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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 24 Dec 2011 06:23:21 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/24/t1324726014fnfqspxr9tewowp.htm/, Retrieved Thu, 02 May 2024 16:41:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160746, Retrieved Thu, 02 May 2024 16:41:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 oefening 2] [2011-12-24 11:23:21] [060caeb40c68cbb867cbfbfe8deeeb10] [Current]
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Dataseries X:
74,96
75,19
74,98
75,54
75,61
75,59
75,58
75,44
75,37
75,22
75,33
75,33
78,33
78,09
77,88
77,61
77,43
77,47
77,47
77,46
77,76
78,29
78,56
78,55
78,55
78,59
77,95
78,5
78,45
78,31
78,31
78,33
78,28
79,06
79,2
79,26
79,26
79,38
79,35
78,91
79,11
79,22
79,22
79,21
79,26
79,82
80,04
80,2
80,2
80,27
80,37
80,57
79,99
79,86
79,86
79,81
79,88
80,2
80,53
80,52
80,52
80,48
80,29
79,54
79,39
79,3
79,3
79,49
79,63
79,74
80,17
80,06




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160746&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160746&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160746&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.551043025023764
beta0.0241668840555601
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.551043025023764 \tabularnewline
beta & 0.0241668840555601 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160746&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]0.551043025023764[/C][/ROW]
[ROW][C]beta[/C][C]0.0241668840555601[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160746&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160746&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
alpha0.551043025023764
beta0.0241668840555601
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1378.3377.22513888888891.10486111111112
1478.0977.63970105262640.450298947373554
1577.8877.70873459614160.171265403858399
1677.6177.52253939192140.0874606080785583
1777.4377.34632885181970.0836711481803007
1877.4777.38289440435830.0871055956417308
1977.4778.0500124698136-0.580012469813596
2077.4677.5417957564927-0.0817957564926814
2177.7677.39661194782270.363388052177257
2278.2977.45616614121630.833833858783663
2378.5678.09106037456540.468939625434587
2478.5578.4290437180830.120956281916961
2578.5582.0700024768244-3.52000247682442
2678.5979.6220217746744-1.03202177467443
2777.9578.7090449182154-0.759044918215423
2878.577.92028116672960.579718833270434
2978.4577.96787739738770.482122602612264
3078.3178.18510755274250.124892447257508
3178.3178.5336024867319-0.223602486731878
3278.3378.4102691824771-0.0802691824770676
3378.2878.4306235925397-0.150623592539731
3479.0678.37612872585470.683871274145275
3579.278.72055180635880.479448193641176
3679.2678.86422271099530.395777289004741
3779.2680.9817720650368-1.72177206503684
3879.3880.6254232266948-1.24542322669481
3979.3579.6982992348342-0.348299234834229
4078.9179.7232826312064-0.813282631206363
4179.1178.92726930182290.18273069817711
4279.2278.7829643559990.437035644001014
4379.2279.11498488816470.105015111835272
4479.2179.2094412025780.000558797421959412
4579.2679.2161822860930.0438177139070461
4679.8279.61950769159870.200492308401309
4780.0479.5753762980120.464623701988032
