Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 30 Dec 2015 14:40:21 +0000
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/Dec/30/t1451486478absykcrzumns0da.htm/, Retrieved Thu, 16 May 2024 22:08:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287211, Retrieved Thu, 16 May 2024 22:08:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [] [2015-11-26 09:35:52] [1abbea75cc6be7d57004024c66566ad0]
- RMPD  [Exponential Smoothing] [] [2015-11-30 14:08:36] [1abbea75cc6be7d57004024c66566ad0]
- R P       [Exponential Smoothing] [] [2015-12-30 14:40:21] [663b8bcb3523d59827bca0af0b37f04c] [Current]
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Dataseries X:
91.99
92.17
92.19
92.24
92.19
92.21
92.22
92.14
92.43
92.93
93.01
93.07
93.08
93.11
93.21
93.49
93.48
93.51
93.52
93.49
93.76
94.25
94.42
94.45
94.45
94.53
94.78
95.05
95.21
95.23
95.23
95.34
95.93
96.75
97.15
97.21
97.21
97.35
97.44
97.34
97.44
97.43
97.43
97.47
97.69
98.54
98.64
98.72
98.72
98.73
98.68
98.75
98.73
98.74
98.75
98.85
99.14
99.83
99.93
100
100
100.08
100.25
100.4
100.33
100.29
100.29
100.32
100.82
101.42
101.46
101.55
101.56
101.56
101.6
101.66
101.82
101.94
101.95
101.93
102.26
102.65
102.9
102.94
99.14
99.18
99.23
99.32
99.46
99.5
99.95
100.13
100.43
101.09
101.27
101.29
101.04
101.14
101.11
101.01
101.08
101.06
101.26
101.32
101.4
101.85
102.12
102.15




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287211&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287211&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287211&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0157922109007943
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0157922109007943 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287211&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0157922109007943[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287211&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287211&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
alpha1
beta0.0157922109007943
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
392.1992.35-0.160000000000011
492.2492.3674732462559-0.127473246255889
592.1992.4154601618668-0.225460161866792
692.2192.3618996474409-0.151899647440871
792.2292.3795008161727-0.159500816172724
892.1492.3869819456449-0.246981945644876
992.4392.30308155467060.126918445329437
1092.9392.59508587752640.334914122473592
1193.0193.1003749119822-0.0903749119821669
1293.0793.178947692312-0.108947692312015
1393.0893.2372271673779-0.157227167377854
1493.1193.2447442027913-0.134744202791296
1593.2193.2726162939232-0.0626162939231563
1693.4993.37162744420370.118372555796313
1793.4893.6534968085697-0.173496808569681
1893.5193.6407569103781-0.130756910378139
1993.5293.6686919696727-0.148691969672726
2093.4993.6763437947284-0.186343794728387
2193.7693.6434010142220.116598985778026
2294.2593.91524236999620.334757630003779
2394.4294.41052893308990.00947106691012323
2494.4594.580678502176-0.130678502175982
2594.4594.6086147997094-0.158614799709426
2694.5394.6061099213404-0.0761099213404179
2794.7894.6849079774110.0950920225890286
2895.0594.93640969068670.113590309313324
2995.2195.20820353280760.00179646719234938
3095.2395.3682319029964-0.138231902996409
3195.2395.3860489156311-0.156048915631075
3295.3495.3835845582446-0.0435845582446035
3395.9395.49289626170880.437103738291228
3496.7596.08979909612940.660200903870589
3597.1596.92022512804020.229774871959791
3697.2197.3238537812779-0.113853781277925
3797.2197.3820557783521-0.172055778352117
3897.3597.3793386372137-0.0293386372136837
3997.4497.5188753152673-0.0788753152672541
4097.3497.6076296996537-0.267629699653682
4197.4497.5034032349934-0.0634032349934444
4297.4397.6024019577346-0.172401957734621
4397.4397.5896793496584-0.159679349658376
4497.4797.5871576596921-0.117157659692083
4597.6997.62530748122160.0646925187784291
