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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 01 Apr 2015 15:00:26 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/01/t142789688094u380bdpacbbtb.htm/, Retrieved Thu, 09 May 2024 18:06:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278513, Retrieved Thu, 09 May 2024 18:06:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-01 14:00:26] [aed7930eb470b174eb4d45bdfa14c6e0] [Current]
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Dataseries X:
100,8
100,9
101,5
101,8
102,3
102,7
103,3
104,3
103,9
104,1
104,5
104
105,3
105,3
105,7
105,7
105,3
105,6
106,5
107
106,6
106,4
105,6
105,8
106,3
105,2
104,1
103,4
102,6
101,6
101,7
101
100,7
100,8
100,3
99,8
100
100,3
100,1
100,8
100,1
99,9
100,5
100,6
99,9
99,5
99,2
98,9
98,8
98,4
98,9
98,4
98,3
98,1
98,2
97,6
96,8
96,6
96
94,9
95,2
95
93,7
92,9
92,3
93,2
89,6
89,2
88,7
88,4
88,9
88,3
85,8
86,8
86,9
85,7
84,5
84
85
85,2
85
84,8
84,5
85




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=278513&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=278513&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278513&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
alpha0.618538538747077
beta0.254716554081614
gamma0.27364319057624

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.618538538747077 \tabularnewline
beta & 0.254716554081614 \tabularnewline
gamma & 0.27364319057624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278513&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]0.618538538747077[/C][/ROW]
[ROW][C]beta[/C][C]0.254716554081614[/C][/ROW]
[ROW][C]gamma[/C][C]0.27364319057624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278513&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278513&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
alpha0.618538538747077
beta0.254716554081614
gamma0.27364319057624







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13105.3103.557024572651.74297542735037
14105.3104.9188076603990.381192339601427
15105.7105.919166377749-0.219166377748593
16105.7106.130316655734-0.430316655734373
17105.3105.809731764022-0.509731764022334
18105.6106.080549639095-0.480549639095187
19106.5106.610372890528-0.110372890528083
20107107.485108590214-0.485108590213514
21106.6106.664125986692-0.0641259866925026
22106.4106.714267503139-0.314267503138581
23105.6106.810173376247-1.2101733762472
24105.8105.30292836440.49707163559961
25106.3106.903600811551-0.603600811550749
26105.2106.112611605193-0.912611605192978
27104.1105.487017632854-1.38701763285434
28103.4104.006751769511-0.606751769511064
29102.6102.5939332094650.00606679053483106
30101.6102.293291563989-0.693291563988552
31101.7101.803101510226-0.103101510225684
32101101.717299045746-0.717299045745946
33100.799.8341403552040.865859644796032
34100.899.61742274176111.18257725823888
35100.399.96551691584760.334483084152382
3699.899.25512547054140.544874529458568
37100100.441218721833-0.441218721832911
38100.399.41474266417840.885257335821578
39100.199.83126667343950.268733326560451
40100.899.69704831311551.10295168688451
41100.199.91553728772160.184462712278361
