Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 30 Nov 2015 14:08:36 +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/Nov/30/t1448892605x71wt1iwwwih6jt.htm/, Retrieved Tue, 14 May 2024 16:34:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284596, Retrieved Tue, 14 May 2024 16:34:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117
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] [663b8bcb3523d59827bca0af0b37f04c] [Current]
- R P       [Exponential Smoothing] [] [2015-12-30 14:40:21] [1abbea75cc6be7d57004024c66566ad0]
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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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284596&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284596&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284596&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999934512330295
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999934512330295 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284596&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]0.999934512330295[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284596&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284596&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
alpha0.999934512330295
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
292.1791.990.180000000000007
392.1992.16998821221950.0200117877805326
492.2492.18999868947460.0500013105253458
592.1992.2399967255307-0.0499967255306899
692.2192.1900032741690.0199967258309499
792.2292.2099986904610.0100013095389784
892.1492.2199993450376-0.0799993450375496
992.4392.14000523897070.28999476102932
1092.9392.42998100891890.50001899108112
1193.0192.92996725492150.0800327450785261
1293.0793.0099947588420.0600052411579526
1393.0893.06999607039660.010003929603414
1493.1193.0799993448660.0300006551340459
1593.2193.1099980353270.100001964672984
1693.4993.20999345110440.280006548895642
1793.4893.4899816630236-0.00998166302360914
1893.5193.48000065367590.0299993463241464
1993.5293.50999803541270.0100019645872749
2093.4993.5199993449946-0.0299993449946498
2193.7693.49000196458720.269998035412812
2294.2593.75998231845780.49001768154217
2394.4294.24996790988390.170032090116081
2494.4594.41998886499470.0300111350053527
2594.4594.44999803464071.96535928864705e-06
2694.5394.44999999987130.080000000128706
2794.7894.52999476098640.250005239013575
2895.0594.77998362773950.2700163722605
2995.2195.0499823172570.160017682743003
3095.2395.20998952081480.0200104791851601
3195.2395.22999868956031.31043965723165e-06
3295.3495.22999999991420.110000000085819
3395.9395.33999279635630.59000720364368
3496.7595.92996136180310.820038638196863
3597.1596.74994629758050.400053702419498
3697.2197.14997380141530.0600261985847084
3797.2197.20999606902413.93097586481872e-06
3897.3597.20999999974260.14000000025743
3997.4497.34999083172620.0900091682737667
4097.3497.4399941055093-0.0999941055093103
4197.4497.3400065483810.0999934516190422
4297.4397.4399934516619-0.00999345166187027
4397.4397.4300006544479-6.54447859460561e-07
4497.4797.43000000004290.0399999999571463
4597.6997.46999738049320.220002619506786
4698.5497.68998559254110.850014407458886
4798.6498.53994433453730.100055665462747
4898.7298.63999344758760.080006552412371
4998.7298.71999476055735.23944268593368e-06
5098.7398.71999999965690.0100000003431262
5198.6898.7299993451233-0.0499993451232683
5298.7598.68000327434060.0699967256593936
5398.7398.7499954160776-0.0199954160775491
5498.7498.73000130945320.00999869054679436
5598.7598.73999934520910.010000654790943
5698.8598.74999934508040.100000654919569
5799.1498.84999345119010.29000654880987
5899.8399.13998100814690.69001899185308
5999.9399.82995481226420.100045187735844
