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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 Dec 2016 09:22:32 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/16/t14818766191ifya4cmijalojk.htm/, Retrieved Thu, 02 May 2024 23:33:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300105, Retrieved Thu, 02 May 2024 23:33:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-16 08:22:32] [c0b73e623858a81821526bb2f691ccd9] [Current]
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Dataseries X:
3300
4100
3550
3650
3400
4050
2950
3300
3950
3950
3900
3700
3850
4350
4350
3550
3800
4150
3500
3850
4250
4150
4200
4100
4200
4350
4150
4200
3850
4100
3800
4250
4400
4400
4450
4050
4100
4450
4600
4100
4300
4850
3800
4450
4800
4900
4900
4350
4500
5050
5150
4450
4900
5450
4100
5050
5550
5450
5500
4950
5400
5750
5950
5950
5750
6450
5000
5950
6250
6300
6400
5700
5750
6450
6500
5950
6200
6750
5300
6450
6900
6800
6750
6050
6100
7400
7300
6200
6550
7500
5400
6750
7400
7450
7200
6500
7150
8000
7000
7600
7100
8050
5700
7550
7800
7800
8250
7150
7350
7800
8250
7500
8150
8550




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=300105&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=300105&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300105&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
alpha0.170865758239341
beta0.0337359057263226
gamma0.495826847482226

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.170865758239341 \tabularnewline
beta & 0.0337359057263226 \tabularnewline
gamma & 0.495826847482226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300105&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]0.170865758239341[/C][/ROW]
[ROW][C]beta[/C][C]0.0337359057263226[/C][/ROW]
[ROW][C]gamma[/C][C]0.495826847482226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300105&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300105&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
alpha0.170865758239341
beta0.0337359057263226
gamma0.495826847482226







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1338503712.31303418803137.686965811965
1443504219.36870649417130.631293505832
1543504236.3884720852113.611527914803
1635503465.7383680495884.2616319504164
1738003740.5590820471259.4409179528789
1841504103.1480885379546.8519114620531
1935003261.77280054976238.227199450245
2038503652.38687861153197.613121388467
2142504326.78383827489-76.7838382748878
2241504318.43648076795-168.43648076795
2342004260.12457139574-60.1245713957378
2441004061.6395484764338.3604515235656
2542004280.55744307708-80.5574430770757
2643504750.4372690613-400.437269061298
2741504669.67269903052-519.672699030515
2842003775.05365194898424.946348051019
2938504096.14915603925-246.149156039246
3041004397.8537451122-297.853745112197
3138003570.77468810781229.225311892189
3242503937.62093020338312.379069796616
3344004513.94950253514-113.949502535142
3444004456.48708419395-56.4870841939528
3544504457.39091354189-7.39091354188986
3640504304.26775847822-254.267758478218
3741004418.47433851473-318.474338514732
3844504709.0028529898-259.002852989801
3946004597.006712076122.99328792388496
4041004176.66636572071-76.6663657207127
4143004129.90337211913170.096627880873
4248504477.61537343548372.384626564519
4338003981.7478456235-181.747845623499
4444504310.19380643367139.806193566326
4548004678.4100174426121.589982557401
4649004682.81525985319217.184740146806
4749004750.24036741714149.759632582858
4843504522.95827503571-172.95827503571
4945004625.61299797239-125.612997972386
5050504975.6066813922774.3933186077265