4698.5497.84632911912180.693670880878187
4798.6498.7072837159684-0.0672837159684008
4898.7298.8062211573356-0.0862211573356291
4998.7298.8848595346349-0.164859534634871
5098.7398.8822560380949-0.152256038094905
5198.6898.8898515786304-0.209851578630406
5298.7598.8365375582428-0.0865375582428101
5398.7398.9051709388722-0.175170938872199
5498.7498.8824046024618-0.142404602461852
5598.7598.8901557189465-0.140155718946517
5698.8598.897942350274-0.0479423502739706
5799.1498.99718523456740.142814765432647
5899.8399.28944059546280.540559404537191
5999.9399.9879772235837-0.0579772235836629
60100100.087061635041-0.0870616350414082
61100100.155686739339-0.155686739339458
62100.08100.153228101517-0.0732281015173442
63100.25100.2320716678940.0179283321056829
64100.4100.402354795896-0.00235479589602505
65100.33100.552317608463-0.222317608462617
66100.29100.478806721903-0.188806721902807
67100.29100.435825046331-0.145825046331041
68100.32100.433522146445-0.11352214644478
69100.82100.4617293807660.358270619233807
70101.42100.9673872659450.452612734055322
71101.46101.574535021697-0.114535021697279
72101.55101.612726260479-0.0627262604791099
73101.56101.701735674145-0.141735674144599
74101.56101.709497354486-0.149497354486343
75101.6101.707136460735-0.107136460735191
76101.66101.745444539152-0.0854445391520926
77101.82101.8040951809690.01590481903051
78101.94101.964346353226-0.0243463532259511
79101.95102.083961870481-0.13396187048113
80101.93102.09184631637-0.161846316369832
81102.26102.0692904052080.190709594791784
82102.65102.402302131350.247697868650036
83102.9102.7962138283310.103786171668631
84102.94103.047852841443-0.107852841442948
8599.14103.086149606625-3.94614960662462
8699.1899.2238311797907-0.0438311797907147
8799.2399.2631389885554-0.0331389885554358
8899.3299.31261565065910.00738434934085319
8999.4699.40273226586130.0572677341387191
9099.599.5436366499966-0.0436366499966141
9199.9599.58294753081690.367052469183136
92100.13100.0387441008220.0912558991781367
93100.43100.2201852332280.209814766772382
94101.09100.5234986722750.566501327725405
95101.27101.1924449807180.0775550192823857
96101.29101.373669745939-0.0836697459385221
97101.04101.392348415665-0.352348415664665
98101.14101.1367840551740.00321594482606713
99101.11101.236834842053-0.126834842052858
100101.01101.204831839478-0.194831839477587
101101.08101.101755013978-0.0217550139783782
102101.06101.171411454209-0.111411454209474
103101.26101.1496520210280.110347978972172
104101.32101.351394659584-0.0313946595842509
105101.4101.410898868499-0.0108988684989129
106101.85101.4907267512690.359273248730972
107102.12101.9464004701840.17359952981603
108102.15102.219141990571-0.0691419905711257

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 92.19 & 92.35 & -0.160000000000011 \tabularnewline
4 & 92.24 & 92.3674732462559 & -0.127473246255889 \tabularnewline
5 & 92.19 & 92.4154601618668 & -0.225460161866792 \tabularnewline
6 & 92.21 & 92.3618996474409 & -0.151899647440871 \tabularnewline
7 & 92.22 & 92.3795008161727 & -0.159500816172724 \tabularnewline
8 & 92.14 & 92.3869819456449 & -0.246981945644876 \tabularnewline
9 & 92.43 & 92.3030815546706 & 0.126918445329437 \tabularnewline
10 & 92.93 & 92.5950858775264 & 0.334914122473592 \tabularnewline
11 & 93.01 & 93.1003749119822 & -0.0903749119821669 \tabularnewline
12 & 93.07 & 93.178947692312 & -0.108947692312015 \tabularnewline
13 & 93.08 & 93.2372271673779 & -0.157227167377854 \tabularnewline
14 & 93.11 & 93.2447442027913 & -0.134744202791296 \tabularnewline
15 & 93.21 & 93.2726162939232 & -0.0626162939231563 \tabularnewline
16 & 93.49 & 93.3716274442037 & 0.118372555796313 \tabularnewline
17 & 93.48 & 93.6534968085697 & -0.173496808569681 \tabularnewline
18 & 93.51 & 93.6407569103781 & -0.130756910378139 \tabularnewline