6010099.92999344827380.0700065517261947
6110099.99999541543414.58456594287782e-06
62100.0899.99999999969980.080000000300231
63100.25100.0799947609860.170005239013605
64100.4100.2499888667530.150011133246949
65100.33100.39999017612-0.0699901761204558
66100.29100.330004583494-0.040004583493527
67100.29100.290002619807-2.61980694915565e-06
68100.32100.2900000001720.0299999998284335
69100.82100.319998035370.500001964630087
70101.42100.8199672560360.600032743963524
71101.46101.4199607052540.040039294746137
72101.55101.459997377920.0900026220801209
73101.56101.5499941059380.0100058940619903
74101.56101.5599993447376.55262695659076e-07
75101.6101.5599999999570.0400000000429088
76101.66101.5999973804930.060002619506804
77101.82101.6599960705680.160003929431724
78101.94101.8199895217160.120010478284485
79101.95101.9399921407930.0100078592065813
80101.93101.949999344609-0.0199993446086211
81102.26101.930001309710.329998690289528
82102.65102.2599783891550.390021610845238
83102.9102.6499744583940.250025541606433
84102.94102.899983626410.0400163735900776
8599.14102.939997379421-3.79999737942094
8699.1899.14024885297330.0397511470267489
8799.2399.179997396790.0500026032099896
8899.3299.2299967254460.0900032745539505
8999.4699.31999410589530.140005894104718
9099.599.45999083134020.0400091686597506
9199.9599.49999737989280.450002620107213
92100.1399.9499705303770.180029469622951
93100.43100.129988210290.300011789710453
94101.09100.4299803529270.660019647072986
95101.27101.0899567768510.180043223148644
96101.29101.2699882093890.0200117906111359
97101.04101.289998689474-0.249998689474467
98101.14101.0400163718320.0999836281683883
99101.11101.139993452305-0.0299934523051775
100101.01101.110001964201-0.100001964201297
101101.08101.0100065488960.0699934511043949
102101.06101.079995416292-0.0199954162919909
103101.26101.0600013094530.199998690546778
104101.32101.2599869025520.0600130974481772
105101.4101.3199960698820.0800039301179112
106101.85101.3999947607290.450005239270936
107102.12101.8499705302060.270029469794494
108102.15102.1199823163990.0300176836007324

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 92.17 & 91.99 & 0.180000000000007 \tabularnewline
3 & 92.19 & 92.1699882122195 & 0.0200117877805326 \tabularnewline
4 & 92.24 & 92.1899986894746 & 0.0500013105253458 \tabularnewline
5 & 92.19 & 92.2399967255307 & -0.0499967255306899 \tabularnewline
6 & 92.21 & 92.190003274169 & 0.0199967258309499 \tabularnewline
7 & 92.22 & 92.209998690461 & 0.0100013095389784 \tabularnewline
8 & 92.14 & 92.2199993450376 & -0.0799993450375496 \tabularnewline
9 & 92.43 & 92.1400052389707 & 0.28999476102932 \tabularnewline
10 & 92.93 & 92.4299810089189 & 0.50001899108112 \tabularnewline
11 & 93.01 & 92.9299672549215 & 0.0800327450785261 \tabularnewline
12 & 93.07 & 93.009994758842 & 0.0600052411579526 \tabularnewline
13 & 93.08 & 93.0699960703966 & 0.010003929603414 \tabularnewline
14 & 93.11 & 93.079999344866 & 0.0300006551340459 \tabularnewline
15 & 93.21 & 93.109998035327 & 0.100001964672984 \tabularnewline
16 & 93.49 & 93.2099934511044 & 0.280006548895642 \tabularnewline
17 & 93.48 & 93.4899816630236 & -0.00998166302360914 \tabularnewline
18 & 93.51 & 93.4800006536759 & 0.0299993463241464 \tabularnewline
19 & 93.52 & 93.5099980354127 & 0.0100019645872749 \tabularnewline
20 & 93.49 & 93.5199993449946 & -0.0299993449946498 \tabularnewline
21 & 93.76 & 93.4900019645872 & 0.269998035412812 \tabularnewline
22 & 94.25 & 93.7599823184578 & 0.49001768154217 \tabularnewline
23 & 94.42 & 94.2499679098839 & 0.170032090116081 \tabularnewline
24 & 94.45 & 94.4199888649947 & 0.0300111350053527 \tabularnewline
25 & 94.45 & 94.4499980346407 & 1.96535928864705e-06 \tabularnewline
26 & 94.53 & 94.4499999998713 & 0.080000000128706 \tabularnewline