5151505032.26940614003117.730593859975
5244504603.43089947581-153.430899475812
5349004649.20078473371250.799215266295
5454505098.53261628009351.467383719913
5541004375.83123230528-275.831232305277
5650504824.40029211978225.599707880224
5755505204.28701161598345.712988384018
5854505292.07893852966157.921061470342
5955005327.1094250799172.890574920105
6049504976.69180347585-26.6918034758473
6154005130.22934024589269.770659754112
6257505638.71057341886111.289426581136
6359505728.4125392841221.587460715904
6459505215.36058719048734.639412809524
6557505593.68959502319156.310404976813
6664506082.35373046784367.646269532162
6750005118.71497691871-118.714976918712
6859505815.36234576734134.637654232662
6962506243.652586655696.34741334431328
7063006208.8661787628291.1338212371757
7164006250.86430288928149.135697110717
7257005826.42635729159-126.426357291588
7357506096.31385937361-346.31385937361
7464506442.336680642657.66331935734797
7565006567.04153947532-67.0415394753209
7659506221.29303530326-271.293035303256
7762006189.8900148534810.1099851465233
7867506739.5149125063410.4850874936619
7953005511.90398416465-211.903984164654
8064506293.24737941677156.752620583233
8169006669.16656235944230.833437640557
8268006705.4786935889794.5213064110285
8367506769.80540475708-19.8054047570813
8460506200.14669000731-150.146690007306
8561006372.37814753318-272.378147533177
8674006873.77698401481526.223015985194
8773007056.58381796996243.416182030039
8862006681.91183051627-481.911830516269
8965506730.99309998552-180.993099985518
9075007247.80272735082252.197272649182
9154005971.1432271701-571.143227170098
9267506841.66828746026-91.6682874602566
9374007203.17004544427196.82995455573
9474507175.01132353824274.988676461764
9572007221.59153704257-21.5915370425691
9665006596.45144215525-96.4514421552503
9771506726.32491082881423.675089171189
9880007677.69576289843322.304237101574
9970007710.95034406901-710.950344069007
10076006871.07545312014728.924546879859
10171007253.78973001697-153.789730016973
10280507956.5246224561293.4753775438803
10357006316.53854453874-616.53854453874
10475507378.43555534184171.564444658157
10578007907.04872434139-107.048724341388
10678007860.87778823776-60.8777882377617
10782507727.98632549726522.013674502737
10871507167.93043338066-17.9304333806613
10973507528.47685857461-178.476858574607
11078008335.24403966705-535.244039667052
11182507792.20934711223457.790652887767
11275007745.72650283187-245.726502831865
11381507595.14962221518554.850377784817
11485508520.8374534323929.1625465676061

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3850 & 3712.31303418803 & 137.686965811965 \tabularnewline
14 & 4350 & 4219.36870649417 & 130.631293505832 \tabularnewline
15 & 4350 & 4236.3884720852 & 113.611527914803 \tabularnewline
16 & 3550 & 3465.73836804958 & 84.2616319504164 \tabularnewline
17 & 3800 & 3740.55908204712 & 59.4409179528789 \tabularnewline
18 & 4150 & 4103.14808853795 & 46.8519114620531 \tabularnewline
19 & 3500 & 3261.77280054976 & 238.227199450245 \tabularnewline
20 & 3850 & 3652.38687861153 & 197.613121388467 \tabularnewline
21 & 4250 & 4326.78383827489 & -76.7838382748878 \tabularnewline
22 & 4150 & 4318.43648076795 & -168.43648076795 \tabularnewline
23 & 4200 & 4260.12457139574 & -60.1245713957378 \tabularnewline
24 & 4100 & 4061.63954847643 & 38.3604515235656 \tabularnewline
25 & 4200 & 4280.55744307708 & -80.5574430770757 \tabularnewline
26 & 4350 & 4750.4372690613 & -400.437269061298 \tabularnewline
27 & 4150 & 4669.67269903052 & -519.672699030515 \tabularnewline
28 & 4200 & 3775.05365194898 & 424.946348051019 \tabularnewline
