C][C]-385433.181659215[/C][/ROW]
[ROW][C]44[/C][C]6410950[/C][C]6504532.99108277[/C][C]-93582.9910827652[/C][/ROW]
[ROW][C]45[/C][C]6674850[/C][C]6630415.11321081[/C][C]44434.8867891897[/C][/ROW]
[ROW][C]46[/C][C]6316050[/C][C]6323364.6567471[/C][C]-7314.65674709901[/C][/ROW]
[ROW][C]47[/C][C]6579950[/C][C]6527291.21394647[/C][C]52658.7860535327[/C][/ROW]
[ROW][C]48[/C][C]6626425[/C][C]6508396.7298343[/C][C]118028.270165703[/C][/ROW]
[ROW][C]49[/C][C]6723600[/C][C]6616549.90122019[/C][C]107050.098779807[/C][/ROW]
[ROW][C]50[/C][C]6508450[/C][C]6473153.64162595[/C][C]35296.3583740471[/C][/ROW]
[ROW][C]51[/C][C]6626425[/C][C]6720932.04402042[/C][C]-94507.0440204199[/C][/ROW]
[ROW][C]52[/C][C]6698250[/C][C]6572832.23663903[/C][C]125417.763360973[/C][/ROW]
[ROW][C]53[/C][C]6962150[/C][C]7061709.9613827[/C][C]-99559.9613827011[/C][/ROW]
[ROW][C]54[/C][C]6746675[/C][C]7034245.6584954[/C][C]-287570.658495402[/C][/ROW]
[ROW][C]55[/C][C]6459700[/C][C]6679352.40826101[/C][C]-219652.408261008[/C][/ROW]
[ROW][C]56[/C][C]6149325[/C][C]6427500.50275537[/C][C]-278175.502755372[/C][/ROW]
[ROW][C]57[/C][C]6436625[/C][C]6547454.52482519[/C][C]-110829.524825186[/C][/ROW]
[ROW][C]58[/C][C]5646875[/C][C]6129456.8232812[/C][C]-482581.823281201[/C][/ROW]
[ROW][C]59[/C][C]6029075[/C][C]6146732.66598762[/C][C]-117657.665987621[/C][/ROW]
[ROW][C]60[/C][C]6244225[/C][C]6063551.689976[/C][C]180673.310024[/C][/ROW]
[ROW][C]61[/C][C]6459700[/C][C]6158085.33983647[/C][C]301614.660163535[/C][/ROW]
[ROW][C]62[/C][C]6149325[/C][C]6023489.95535205[/C][C]125835.044647945[/C][/ROW]
[ROW][C]63[/C][C]6149325[/C][C]6205751.25199757[/C][C]-56426.2519975677[/C][/ROW]
[ROW][C]64[/C][C]6149325[/C][C]6179835.13554007[/C][C]-30510.1355400737[/C][/ROW]
[ROW][C]65[/C][C]6316050[/C][C]6443614.16997272[/C][C]-127564.16997272[/C][/ROW]
[ROW][C]66[/C][C]6077825[/C][C]6264154.4697051[/C][C]-186329.469705104[/C][/ROW]
[ROW][C]67[/C][C]5765175[/C][C]5964492.19406431[/C][C]-199317.194064305[/C][/ROW]
[ROW][C]68[/C][C]5503550[/C][C]5660419.17973861[/C][C]-156869.179738613[/C][/ROW]
[ROW][C]69[/C][C]5693350[/C][C]5906567.11937351[/C][C]-213217.119373509[/C][/ROW]
[ROW][C]70[/C][C]4952350[/C][C]5200834.31219532[/C][C]-248484.312195321[/C][/ROW]
[ROW][C]71[/C][C]5406375[/C][C]5510958.98821435[/C][C]-104583.98821435[/C][/ROW]
[ROW][C]72[/C][C]5670275[/C][C]5591778.1900942[/C][C]78496.8099058019[/C][/ROW]
[ROW][C]73[/C][C]5718700[/C][C]5695438.00649644[/C][C]23261.9935035622[/C][/ROW]
[ROW][C]74[/C][C]5454800[/C][C]5314830.182048[/C][C]139969.817951996[/C][/ROW]
[ROW][C]75[/C][C]5477875[/C][C]5366152.05906553[/C][C]111722.940934474[/C][/ROW]
[ROW][C]76[/C][C]5406375[/C][C]5399916.87562866[/C][C]6458.12437133584[/C][/ROW]
[ROW][C]77[/C][C]5646875[/C][C]5598045.32332427[/C][C]48829.6766757295[/C][/ROW]
[ROW][C]78[/C][C]5477875[/C][C]5436832.03489904[/C][C]41042.9651009627[/C][/ROW]
[ROW][C]79[/C][C]5144750[/C][C]5209248.30924968[/C][C]-64498.3092496786[/C][/ROW]