4880.279.64270151729830.557298482701654
4980.280.8701063063697-0.670106306369689
5080.2781.2926745681324-1.02267456813242
5180.3780.8795749724133-0.509574972413319
5280.5780.5932934795289-0.0232934795289452
5379.9980.6766480934295-0.686648093429497
5479.8680.1527552964063-0.292755296406284
5579.8679.9091533554359-0.0491533554359194
5679.8179.8452934280133-0.0352934280133326
5779.8879.82475594889370.0552440511062713
5880.280.277926238103-0.0779262381029753
5980.5380.16845850837160.361541491628401
6080.5280.18871586926090.331284130739135
6180.5280.7056431388556-0.185643138855653
6280.4881.2084531161446-0.728453116144607
6380.2981.1633296331575-0.873329633157468
6479.5480.8655668128958-1.32556681289576
6579.3979.8867964174618-0.496796417461823
6679.379.6001905427912-0.300190542791242
6779.379.4175887984593-0.117588798459309
6879.4979.27705970105660.212940298943423
6979.6379.39208203775120.237917962248801
7079.7479.8466833677777-0.106683367777663
7180.1779.87884595279610.291154047203946
7280.0679.80596982900990.254030170990134

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 78.33 & 77.2251388888889 & 1.10486111111112 \tabularnewline
14 & 78.09 & 77.6397010526264 & 0.450298947373554 \tabularnewline
15 & 77.88 & 77.7087345961416 & 0.171265403858399 \tabularnewline
16 & 77.61 & 77.5225393919214 & 0.0874606080785583 \tabularnewline
17 & 77.43 & 77.3463288518197 & 0.0836711481803007 \tabularnewline
18 & 77.47 & 77.3828944043583 & 0.0871055956417308 \tabularnewline
19 & 77.47 & 78.0500124698136 & -0.580012469813596 \tabularnewline
20 & 77.46 & 77.5417957564927 & -0.0817957564926814 \tabularnewline
21 & 77.76 & 77.3966119478227 & 0.363388052177257 \tabularnewline
22 & 78.29 & 77.4561661412163 & 0.833833858783663 \tabularnewline
23 & 78.56 & 78.0910603745654 & 0.468939625434587 \tabularnewline
24 & 78.55 & 78.429043718083 & 0.120956281916961 \tabularnewline
25 & 78.55 & 82.0700024768244 & -3.52000247682442 \tabularnewline
26 & 78.59 & 79.6220217746744 & -1.03202177467443 \tabularnewline
27 & 77.95 & 78.7090449182154 & -0.759044918215423 \tabularnewline
28 & 78.5 & 77.9202811667296 & 0.579718833270434 \tabularnewline
29 & 78.45 & 77.9678773973877 & 0.482122602612264 \tabularnewline
30 & 78.31 & 78.1851075527425 & 0.124892447257508 \tabularnewline
31 & 78.31 & 78.5336024867319 & -0.223602486731878 \tabularnewline
32 & 78.33 & 78.4102691824771 & -0.0802691824770676 \tabularnewline
33 & 78.28 & 78.4306235925397 & -0.150623592539731 \tabularnewline
34 & 79.06 & 78.3761287258547 & 0.683871274145275 \tabularnewline
35 & 79.2 & 78.7205518063588 & 0.479448193641176 \tabularnewline
36 & 79.26 & 78.8642227109953 & 0.395777289004741 \tabularnewline
37 & 79.26 & 80.9817720650368 & -1.72177206503684 \tabularnewline
38 & 79.38 & 80.6254232266948 & -1.24542322669481 \tabularnewline
39 & 79.35 & 79.6982992348342 & -0.348299234834229 \tabularnewline
40 & 78.91 & 79.7232826312064 & -0.813282631206363 \tabularnewline
41 & 79.11 & 78.9272693018229 & 0.18273069817711 \tabularnewline
42 & 79.22 & 78.782964355999 & 0.437035644001014 \tabularnewline
43 & 79.22 & 79.1149848881647 & 0.105015111835272 \tabularnewline
44 & 79.21 & 79.209441202578 & 0.000558797421959412 \tabularnewline
45 & 79.26 & 79.216182286093 & 0.0438177139070461 \tabularnewline