19 & 93.52 & 93.6686919696727 & -0.148691969672726 \tabularnewline
20 & 93.49 & 93.6763437947284 & -0.186343794728387 \tabularnewline
21 & 93.76 & 93.643401014222 & 0.116598985778026 \tabularnewline
22 & 94.25 & 93.9152423699962 & 0.334757630003779 \tabularnewline
23 & 94.42 & 94.4105289330899 & 0.00947106691012323 \tabularnewline
24 & 94.45 & 94.580678502176 & -0.130678502175982 \tabularnewline
25 & 94.45 & 94.6086147997094 & -0.158614799709426 \tabularnewline
26 & 94.53 & 94.6061099213404 & -0.0761099213404179 \tabularnewline
27 & 94.78 & 94.684907977411 & 0.0950920225890286 \tabularnewline
28 & 95.05 & 94.9364096906867 & 0.113590309313324 \tabularnewline
29 & 95.21 & 95.2082035328076 & 0.00179646719234938 \tabularnewline
30 & 95.23 & 95.3682319029964 & -0.138231902996409 \tabularnewline
31 & 95.23 & 95.3860489156311 & -0.156048915631075 \tabularnewline
32 & 95.34 & 95.3835845582446 & -0.0435845582446035 \tabularnewline
33 & 95.93 & 95.4928962617088 & 0.437103738291228 \tabularnewline
34 & 96.75 & 96.0897990961294 & 0.660200903870589 \tabularnewline
35 & 97.15 & 96.9202251280402 & 0.229774871959791 \tabularnewline
36 & 97.21 & 97.3238537812779 & -0.113853781277925 \tabularnewline
37 & 97.21 & 97.3820557783521 & -0.172055778352117 \tabularnewline
38 & 97.35 & 97.3793386372137 & -0.0293386372136837 \tabularnewline
39 & 97.44 & 97.5188753152673 & -0.0788753152672541 \tabularnewline
40 & 97.34 & 97.6076296996537 & -0.267629699653682 \tabularnewline
41 & 97.44 & 97.5034032349934 & -0.0634032349934444 \tabularnewline
42 & 97.43 & 97.6024019577346 & -0.172401957734621 \tabularnewline
43 & 97.43 & 97.5896793496584 & -0.159679349658376 \tabularnewline
44 & 97.47 & 97.5871576596921 & -0.117157659692083 \tabularnewline
45 & 97.69 & 97.6253074812216 & 0.0646925187784291 \tabularnewline
46 & 98.54 & 97.8463291191218 & 0.693670880878187 \tabularnewline
47 & 98.64 & 98.7072837159684 & -0.0672837159684008 \tabularnewline
48 & 98.72 & 98.8062211573356 & -0.0862211573356291 \tabularnewline
49 & 98.72 & 98.8848595346349 & -0.164859534634871 \tabularnewline
50 & 98.73 & 98.8822560380949 & -0.152256038094905 \tabularnewline
51 & 98.68 & 98.8898515786304 & -0.209851578630406 \tabularnewline
52 & 98.75 & 98.8365375582428 & -0.0865375582428101 \tabularnewline
53 & 98.73 & 98.9051709388722 & -0.175170938872199 \tabularnewline
54 & 98.74 & 98.8824046024618 & -0.142404602461852 \tabularnewline
55 & 98.75 & 98.8901557189465 & -0.140155718946517 \tabularnewline
56 & 98.85 & 98.897942350274 & -0.0479423502739706 \tabularnewline
57 & 99.14 & 98.9971852345674 & 0.142814765432647 \tabularnewline
58 & 99.83 & 99.2894405954628 & 0.540559404537191 \tabularnewline
59 & 99.93 & 99.9879772235837 & -0.0579772235836629 \tabularnewline
60 & 100 & 100.087061635041 & -0.0870616350414082 \tabularnewline
61 & 100 & 100.155686739339 & -0.155686739339458 \tabularnewline
62 & 100.08 & 100.153228101517 & -0.0732281015173442 \tabularnewline
63 & 100.25 & 100.232071667894 & 0.0179283321056829 \tabularnewline
64 & 100.4 & 100.402354795896 & -0.00235479589602505 \tabularnewline
65 & 100.33 & 100.552317608463 & -0.222317608462617 \tabularnewline
66 & 100.29 & 100.478806721903 & -0.188806721902807 \tabularnewline
67 & 100.29 & 100.435825046331 & -0.145825046331041 \tabularnewline
68 & 100.32 & 100.433522146445 & -0.11352214644478 \tabularnewline
69 & 100.82 & 100.461729380766 & 0.358270619233807 \tabularnewline
70 & 101.42 & 100.967387265945 & 0.452612734055322 \tabularnewline
71 & 101.46 & 101.574535021697 & -0.114535021697279 \tabularnewline
72 & 101.55 & 101.612726260479 & -0.0627262604791099 \tabularnewline
73 & 101.56 & 101.701735674145 & -0.141735674144599 \tabularnewline
74 & 101.56 & 101.709497354486 & -0.149497354486343 \tabularnewline
75 & 101.6 & 101.707136460735 & -0.107136460735191 \tabularnewline
76 & 101.66 & 101.745444539152 & -0.0854445391520926 \tabularnewline