[ROW][C]80[/C][C]4903925[/C][C]4976229.01845901[/C][C]-72304.0184590071[/C][/ROW]
[ROW][C]81[/C][C]5311150[/C][C]5216522.57557002[/C][C]94627.4244299792[/C][/ROW]
[ROW][C]82[/C][C]4426825[/C][C]4616026.85410491[/C][C]-189201.854104912[/C][/ROW]
[ROW][C]83[/C][C]5001100[/C][C]5038729.31877267[/C][C]-37629.3187726736[/C][/ROW]
[ROW][C]84[/C][C]5262725[/C][C]5260286.16484956[/C][C]2438.8351504365[/C][/ROW]
[ROW][C]85[/C][C]5262725[/C][C]5303009.29316336[/C][C]-40284.293163362[/C][/ROW]
[ROW][C]86[/C][C]4952350[/C][C]4967121.30308777[/C][C]-14771.3030877728[/C][/ROW]
[ROW][C]87[/C][C]4665375[/C][C]4935952.62425971[/C][C]-270577.624259709[/C][/ROW]
[ROW][C]88[/C][C]4642300[/C][C]4739189.86590178[/C][C]-96889.865901784[/C][/ROW]
[ROW][C]89[/C][C]4903925[/C][C]4904952.39941553[/C][C]-1027.39941553213[/C][/ROW]
[ROW][C]90[/C][C]4665375[/C][C]4701924.51234132[/C][C]-36549.5123413187[/C][/ROW]
[ROW][C]91[/C][C]4211675[/C][C]4361124.16134024[/C][C]-149449.161340239[/C][/ROW]
[ROW][C]92[/C][C]3899025[/C][C]4067803.03598446[/C][C]-168778.035984464[/C][/ROW]
[ROW][C]93[/C][C]4234750[/C][C]4344509.5528951[/C][C]-109759.552895103[/C][/ROW]
[ROW][C]94[/C][C]3445325[/C][C]3463291.77046686[/C][C]-17966.7704668613[/C][/ROW]
[ROW][C]95[/C][C]4162925[/C][C]4020920.91736093[/C][C]142004.082639067[/C][/ROW]
[ROW][C]96[/C][C]4544800[/C][C]4319199.65556911[/C][C]225600.34443089[/C][/ROW]
[ROW][C]97[/C][C]4665375[/C][C]4412892.31680861[/C][C]252482.683191394[/C][/ROW]
[ROW][C]98[/C][C]4401475[/C][C]4204421.63651676[/C][C]197053.363483237[/C][/ROW]
[ROW][C]99[/C][C]4068025[/C][C]4106112.12645349[/C][C]-38087.1264534853[/C][/ROW]
[ROW][C]100[/C][C]4306575[/C][C]4112067.1658566[/C][C]194507.834143396[/C][/ROW]
[ROW][C]101[/C][C]4401475[/C][C]4465766.55742258[/C][C]-64291.5574225849[/C][/ROW]
[ROW][C]102[/C][C]4329650[/C][C]4227132.54756936[/C][C]102517.452430643[/C][/ROW]
[ROW][C]103[/C][C]3611725[/C][C]3890363.44079473[/C][C]-278638.440794731[/C][/ROW]
[ROW][C]104[/C][C]3278600[/C][C]3544601.6551148[/C][C]-266001.655114796[/C][/ROW]
[ROW][C]105[/C][C]3516825[/C][C]3825871.72753892[/C][C]-309046.727538923[/C][/ROW]
[ROW][C]106[/C][C]2799225[/C][C]2922124.35155239[/C][C]-122899.351552392[/C][/ROW]
[ROW][C]107[/C][C]3540225[/C][C]3533268.19151763[/C][C]6956.80848237127[/C][/ROW]
[ROW][C]108[/C][C]3804125[/C][C]3823906.32712662[/C][C]-19781.327126618[/C][/ROW]
[ROW][C]109[/C][C]4019275[/C][C]3825092.42259565[/C][C]194182.577404354[/C][/ROW]
[ROW][C]110[/C][C]3660475[/C][C]3549475.48001378[/C][C]110999.519986217[/C][/ROW]
[ROW][C]111[/C][C]3324750[/C][C]3263652.89202194[/C][C]61097.1079780567[/C][/ROW]
[ROW][C]112[/C][C]3516825[/C][C]3437915.89139968[/C][C]78909.1086003152[/C][/ROW]
[ROW][C]113[/C][C]3611725[/C][C]3577628.18165894[/C][C]34096.8183410624[/C][/ROW]
[ROW][C]114[/C][C]3421925[/C][C]3467409.36556636[/C][C]-45484.3655663598[/C][/ROW]
[ROW][C]115[/C][C]2704325[/C][C]2829461.12281807[/C][C]-125136.122818071[/C][/ROW]