4299.9100.190166377397-0.290166377397469
43100.5100.612372599684-0.112372599684406
44100.6101.056703549367-0.456703549367219
4599.9100.141028060009-0.241028060008887
4699.599.7393636043401-0.239363604340085
4799.299.3620206826732-0.162020682673202
4898.998.53087480010460.369125199895379
4998.899.6420286807652-0.842028680765225
5098.498.5796521679337-0.179652167933654
5198.998.17890716957680.721092830423174
5298.498.38861407557260.0113859244273726
5398.397.64111748050950.658882519490518
5498.198.03946123568710.0605387643128523
5598.298.6322168581127-0.432216858112653
5697.698.7274428170167-1.12744281701666
5796.897.1983998317519-0.39839983175186
5896.696.45377182409080.146228175909172
599696.137959636694-0.137959636693964
6094.995.1958845809815-0.295884580981479
6195.295.4832500059587-0.283250005958664
629594.63764927858020.362350721419773
6393.794.553579172848-0.853579172848015
6492.993.3545172996132-0.454517299613201
6592.391.95233493862590.34766506137413
6693.291.6125928890181.58740711098199
6789.692.8557725307039-3.25577253070392
6889.290.4445260044882-1.24452600448818
6988.788.21329274063670.486707259363314
7088.487.50656812770970.893431872290293
7188.987.17456882620331.72543117379666
7288.387.21347222657571.08652777342427
7385.888.4199179760084-2.61991797600845
7486.885.89092808822180.90907191177817
7586.985.79877853059411.10122146940593
7685.785.9391512087159-0.239151208715924
7784.584.8765069154696-0.376506915469605
788484.2267420585729-0.226742058572853
798583.56492144027261.43507855972736
8085.284.7268156968690.473184303130992
818584.47112076662480.528879233375207
8284.884.57193578400830.228064215991722
8384.584.5493975893613-0.0493975893612912
848583.77835061931441.22164938068565

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 105.3 & 103.55702457265 & 1.74297542735037 \tabularnewline
14 & 105.3 & 104.918807660399 & 0.381192339601427 \tabularnewline
15 & 105.7 & 105.919166377749 & -0.219166377748593 \tabularnewline
16 & 105.7 & 106.130316655734 & -0.430316655734373 \tabularnewline
17 & 105.3 & 105.809731764022 & -0.509731764022334 \tabularnewline
18 & 105.6 & 106.080549639095 & -0.480549639095187 \tabularnewline
19 & 106.5 & 106.610372890528 & -0.110372890528083 \tabularnewline
20 & 107 & 107.485108590214 & -0.485108590213514 \tabularnewline
21 & 106.6 & 106.664125986692 & -0.0641259866925026 \tabularnewline
22 & 106.4 & 106.714267503139 & -0.314267503138581 \tabularnewline
23 & 105.6 & 106.810173376247 & -1.2101733762472 \tabularnewline
24 & 105.8 & 105.3029283644 & 0.49707163559961 \tabularnewline
25 & 106.3 & 106.903600811551 & -0.603600811550749 \tabularnewline
26 & 105.2 & 106.112611605193 & -0.912611605192978 \tabularnewline
27 & 104.1 & 105.487017632854 & -1.38701763285434 \tabularnewline
28 & 103.4 & 104.006751769511 & -0.606751769511064 \tabularnewline
29 & 102.6 & 102.593933209465 & 0.00606679053483106 \tabularnewline
30 & 101.6 & 102.293291563989 & -0.693291563988552 \tabularnewline
31 & 101.7 & 101.803101510226 & -0.103101510225684 \tabularnewline
32 & 101 & 101.717299045746 & -0.717299045745946 \tabularnewline
33 & 100.7 & 99.834140355204 & 0.865859644796032 \tabularnewline