77 & 101.82 & 101.804095180969 & 0.01590481903051 \tabularnewline
78 & 101.94 & 101.964346353226 & -0.0243463532259511 \tabularnewline
79 & 101.95 & 102.083961870481 & -0.13396187048113 \tabularnewline
80 & 101.93 & 102.09184631637 & -0.161846316369832 \tabularnewline
81 & 102.26 & 102.069290405208 & 0.190709594791784 \tabularnewline
82 & 102.65 & 102.40230213135 & 0.247697868650036 \tabularnewline
83 & 102.9 & 102.796213828331 & 0.103786171668631 \tabularnewline
84 & 102.94 & 103.047852841443 & -0.107852841442948 \tabularnewline
85 & 99.14 & 103.086149606625 & -3.94614960662462 \tabularnewline
86 & 99.18 & 99.2238311797907 & -0.0438311797907147 \tabularnewline
87 & 99.23 & 99.2631389885554 & -0.0331389885554358 \tabularnewline
88 & 99.32 & 99.3126156506591 & 0.00738434934085319 \tabularnewline
89 & 99.46 & 99.4027322658613 & 0.0572677341387191 \tabularnewline
90 & 99.5 & 99.5436366499966 & -0.0436366499966141 \tabularnewline
91 & 99.95 & 99.5829475308169 & 0.367052469183136 \tabularnewline
92 & 100.13 & 100.038744100822 & 0.0912558991781367 \tabularnewline
93 & 100.43 & 100.220185233228 & 0.209814766772382 \tabularnewline
94 & 101.09 & 100.523498672275 & 0.566501327725405 \tabularnewline
95 & 101.27 & 101.192444980718 & 0.0775550192823857 \tabularnewline
96 & 101.29 & 101.373669745939 & -0.0836697459385221 \tabularnewline
97 & 101.04 & 101.392348415665 & -0.352348415664665 \tabularnewline
98 & 101.14 & 101.136784055174 & 0.00321594482606713 \tabularnewline
99 & 101.11 & 101.236834842053 & -0.126834842052858 \tabularnewline
100 & 101.01 & 101.204831839478 & -0.194831839477587 \tabularnewline
101 & 101.08 & 101.101755013978 & -0.0217550139783782 \tabularnewline
102 & 101.06 & 101.171411454209 & -0.111411454209474 \tabularnewline
103 & 101.26 & 101.149652021028 & 0.110347978972172 \tabularnewline
104 & 101.32 & 101.351394659584 & -0.0313946595842509 \tabularnewline
105 & 101.4 & 101.410898868499 & -0.0108988684989129 \tabularnewline
106 & 101.85 & 101.490726751269 & 0.359273248730972 \tabularnewline
107 & 102.12 & 101.946400470184 & 0.17359952981603 \tabularnewline
108 & 102.15 & 102.219141990571 & -0.0691419905711257 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287211&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]92.19[/C][C]92.35[/C][C]-0.160000000000011[/C][/ROW]
[ROW][C]4[/C][C]92.24[/C][C]92.3674732462559[/C][C]-0.127473246255889[/C][/ROW]
[ROW][C]5[/C][C]92.19[/C][C]92.4154601618668[/C][C]-0.225460161866792[/C][/ROW]
[ROW][C]6[/C][C]92.21[/C][C]92.3618996474409[/C][C]-0.151899647440871[/C][/ROW]
[ROW][C]7[/C][C]92.22[/C][C]92.3795008161727[/C][C]-0.159500816172724[/C][/ROW]
[ROW][C]8[/C][C]92.14[/C][C]92.3869819456449[/C][C]-0.246981945644876[/C][/ROW]
[ROW][C]9[/C][C]92.43[/C][C]92.3030815546706[/C][C]0.126918445329437[/C][/ROW]
[ROW][C]10[/C][C]92.93[/C][C]92.5950858775264[/C][C]0.334914122473592[/C][/ROW]
[ROW][C]11[/C][C]93.01[/C][C]93.1003749119822[/C][C]-0.0903749119821669[/C][/ROW]
[ROW][C]12[/C][C]93.07[/C][C]93.178947692312[/C][C]-0.108947692312015[/C][/ROW]
[ROW][C]13[/C][C]93.08[/C][C]93.2372271673779[/C][C]-0.157227167377854[/C][/ROW]
[ROW][C]14[/C][C]93.11[/C][C]93.2447442027913[/C][C]-0.134744202791296[/C][/ROW]
[ROW][C]15[/C][C]93.21[/C][C]93.2726162939232[/C][C]-0.0626162939231563[/C][/ROW]
[ROW][C]16[/C][C]93.49[/C][C]93.3716274442037[/C][C]0.118372555796313[/C][/ROW]
[ROW][C]17[/C][C]93.48[/C][C]93.6534968085697[/C][C]-0.173496808569681[/C][/ROW]
[ROW][C]18[/C][C]93.51[/C][C]93.6407569103781[/C][C]-0.130756910378139[/C][/ROW]
[ROW][C]19[/C][C]93.52[/C][C]93.6686919696727[/C][C]-0.148691969672726[/C][/ROW]
[ROW][C]20[/C][C]93.49[/C][C]93.6763437947284[/C][C]-0.186343794728387[/C][/ROW]
[ROW][C]21[/C][C]93.76[/C][C]93.643401014222[/C][C]0.116598985778026[/C][/ROW]
[ROW][C]22[/C][C]94.25[/C][C]93.9152423699962[/C][C]0.334757630003779[/C][/ROW]