29 & 3850 & 4096.14915603925 & -246.149156039246 \tabularnewline
30 & 4100 & 4397.8537451122 & -297.853745112197 \tabularnewline
31 & 3800 & 3570.77468810781 & 229.225311892189 \tabularnewline
32 & 4250 & 3937.62093020338 & 312.379069796616 \tabularnewline
33 & 4400 & 4513.94950253514 & -113.949502535142 \tabularnewline
34 & 4400 & 4456.48708419395 & -56.4870841939528 \tabularnewline
35 & 4450 & 4457.39091354189 & -7.39091354188986 \tabularnewline
36 & 4050 & 4304.26775847822 & -254.267758478218 \tabularnewline
37 & 4100 & 4418.47433851473 & -318.474338514732 \tabularnewline
38 & 4450 & 4709.0028529898 & -259.002852989801 \tabularnewline
39 & 4600 & 4597.00671207612 & 2.99328792388496 \tabularnewline
40 & 4100 & 4176.66636572071 & -76.6663657207127 \tabularnewline
41 & 4300 & 4129.90337211913 & 170.096627880873 \tabularnewline
42 & 4850 & 4477.61537343548 & 372.384626564519 \tabularnewline
43 & 3800 & 3981.7478456235 & -181.747845623499 \tabularnewline
44 & 4450 & 4310.19380643367 & 139.806193566326 \tabularnewline
45 & 4800 & 4678.4100174426 & 121.589982557401 \tabularnewline
46 & 4900 & 4682.81525985319 & 217.184740146806 \tabularnewline
47 & 4900 & 4750.24036741714 & 149.759632582858 \tabularnewline
48 & 4350 & 4522.95827503571 & -172.95827503571 \tabularnewline
49 & 4500 & 4625.61299797239 & -125.612997972386 \tabularnewline
50 & 5050 & 4975.60668139227 & 74.3933186077265 \tabularnewline
51 & 5150 & 5032.26940614003 & 117.730593859975 \tabularnewline
52 & 4450 & 4603.43089947581 & -153.430899475812 \tabularnewline
53 & 4900 & 4649.20078473371 & 250.799215266295 \tabularnewline
54 & 5450 & 5098.53261628009 & 351.467383719913 \tabularnewline
55 & 4100 & 4375.83123230528 & -275.831232305277 \tabularnewline
56 & 5050 & 4824.40029211978 & 225.599707880224 \tabularnewline
57 & 5550 & 5204.28701161598 & 345.712988384018 \tabularnewline
58 & 5450 & 5292.07893852966 & 157.921061470342 \tabularnewline
59 & 5500 & 5327.1094250799 & 172.890574920105 \tabularnewline
60 & 4950 & 4976.69180347585 & -26.6918034758473 \tabularnewline
61 & 5400 & 5130.22934024589 & 269.770659754112 \tabularnewline
62 & 5750 & 5638.71057341886 & 111.289426581136 \tabularnewline
63 & 5950 & 5728.4125392841 & 221.587460715904 \tabularnewline
64 & 5950 & 5215.36058719048 & 734.639412809524 \tabularnewline
65 & 5750 & 5593.68959502319 & 156.310404976813 \tabularnewline
66 & 6450 & 6082.35373046784 & 367.646269532162 \tabularnewline
67 & 5000 & 5118.71497691871 & -118.714976918712 \tabularnewline
68 & 5950 & 5815.36234576734 & 134.637654232662 \tabularnewline
69 & 6250 & 6243.65258665569 & 6.34741334431328 \tabularnewline
70 & 6300 & 6208.86617876282 & 91.1338212371757 \tabularnewline
71 & 6400 & 6250.86430288928 & 149.135697110717 \tabularnewline
72 & 5700 & 5826.42635729159 & -126.426357291588 \tabularnewline
73 & 5750 & 6096.31385937361 & -346.31385937361 \tabularnewline
74 & 6450 & 6442.33668064265 & 7.66331935734797 \tabularnewline
75 & 6500 & 6567.04153947532 & -67.0415394753209 \tabularnewline
76 & 5950 & 6221.29303530326 & -271.293035303256 \tabularnewline
77 & 6200 & 6189.89001485348 & 10.1099851465233 \tabularnewline
78 & 6750 & 6739.51491250634 & 10.4850874936619 \tabularnewline
79 & 5300 & 5511.90398416465 & -211.903984164654 \tabularnewline
80 & 6450 & 6293.24737941677 & 156.752620583233 \tabularnewline
81 & 6900 & 6669.16656235944 & 230.833437640557 \tabularnewline
82 & 6800 & 6705.47869358897 & 94.5213064110285 \tabularnewline
83 & 6750 & 6769.80540475708 & -19.8054047570813 \tabularnewline
84 & 6050 & 6200.14669000731 & -150.146690007306 \tabularnewline