46 & 79.82 & 79.6195076915987 & 0.200492308401309 \tabularnewline
47 & 80.04 & 79.575376298012 & 0.464623701988032 \tabularnewline
48 & 80.2 & 79.6427015172983 & 0.557298482701654 \tabularnewline
49 & 80.2 & 80.8701063063697 & -0.670106306369689 \tabularnewline
50 & 80.27 & 81.2926745681324 & -1.02267456813242 \tabularnewline
51 & 80.37 & 80.8795749724133 & -0.509574972413319 \tabularnewline
52 & 80.57 & 80.5932934795289 & -0.0232934795289452 \tabularnewline
53 & 79.99 & 80.6766480934295 & -0.686648093429497 \tabularnewline
54 & 79.86 & 80.1527552964063 & -0.292755296406284 \tabularnewline
55 & 79.86 & 79.9091533554359 & -0.0491533554359194 \tabularnewline
56 & 79.81 & 79.8452934280133 & -0.0352934280133326 \tabularnewline
57 & 79.88 & 79.8247559488937 & 0.0552440511062713 \tabularnewline
58 & 80.2 & 80.277926238103 & -0.0779262381029753 \tabularnewline
59 & 80.53 & 80.1684585083716 & 0.361541491628401 \tabularnewline
60 & 80.52 & 80.1887158692609 & 0.331284130739135 \tabularnewline
61 & 80.52 & 80.7056431388556 & -0.185643138855653 \tabularnewline
62 & 80.48 & 81.2084531161446 & -0.728453116144607 \tabularnewline
63 & 80.29 & 81.1633296331575 & -0.873329633157468 \tabularnewline
64 & 79.54 & 80.8655668128958 & -1.32556681289576 \tabularnewline
65 & 79.39 & 79.8867964174618 & -0.496796417461823 \tabularnewline
66 & 79.3 & 79.6001905427912 & -0.300190542791242 \tabularnewline
67 & 79.3 & 79.4175887984593 & -0.117588798459309 \tabularnewline
68 & 79.49 & 79.2770597010566 & 0.212940298943423 \tabularnewline
69 & 79.63 & 79.3920820377512 & 0.237917962248801 \tabularnewline
70 & 79.74 & 79.8466833677777 & -0.106683367777663 \tabularnewline
71 & 80.17 & 79.8788459527961 & 0.291154047203946 \tabularnewline
72 & 80.06 & 79.8059698290099 & 0.254030170990134 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160746&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]78.33[/C][C]77.2251388888889[/C][C]1.10486111111112[/C][/ROW]
[ROW][C]14[/C][C]78.09[/C][C]77.6397010526264[/C][C]0.450298947373554[/C][/ROW]
[ROW][C]15[/C][C]77.88[/C][C]77.7087345961416[/C][C]0.171265403858399[/C][/ROW]
[ROW][C]16[/C][C]77.61[/C][C]77.5225393919214[/C][C]0.0874606080785583[/C][/ROW]
[ROW][C]17[/C][C]77.43[/C][C]77.3463288518197[/C][C]0.0836711481803007[/C][/ROW]
[ROW][C]18[/C][C]77.47[/C][C]77.3828944043583[/C][C]0.0871055956417308[/C][/ROW]
[ROW][C]19[/C][C]77.47[/C][C]78.0500124698136[/C][C]-0.580012469813596[/C][/ROW]
[ROW][C]20[/C][C]77.46[/C][C]77.5417957564927[/C][C]-0.0817957564926814[/C][/ROW]
[ROW][C]21[/C][C]77.76[/C][C]77.3966119478227[/C][C]0.363388052177257[/C][/ROW]
[ROW][C]22[/C][C]78.29[/C][C]77.4561661412163[/C][C]0.833833858783663[/C][/ROW]
[ROW][C]23[/C][C]78.56[/C][C]78.0910603745654[/C][C]0.468939625434587[/C][/ROW]
[ROW][C]24[/C][C]78.55[/C][C]78.429043718083[/C][C]0.120956281916961[/C][/ROW]
[ROW][C]25[/C][C]78.55[/C][C]82.0700024768244[/C][C]-3.52000247682442[/C][/ROW]
[ROW][C]26[/C][C]78.59[/C][C]79.6220217746744[/C][C]-1.03202177467443[/C][/ROW]
[ROW][C]27[/C][C]77.95[/C][C]78.7090449182154[/C][C]-0.759044918215423[/C][/ROW]
[ROW][C]28[/C][C]78.5[/C][C]77.9202811667296[/C][C]0.579718833270434[/C][/ROW]
[ROW][C]29[/C][C]78.45[/C][C]77.9678773973877[/C][C]0.482122602612264[/C][/ROW]