34 & 100.8 & 99.6174227417611 & 1.18257725823888 \tabularnewline
35 & 100.3 & 99.9655169158476 & 0.334483084152382 \tabularnewline
36 & 99.8 & 99.2551254705414 & 0.544874529458568 \tabularnewline
37 & 100 & 100.441218721833 & -0.441218721832911 \tabularnewline
38 & 100.3 & 99.4147426641784 & 0.885257335821578 \tabularnewline
39 & 100.1 & 99.8312666734395 & 0.268733326560451 \tabularnewline
40 & 100.8 & 99.6970483131155 & 1.10295168688451 \tabularnewline
41 & 100.1 & 99.9155372877216 & 0.184462712278361 \tabularnewline
42 & 99.9 & 100.190166377397 & -0.290166377397469 \tabularnewline
43 & 100.5 & 100.612372599684 & -0.112372599684406 \tabularnewline
44 & 100.6 & 101.056703549367 & -0.456703549367219 \tabularnewline
45 & 99.9 & 100.141028060009 & -0.241028060008887 \tabularnewline
46 & 99.5 & 99.7393636043401 & -0.239363604340085 \tabularnewline
47 & 99.2 & 99.3620206826732 & -0.162020682673202 \tabularnewline
48 & 98.9 & 98.5308748001046 & 0.369125199895379 \tabularnewline
49 & 98.8 & 99.6420286807652 & -0.842028680765225 \tabularnewline
50 & 98.4 & 98.5796521679337 & -0.179652167933654 \tabularnewline
51 & 98.9 & 98.1789071695768 & 0.721092830423174 \tabularnewline
52 & 98.4 & 98.3886140755726 & 0.0113859244273726 \tabularnewline
53 & 98.3 & 97.6411174805095 & 0.658882519490518 \tabularnewline
54 & 98.1 & 98.0394612356871 & 0.0605387643128523 \tabularnewline
55 & 98.2 & 98.6322168581127 & -0.432216858112653 \tabularnewline
56 & 97.6 & 98.7274428170167 & -1.12744281701666 \tabularnewline
57 & 96.8 & 97.1983998317519 & -0.39839983175186 \tabularnewline
58 & 96.6 & 96.4537718240908 & 0.146228175909172 \tabularnewline
59 & 96 & 96.137959636694 & -0.137959636693964 \tabularnewline
60 & 94.9 & 95.1958845809815 & -0.295884580981479 \tabularnewline
61 & 95.2 & 95.4832500059587 & -0.283250005958664 \tabularnewline
62 & 95 & 94.6376492785802 & 0.362350721419773 \tabularnewline
63 & 93.7 & 94.553579172848 & -0.853579172848015 \tabularnewline
64 & 92.9 & 93.3545172996132 & -0.454517299613201 \tabularnewline
65 & 92.3 & 91.9523349386259 & 0.34766506137413 \tabularnewline
66 & 93.2 & 91.612592889018 & 1.58740711098199 \tabularnewline
67 & 89.6 & 92.8557725307039 & -3.25577253070392 \tabularnewline
68 & 89.2 & 90.4445260044882 & -1.24452600448818 \tabularnewline
69 & 88.7 & 88.2132927406367 & 0.486707259363314 \tabularnewline
70 & 88.4 & 87.5065681277097 & 0.893431872290293 \tabularnewline
71 & 88.9 & 87.1745688262033 & 1.72543117379666 \tabularnewline
72 & 88.3 & 87.2134722265757 & 1.08652777342427 \tabularnewline
73 & 85.8 & 88.4199179760084 & -2.61991797600845 \tabularnewline
74 & 86.8 & 85.8909280882218 & 0.90907191177817 \tabularnewline
75 & 86.9 & 85.7987785305941 & 1.10122146940593 \tabularnewline
76 & 85.7 & 85.9391512087159 & -0.239151208715924 \tabularnewline
77 & 84.5 & 84.8765069154696 & -0.376506915469605 \tabularnewline
78 & 84 & 84.2267420585729 & -0.226742058572853 \tabularnewline
79 & 85 & 83.5649214402726 & 1.43507855972736 \tabularnewline
80 & 85.2 & 84.726815696869 & 0.473184303130992 \tabularnewline
81 & 85 & 84.4711207666248 & 0.528879233375207 \tabularnewline
82 & 84.8 & 84.5719357840083 & 0.228064215991722 \tabularnewline