27 & 94.78 & 94.5299947609864 & 0.250005239013575 \tabularnewline
28 & 95.05 & 94.7799836277395 & 0.2700163722605 \tabularnewline
29 & 95.21 & 95.049982317257 & 0.160017682743003 \tabularnewline
30 & 95.23 & 95.2099895208148 & 0.0200104791851601 \tabularnewline
31 & 95.23 & 95.2299986895603 & 1.31043965723165e-06 \tabularnewline
32 & 95.34 & 95.2299999999142 & 0.110000000085819 \tabularnewline
33 & 95.93 & 95.3399927963563 & 0.59000720364368 \tabularnewline
34 & 96.75 & 95.9299613618031 & 0.820038638196863 \tabularnewline
35 & 97.15 & 96.7499462975805 & 0.400053702419498 \tabularnewline
36 & 97.21 & 97.1499738014153 & 0.0600261985847084 \tabularnewline
37 & 97.21 & 97.2099960690241 & 3.93097586481872e-06 \tabularnewline
38 & 97.35 & 97.2099999997426 & 0.14000000025743 \tabularnewline
39 & 97.44 & 97.3499908317262 & 0.0900091682737667 \tabularnewline
40 & 97.34 & 97.4399941055093 & -0.0999941055093103 \tabularnewline
41 & 97.44 & 97.340006548381 & 0.0999934516190422 \tabularnewline
42 & 97.43 & 97.4399934516619 & -0.00999345166187027 \tabularnewline
43 & 97.43 & 97.4300006544479 & -6.54447859460561e-07 \tabularnewline
44 & 97.47 & 97.4300000000429 & 0.0399999999571463 \tabularnewline
45 & 97.69 & 97.4699973804932 & 0.220002619506786 \tabularnewline
46 & 98.54 & 97.6899855925411 & 0.850014407458886 \tabularnewline
47 & 98.64 & 98.5399443345373 & 0.100055665462747 \tabularnewline
48 & 98.72 & 98.6399934475876 & 0.080006552412371 \tabularnewline
49 & 98.72 & 98.7199947605573 & 5.23944268593368e-06 \tabularnewline
50 & 98.73 & 98.7199999996569 & 0.0100000003431262 \tabularnewline
51 & 98.68 & 98.7299993451233 & -0.0499993451232683 \tabularnewline
52 & 98.75 & 98.6800032743406 & 0.0699967256593936 \tabularnewline
53 & 98.73 & 98.7499954160776 & -0.0199954160775491 \tabularnewline
54 & 98.74 & 98.7300013094532 & 0.00999869054679436 \tabularnewline
55 & 98.75 & 98.7399993452091 & 0.010000654790943 \tabularnewline
56 & 98.85 & 98.7499993450804 & 0.100000654919569 \tabularnewline
57 & 99.14 & 98.8499934511901 & 0.29000654880987 \tabularnewline
58 & 99.83 & 99.1399810081469 & 0.69001899185308 \tabularnewline
59 & 99.93 & 99.8299548122642 & 0.100045187735844 \tabularnewline
60 & 100 & 99.9299934482738 & 0.0700065517261947 \tabularnewline
61 & 100 & 99.9999954154341 & 4.58456594287782e-06 \tabularnewline
62 & 100.08 & 99.9999999996998 & 0.080000000300231 \tabularnewline
63 & 100.25 & 100.079994760986 & 0.170005239013605 \tabularnewline
64 & 100.4 & 100.249988866753 & 0.150011133246949 \tabularnewline
65 & 100.33 & 100.39999017612 & -0.0699901761204558 \tabularnewline
66 & 100.29 & 100.330004583494 & -0.040004583493527 \tabularnewline
67 & 100.29 & 100.290002619807 & -2.61980694915565e-06 \tabularnewline
68 & 100.32 & 100.290000000172 & 0.0299999998284335 \tabularnewline
69 & 100.82 & 100.31999803537 & 0.500001964630087 \tabularnewline
70 & 101.42 & 100.819967256036 & 0.600032743963524 \tabularnewline
71 & 101.46 & 101.419960705254 & 0.040039294746137 \tabularnewline
72 & 101.55 & 101.45999737792 & 0.0900026220801209 \tabularnewline
73 & 101.56 & 101.549994105938 & 0.0100058940619903 \tabularnewline
74 & 101.56 & 101.559999344737 & 6.55262695659076e-07 \tabularnewline
75 & 101.6 & 101.559999999957 & 0.0400000000429088 \tabularnewline
76 & 101.66 & 101.599997380493 & 0.060002619506804 \tabularnewline
77 & 101.82 & 101.659996070568 & 0.160003929431724 \tabularnewline
78 & 101.94 & 101.819989521716 & 0.120010478284485 \tabularnewline
79 & 101.95 & 101.939992140793 & 0.0100078592065813 \tabularnewline
80 & 101.93 & 101.949999344609 & -0.0199993446086211 \tabularnewline
81 & 102.26 & 101.93000130971 & 0.329998690289528 \tabularnewline
82 & 102.65 & 102.259978389155 & 0.390021610845238 \tabularnewline
