Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Aug 2017 18:40:32 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/06/t1502037642p4qss8alcstnxqi.htm/, Retrieved Sat, 11 May 2024 22:35:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=306962, Retrieved Sat, 11 May 2024 22:35:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-06 16:40:32] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
6195800.00
6172725.00
6149325.00
6100900.00
6579950.00
6554600.00
6195800.00
5957250.00
5980325.00
5980325.00
6006000.00
6052150.00
6123975.00
6123975.00
6077825.00
5957250.00
6579950.00
6674850.00
6531525.00
6195800.00
6339450.00
6123975.00
6221150.00
6267625.00
6316050.00
6195800.00
6221150.00
6052150.00
6579950.00
6746675.00
6603350.00
6339450.00
6626425.00
6316050.00
6603350.00
6579950.00
6651775.00
6387875.00
6674850.00
6651775.00
7082400.00
6985225.00
6603350.00
6410950.00
6674850.00
6316050.00
6579950.00
6626425.00
6723600.00
6508450.00
6626425.00
6698250.00
6962150.00
6746675.00
6459700.00
6149325.00
6436625.00
5646875.00
6029075.00
6244225.00
6459700.00
6149325.00
6149325.00
6149325.00
6316050.00
6077825.00
5765175.00
5503550.00
5693350.00
4952350.00
5406375.00
5670275.00
5718700.00
5454800.00
5477875.00
5406375.00
5646875.00
5477875.00
5144750.00
4903925.00
5311150.00
4426825.00
5001100.00
5262725.00
5262725.00
4952350.00
4665375.00
4642300.00
4903925.00
4665375.00
4211675.00
3899025.00
4234750.00
3445325.00
4162925.00
4544800.00
4665375.00
4401475.00
4068025.00
4306575.00
4401475.00
4329650.00
3611725.00
3278600.00
3516825.00
2799225.00
3540225.00
3804125.00
4019275.00
3660475.00
3324750.00
3516825.00
3611725.00
3421925.00
2704325.00
2391675.00
2678650.00
1889225.00
2750475.00
3278600.00




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306962&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=306962&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306962&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







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=306962&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=306962&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306962&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=306962&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=306962&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306962&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=306962&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=306962&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306962&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):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')