83 & 84.5 & 84.5493975893613 & -0.0493975893612912 \tabularnewline
84 & 85 & 83.7783506193144 & 1.22164938068565 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278513&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]105.3[/C][C]103.55702457265[/C][C]1.74297542735037[/C][/ROW]
[ROW][C]14[/C][C]105.3[/C][C]104.918807660399[/C][C]0.381192339601427[/C][/ROW]
[ROW][C]15[/C][C]105.7[/C][C]105.919166377749[/C][C]-0.219166377748593[/C][/ROW]
[ROW][C]16[/C][C]105.7[/C][C]106.130316655734[/C][C]-0.430316655734373[/C][/ROW]
[ROW][C]17[/C][C]105.3[/C][C]105.809731764022[/C][C]-0.509731764022334[/C][/ROW]
[ROW][C]18[/C][C]105.6[/C][C]106.080549639095[/C][C]-0.480549639095187[/C][/ROW]
[ROW][C]19[/C][C]106.5[/C][C]106.610372890528[/C][C]-0.110372890528083[/C][/ROW]
[ROW][C]20[/C][C]107[/C][C]107.485108590214[/C][C]-0.485108590213514[/C][/ROW]
[ROW][C]21[/C][C]106.6[/C][C]106.664125986692[/C][C]-0.0641259866925026[/C][/ROW]
[ROW][C]22[/C][C]106.4[/C][C]106.714267503139[/C][C]-0.314267503138581[/C][/ROW]
[ROW][C]23[/C][C]105.6[/C][C]106.810173376247[/C][C]-1.2101733762472[/C][/ROW]
[ROW][C]24[/C][C]105.8[/C][C]105.3029283644[/C][C]0.49707163559961[/C][/ROW]
[ROW][C]25[/C][C]106.3[/C][C]106.903600811551[/C][C]-0.603600811550749[/C][/ROW]
[ROW][C]26[/C][C]105.2[/C][C]106.112611605193[/C][C]-0.912611605192978[/C][/ROW]
[ROW][C]27[/C][C]104.1[/C][C]105.487017632854[/C][C]-1.38701763285434[/C][/ROW]
[ROW][C]28[/C][C]103.4[/C][C]104.006751769511[/C][C]-0.606751769511064[/C][/ROW]
[ROW][C]29[/C][C]102.6[/C][C]102.593933209465[/C][C]0.00606679053483106[/C][/ROW]
[ROW][C]30[/C][C]101.6[/C][C]102.293291563989[/C][C]-0.693291563988552[/C][/ROW]
[ROW][C]31[/C][C]101.7[/C][C]101.803101510226[/C][C]-0.103101510225684[/C][/ROW]
[ROW][C]32[/C][C]101[/C][C]101.717299045746[/C][C]-0.717299045745946[/C][/ROW]
[ROW][C]33[/C][C]100.7[/C][C]99.834140355204[/C][C]0.865859644796032[/C][/ROW]
[ROW][C]34[/C][C]100.8[/C][C]99.6174227417611[/C][C]1.18257725823888[/C][/ROW]
[ROW][C]35[/C][C]100.3[/C][C]99.9655169158476[/C][C]0.334483084152382[/C][/ROW]
[ROW][C]36[/C][C]99.8[/C][C]99.2551254705414[/C][C]0.544874529458568[/C][/ROW]
[ROW][C]37[/C][C]100[/C][C]100.441218721833[/C][C]-0.441218721832911[/C][/ROW]
[ROW][C]38[/C][C]100.3[/C][C]99.4147426641784[/C][C]0.885257335821578[/C][/ROW]
[ROW][C]39[/C][C]100.1[/C][C]99.8312666734395[/C][C]0.268733326560451[/C][/ROW]
[ROW][C]40[/C][C]100.8[/C][C]99.6970483131155[/C][C]1.10295168688451[/C][/ROW]
[ROW][C]41[/C][C]100.1[/C][C]99.9155372877216[/C][C]0.184462712278361[/C][/ROW]
[ROW][C]42[/C][C]99.9[/C][C]100.190166377397[/C][C]-0.290166377397469[/C][/ROW]
[ROW][C]43[/C][C]100.5[/C][C]100.612372599684[/C][C]-0.112372599684406[/C][/ROW]
[ROW][C]44[/C][C]100.6[/C][C]101.056703549367[/C][C]-0.456703549367219[/C][/ROW]
[ROW][C]45[/C][C]99.9[/C][C]100.141028060009[/C][C]-0.241028060008887[/C][/ROW]
[ROW][C]46[/C][C]99.5[/C][C]99.7393636043401[/C][C]-0.239363604340085[/C][/ROW]
[ROW][C]47[/C][C]99.2[/C][C]99.3620206826732[/C][C]-0.162020682673202[/C][/ROW]
[ROW][C]48[/C][C]98.9[/C][C]98.5308748001046[/C][C]0.369125199895379[/C][/ROW]
[ROW][C]49[/C][C]98.8[/C][C]99.6420286807652[/C][C]-0.842028680765225[/C][/ROW]