83 & 102.9 & 102.649974458394 & 0.250025541606433 \tabularnewline
84 & 102.94 & 102.89998362641 & 0.0400163735900776 \tabularnewline
85 & 99.14 & 102.939997379421 & -3.79999737942094 \tabularnewline
86 & 99.18 & 99.1402488529733 & 0.0397511470267489 \tabularnewline
87 & 99.23 & 99.17999739679 & 0.0500026032099896 \tabularnewline
88 & 99.32 & 99.229996725446 & 0.0900032745539505 \tabularnewline
89 & 99.46 & 99.3199941058953 & 0.140005894104718 \tabularnewline
90 & 99.5 & 99.4599908313402 & 0.0400091686597506 \tabularnewline
91 & 99.95 & 99.4999973798928 & 0.450002620107213 \tabularnewline
92 & 100.13 & 99.949970530377 & 0.180029469622951 \tabularnewline
93 & 100.43 & 100.12998821029 & 0.300011789710453 \tabularnewline
94 & 101.09 & 100.429980352927 & 0.660019647072986 \tabularnewline
95 & 101.27 & 101.089956776851 & 0.180043223148644 \tabularnewline
96 & 101.29 & 101.269988209389 & 0.0200117906111359 \tabularnewline
97 & 101.04 & 101.289998689474 & -0.249998689474467 \tabularnewline
98 & 101.14 & 101.040016371832 & 0.0999836281683883 \tabularnewline
99 & 101.11 & 101.139993452305 & -0.0299934523051775 \tabularnewline
100 & 101.01 & 101.110001964201 & -0.100001964201297 \tabularnewline
101 & 101.08 & 101.010006548896 & 0.0699934511043949 \tabularnewline
102 & 101.06 & 101.079995416292 & -0.0199954162919909 \tabularnewline
103 & 101.26 & 101.060001309453 & 0.199998690546778 \tabularnewline
104 & 101.32 & 101.259986902552 & 0.0600130974481772 \tabularnewline
105 & 101.4 & 101.319996069882 & 0.0800039301179112 \tabularnewline
106 & 101.85 & 101.399994760729 & 0.450005239270936 \tabularnewline
107 & 102.12 & 101.849970530206 & 0.270029469794494 \tabularnewline
108 & 102.15 & 102.119982316399 & 0.0300176836007324 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284596&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]92.17[/C][C]91.99[/C][C]0.180000000000007[/C][/ROW]
[ROW][C]3[/C][C]92.19[/C][C]92.1699882122195[/C][C]0.0200117877805326[/C][/ROW]
[ROW][C]4[/C][C]92.24[/C][C]92.1899986894746[/C][C]0.0500013105253458[/C][/ROW]
[ROW][C]5[/C][C]92.19[/C][C]92.2399967255307[/C][C]-0.0499967255306899[/C][/ROW]
[ROW][C]6[/C][C]92.21[/C][C]92.190003274169[/C][C]0.0199967258309499[/C][/ROW]
[ROW][C]7[/C][C]92.22[/C][C]92.209998690461[/C][C]0.0100013095389784[/C][/ROW]
[ROW][C]8[/C][C]92.14[/C][C]92.2199993450376[/C][C]-0.0799993450375496[/C][/ROW]
[ROW][C]9[/C][C]92.43[/C][C]92.1400052389707[/C][C]0.28999476102932[/C][/ROW]
[ROW][C]10[/C][C]92.93[/C][C]92.4299810089189[/C][C]0.50001899108112[/C][/ROW]
[ROW][C]11[/C][C]93.01[/C][C]92.9299672549215[/C][C]0.0800327450785261[/C][/ROW]
[ROW][C]12[/C][C]93.07[/C][C]93.009994758842[/C][C]0.0600052411579526[/C][/ROW]
[ROW][C]13[/C][C]93.08[/C][C]93.0699960703966[/C][C]0.010003929603414[/C][/ROW]
[ROW][C]14[/C][C]93.11[/C][C]93.079999344866[/C][C]0.0300006551340459[/C][/ROW]
[ROW][C]15[/C][C]93.21[/C][C]93.109998035327[/C][C]0.100001964672984[/C][/ROW]
[ROW][C]16[/C][C]93.49[/C][C]93.2099934511044[/C][C]0.280006548895642[/C][/ROW]
[ROW][C]17[/C][C]93.48[/C][C]93.4899816630236[/C][C]-0.00998166302360914[/C][/ROW]
[ROW][C]18[/C][C]93.51[/C][C]93.4800006536759[/C][C]0.0299993463241464[/C][/ROW]
[ROW][C]19[/C][C]93.52[/C][C]93.5099980354127[/C][C]0.0100019645872749[/C][/ROW]
[ROW][C]20[/C][C]93.49[/C][C]93.5199993449946[/C][C]-0.0299993449946498[/C][/ROW]
[ROW][C]21[/C][C]93.76[/C][C]93.4900019645872[/C][C]0.269998035412812[/C][/ROW]
[ROW][C]22[/C][C]94.25[/C][C]93.7599823184578[/C][C]0.49001768154217[/C][/ROW]
[ROW][C]23[/C][C]94.42[/C][C]94.2499679098839[/C][C]0.170032090116081[/C][/ROW]
[ROW][C]24[/C][C]94.45[/C][C]94.4199888649947[/C][C]0.0300111350053527[/C][/ROW]
[ROW][C]25[/C][C]94.45[/C][C]94.4499980346407[/C][C]1.96535928864705e-06[/C][/ROW]