85 & 6100 & 6372.37814753318 & -272.378147533177 \tabularnewline
86 & 7400 & 6873.77698401481 & 526.223015985194 \tabularnewline
87 & 7300 & 7056.58381796996 & 243.416182030039 \tabularnewline
88 & 6200 & 6681.91183051627 & -481.911830516269 \tabularnewline
89 & 6550 & 6730.99309998552 & -180.993099985518 \tabularnewline
90 & 7500 & 7247.80272735082 & 252.197272649182 \tabularnewline
91 & 5400 & 5971.1432271701 & -571.143227170098 \tabularnewline
92 & 6750 & 6841.66828746026 & -91.6682874602566 \tabularnewline
93 & 7400 & 7203.17004544427 & 196.82995455573 \tabularnewline
94 & 7450 & 7175.01132353824 & 274.988676461764 \tabularnewline
95 & 7200 & 7221.59153704257 & -21.5915370425691 \tabularnewline
96 & 6500 & 6596.45144215525 & -96.4514421552503 \tabularnewline
97 & 7150 & 6726.32491082881 & 423.675089171189 \tabularnewline
98 & 8000 & 7677.69576289843 & 322.304237101574 \tabularnewline
99 & 7000 & 7710.95034406901 & -710.950344069007 \tabularnewline
100 & 7600 & 6871.07545312014 & 728.924546879859 \tabularnewline
101 & 7100 & 7253.78973001697 & -153.789730016973 \tabularnewline
102 & 8050 & 7956.52462245612 & 93.4753775438803 \tabularnewline
103 & 5700 & 6316.53854453874 & -616.53854453874 \tabularnewline
104 & 7550 & 7378.43555534184 & 171.564444658157 \tabularnewline
105 & 7800 & 7907.04872434139 & -107.048724341388 \tabularnewline
106 & 7800 & 7860.87778823776 & -60.8777882377617 \tabularnewline
107 & 8250 & 7727.98632549726 & 522.013674502737 \tabularnewline
108 & 7150 & 7167.93043338066 & -17.9304333806613 \tabularnewline
109 & 7350 & 7528.47685857461 & -178.476858574607 \tabularnewline
110 & 7800 & 8335.24403966705 & -535.244039667052 \tabularnewline
111 & 8250 & 7792.20934711223 & 457.790652887767 \tabularnewline
112 & 7500 & 7745.72650283187 & -245.726502831865 \tabularnewline
113 & 8150 & 7595.14962221518 & 554.850377784817 \tabularnewline
114 & 8550 & 8520.83745343239 & 29.1625465676061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300105&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]3850[/C][C]3712.31303418803[/C][C]137.686965811965[/C][/ROW]
[ROW][C]14[/C][C]4350[/C][C]4219.36870649417[/C][C]130.631293505832[/C][/ROW]
[ROW][C]15[/C][C]4350[/C][C]4236.3884720852[/C][C]113.611527914803[/C][/ROW]
[ROW][C]16[/C][C]3550[/C][C]3465.73836804958[/C][C]84.2616319504164[/C][/ROW]
[ROW][C]17[/C][C]3800[/C][C]3740.55908204712[/C][C]59.4409179528789[/C][/ROW]
[ROW][C]18[/C][C]4150[/C][C]4103.14808853795[/C][C]46.8519114620531[/C][/ROW]
[ROW][C]19[/C][C]3500[/C][C]3261.77280054976[/C][C]238.227199450245[/C][/ROW]
[ROW][C]20[/C][C]3850[/C][C]3652.38687861153[/C][C]197.613121388467[/C][/ROW]
[ROW][C]21[/C][C]4250[/C][C]4326.78383827489[/C][C]-76.7838382748878[/C][/ROW]
[ROW][C]22[/C][C]4150[/C][C]4318.43648076795[/C][C]-168.43648076795[/C][/ROW]
[ROW][C]23[/C][C]4200[/C][C]4260.12457139574[/C][C]-60.1245713957378[/C][/ROW]
[ROW][C]24[/C][C]4100[/C][C]4061.63954847643[/C][C]38.3604515235656[/C][/ROW]
[ROW][C]25[/C][C]4200[/C][C]4280.55744307708[/C][C]-80.5574430770757[/C][/ROW]
[ROW][C]26[/C][C]4350[/C][C]4750.4372690613[/C][C]-400.437269061298[/C][/ROW]
[ROW][C]27[/C][C]4150[/C][C]4669.67269903052[/C][C]-519.672699030515[/C][/ROW]
[ROW][C]28[/C][C]4200[/C][C]3775.05365194898[/C][C]424.946348051019[/C][/ROW]
[ROW][C]29[/C][C]3850[/C][C]4096.14915603925[/C][C]-246.149156039246[/C][/ROW]
[ROW][C]30[/C][C]4100[/C][C]4397.8537451122[/C][C]-297.853745112197[/C][/ROW]
[ROW][C]31[/C][C]3800[/C][C]3570.77468810781[/C][C]229.225311892189[/C][/ROW]
[ROW][C]32[/C][C]4250[/C][C]3937.62093020338[/C][C]312.379069796616[/C][/ROW]