[ROW][C]116[/C][C]2391675[/C][C]2542918.84182833[/C][C]-151243.84182833[/C][/ROW]
[ROW][C]117[/C][C]2678650[/C][C]2837593.20780428[/C][C]-158943.207804284[/C][/ROW]
[ROW][C]118[/C][C]1889225[/C][C]2101793.74300563[/C][C]-212568.74300563[/C][/ROW]
[ROW][C]119[/C][C]2750475[/C][C]2747876.17389107[/C][C]2598.8261089283[/C][/ROW]
[ROW][C]120[/C][C]3278600[/C][C]3014799.41704229[/C][C]263800.582957708[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279998&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279998&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
1361239756123708.68055556266.319444443099
1461239756110268.3878775913706.6121224128
1560778256055509.486623622315.5133763989
1659572505934352.9174634422897.0825365577
1765799506563304.8586885916645.1413114108
1866748506659365.2238205715484.7761794291
1965315256301050.83442701230474.165572989
2061958006179734.4180500116065.5819499856
2163394506233540.59692667105909.403073328
2261239756307413.30746203-183438.307462034
2362211506281899.40241039-60749.4024103899
2462676256314007.00144481-46382.0014448082
2563160506362570.14543118-46520.1454311786
2661958006340940.50206261-145140.502062611
2762211506225541.9725099-4391.97250990011
2860521506091835.67067624-39685.6706762398
2965799506687995.79740224-108045.797402243
3067466756725855.9851861120819.0148138925
3166033506490720.68222516112629.31777484
3263394506184227.11899154155222.881008461
3366264256341595.31238741284829.687612592
3463160506314338.008989311711.99101068638
3566033506440081.99151761163268.008482393
3665799506580646.47596927-696.47596926894
3766517756657949.89265374-6174.89265373908
3863878756605387.8740925-217512.874092504
3966748506553817.33014531121032.66985469
4066517756462710.08099936189064.919000644
4170824007129670.93787315-47270.9378731493
4269852257289114.67658255-303889.676582552
4366033506988783.18165922-385433.181659215
4464109506504532.99108277-93582.9910827652
4566748506630415.1132108144434.8867891897
4663160506323364.6567471-7314.65674709901
4765799506527291.2139464752658.7860535327
4866264256508396.7298343118028.270165703
4967236006616549.90122019107050.098779807
5065084506473153.6416259535296.3583740471
5166264256720932.04402042-94507.0440204199
5266982506572832.23663903125417.763360973
5369621507061709.9613827-99559.9613827011
5467466757034245.6584954-287570.658495402
5564597006679352.40826101-219652.408261008
5661493256427500.50275537-278175.502755372
5764366256547454.52482519-110829.524825186
5856468756129456.8232812-482581.823281201
5960290756146732.66598762-117657.665987621
6062442256063551.689976180673.310024
6164597006158085.33983647301614.660163535
6261493256023489.95535205125835.044647945
6361493256205751.25199757-56426.2519975677
6461493256179835.13554007-30510.1355400737
6563160506443614.16997272-127564.16997272
6660778256264154.4697051-186329.469705104
6757651755964492.19406431-199317.194064305
6855035505660419.17973861-156869.179738613