[ROW][C]30[/C][C]78.31[/C][C]78.1851075527425[/C][C]0.124892447257508[/C][/ROW]
[ROW][C]31[/C][C]78.31[/C][C]78.5336024867319[/C][C]-0.223602486731878[/C][/ROW]
[ROW][C]32[/C][C]78.33[/C][C]78.4102691824771[/C][C]-0.0802691824770676[/C][/ROW]
[ROW][C]33[/C][C]78.28[/C][C]78.4306235925397[/C][C]-0.150623592539731[/C][/ROW]
[ROW][C]34[/C][C]79.06[/C][C]78.3761287258547[/C][C]0.683871274145275[/C][/ROW]
[ROW][C]35[/C][C]79.2[/C][C]78.7205518063588[/C][C]0.479448193641176[/C][/ROW]
[ROW][C]36[/C][C]79.26[/C][C]78.8642227109953[/C][C]0.395777289004741[/C][/ROW]
[ROW][C]37[/C][C]79.26[/C][C]80.9817720650368[/C][C]-1.72177206503684[/C][/ROW]
[ROW][C]38[/C][C]79.38[/C][C]80.6254232266948[/C][C]-1.24542322669481[/C][/ROW]
[ROW][C]39[/C][C]79.35[/C][C]79.6982992348342[/C][C]-0.348299234834229[/C][/ROW]
[ROW][C]40[/C][C]78.91[/C][C]79.7232826312064[/C][C]-0.813282631206363[/C][/ROW]
[ROW][C]41[/C][C]79.11[/C][C]78.9272693018229[/C][C]0.18273069817711[/C][/ROW]
[ROW][C]42[/C][C]79.22[/C][C]78.782964355999[/C][C]0.437035644001014[/C][/ROW]
[ROW][C]43[/C][C]79.22[/C][C]79.1149848881647[/C][C]0.105015111835272[/C][/ROW]
[ROW][C]44[/C][C]79.21[/C][C]79.209441202578[/C][C]0.000558797421959412[/C][/ROW]
[ROW][C]45[/C][C]79.26[/C][C]79.216182286093[/C][C]0.0438177139070461[/C][/ROW]
[ROW][C]46[/C][C]79.82[/C][C]79.6195076915987[/C][C]0.200492308401309[/C][/ROW]
[ROW][C]47[/C][C]80.04[/C][C]79.575376298012[/C][C]0.464623701988032[/C][/ROW]
[ROW][C]48[/C][C]80.2[/C][C]79.6427015172983[/C][C]0.557298482701654[/C][/ROW]
[ROW][C]49[/C][C]80.2[/C][C]80.8701063063697[/C][C]-0.670106306369689[/C][/ROW]
[ROW][C]50[/C][C]80.27[/C][C]81.2926745681324[/C][C]-1.02267456813242[/C][/ROW]
[ROW][C]51[/C][C]80.37[/C][C]80.8795749724133[/C][C]-0.509574972413319[/C][/ROW]
[ROW][C]52[/C][C]80.57[/C][C]80.5932934795289[/C][C]-0.0232934795289452[/C][/ROW]
[ROW][C]53[/C][C]79.99[/C][C]80.6766480934295[/C][C]-0.686648093429497[/C][/ROW]
[ROW][C]54[/C][C]79.86[/C][C]80.1527552964063[/C][C]-0.292755296406284[/C][/ROW]
[ROW][C]55[/C][C]79.86[/C][C]79.9091533554359[/C][C]-0.0491533554359194[/C][/ROW]
[ROW][C]56[/C][C]79.81[/C][C]79.8452934280133[/C][C]-0.0352934280133326[/C][/ROW]
[ROW][C]57[/C][C]79.88[/C][C]79.8247559488937[/C][C]0.0552440511062713[/C][/ROW]
[ROW][C]58[/C][C]80.2[/C][C]80.277926238103[/C][C]-0.0779262381029753[/C][/ROW]
[ROW][C]59[/C][C]80.53[/C][C]80.1684585083716[/C][C]0.361541491628401[/C][/ROW]
[ROW][C]60[/C][C]80.52[/C][C]80.1887158692609[/C][C]0.331284130739135[/C][/ROW]
[ROW][C]61[/C][C]80.52[/C][C]80.7056431388556[/C][C]-0.185643138855653[/C][/ROW]
[ROW][C]62[/C][C]80.48[/C][C]81.2084531161446[/C][C]-0.728453116144607[/C][/ROW]
[ROW][C]63[/C][C]80.29[/C][C]81.1633296331575[/C][C]-0.873329633157468[/C][/ROW]
[ROW][C]64[/C][C]79.54[/C][C]80.8655668128958[/C][C]-1.32556681289576[/C][/ROW]
[ROW][C]65[/C][C]79.39[/C][C]79.8867964174618[/C][C]-0.496796417461823[/C][/ROW]
[ROW][C]66[/C][C]79.3[/C][C]79.6001905427912[/C][C]-0.300190542791242[/C][/ROW]
[ROW][C]67[/C][C]79.3[/C][C]79.4175887984593[/C][C]-0.117588798459309[/C][/ROW]
[ROW][C]68[/C][C]79.49[/C][C]79.2770597010566[/C][C]0.212940298943423[/C][/ROW]
[ROW][C]69[/C][C]79.63[/C][C]79.3920820377512[/C][C]0.237917962248801[/C][/ROW]