[ROW][C]23[/C][C]94.42[/C][C]94.4105289330899[/C][C]0.00947106691012323[/C][/ROW]
[ROW][C]24[/C][C]94.45[/C][C]94.580678502176[/C][C]-0.130678502175982[/C][/ROW]
[ROW][C]25[/C][C]94.45[/C][C]94.6086147997094[/C][C]-0.158614799709426[/C][/ROW]
[ROW][C]26[/C][C]94.53[/C][C]94.6061099213404[/C][C]-0.0761099213404179[/C][/ROW]
[ROW][C]27[/C][C]94.78[/C][C]94.684907977411[/C][C]0.0950920225890286[/C][/ROW]
[ROW][C]28[/C][C]95.05[/C][C]94.9364096906867[/C][C]0.113590309313324[/C][/ROW]
[ROW][C]29[/C][C]95.21[/C][C]95.2082035328076[/C][C]0.00179646719234938[/C][/ROW]
[ROW][C]30[/C][C]95.23[/C][C]95.3682319029964[/C][C]-0.138231902996409[/C][/ROW]
[ROW][C]31[/C][C]95.23[/C][C]95.3860489156311[/C][C]-0.156048915631075[/C][/ROW]
[ROW][C]32[/C][C]95.34[/C][C]95.3835845582446[/C][C]-0.0435845582446035[/C][/ROW]
[ROW][C]33[/C][C]95.93[/C][C]95.4928962617088[/C][C]0.437103738291228[/C][/ROW]
[ROW][C]34[/C][C]96.75[/C][C]96.0897990961294[/C][C]0.660200903870589[/C][/ROW]
[ROW][C]35[/C][C]97.15[/C][C]96.9202251280402[/C][C]0.229774871959791[/C][/ROW]
[ROW][C]36[/C][C]97.21[/C][C]97.3238537812779[/C][C]-0.113853781277925[/C][/ROW]
[ROW][C]37[/C][C]97.21[/C][C]97.3820557783521[/C][C]-0.172055778352117[/C][/ROW]
[ROW][C]38[/C][C]97.35[/C][C]97.3793386372137[/C][C]-0.0293386372136837[/C][/ROW]
[ROW][C]39[/C][C]97.44[/C][C]97.5188753152673[/C][C]-0.0788753152672541[/C][/ROW]
[ROW][C]40[/C][C]97.34[/C][C]97.6076296996537[/C][C]-0.267629699653682[/C][/ROW]
[ROW][C]41[/C][C]97.44[/C][C]97.5034032349934[/C][C]-0.0634032349934444[/C][/ROW]
[ROW][C]42[/C][C]97.43[/C][C]97.6024019577346[/C][C]-0.172401957734621[/C][/ROW]
[ROW][C]43[/C][C]97.43[/C][C]97.5896793496584[/C][C]-0.159679349658376[/C][/ROW]
[ROW][C]44[/C][C]97.47[/C][C]97.5871576596921[/C][C]-0.117157659692083[/C][/ROW]
[ROW][C]45[/C][C]97.69[/C][C]97.6253074812216[/C][C]0.0646925187784291[/C][/ROW]
[ROW][C]46[/C][C]98.54[/C][C]97.8463291191218[/C][C]0.693670880878187[/C][/ROW]
[ROW][C]47[/C][C]98.64[/C][C]98.7072837159684[/C][C]-0.0672837159684008[/C][/ROW]
[ROW][C]48[/C][C]98.72[/C][C]98.8062211573356[/C][C]-0.0862211573356291[/C][/ROW]
[ROW][C]49[/C][C]98.72[/C][C]98.8848595346349[/C][C]-0.164859534634871[/C][/ROW]
[ROW][C]50[/C][C]98.73[/C][C]98.8822560380949[/C][C]-0.152256038094905[/C][/ROW]
[ROW][C]51[/C][C]98.68[/C][C]98.8898515786304[/C][C]-0.209851578630406[/C][/ROW]
[ROW][C]52[/C][C]98.75[/C][C]98.8365375582428[/C][C]-0.0865375582428101[/C][/ROW]
[ROW][C]53[/C][C]98.73[/C][C]98.9051709388722[/C][C]-0.175170938872199[/C][/ROW]
[ROW][C]54[/C][C]98.74[/C][C]98.8824046024618[/C][C]-0.142404602461852[/C][/ROW]
[ROW][C]55[/C][C]98.75[/C][C]98.8901557189465[/C][C]-0.140155718946517[/C][/ROW]
[ROW][C]56[/C][C]98.85[/C][C]98.897942350274[/C][C]-0.0479423502739706[/C][/ROW]
[ROW][C]57[/C][C]99.14[/C][C]98.9971852345674[/C][C]0.142814765432647[/C][/ROW]
[ROW][C]58[/C][C]99.83[/C][C]99.2894405954628[/C][C]0.540559404537191[/C][/ROW]
[ROW][C]59[/C][C]99.93[/C][C]99.9879772235837[/C][C]-0.0579772235836629[/C][/ROW]
[ROW][C]60[/C][C]100[/C][C]100.087061635041[/C][C]-0.0870616350414082[/C][/ROW]
[ROW][C]61[/C][C]100[/C][C]100.155686739339[/C][C]-0.155686739339458[/C][/ROW]
[ROW][C]62[/C][C]100.08[/C][C]100.153228101517[/C][C]-0.0732281015173442[/C][/ROW]
[ROW][C]63[/C][C]100.25[/C][C]100.232071667894[/C][C]0.0179283321056829[/C][/ROW]
[ROW][C]64[/C][C]100.4[/C][C]100.402354795896[/C][C]-0.00235479589602505[/C][/ROW]
[ROW][C]65[/C][C]100.33[/C][C]100.552317608463[/C][C]-0.222317608462617[/C][/ROW]
[ROW][C]66[/C][C]100.29[/C][C]100.478806721903[/C][C]-0.188806721902807[/C][/ROW]
[ROW][C]67[/C][C]100.29[/C][C]100.435825046331[/C][C]-0.145825046331041[/C][/ROW]
[ROW][C]68[/C][C]100.32[/C][C]100.433522146445[/C][C]-0.11352214644478[/C][/ROW]
[ROW][C]69[/C][C]100.82[/C][C]100.461729380766[/C][C]0.358270619233807[/C][/ROW]