[ROW][C]33[/C][C]4400[/C][C]4513.94950253514[/C][C]-113.949502535142[/C][/ROW]
[ROW][C]34[/C][C]4400[/C][C]4456.48708419395[/C][C]-56.4870841939528[/C][/ROW]
[ROW][C]35[/C][C]4450[/C][C]4457.39091354189[/C][C]-7.39091354188986[/C][/ROW]
[ROW][C]36[/C][C]4050[/C][C]4304.26775847822[/C][C]-254.267758478218[/C][/ROW]
[ROW][C]37[/C][C]4100[/C][C]4418.47433851473[/C][C]-318.474338514732[/C][/ROW]
[ROW][C]38[/C][C]4450[/C][C]4709.0028529898[/C][C]-259.002852989801[/C][/ROW]
[ROW][C]39[/C][C]4600[/C][C]4597.00671207612[/C][C]2.99328792388496[/C][/ROW]
[ROW][C]40[/C][C]4100[/C][C]4176.66636572071[/C][C]-76.6663657207127[/C][/ROW]
[ROW][C]41[/C][C]4300[/C][C]4129.90337211913[/C][C]170.096627880873[/C][/ROW]
[ROW][C]42[/C][C]4850[/C][C]4477.61537343548[/C][C]372.384626564519[/C][/ROW]
[ROW][C]43[/C][C]3800[/C][C]3981.7478456235[/C][C]-181.747845623499[/C][/ROW]
[ROW][C]44[/C][C]4450[/C][C]4310.19380643367[/C][C]139.806193566326[/C][/ROW]
[ROW][C]45[/C][C]4800[/C][C]4678.4100174426[/C][C]121.589982557401[/C][/ROW]
[ROW][C]46[/C][C]4900[/C][C]4682.81525985319[/C][C]217.184740146806[/C][/ROW]
[ROW][C]47[/C][C]4900[/C][C]4750.24036741714[/C][C]149.759632582858[/C][/ROW]
[ROW][C]48[/C][C]4350[/C][C]4522.95827503571[/C][C]-172.95827503571[/C][/ROW]
[ROW][C]49[/C][C]4500[/C][C]4625.61299797239[/C][C]-125.612997972386[/C][/ROW]
[ROW][C]50[/C][C]5050[/C][C]4975.60668139227[/C][C]74.3933186077265[/C][/ROW]
[ROW][C]51[/C][C]5150[/C][C]5032.26940614003[/C][C]117.730593859975[/C][/ROW]
[ROW][C]52[/C][C]4450[/C][C]4603.43089947581[/C][C]-153.430899475812[/C][/ROW]
[ROW][C]53[/C][C]4900[/C][C]4649.20078473371[/C][C]250.799215266295[/C][/ROW]
[ROW][C]54[/C][C]5450[/C][C]5098.53261628009[/C][C]351.467383719913[/C][/ROW]
[ROW][C]55[/C][C]4100[/C][C]4375.83123230528[/C][C]-275.831232305277[/C][/ROW]
[ROW][C]56[/C][C]5050[/C][C]4824.40029211978[/C][C]225.599707880224[/C][/ROW]
[ROW][C]57[/C][C]5550[/C][C]5204.28701161598[/C][C]345.712988384018[/C][/ROW]
[ROW][C]58[/C][C]5450[/C][C]5292.07893852966[/C][C]157.921061470342[/C][/ROW]
[ROW][C]59[/C][C]5500[/C][C]5327.1094250799[/C][C]172.890574920105[/C][/ROW]
[ROW][C]60[/C][C]4950[/C][C]4976.69180347585[/C][C]-26.6918034758473[/C][/ROW]
[ROW][C]61[/C][C]5400[/C][C]5130.22934024589[/C][C]269.770659754112[/C][/ROW]
[ROW][C]62[/C][C]5750[/C][C]5638.71057341886[/C][C]111.289426581136[/C][/ROW]
[ROW][C]63[/C][C]5950[/C][C]5728.4125392841[/C][C]221.587460715904[/C][/ROW]
[ROW][C]64[/C][C]5950[/C][C]5215.36058719048[/C][C]734.639412809524[/C][/ROW]
[ROW][C]65[/C][C]5750[/C][C]5593.68959502319[/C][C]156.310404976813[/C][/ROW]
[ROW][C]66[/C][C]6450[/C][C]6082.35373046784[/C][C]367.646269532162[/C][/ROW]
[ROW][C]67[/C][C]5000[/C][C]5118.71497691871[/C][C]-118.714976918712[/C][/ROW]
[ROW][C]68[/C][C]5950[/C][C]5815.36234576734[/C][C]134.637654232662[/C][/ROW]
[ROW][C]69[/C][C]6250[/C][C]6243.65258665569[/C][C]6.34741334431328[/C][/ROW]
[ROW][C]70[/C][C]6300[/C][C]6208.86617876282[/C][C]91.1338212371757[/C][/ROW]
[ROW][C]71[/C][C]6400[/C][C]6250.86430288928[/C][C]149.135697110717[/C][/ROW]
[ROW][C]72[/C][C]5700[/C][C]5826.42635729159[/C][C]-126.426357291588[/C][/ROW]
[ROW][C]73[/C][C]5750[/C][C]6096.31385937361[/C][C]-346.31385937361[/C][/ROW]
[ROW][C]74[/C][C]6450[/C][C]6442.33668064265[/C][C]7.66331935734797[/C][/ROW]
[ROW][C]75[/C][C]6500[/C][C]6567.04153947532[/C][C]-67.0415394753209[/C][/ROW]
[ROW][C]76[/C][C]5950[/C][C]6221.29303530326[/C][C]-271.293035303256[/C][/ROW]
[ROW][C]77[/C][C]6200[/C][C]6189.89001485348[/C][C]10.1099851465233[/C][/ROW]
[ROW][C]78[/C][C]6750[/C][C]6739.51491250634[/C][C]10.4850874936619[/C][/ROW]