[ROW][C]70[/C][C]79.74[/C][C]79.8466833677777[/C][C]-0.106683367777663[/C][/ROW]
[ROW][C]71[/C][C]80.17[/C][C]79.8788459527961[/C][C]0.291154047203946[/C][/ROW]
[ROW][C]72[/C][C]80.06[/C][C]79.8059698290099[/C][C]0.254030170990134[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160746&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160746&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
1378.3377.22513888888891.10486111111112
1478.0977.63970105262640.450298947373554
1577.8877.70873459614160.171265403858399
1677.6177.52253939192140.0874606080785583
1777.4377.34632885181970.0836711481803007
1877.4777.38289440435830.0871055956417308
1977.4778.0500124698136-0.580012469813596
2077.4677.5417957564927-0.0817957564926814
2177.7677.39661194782270.363388052177257
2278.2977.45616614121630.833833858783663
2378.5678.09106037456540.468939625434587
2478.5578.4290437180830.120956281916961
2578.5582.0700024768244-3.52000247682442
2678.5979.6220217746744-1.03202177467443
2777.9578.7090449182154-0.759044918215423
2878.577.92028116672960.579718833270434
2978.4577.96787739738770.482122602612264
3078.3178.18510755274250.124892447257508
3178.3178.5336024867319-0.223602486731878
3278.3378.4102691824771-0.0802691824770676
3378.2878.4306235925397-0.150623592539731
3479.0678.37612872585470.683871274145275
3579.278.72055180635880.479448193641176
3679.2678.86422271099530.395777289004741
3779.2680.9817720650368-1.72177206503684
3879.3880.6254232266948-1.24542322669481
3979.3579.6982992348342-0.348299234834229
4078.9179.7232826312064-0.813282631206363
4179.1178.92726930182290.18273069817711
4279.2278.7829643559990.437035644001014
4379.2279.11498488816470.105015111835272
4479.2179.2094412025780.000558797421959412
4579.2679.2161822860930.0438177139070461
4679.8279.61950769159870.200492308401309
4780.0479.5753762980120.464623701988032
4880.279.64270151729830.557298482701654
4980.280.8701063063697-0.670106306369689
5080.2781.2926745681324-1.02267456813242
5180.3780.8795749724133-0.509574972413319
5280.5780.5932934795289-0.0232934795289452
5379.9980.6766480934295-0.686648093429497
5479.8680.1527552964063-0.292755296406284
5579.8679.9091533554359-0.0491533554359194
5679.8179.8452934280133-0.0352934280133326
5779.8879.82475594889370.0552440511062713
5880.280.277926238103-0.0779262381029753
5980.5380.16845850837160.361541491628401
6080.5280.18871586926090.331284130739135
6180.5280.7056431388556-0.185643138855653
6280.4881.2084531161446-0.728453116144607
6380.2981.1633296331575-0.873329633157468
6479.5480.8655668128958-1.32556681289576
6579.3979.8867964174618-0.496796417461823
6679.379.6001905427912-0.300190542791242
6779.379.4175887984593-0.117588798459309
6879.4979.27705970105660.212940298943423
6979.6379.39208203775120.237917962248801
7079.7479.8466833677777-0.106683367777663
7180.1779.87884595279610.291154047203946
7280.0679.80596982900990.254030170990134







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7380.006457228095978.613989389956981.3989250662349
7480.328546933571878.729631084795181.9274627823486
7580.590170638209878.800314254166482.3800270222531
7680.552626610918978.582647840991282.5226053808467
7780.676047001707778.533872627739582.818221375676
7880.757744930942478.449378044877483.0661118170075