[ROW][C]26[/C][C]94.53[/C][C]94.4499999998713[/C][C]0.080000000128706[/C][/ROW]
[ROW][C]27[/C][C]94.78[/C][C]94.5299947609864[/C][C]0.250005239013575[/C][/ROW]
[ROW][C]28[/C][C]95.05[/C][C]94.7799836277395[/C][C]0.2700163722605[/C][/ROW]
[ROW][C]29[/C][C]95.21[/C][C]95.049982317257[/C][C]0.160017682743003[/C][/ROW]
[ROW][C]30[/C][C]95.23[/C][C]95.2099895208148[/C][C]0.0200104791851601[/C][/ROW]
[ROW][C]31[/C][C]95.23[/C][C]95.2299986895603[/C][C]1.31043965723165e-06[/C][/ROW]
[ROW][C]32[/C][C]95.34[/C][C]95.2299999999142[/C][C]0.110000000085819[/C][/ROW]
[ROW][C]33[/C][C]95.93[/C][C]95.3399927963563[/C][C]0.59000720364368[/C][/ROW]
[ROW][C]34[/C][C]96.75[/C][C]95.9299613618031[/C][C]0.820038638196863[/C][/ROW]
[ROW][C]35[/C][C]97.15[/C][C]96.7499462975805[/C][C]0.400053702419498[/C][/ROW]
[ROW][C]36[/C][C]97.21[/C][C]97.1499738014153[/C][C]0.0600261985847084[/C][/ROW]
[ROW][C]37[/C][C]97.21[/C][C]97.2099960690241[/C][C]3.93097586481872e-06[/C][/ROW]
[ROW][C]38[/C][C]97.35[/C][C]97.2099999997426[/C][C]0.14000000025743[/C][/ROW]
[ROW][C]39[/C][C]97.44[/C][C]97.3499908317262[/C][C]0.0900091682737667[/C][/ROW]
[ROW][C]40[/C][C]97.34[/C][C]97.4399941055093[/C][C]-0.0999941055093103[/C][/ROW]
[ROW][C]41[/C][C]97.44[/C][C]97.340006548381[/C][C]0.0999934516190422[/C][/ROW]
[ROW][C]42[/C][C]97.43[/C][C]97.4399934516619[/C][C]-0.00999345166187027[/C][/ROW]
[ROW][C]43[/C][C]97.43[/C][C]97.4300006544479[/C][C]-6.54447859460561e-07[/C][/ROW]
[ROW][C]44[/C][C]97.47[/C][C]97.4300000000429[/C][C]0.0399999999571463[/C][/ROW]
[ROW][C]45[/C][C]97.69[/C][C]97.4699973804932[/C][C]0.220002619506786[/C][/ROW]
[ROW][C]46[/C][C]98.54[/C][C]97.6899855925411[/C][C]0.850014407458886[/C][/ROW]
[ROW][C]47[/C][C]98.64[/C][C]98.5399443345373[/C][C]0.100055665462747[/C][/ROW]
[ROW][C]48[/C][C]98.72[/C][C]98.6399934475876[/C][C]0.080006552412371[/C][/ROW]
[ROW][C]49[/C][C]98.72[/C][C]98.7199947605573[/C][C]5.23944268593368e-06[/C][/ROW]
[ROW][C]50[/C][C]98.73[/C][C]98.7199999996569[/C][C]0.0100000003431262[/C][/ROW]
[ROW][C]51[/C][C]98.68[/C][C]98.7299993451233[/C][C]-0.0499993451232683[/C][/ROW]
[ROW][C]52[/C][C]98.75[/C][C]98.6800032743406[/C][C]0.0699967256593936[/C][/ROW]
[ROW][C]53[/C][C]98.73[/C][C]98.7499954160776[/C][C]-0.0199954160775491[/C][/ROW]
[ROW][C]54[/C][C]98.74[/C][C]98.7300013094532[/C][C]0.00999869054679436[/C][/ROW]
[ROW][C]55[/C][C]98.75[/C][C]98.7399993452091[/C][C]0.010000654790943[/C][/ROW]
[ROW][C]56[/C][C]98.85[/C][C]98.7499993450804[/C][C]0.100000654919569[/C][/ROW]
[ROW][C]57[/C][C]99.14[/C][C]98.8499934511901[/C][C]0.29000654880987[/C][/ROW]
[ROW][C]58[/C][C]99.83[/C][C]99.1399810081469[/C][C]0.69001899185308[/C][/ROW]
[ROW][C]59[/C][C]99.93[/C][C]99.8299548122642[/C][C]0.100045187735844[/C][/ROW]
[ROW][C]60[/C][C]100[/C][C]99.9299934482738[/C][C]0.0700065517261947[/C][/ROW]
[ROW][C]61[/C][C]100[/C][C]99.9999954154341[/C][C]4.58456594287782e-06[/C][/ROW]
[ROW][C]62[/C][C]100.08[/C][C]99.9999999996998[/C][C]0.080000000300231[/C][/ROW]
[ROW][C]63[/C][C]100.25[/C][C]100.079994760986[/C][C]0.170005239013605[/C][/ROW]
[ROW][C]64[/C][C]100.4[/C][C]100.249988866753[/C][C]0.150011133246949[/C][/ROW]
[ROW][C]65[/C][C]100.33[/C][C]100.39999017612[/C][C]-0.0699901761204558[/C][/ROW]
[ROW][C]66[/C][C]100.29[/C][C]100.330004583494[/C][C]-0.040004583493527[/C][/ROW]
[ROW][C]67[/C][C]100.29[/C][C]100.290002619807[/C][C]-2.61980694915565e-06[/C][/ROW]
[ROW][C]68[/C][C]100.32[/C][C]100.290000000172[/C][C]0.0299999998284335[/C][/ROW]
[ROW][C]69[/C][C]100.82[/C][C]100.31999803537[/C][C]0.500001964630087[/C][/ROW]
[ROW][C]70[/C][C]101.42[/C][C]100.819967256036[/C][C]0.600032743963524[/C][/ROW]
[ROW][C]71[/C][C]101.46[/C][C]101.419960705254[/C][C]0.040039294746137[/C][/ROW]
[ROW][C]72[/C][C]101.55[/C][C]101.45999737792[/C][C]0.0900026220801209[/C][/ROW]