[ROW][C]50[/C][C]98.4[/C][C]98.5796521679337[/C][C]-0.179652167933654[/C][/ROW]
[ROW][C]51[/C][C]98.9[/C][C]98.1789071695768[/C][C]0.721092830423174[/C][/ROW]
[ROW][C]52[/C][C]98.4[/C][C]98.3886140755726[/C][C]0.0113859244273726[/C][/ROW]
[ROW][C]53[/C][C]98.3[/C][C]97.6411174805095[/C][C]0.658882519490518[/C][/ROW]
[ROW][C]54[/C][C]98.1[/C][C]98.0394612356871[/C][C]0.0605387643128523[/C][/ROW]
[ROW][C]55[/C][C]98.2[/C][C]98.6322168581127[/C][C]-0.432216858112653[/C][/ROW]
[ROW][C]56[/C][C]97.6[/C][C]98.7274428170167[/C][C]-1.12744281701666[/C][/ROW]
[ROW][C]57[/C][C]96.8[/C][C]97.1983998317519[/C][C]-0.39839983175186[/C][/ROW]
[ROW][C]58[/C][C]96.6[/C][C]96.4537718240908[/C][C]0.146228175909172[/C][/ROW]
[ROW][C]59[/C][C]96[/C][C]96.137959636694[/C][C]-0.137959636693964[/C][/ROW]
[ROW][C]60[/C][C]94.9[/C][C]95.1958845809815[/C][C]-0.295884580981479[/C][/ROW]
[ROW][C]61[/C][C]95.2[/C][C]95.4832500059587[/C][C]-0.283250005958664[/C][/ROW]
[ROW][C]62[/C][C]95[/C][C]94.6376492785802[/C][C]0.362350721419773[/C][/ROW]
[ROW][C]63[/C][C]93.7[/C][C]94.553579172848[/C][C]-0.853579172848015[/C][/ROW]
[ROW][C]64[/C][C]92.9[/C][C]93.3545172996132[/C][C]-0.454517299613201[/C][/ROW]
[ROW][C]65[/C][C]92.3[/C][C]91.9523349386259[/C][C]0.34766506137413[/C][/ROW]
[ROW][C]66[/C][C]93.2[/C][C]91.612592889018[/C][C]1.58740711098199[/C][/ROW]
[ROW][C]67[/C][C]89.6[/C][C]92.8557725307039[/C][C]-3.25577253070392[/C][/ROW]
[ROW][C]68[/C][C]89.2[/C][C]90.4445260044882[/C][C]-1.24452600448818[/C][/ROW]
[ROW][C]69[/C][C]88.7[/C][C]88.2132927406367[/C][C]0.486707259363314[/C][/ROW]
[ROW][C]70[/C][C]88.4[/C][C]87.5065681277097[/C][C]0.893431872290293[/C][/ROW]
[ROW][C]71[/C][C]88.9[/C][C]87.1745688262033[/C][C]1.72543117379666[/C][/ROW]
[ROW][C]72[/C][C]88.3[/C][C]87.2134722265757[/C][C]1.08652777342427[/C][/ROW]
[ROW][C]73[/C][C]85.8[/C][C]88.4199179760084[/C][C]-2.61991797600845[/C][/ROW]
[ROW][C]74[/C][C]86.8[/C][C]85.8909280882218[/C][C]0.90907191177817[/C][/ROW]
[ROW][C]75[/C][C]86.9[/C][C]85.7987785305941[/C][C]1.10122146940593[/C][/ROW]
[ROW][C]76[/C][C]85.7[/C][C]85.9391512087159[/C][C]-0.239151208715924[/C][/ROW]
[ROW][C]77[/C][C]84.5[/C][C]84.8765069154696[/C][C]-0.376506915469605[/C][/ROW]
[ROW][C]78[/C][C]84[/C][C]84.2267420585729[/C][C]-0.226742058572853[/C][/ROW]
[ROW][C]79[/C][C]85[/C][C]83.5649214402726[/C][C]1.43507855972736[/C][/ROW]
[ROW][C]80[/C][C]85.2[/C][C]84.726815696869[/C][C]0.473184303130992[/C][/ROW]
[ROW][C]81[/C][C]85[/C][C]84.4711207666248[/C][C]0.528879233375207[/C][/ROW]
[ROW][C]82[/C][C]84.8[/C][C]84.5719357840083[/C][C]0.228064215991722[/C][/ROW]
[ROW][C]83[/C][C]84.5[/C][C]84.5493975893613[/C][C]-0.0493975893612912[/C][/ROW]
[ROW][C]84[/C][C]85[/C][C]83.7783506193144[/C][C]1.22164938068565[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278513&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278513&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
13105.3103.557024572651.74297542735037
14105.3104.9188076603990.381192339601427
15105.7105.919166377749-0.219166377748593
16105.7106.130316655734-0.430316655734373
17105.3105.809731764022-0.509731764022334