[ROW][C]79[/C][C]5300[/C][C]5511.90398416465[/C][C]-211.903984164654[/C][/ROW]
[ROW][C]80[/C][C]6450[/C][C]6293.24737941677[/C][C]156.752620583233[/C][/ROW]
[ROW][C]81[/C][C]6900[/C][C]6669.16656235944[/C][C]230.833437640557[/C][/ROW]
[ROW][C]82[/C][C]6800[/C][C]6705.47869358897[/C][C]94.5213064110285[/C][/ROW]
[ROW][C]83[/C][C]6750[/C][C]6769.80540475708[/C][C]-19.8054047570813[/C][/ROW]
[ROW][C]84[/C][C]6050[/C][C]6200.14669000731[/C][C]-150.146690007306[/C][/ROW]
[ROW][C]85[/C][C]6100[/C][C]6372.37814753318[/C][C]-272.378147533177[/C][/ROW]
[ROW][C]86[/C][C]7400[/C][C]6873.77698401481[/C][C]526.223015985194[/C][/ROW]
[ROW][C]87[/C][C]7300[/C][C]7056.58381796996[/C][C]243.416182030039[/C][/ROW]
[ROW][C]88[/C][C]6200[/C][C]6681.91183051627[/C][C]-481.911830516269[/C][/ROW]
[ROW][C]89[/C][C]6550[/C][C]6730.99309998552[/C][C]-180.993099985518[/C][/ROW]
[ROW][C]90[/C][C]7500[/C][C]7247.80272735082[/C][C]252.197272649182[/C][/ROW]
[ROW][C]91[/C][C]5400[/C][C]5971.1432271701[/C][C]-571.143227170098[/C][/ROW]
[ROW][C]92[/C][C]6750[/C][C]6841.66828746026[/C][C]-91.6682874602566[/C][/ROW]
[ROW][C]93[/C][C]7400[/C][C]7203.17004544427[/C][C]196.82995455573[/C][/ROW]
[ROW][C]94[/C][C]7450[/C][C]7175.01132353824[/C][C]274.988676461764[/C][/ROW]
[ROW][C]95[/C][C]7200[/C][C]7221.59153704257[/C][C]-21.5915370425691[/C][/ROW]
[ROW][C]96[/C][C]6500[/C][C]6596.45144215525[/C][C]-96.4514421552503[/C][/ROW]
[ROW][C]97[/C][C]7150[/C][C]6726.32491082881[/C][C]423.675089171189[/C][/ROW]
[ROW][C]98[/C][C]8000[/C][C]7677.69576289843[/C][C]322.304237101574[/C][/ROW]
[ROW][C]99[/C][C]7000[/C][C]7710.95034406901[/C][C]-710.950344069007[/C][/ROW]
[ROW][C]100[/C][C]7600[/C][C]6871.07545312014[/C][C]728.924546879859[/C][/ROW]
[ROW][C]101[/C][C]7100[/C][C]7253.78973001697[/C][C]-153.789730016973[/C][/ROW]
[ROW][C]102[/C][C]8050[/C][C]7956.52462245612[/C][C]93.4753775438803[/C][/ROW]
[ROW][C]103[/C][C]5700[/C][C]6316.53854453874[/C][C]-616.53854453874[/C][/ROW]
[ROW][C]104[/C][C]7550[/C][C]7378.43555534184[/C][C]171.564444658157[/C][/ROW]
[ROW][C]105[/C][C]7800[/C][C]7907.04872434139[/C][C]-107.048724341388[/C][/ROW]
[ROW][C]106[/C][C]7800[/C][C]7860.87778823776[/C][C]-60.8777882377617[/C][/ROW]
[ROW][C]107[/C][C]8250[/C][C]7727.98632549726[/C][C]522.013674502737[/C][/ROW]
[ROW][C]108[/C][C]7150[/C][C]7167.93043338066[/C][C]-17.9304333806613[/C][/ROW]
[ROW][C]109[/C][C]7350[/C][C]7528.47685857461[/C][C]-178.476858574607[/C][/ROW]
[ROW][C]110[/C][C]7800[/C][C]8335.24403966705[/C][C]-535.244039667052[/C][/ROW]
[ROW][C]111[/C][C]8250[/C][C]7792.20934711223[/C][C]457.790652887767[/C][/ROW]
[ROW][C]112[/C][C]7500[/C][C]7745.72650283187[/C][C]-245.726502831865[/C][/ROW]
[ROW][C]113[/C][C]8150[/C][C]7595.14962221518[/C][C]554.850377784817[/C][/ROW]
[ROW][C]114[/C][C]8550[/C][C]8520.83745343239[/C][C]29.1625465676061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300105&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300105&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
1338503712.31303418803137.686965811965
1443504219.36870649417130.631293505832
1543504236.3884720852113.611527914803
1635503465.7383680495884.2616319504164
1738003740.5590820471259.4409179528789
1841504103.1480885379546.8519114620531
1935003261.77280054976238.227199450245
2038503652.38687861153197.613121388467
2142504326.78383827489-76.7838382748878
2241504318.43648076795-168.43648076795
2342004260.12457139574-60.1245713957378
2441004061.6395484764338.3604515235656
2542004280.55744307708-80.5574430770757
2643504750.4372690613-400.437269061298
2741504669.67269903052-519.672699030515