[ROW][C]73[/C][C]101.56[/C][C]101.549994105938[/C][C]0.0100058940619903[/C][/ROW]
[ROW][C]74[/C][C]101.56[/C][C]101.559999344737[/C][C]6.55262695659076e-07[/C][/ROW]
[ROW][C]75[/C][C]101.6[/C][C]101.559999999957[/C][C]0.0400000000429088[/C][/ROW]
[ROW][C]76[/C][C]101.66[/C][C]101.599997380493[/C][C]0.060002619506804[/C][/ROW]
[ROW][C]77[/C][C]101.82[/C][C]101.659996070568[/C][C]0.160003929431724[/C][/ROW]
[ROW][C]78[/C][C]101.94[/C][C]101.819989521716[/C][C]0.120010478284485[/C][/ROW]
[ROW][C]79[/C][C]101.95[/C][C]101.939992140793[/C][C]0.0100078592065813[/C][/ROW]
[ROW][C]80[/C][C]101.93[/C][C]101.949999344609[/C][C]-0.0199993446086211[/C][/ROW]
[ROW][C]81[/C][C]102.26[/C][C]101.93000130971[/C][C]0.329998690289528[/C][/ROW]
[ROW][C]82[/C][C]102.65[/C][C]102.259978389155[/C][C]0.390021610845238[/C][/ROW]
[ROW][C]83[/C][C]102.9[/C][C]102.649974458394[/C][C]0.250025541606433[/C][/ROW]
[ROW][C]84[/C][C]102.94[/C][C]102.89998362641[/C][C]0.0400163735900776[/C][/ROW]
[ROW][C]85[/C][C]99.14[/C][C]102.939997379421[/C][C]-3.79999737942094[/C][/ROW]
[ROW][C]86[/C][C]99.18[/C][C]99.1402488529733[/C][C]0.0397511470267489[/C][/ROW]
[ROW][C]87[/C][C]99.23[/C][C]99.17999739679[/C][C]0.0500026032099896[/C][/ROW]
[ROW][C]88[/C][C]99.32[/C][C]99.229996725446[/C][C]0.0900032745539505[/C][/ROW]
[ROW][C]89[/C][C]99.46[/C][C]99.3199941058953[/C][C]0.140005894104718[/C][/ROW]
[ROW][C]90[/C][C]99.5[/C][C]99.4599908313402[/C][C]0.0400091686597506[/C][/ROW]
[ROW][C]91[/C][C]99.95[/C][C]99.4999973798928[/C][C]0.450002620107213[/C][/ROW]
[ROW][C]92[/C][C]100.13[/C][C]99.949970530377[/C][C]0.180029469622951[/C][/ROW]
[ROW][C]93[/C][C]100.43[/C][C]100.12998821029[/C][C]0.300011789710453[/C][/ROW]
[ROW][C]94[/C][C]101.09[/C][C]100.429980352927[/C][C]0.660019647072986[/C][/ROW]
[ROW][C]95[/C][C]101.27[/C][C]101.089956776851[/C][C]0.180043223148644[/C][/ROW]
[ROW][C]96[/C][C]101.29[/C][C]101.269988209389[/C][C]0.0200117906111359[/C][/ROW]
[ROW][C]97[/C][C]101.04[/C][C]101.289998689474[/C][C]-0.249998689474467[/C][/ROW]
[ROW][C]98[/C][C]101.14[/C][C]101.040016371832[/C][C]0.0999836281683883[/C][/ROW]
[ROW][C]99[/C][C]101.11[/C][C]101.139993452305[/C][C]-0.0299934523051775[/C][/ROW]
[ROW][C]100[/C][C]101.01[/C][C]101.110001964201[/C][C]-0.100001964201297[/C][/ROW]
[ROW][C]101[/C][C]101.08[/C][C]101.010006548896[/C][C]0.0699934511043949[/C][/ROW]
[ROW][C]102[/C][C]101.06[/C][C]101.079995416292[/C][C]-0.0199954162919909[/C][/ROW]
[ROW][C]103[/C][C]101.26[/C][C]101.060001309453[/C][C]0.199998690546778[/C][/ROW]
[ROW][C]104[/C][C]101.32[/C][C]101.259986902552[/C][C]0.0600130974481772[/C][/ROW]
[ROW][C]105[/C][C]101.4[/C][C]101.319996069882[/C][C]0.0800039301179112[/C][/ROW]
[ROW][C]106[/C][C]101.85[/C][C]101.399994760729[/C][C]0.450005239270936[/C][/ROW]
[ROW][C]107[/C][C]102.12[/C][C]101.849970530206[/C][C]0.270029469794494[/C][/ROW]
[ROW][C]108[/C][C]102.15[/C][C]102.119982316399[/C][C]0.0300176836007324[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284596&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284596&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
292.1791.990.180000000000007
392.1992.16998821221950.0200117877805326
492.2492.18999868947460.0500013105253458
592.1992.2399967255307-0.0499967255306899
692.2192.1900032741690.0199967258309499
792.2292.2099986904610.0100013095389784
892.1492.2199993450376-0.0799993450375496
992.4392.14000523897070.28999476102932
1092.9392.42998100891890.50001899108112
1193.0192.92996725492150.0800327450785261
1293.0793.0099947588420.0600052411579526
1393.0893.06999607039660.010003929603414
1493.1193.0799993448660.0300006551340459
1593.2193.1099980353270.100001964672984
1693.4993.20999345110440.280006548895642