18105.6106.080549639095-0.480549639095187
19106.5106.610372890528-0.110372890528083
20107107.485108590214-0.485108590213514
21106.6106.664125986692-0.0641259866925026
22106.4106.714267503139-0.314267503138581
23105.6106.810173376247-1.2101733762472
24105.8105.30292836440.49707163559961
25106.3106.903600811551-0.603600811550749
26105.2106.112611605193-0.912611605192978
27104.1105.487017632854-1.38701763285434
28103.4104.006751769511-0.606751769511064
29102.6102.5939332094650.00606679053483106
30101.6102.293291563989-0.693291563988552
31101.7101.803101510226-0.103101510225684
32101101.717299045746-0.717299045745946
33100.799.8341403552040.865859644796032
34100.899.61742274176111.18257725823888
35100.399.96551691584760.334483084152382
3699.899.25512547054140.544874529458568
37100100.441218721833-0.441218721832911
38100.399.41474266417840.885257335821578
39100.199.83126667343950.268733326560451
40100.899.69704831311551.10295168688451
41100.199.91553728772160.184462712278361
4299.9100.190166377397-0.290166377397469
43100.5100.612372599684-0.112372599684406
44100.6101.056703549367-0.456703549367219
4599.9100.141028060009-0.241028060008887
4699.599.7393636043401-0.239363604340085
4799.299.3620206826732-0.162020682673202
4898.998.53087480010460.369125199895379
4998.899.6420286807652-0.842028680765225
5098.498.5796521679337-0.179652167933654
5198.998.17890716957680.721092830423174
5298.498.38861407557260.0113859244273726
5398.397.64111748050950.658882519490518
5498.198.03946123568710.0605387643128523
5598.298.6322168581127-0.432216858112653
5697.698.7274428170167-1.12744281701666
5796.897.1983998317519-0.39839983175186
5896.696.45377182409080.146228175909172
599696.137959636694-0.137959636693964
6094.995.1958845809815-0.295884580981479
6195.295.4832500059587-0.283250005958664
629594.63764927858020.362350721419773
6393.794.553579172848-0.853579172848015
6492.993.3545172996132-0.454517299613201
6592.391.95233493862590.34766506137413
6693.291.6125928890181.58740711098199
6789.692.8557725307039-3.25577253070392
6889.290.4445260044882-1.24452600448818
6988.788.21329274063670.486707259363314
7088.487.50656812770970.893431872290293
7188.987.17456882620331.72543117379666
7288.387.21347222657571.08652777342427
7385.888.4199179760084-2.61991797600845
7486.885.89092808822180.90907191177817
7586.985.79877853059411.10122146940593
7685.785.9391512087159-0.239151208715924
7784.584.8765069154696-0.376506915469605
788484.2267420585729-0.226742058572853
798583.56492144027261.43507855972736
8085.284.7268156968690.473184303130992
818584.47112076662480.528879233375207
8284.884.57193578400830.228064215991722
8384.584.5493975893613-0.0493975893612912
848583.77835061931441.22164938068565







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8585.057309232729283.352576962559386.7620415028992
8685.305813965337383.147918814173587.4637091165012
8785.316802830478582.635434573647287.9981710873098
8885.107991065306181.844548164697488.3714339659148
8984.688489361082280.792111849805188.5848668723594
9084.856117198889780.281283335250789.4309510625286
9185.112612535136179.817673839488790.4075512307836
9285.664948421893579.611202048011991.7186947957751