6956933505906567.11937351-213217.119373509
7049523505200834.31219532-248484.312195321
7154063755510958.98821435-104583.98821435
7256702755591778.190094278496.8099058019
7357187005695438.0064964423261.9935035622
7454548005314830.182048139969.817951996
7554778755366152.05906553111722.940934474
7654063755399916.875628666458.12437133584
7756468755598045.3233242748829.6766757295
7854778755436832.0348990441042.9651009627
7951447505209248.30924968-64498.3092496786
8049039254976229.01845901-72304.0184590071
8153111505216522.5755700294627.4244299792
8244268254616026.85410491-189201.854104912
8350011005038729.31877267-37629.3187726736
8452627255260286.164849562438.8351504365
8552627255303009.29316336-40284.293163362
8649523504967121.30308777-14771.3030877728
8746653754935952.62425971-270577.624259709
8846423004739189.86590178-96889.865901784
8949039254904952.39941553-1027.39941553213
9046653754701924.51234132-36549.5123413187
9142116754361124.16134024-149449.161340239
9238990254067803.03598446-168778.035984464
9342347504344509.5528951-109759.552895103
9434453253463291.77046686-17966.7704668613
9541629254020920.91736093142004.082639067
9645448004319199.65556911225600.34443089
9746653754412892.31680861252482.683191394
9844014754204421.63651676197053.363483237
9940680254106112.12645349-38087.1264534853
10043065754112067.1658566194507.834143396
10144014754465766.55742258-64291.5574225849
10243296504227132.54756936102517.452430643
10336117253890363.44079473-278638.440794731
10432786003544601.6551148-266001.655114796
10535168253825871.72753892-309046.727538923
10627992252922124.35155239-122899.351552392
10735402253533268.191517636956.80848237127
10838041253823906.32712662-19781.327126618
10940192753825092.42259565194182.577404354
11036604753549475.48001378110999.519986217
11133247503263652.8920219461097.1079780567
11235168253437915.8913996878909.1086003152
11336117253577628.1816589434096.8183410624
11434219253467409.36556636-45484.3655663598
11527043252829461.12281807-125136.122818071
11623916752542918.84182833-151243.84182833
11726786502837593.20780428-158943.207804284
11818892252101793.74300563-212568.74300563
11927504752747876.173891072598.8261089283
12032786003014799.41704229263800.582957708







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1213259536.58274142962820.849710123556252.31577269
1222852033.329099112528873.467735893175193.19046233
1232484929.748624212134399.296398682835460.20084974
1242636808.353258832258022.710318633015593.99619902
1252707612.631870982299723.402639853115501.86110212
1262525082.867792992087273.30958442962892.42600159
1271848228.918211551379710.239446612316747.59697649
1281590180.178362111090188.494584062090171.86214016
1291938832.734548311406626.53861352471038.93048312
1301236978.79612775671836.8342897051802120.7579658
1312104142.403628541505361.875213182702922.93204391
1322532236.74089221899131.758464323165341.72332007