[ROW][C]70[/C][C]101.42[/C][C]100.967387265945[/C][C]0.452612734055322[/C][/ROW]
[ROW][C]71[/C][C]101.46[/C][C]101.574535021697[/C][C]-0.114535021697279[/C][/ROW]
[ROW][C]72[/C][C]101.55[/C][C]101.612726260479[/C][C]-0.0627262604791099[/C][/ROW]
[ROW][C]73[/C][C]101.56[/C][C]101.701735674145[/C][C]-0.141735674144599[/C][/ROW]
[ROW][C]74[/C][C]101.56[/C][C]101.709497354486[/C][C]-0.149497354486343[/C][/ROW]
[ROW][C]75[/C][C]101.6[/C][C]101.707136460735[/C][C]-0.107136460735191[/C][/ROW]
[ROW][C]76[/C][C]101.66[/C][C]101.745444539152[/C][C]-0.0854445391520926[/C][/ROW]
[ROW][C]77[/C][C]101.82[/C][C]101.804095180969[/C][C]0.01590481903051[/C][/ROW]
[ROW][C]78[/C][C]101.94[/C][C]101.964346353226[/C][C]-0.0243463532259511[/C][/ROW]
[ROW][C]79[/C][C]101.95[/C][C]102.083961870481[/C][C]-0.13396187048113[/C][/ROW]
[ROW][C]80[/C][C]101.93[/C][C]102.09184631637[/C][C]-0.161846316369832[/C][/ROW]
[ROW][C]81[/C][C]102.26[/C][C]102.069290405208[/C][C]0.190709594791784[/C][/ROW]
[ROW][C]82[/C][C]102.65[/C][C]102.40230213135[/C][C]0.247697868650036[/C][/ROW]
[ROW][C]83[/C][C]102.9[/C][C]102.796213828331[/C][C]0.103786171668631[/C][/ROW]
[ROW][C]84[/C][C]102.94[/C][C]103.047852841443[/C][C]-0.107852841442948[/C][/ROW]
[ROW][C]85[/C][C]99.14[/C][C]103.086149606625[/C][C]-3.94614960662462[/C][/ROW]
[ROW][C]86[/C][C]99.18[/C][C]99.2238311797907[/C][C]-0.0438311797907147[/C][/ROW]
[ROW][C]87[/C][C]99.23[/C][C]99.2631389885554[/C][C]-0.0331389885554358[/C][/ROW]
[ROW][C]88[/C][C]99.32[/C][C]99.3126156506591[/C][C]0.00738434934085319[/C][/ROW]
[ROW][C]89[/C][C]99.46[/C][C]99.4027322658613[/C][C]0.0572677341387191[/C][/ROW]
[ROW][C]90[/C][C]99.5[/C][C]99.5436366499966[/C][C]-0.0436366499966141[/C][/ROW]
[ROW][C]91[/C][C]99.95[/C][C]99.5829475308169[/C][C]0.367052469183136[/C][/ROW]
[ROW][C]92[/C][C]100.13[/C][C]100.038744100822[/C][C]0.0912558991781367[/C][/ROW]
[ROW][C]93[/C][C]100.43[/C][C]100.220185233228[/C][C]0.209814766772382[/C][/ROW]
[ROW][C]94[/C][C]101.09[/C][C]100.523498672275[/C][C]0.566501327725405[/C][/ROW]
[ROW][C]95[/C][C]101.27[/C][C]101.192444980718[/C][C]0.0775550192823857[/C][/ROW]
[ROW][C]96[/C][C]101.29[/C][C]101.373669745939[/C][C]-0.0836697459385221[/C][/ROW]
[ROW][C]97[/C][C]101.04[/C][C]101.392348415665[/C][C]-0.352348415664665[/C][/ROW]
[ROW][C]98[/C][C]101.14[/C][C]101.136784055174[/C][C]0.00321594482606713[/C][/ROW]
[ROW][C]99[/C][C]101.11[/C][C]101.236834842053[/C][C]-0.126834842052858[/C][/ROW]
[ROW][C]100[/C][C]101.01[/C][C]101.204831839478[/C][C]-0.194831839477587[/C][/ROW]
[ROW][C]101[/C][C]101.08[/C][C]101.101755013978[/C][C]-0.0217550139783782[/C][/ROW]
[ROW][C]102[/C][C]101.06[/C][C]101.171411454209[/C][C]-0.111411454209474[/C][/ROW]
[ROW][C]103[/C][C]101.26[/C][C]101.149652021028[/C][C]0.110347978972172[/C][/ROW]
[ROW][C]104[/C][C]101.32[/C][C]101.351394659584[/C][C]-0.0313946595842509[/C][/ROW]
[ROW][C]105[/C][C]101.4[/C][C]101.410898868499[/C][C]-0.0108988684989129[/C][/ROW]
[ROW][C]106[/C][C]101.85[/C][C]101.490726751269[/C][C]0.359273248730972[/C][/ROW]
[ROW][C]107[/C][C]102.12[/C][C]101.946400470184[/C][C]0.17359952981603[/C][/ROW]
[ROW][C]108[/C][C]102.15[/C][C]102.219141990571[/C][C]-0.0691419905711257[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287211&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287211&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
392.1992.35-0.160000000000011
492.2492.3674732462559-0.127473246255889
592.1992.4154601618668-0.225460161866792
692.2192.3618996474409-0.151899647440871
792.2292.3795008161727-0.159500816172724
892.1492.3869819456449-0.246981945644876
992.4392.30308155467060.126918445329437
1092.9392.59508587752640.334914122473592
1193.0193.1003749119822-0.0903749119821669
1293.0793.178947692312-0.108947692312015
1393.0893.2372271673779-0.157227167377854
1493.1193.2447442027913-0.134744202791296