2842003775.05365194898424.946348051019
2938504096.14915603925-246.149156039246
3041004397.8537451122-297.853745112197
3138003570.77468810781229.225311892189
3242503937.62093020338312.379069796616
3344004513.94950253514-113.949502535142
3444004456.48708419395-56.4870841939528
3544504457.39091354189-7.39091354188986
3640504304.26775847822-254.267758478218
3741004418.47433851473-318.474338514732
3844504709.0028529898-259.002852989801
3946004597.006712076122.99328792388496
4041004176.66636572071-76.6663657207127
4143004129.90337211913170.096627880873
4248504477.61537343548372.384626564519
4338003981.7478456235-181.747845623499
4444504310.19380643367139.806193566326
4548004678.4100174426121.589982557401
4649004682.81525985319217.184740146806
4749004750.24036741714149.759632582858
4843504522.95827503571-172.95827503571
4945004625.61299797239-125.612997972386
5050504975.6066813922774.3933186077265
5151505032.26940614003117.730593859975
5244504603.43089947581-153.430899475812
5349004649.20078473371250.799215266295
5454505098.53261628009351.467383719913
5541004375.83123230528-275.831232305277
5650504824.40029211978225.599707880224
5755505204.28701161598345.712988384018
5854505292.07893852966157.921061470342
5955005327.1094250799172.890574920105
6049504976.69180347585-26.6918034758473
6154005130.22934024589269.770659754112
6257505638.71057341886111.289426581136
6359505728.4125392841221.587460715904
6459505215.36058719048734.639412809524
6557505593.68959502319156.310404976813
6664506082.35373046784367.646269532162
6750005118.71497691871-118.714976918712
6859505815.36234576734134.637654232662
6962506243.652586655696.34741334431328
7063006208.8661787628291.1338212371757
7164006250.86430288928149.135697110717
7257005826.42635729159-126.426357291588
7357506096.31385937361-346.31385937361
7464506442.336680642657.66331935734797
7565006567.04153947532-67.0415394753209
7659506221.29303530326-271.293035303256
7762006189.8900148534810.1099851465233
7867506739.5149125063410.4850874936619
7953005511.90398416465-211.903984164654
8064506293.24737941677156.752620583233
8169006669.16656235944230.833437640557
8268006705.4786935889794.5213064110285
8367506769.80540475708-19.8054047570813
8460506200.14669000731-150.146690007306
8561006372.37814753318-272.378147533177
8674006873.77698401481526.223015985194
8773007056.58381796996243.416182030039
8862006681.91183051627-481.911830516269
8965506730.99309998552-180.993099985518
9075007247.80272735082252.197272649182
9154005971.1432271701-571.143227170098
9267506841.66828746026-91.6682874602566
9374007203.17004544427196.82995455573
9474507175.01132353824274.988676461764
9572007221.59153704257-21.5915370425691
9665006596.45144215525-96.4514421552503
9771506726.32491082881423.675089171189
9880007677.69576289843322.304237101574
9970007710.95034406901-710.950344069007
10076006871.07545312014728.924546879859
10171007253.78973001697-153.789730016973
10280507956.5246224561293.4753775438803
10357006316.53854453874-616.53854453874
10475507378.43555534184171.564444658157
10578007907.04872434139-107.048724341388
10678007860.87778823776-60.8777882377617
10782507727.98632549726522.013674502737
10871507167.93043338066-17.9304333806613
10973507528.47685857461-178.476858574607
11078008335.24403966705-535.244039667052
11182507792.20934711223457.790652887767
11275007745.72650283187-245.726502831865
11381507595.14962221518554.850377784817
11485508520.8374534323929.1625465676061







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1156577.818278623976040.954760278237114.68179696972
1168072.456673905437527.282891324438617.63045648642