1793.4893.4899816630236-0.00998166302360914
1893.5193.48000065367590.0299993463241464
1993.5293.50999803541270.0100019645872749
2093.4993.5199993449946-0.0299993449946498
2193.7693.49000196458720.269998035412812
2294.2593.75998231845780.49001768154217
2394.4294.24996790988390.170032090116081
2494.4594.41998886499470.0300111350053527
2594.4594.44999803464071.96535928864705e-06
2694.5394.44999999987130.080000000128706
2794.7894.52999476098640.250005239013575
2895.0594.77998362773950.2700163722605
2995.2195.0499823172570.160017682743003
3095.2395.20998952081480.0200104791851601
3195.2395.22999868956031.31043965723165e-06
3295.3495.22999999991420.110000000085819
3395.9395.33999279635630.59000720364368
3496.7595.92996136180310.820038638196863
3597.1596.74994629758050.400053702419498
3697.2197.14997380141530.0600261985847084
3797.2197.20999606902413.93097586481872e-06
3897.3597.20999999974260.14000000025743
3997.4497.34999083172620.0900091682737667
4097.3497.4399941055093-0.0999941055093103
4197.4497.3400065483810.0999934516190422
4297.4397.4399934516619-0.00999345166187027
4397.4397.4300006544479-6.54447859460561e-07
4497.4797.43000000004290.0399999999571463
4597.6997.46999738049320.220002619506786
4698.5497.68998559254110.850014407458886
4798.6498.53994433453730.100055665462747
4898.7298.63999344758760.080006552412371
4998.7298.71999476055735.23944268593368e-06
5098.7398.71999999965690.0100000003431262
5198.6898.7299993451233-0.0499993451232683
5298.7598.68000327434060.0699967256593936
5398.7398.7499954160776-0.0199954160775491
5498.7498.73000130945320.00999869054679436
5598.7598.73999934520910.010000654790943
5698.8598.74999934508040.100000654919569
5799.1498.84999345119010.29000654880987
5899.8399.13998100814690.69001899185308
5999.9399.82995481226420.100045187735844
6010099.92999344827380.0700065517261947
6110099.99999541543414.58456594287782e-06
62100.0899.99999999969980.080000000300231
63100.25100.0799947609860.170005239013605
64100.4100.2499888667530.150011133246949
65100.33100.39999017612-0.0699901761204558
66100.29100.330004583494-0.040004583493527
67100.29100.290002619807-2.61980694915565e-06
68100.32100.2900000001720.0299999998284335
69100.82100.319998035370.500001964630087
70101.42100.8199672560360.600032743963524
71101.46101.4199607052540.040039294746137
72101.55101.459997377920.0900026220801209
73101.56101.5499941059380.0100058940619903
74101.56101.5599993447376.55262695659076e-07
75101.6101.5599999999570.0400000000429088
76101.66101.5999973804930.060002619506804
77101.82101.6599960705680.160003929431724
78101.94101.8199895217160.120010478284485
79101.95101.9399921407930.0100078592065813
80101.93101.949999344609-0.0199993446086211
81102.26101.930001309710.329998690289528
82102.65102.2599783891550.390021610845238
83102.9102.6499744583940.250025541606433
84102.94102.899983626410.0400163735900776
8599.14102.939997379421-3.79999737942094
8699.1899.14024885297330.0397511470267489
8799.2399.179997396790.0500026032099896
8899.3299.2299967254460.0900032745539505
8999.4699.31999410589530.140005894104718
9099.599.45999083134020.0400091686597506
9199.9599.49999737989280.450002620107213
92100.1399.9499705303770.180029469622951
93100.43100.129988210290.300011789710453
94101.09100.4299803529270.660019647072986
95101.27101.0899567768510.180043223148644
96101.29101.2699882093890.0200117906111359
97101.04101.289998689474-0.249998689474467
98101.14101.0400163718320.0999836281683883
99101.11101.139993452305-0.0299934523051775
100101.01101.110001964201-0.100001964201297
101101.08101.0100065488960.0699934511043949
102101.06101.079995416292-0.0199954162919909
103101.26101.0600013094530.199998690546778
104101.32101.2599869025520.0600130974481772
105101.4101.3199960698820.0800039301179112
106101.85101.3999947607290.450005239270936