1593.2193.2726162939232-0.0626162939231563
1693.4993.37162744420370.118372555796313
1793.4893.6534968085697-0.173496808569681
1893.5193.6407569103781-0.130756910378139
1993.5293.6686919696727-0.148691969672726
2093.4993.6763437947284-0.186343794728387
2193.7693.6434010142220.116598985778026
2294.2593.91524236999620.334757630003779
2394.4294.41052893308990.00947106691012323
2494.4594.580678502176-0.130678502175982
2594.4594.6086147997094-0.158614799709426
2694.5394.6061099213404-0.0761099213404179
2794.7894.6849079774110.0950920225890286
2895.0594.93640969068670.113590309313324
2995.2195.20820353280760.00179646719234938
3095.2395.3682319029964-0.138231902996409
3195.2395.3860489156311-0.156048915631075
3295.3495.3835845582446-0.0435845582446035
3395.9395.49289626170880.437103738291228
3496.7596.08979909612940.660200903870589
3597.1596.92022512804020.229774871959791
3697.2197.3238537812779-0.113853781277925
3797.2197.3820557783521-0.172055778352117
3897.3597.3793386372137-0.0293386372136837
3997.4497.5188753152673-0.0788753152672541
4097.3497.6076296996537-0.267629699653682
4197.4497.5034032349934-0.0634032349934444
4297.4397.6024019577346-0.172401957734621
4397.4397.5896793496584-0.159679349658376
4497.4797.5871576596921-0.117157659692083
4597.6997.62530748122160.0646925187784291
4698.5497.84632911912180.693670880878187
4798.6498.7072837159684-0.0672837159684008
4898.7298.8062211573356-0.0862211573356291
4998.7298.8848595346349-0.164859534634871
5098.7398.8822560380949-0.152256038094905
5198.6898.8898515786304-0.209851578630406
5298.7598.8365375582428-0.0865375582428101
5398.7398.9051709388722-0.175170938872199
5498.7498.8824046024618-0.142404602461852
5598.7598.8901557189465-0.140155718946517
5698.8598.897942350274-0.0479423502739706
5799.1498.99718523456740.142814765432647
5899.8399.28944059546280.540559404537191
5999.9399.9879772235837-0.0579772235836629
60100100.087061635041-0.0870616350414082
61100100.155686739339-0.155686739339458
62100.08100.153228101517-0.0732281015173442
63100.25100.2320716678940.0179283321056829
64100.4100.402354795896-0.00235479589602505
65100.33100.552317608463-0.222317608462617
66100.29100.478806721903-0.188806721902807
67100.29100.435825046331-0.145825046331041
68100.32100.433522146445-0.11352214644478
69100.82100.4617293807660.358270619233807
70101.42100.9673872659450.452612734055322
71101.46101.574535021697-0.114535021697279
72101.55101.612726260479-0.0627262604791099
73101.56101.701735674145-0.141735674144599
74101.56101.709497354486-0.149497354486343
75101.6101.707136460735-0.107136460735191
76101.66101.745444539152-0.0854445391520926
77101.82101.8040951809690.01590481903051
78101.94101.964346353226-0.0243463532259511
79101.95102.083961870481-0.13396187048113
80101.93102.09184631637-0.161846316369832
81102.26102.0692904052080.190709594791784
82102.65102.402302131350.247697868650036
83102.9102.7962138283310.103786171668631
84102.94103.047852841443-0.107852841442948
8599.14103.086149606625-3.94614960662462
8699.1899.2238311797907-0.0438311797907147
8799.2399.2631389885554-0.0331389885554358
8899.3299.31261565065910.00738434934085319
8999.4699.40273226586130.0572677341387191
9099.599.5436366499966-0.0436366499966141
9199.9599.58294753081690.367052469183136
92100.13100.0387441008220.0912558991781367
93100.43100.2201852332280.209814766772382
94101.09100.5234986722750.566501327725405
95101.27101.1924449807180.0775550192823857
96101.29101.373669745939-0.0836697459385221
97101.04101.392348415665-0.352348415664665
98101.14101.1367840551740.00321594482606713
99101.11101.236834842053-0.126834842052858
100101.01101.204831839478-0.194831839477587
101101.08101.101755013978-0.0217550139783782
102101.06101.171411454209-0.111411454209474
103101.26101.1496520210280.110347978972172
104101.32101.351394659584-0.0313946595842509