9385.426333020794178.577406995324692.2752590462635
9485.389238070350877.71066540764493.0678107330576
9585.381361324051176.84027291693293.9224497311703
9684.966019364339375.53091461959994.4011241090797

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 85.0573092327292 & 83.3525769625593 & 86.7620415028992 \tabularnewline
86 & 85.3058139653373 & 83.1479188141735 & 87.4637091165012 \tabularnewline
87 & 85.3168028304785 & 82.6354345736472 & 87.9981710873098 \tabularnewline
88 & 85.1079910653061 & 81.8445481646974 & 88.3714339659148 \tabularnewline
89 & 84.6884893610822 & 80.7921118498051 & 88.5848668723594 \tabularnewline
90 & 84.8561171988897 & 80.2812833352507 & 89.4309510625286 \tabularnewline
91 & 85.1126125351361 & 79.8176738394887 & 90.4075512307836 \tabularnewline
92 & 85.6649484218935 & 79.6112020480119 & 91.7186947957751 \tabularnewline
93 & 85.4263330207941 & 78.5774069953246 & 92.2752590462635 \tabularnewline
94 & 85.3892380703508 & 77.710665407644 & 93.0678107330576 \tabularnewline
95 & 85.3813613240511 & 76.840272916932 & 93.9224497311703 \tabularnewline
96 & 84.9660193643393 & 75.530914619599 & 94.4011241090797 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278513&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]85[/C][C]85.0573092327292[/C][C]83.3525769625593[/C][C]86.7620415028992[/C][/ROW]
[ROW][C]86[/C][C]85.3058139653373[/C][C]83.1479188141735[/C][C]87.4637091165012[/C][/ROW]
[ROW][C]87[/C][C]85.3168028304785[/C][C]82.6354345736472[/C][C]87.9981710873098[/C][/ROW]
[ROW][C]88[/C][C]85.1079910653061[/C][C]81.8445481646974[/C][C]88.3714339659148[/C][/ROW]
[ROW][C]89[/C][C]84.6884893610822[/C][C]80.7921118498051[/C][C]88.5848668723594[/C][/ROW]
[ROW][C]90[/C][C]84.8561171988897[/C][C]80.2812833352507[/C][C]89.4309510625286[/C][/ROW]
[ROW][C]91[/C][C]85.1126125351361[/C][C]79.8176738394887[/C][C]90.4075512307836[/C][/ROW]
[ROW][C]92[/C][C]85.6649484218935[/C][C]79.6112020480119[/C][C]91.7186947957751[/C][/ROW]
[ROW][C]93[/C][C]85.4263330207941[/C][C]78.5774069953246[/C][C]92.2752590462635[/C][/ROW]
[ROW][C]94[/C][C]85.3892380703508[/C][C]77.710665407644[/C][C]93.0678107330576[/C][/ROW]
[ROW][C]95[/C][C]85.3813613240511[/C][C]76.840272916932[/C][C]93.9224497311703[/C][/ROW]
[ROW][C]96[/C][C]84.9660193643393[/C][C]75.530914619599[/C][C]94.4011241090797[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278513&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278513&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
8585.057309232729283.352576962559386.7620415028992
8685.305813965337383.147918814173587.4637091165012
8785.316802830478582.635434573647287.9981710873098
8885.107991065306181.844548164697488.3714339659148
8984.688489361082280.792111849805188.5848668723594
9084.856117198889780.281283335250789.4309510625286
9185.112612535136179.817673839488790.4075512307836
9285.664948421893579.611202048011991.7186947957751
9385.426333020794178.577406995324692.2752590462635
9485.389238070350877.71066540764493.0678107330576
9585.381361324051176.84027291693293.9224497311703
9684.966019364339375.53091461959994.4011241090797



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