7980.832819077931478.362911392981983.3027267628809
8080.917323400422978.289537708137583.5451090927083
8180.935228231320478.15248023347383.7179762291678
8281.109854869729978.174481295783284.0452284436766
8381.386676677171178.300556108641184.472797245701
8481.140078041283777.904720166831384.375435915736

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 80.0064572280959 & 78.6139893899569 & 81.3989250662349 \tabularnewline
74 & 80.3285469335718 & 78.7296310847951 & 81.9274627823486 \tabularnewline
75 & 80.5901706382098 & 78.8003142541664 & 82.3800270222531 \tabularnewline
76 & 80.5526266109189 & 78.5826478409912 & 82.5226053808467 \tabularnewline
77 & 80.6760470017077 & 78.5338726277395 & 82.818221375676 \tabularnewline
78 & 80.7577449309424 & 78.4493780448774 & 83.0661118170075 \tabularnewline
79 & 80.8328190779314 & 78.3629113929819 & 83.3027267628809 \tabularnewline
80 & 80.9173234004229 & 78.2895377081375 & 83.5451090927083 \tabularnewline
81 & 80.9352282313204 & 78.152480233473 & 83.7179762291678 \tabularnewline
82 & 81.1098548697299 & 78.1744812957832 & 84.0452284436766 \tabularnewline
83 & 81.3866766771711 & 78.3005561086411 & 84.472797245701 \tabularnewline
84 & 81.1400780412837 & 77.9047201668313 & 84.375435915736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160746&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]73[/C][C]80.0064572280959[/C][C]78.6139893899569[/C][C]81.3989250662349[/C][/ROW]
[ROW][C]74[/C][C]80.3285469335718[/C][C]78.7296310847951[/C][C]81.9274627823486[/C][/ROW]
[ROW][C]75[/C][C]80.5901706382098[/C][C]78.8003142541664[/C][C]82.3800270222531[/C][/ROW]
[ROW][C]76[/C][C]80.5526266109189[/C][C]78.5826478409912[/C][C]82.5226053808467[/C][/ROW]
[ROW][C]77[/C][C]80.6760470017077[/C][C]78.5338726277395[/C][C]82.818221375676[/C][/ROW]
[ROW][C]78[/C][C]80.7577449309424[/C][C]78.4493780448774[/C][C]83.0661118170075[/C][/ROW]
[ROW][C]79[/C][C]80.8328190779314[/C][C]78.3629113929819[/C][C]83.3027267628809[/C][/ROW]
[ROW][C]80[/C][C]80.9173234004229[/C][C]78.2895377081375[/C][C]83.5451090927083[/C][/ROW]
[ROW][C]81[/C][C]80.9352282313204[/C][C]78.152480233473[/C][C]83.7179762291678[/C][/ROW]
[ROW][C]82[/C][C]81.1098548697299[/C][C]78.1744812957832[/C][C]84.0452284436766[/C][/ROW]
[ROW][C]83[/C][C]81.3866766771711[/C][C]78.3005561086411[/C][C]84.472797245701[/C][/ROW]
[ROW][C]84[/C][C]81.1400780412837[/C][C]77.9047201668313[/C][C]84.375435915736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160746&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160746&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
7380.006457228095978.613989389956981.3989250662349
7480.328546933571878.729631084795181.9274627823486
7580.590170638209878.800314254166482.3800270222531
7680.552626610918978.582647840991282.5226053808467
7780.676047001707778.533872627739582.818221375676
7880.757744930942478.449378044877483.0661118170075
7980.832819077931478.362911392981983.3027267628809
8080.917323400422978.289537708137583.5451090927083
8180.935228231320478.15248023347383.7179762291678
8281.109854869729978.174481295783284.0452284436766
8381.386676677171178.300556108641184.472797245701
8481.140078041283777.904720166831384.375435915736



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')