1178459.627963699717905.730000459799013.52592693963
1188453.758685611887890.724856761169016.7925144626
1198574.280342185148001.701943048989146.85874132131
1207703.426746124557120.898721426018285.95477082309
1218001.509833046347408.631367142428594.38829895026
1228693.60662900278089.981659195879297.23159880954
1238654.859181518428040.096837371459269.6215256654
1248242.884738936797616.599711293898869.16976657969
1258466.783309190297828.596153195429104.97046518516
1269081.720355602418431.25773241859732.18297878631

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
115 & 6577.81827862397 & 6040.95476027823 & 7114.68179696972 \tabularnewline
116 & 8072.45667390543 & 7527.28289132443 & 8617.63045648642 \tabularnewline
117 & 8459.62796369971 & 7905.73000045979 & 9013.52592693963 \tabularnewline
118 & 8453.75868561188 & 7890.72485676116 & 9016.7925144626 \tabularnewline
119 & 8574.28034218514 & 8001.70194304898 & 9146.85874132131 \tabularnewline
120 & 7703.42674612455 & 7120.89872142601 & 8285.95477082309 \tabularnewline
121 & 8001.50983304634 & 7408.63136714242 & 8594.38829895026 \tabularnewline
122 & 8693.6066290027 & 8089.98165919587 & 9297.23159880954 \tabularnewline
123 & 8654.85918151842 & 8040.09683737145 & 9269.6215256654 \tabularnewline
124 & 8242.88473893679 & 7616.59971129389 & 8869.16976657969 \tabularnewline
125 & 8466.78330919029 & 7828.59615319542 & 9104.97046518516 \tabularnewline
126 & 9081.72035560241 & 8431.2577324185 & 9732.18297878631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300105&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]115[/C][C]6577.81827862397[/C][C]6040.95476027823[/C][C]7114.68179696972[/C][/ROW]
[ROW][C]116[/C][C]8072.45667390543[/C][C]7527.28289132443[/C][C]8617.63045648642[/C][/ROW]
[ROW][C]117[/C][C]8459.62796369971[/C][C]7905.73000045979[/C][C]9013.52592693963[/C][/ROW]
[ROW][C]118[/C][C]8453.75868561188[/C][C]7890.72485676116[/C][C]9016.7925144626[/C][/ROW]
[ROW][C]119[/C][C]8574.28034218514[/C][C]8001.70194304898[/C][C]9146.85874132131[/C][/ROW]
[ROW][C]120[/C][C]7703.42674612455[/C][C]7120.89872142601[/C][C]8285.95477082309[/C][/ROW]
[ROW][C]121[/C][C]8001.50983304634[/C][C]7408.63136714242[/C][C]8594.38829895026[/C][/ROW]
[ROW][C]122[/C][C]8693.6066290027[/C][C]8089.98165919587[/C][C]9297.23159880954[/C][/ROW]
[ROW][C]123[/C][C]8654.85918151842[/C][C]8040.09683737145[/C][C]9269.6215256654[/C][/ROW]
[ROW][C]124[/C][C]8242.88473893679[/C][C]7616.59971129389[/C][C]8869.16976657969[/C][/ROW]
[ROW][C]125[/C][C]8466.78330919029[/C][C]7828.59615319542[/C][C]9104.97046518516[/C][/ROW]
[ROW][C]126[/C][C]9081.72035560241[/C][C]8431.2577324185[/C][C]9732.18297878631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300105&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300105&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
1156577.818278623976040.954760278237114.68179696972
1168072.456673905437527.282891324438617.63045648642
1178459.627963699717905.730000459799013.52592693963
1188453.758685611887890.724856761169016.7925144626
1198574.280342185148001.701943048989146.85874132131
1207703.426746124557120.898721426018285.95477082309
1218001.509833046347408.631367142428594.38829895026
1228693.60662900278089.981659195879297.23159880954
1238654.859181518428040.096837371459269.6215256654
1248242.884738936797616.599711293898869.16976657969
1258466.783309190297828.596153195429104.97046518516
1269081.720355602418431.25773241859732.18297878631



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Double'
par1 <- '1'
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')