105101.4101.410898868499-0.0108988684989129
106101.85101.4907267512690.359273248730972
107102.12101.9464004701840.17359952981603
108102.15102.219141990571-0.0691419905711257







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109102.248050085674101.401951122603103.094149048745
110102.346100171348101.140050332984103.552150009711
111102.444150257022100.955400665622103.932899848421
112102.542200342696100.809659454548104.274741230844
113102.64025042837100.688102627555104.592398229184
114102.738300514044100.583240946138104.893360081949
115102.836350599717100.490661549978105.182039649457
116102.934400685391100.407512432871105.461288937912
117103.032450771065100.33182858661105.733072955521
118103.130500856739100.262190898005105.998810815474
119103.228550942413100.197536784857106.259565099969
120103.326601028087100.137047506209106.516154549965

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 102.248050085674 & 101.401951122603 & 103.094149048745 \tabularnewline
110 & 102.346100171348 & 101.140050332984 & 103.552150009711 \tabularnewline
111 & 102.444150257022 & 100.955400665622 & 103.932899848421 \tabularnewline
112 & 102.542200342696 & 100.809659454548 & 104.274741230844 \tabularnewline
113 & 102.64025042837 & 100.688102627555 & 104.592398229184 \tabularnewline
114 & 102.738300514044 & 100.583240946138 & 104.893360081949 \tabularnewline
115 & 102.836350599717 & 100.490661549978 & 105.182039649457 \tabularnewline
116 & 102.934400685391 & 100.407512432871 & 105.461288937912 \tabularnewline
117 & 103.032450771065 & 100.33182858661 & 105.733072955521 \tabularnewline
118 & 103.130500856739 & 100.262190898005 & 105.998810815474 \tabularnewline
119 & 103.228550942413 & 100.197536784857 & 106.259565099969 \tabularnewline
120 & 103.326601028087 & 100.137047506209 & 106.516154549965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287211&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]109[/C][C]102.248050085674[/C][C]101.401951122603[/C][C]103.094149048745[/C][/ROW]
[ROW][C]110[/C][C]102.346100171348[/C][C]101.140050332984[/C][C]103.552150009711[/C][/ROW]
[ROW][C]111[/C][C]102.444150257022[/C][C]100.955400665622[/C][C]103.932899848421[/C][/ROW]
[ROW][C]112[/C][C]102.542200342696[/C][C]100.809659454548[/C][C]104.274741230844[/C][/ROW]
[ROW][C]113[/C][C]102.64025042837[/C][C]100.688102627555[/C][C]104.592398229184[/C][/ROW]
[ROW][C]114[/C][C]102.738300514044[/C][C]100.583240946138[/C][C]104.893360081949[/C][/ROW]
[ROW][C]115[/C][C]102.836350599717[/C][C]100.490661549978[/C][C]105.182039649457[/C][/ROW]
[ROW][C]116[/C][C]102.934400685391[/C][C]100.407512432871[/C][C]105.461288937912[/C][/ROW]
[ROW][C]117[/C][C]103.032450771065[/C][C]100.33182858661[/C][C]105.733072955521[/C][/ROW]
[ROW][C]118[/C][C]103.130500856739[/C][C]100.262190898005[/C][C]105.998810815474[/C][/ROW]
[ROW][C]119[/C][C]103.228550942413[/C][C]100.197536784857[/C][C]106.259565099969[/C][/ROW]
[ROW][C]120[/C][C]103.326601028087[/C][C]100.137047506209[/C][C]106.516154549965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287211&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287211&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
109102.248050085674101.401951122603103.094149048745
110102.346100171348101.140050332984103.552150009711
111102.444150257022100.955400665622103.932899848421
112102.542200342696100.809659454548104.274741230844
113102.64025042837100.688102627555104.592398229184
114102.738300514044100.583240946138104.893360081949
115102.836350599717100.490661549978105.182039649457
116102.934400685391100.407512432871105.461288937912
117103.032450771065100.33182858661105.733072955521
118103.130500856739100.262190898005105.998810815474
119103.228550942413100.197536784857106.259565099969
120103.326601028087100.137047506209106.516154549965



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