107102.12101.8499705302060.270029469794494
108102.15102.1199823163990.0300176836007324







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109102.149998034212101.311729035799102.988267032625
110102.149998034212100.964545464638103.335450603786
111102.149998034212100.698136926627103.601859141797
112102.149998034212100.473542381137103.826453687287
113102.149998034212100.275669771144104.02432629728
114102.149998034212100.096778776864104.20321729156
115102.14999803421299.9322712251223104.367724843301
116102.14999803421299.7791511220804104.520844946343
117102.14999803421299.6353374285292104.664658639895
118102.14999803421299.4993149443685104.800681124055
119102.14999803421299.3699398111182104.930056257305
120102.14999803421299.2463233615256105.053672706898

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 102.149998034212 & 101.311729035799 & 102.988267032625 \tabularnewline
110 & 102.149998034212 & 100.964545464638 & 103.335450603786 \tabularnewline
111 & 102.149998034212 & 100.698136926627 & 103.601859141797 \tabularnewline
112 & 102.149998034212 & 100.473542381137 & 103.826453687287 \tabularnewline
113 & 102.149998034212 & 100.275669771144 & 104.02432629728 \tabularnewline
114 & 102.149998034212 & 100.096778776864 & 104.20321729156 \tabularnewline
115 & 102.149998034212 & 99.9322712251223 & 104.367724843301 \tabularnewline
116 & 102.149998034212 & 99.7791511220804 & 104.520844946343 \tabularnewline
117 & 102.149998034212 & 99.6353374285292 & 104.664658639895 \tabularnewline
118 & 102.149998034212 & 99.4993149443685 & 104.800681124055 \tabularnewline
119 & 102.149998034212 & 99.3699398111182 & 104.930056257305 \tabularnewline
120 & 102.149998034212 & 99.2463233615256 & 105.053672706898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284596&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]102.149998034212[/C][C]101.311729035799[/C][C]102.988267032625[/C][/ROW]
[ROW][C]110[/C][C]102.149998034212[/C][C]100.964545464638[/C][C]103.335450603786[/C][/ROW]
[ROW][C]111[/C][C]102.149998034212[/C][C]100.698136926627[/C][C]103.601859141797[/C][/ROW]
[ROW][C]112[/C][C]102.149998034212[/C][C]100.473542381137[/C][C]103.826453687287[/C][/ROW]
[ROW][C]113[/C][C]102.149998034212[/C][C]100.275669771144[/C][C]104.02432629728[/C][/ROW]
[ROW][C]114[/C][C]102.149998034212[/C][C]100.096778776864[/C][C]104.20321729156[/C][/ROW]
[ROW][C]115[/C][C]102.149998034212[/C][C]99.9322712251223[/C][C]104.367724843301[/C][/ROW]
[ROW][C]116[/C][C]102.149998034212[/C][C]99.7791511220804[/C][C]104.520844946343[/C][/ROW]
[ROW][C]117[/C][C]102.149998034212[/C][C]99.6353374285292[/C][C]104.664658639895[/C][/ROW]
[ROW][C]118[/C][C]102.149998034212[/C][C]99.4993149443685[/C][C]104.800681124055[/C][/ROW]
[ROW][C]119[/C][C]102.149998034212[/C][C]99.3699398111182[/C][C]104.930056257305[/C][/ROW]
[ROW][C]120[/C][C]102.149998034212[/C][C]99.2463233615256[/C][C]105.053672706898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284596&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284596&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
109102.149998034212101.311729035799102.988267032625
110102.149998034212100.964545464638103.335450603786
111102.149998034212100.698136926627103.601859141797
112102.149998034212100.473542381137103.826453687287
113102.149998034212100.275669771144104.02432629728
114102.149998034212100.096778776864104.20321729156
115102.14999803421299.9322712251223104.367724843301
116102.14999803421299.7791511220804104.520844946343
117102.14999803421299.6353374285292104.664658639895
118102.14999803421299.4993149443685104.800681124055
119102.14999803421299.3699398111182104.930056257305
120102.14999803421299.2463233615256105.053672706898



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