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 3259536.5827414 & 2962820.84971012 & 3556252.31577269 \tabularnewline
122 & 2852033.32909911 & 2528873.46773589 & 3175193.19046233 \tabularnewline
123 & 2484929.74862421 & 2134399.29639868 & 2835460.20084974 \tabularnewline
124 & 2636808.35325883 & 2258022.71031863 & 3015593.99619902 \tabularnewline
125 & 2707612.63187098 & 2299723.40263985 & 3115501.86110212 \tabularnewline
126 & 2525082.86779299 & 2087273.3095844 & 2962892.42600159 \tabularnewline
127 & 1848228.91821155 & 1379710.23944661 & 2316747.59697649 \tabularnewline
128 & 1590180.17836211 & 1090188.49458406 & 2090171.86214016 \tabularnewline
129 & 1938832.73454831 & 1406626.5386135 & 2471038.93048312 \tabularnewline
130 & 1236978.79612775 & 671836.834289705 & 1802120.7579658 \tabularnewline
131 & 2104142.40362854 & 1505361.87521318 & 2702922.93204391 \tabularnewline
132 & 2532236.7408922 & 1899131.75846432 & 3165341.72332007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279998&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]121[/C][C]3259536.5827414[/C][C]2962820.84971012[/C][C]3556252.31577269[/C][/ROW]
[ROW][C]122[/C][C]2852033.32909911[/C][C]2528873.46773589[/C][C]3175193.19046233[/C][/ROW]
[ROW][C]123[/C][C]2484929.74862421[/C][C]2134399.29639868[/C][C]2835460.20084974[/C][/ROW]
[ROW][C]124[/C][C]2636808.35325883[/C][C]2258022.71031863[/C][C]3015593.99619902[/C][/ROW]
[ROW][C]125[/C][C]2707612.63187098[/C][C]2299723.40263985[/C][C]3115501.86110212[/C][/ROW]
[ROW][C]126[/C][C]2525082.86779299[/C][C]2087273.3095844[/C][C]2962892.42600159[/C][/ROW]
[ROW][C]127[/C][C]1848228.91821155[/C][C]1379710.23944661[/C][C]2316747.59697649[/C][/ROW]
[ROW][C]128[/C][C]1590180.17836211[/C][C]1090188.49458406[/C][C]2090171.86214016[/C][/ROW]
[ROW][C]129[/C][C]1938832.73454831[/C][C]1406626.5386135[/C][C]2471038.93048312[/C][/ROW]
[ROW][C]130[/C][C]1236978.79612775[/C][C]671836.834289705[/C][C]1802120.7579658[/C][/ROW]
[ROW][C]131[/C][C]2104142.40362854[/C][C]1505361.87521318[/C][C]2702922.93204391[/C][/ROW]
[ROW][C]132[/C][C]2532236.7408922[/C][C]1899131.75846432[/C][C]3165341.72332007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279998&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279998&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
1213259536.58274142962820.849710123556252.31577269
1222852033.329099112528873.467735893175193.19046233
1232484929.748624212134399.296398682835460.20084974
1242636808.353258832258022.710318633015593.99619902
1252707612.631870982299723.402639853115501.86110212
1262525082.867792992087273.30958442962892.42600159
1271848228.918211551379710.239446612316747.59697649
1281590180.178362111090188.494584062090171.86214016
1291938832.734548311406626.53861352471038.93048312
1301236978.79612775671836.8342897051802120.7579658
1312104142.403628541505361.875213182702922.93204391
1322532236.74089221899131.758464323165341.72332007



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')