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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 11 Jan 2014 17:46:10 -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/2014/Jan/11/t1389480460r65lqxzv22xz29i.htm/, Retrieved Thu, 23 May 2024 18:13:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232945, Retrieved Thu, 23 May 2024 18:13:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-01-11 22:46:10] [c13b0833c91505664fff70cc44050808] [Current]
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Dataseries X:
47.43
47.43
47.51
47.96
47.99
48.05
48.05
48.01
48
48.06
48.23
48.4
48.4
48.5
48.41
48.35
48.53
48.52
48.52
48.49
48.45
48.65
48.74
48.74
48.74
48.79
48.82
48.82
49.2
49.3
49.3
49.34
49.47
49.65
49.7
49.75
49.75
49.7
50.09
50.19
50.53
50.55
50.55
50.55
50.58
50.61
50.94
51.01
51.01
51.04
51.15
51.31
51.31
51.34
51.34
51.34
51.47
51.95
51.97
51.92
51.92
51.91
51.97
52.14
52.33
52.4
52.4
52.41
52.71
53.17
53.33
53.32
53.32
53.3
53.31
53.72
53.87
53.91
53.91
53.96
54.02
54.33
54.48
54.54




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232945&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]4 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=232945&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232945&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0537865277111642
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0537865277111642 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232945&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]0.0537865277111642[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232945&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232945&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
beta0.0537865277111642
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
347.5147.430.0799999999999983
447.9647.51430292221690.445697077783109
547.9947.98827542044190.00172457955814309
648.0548.01836817958810.0316318204119383
748.0548.0800695453732-0.0300695453731947
848.0148.0784522089377-0.068452208937714
94848.0347704023048-0.0347704023047939
1048.0648.02290022309770.037099776902302
1148.2348.08489569127610.145104308723859
1248.448.26270034819830.137299651801683
1348.448.4400852197247-0.0400852197246877
1448.548.43792917494320.0620708250568427
1548.4148.5412677490951-0.131267749095137
1648.3548.4442073126708-0.0942073126708394
1748.5348.37914022843730.150859771562722
1848.5248.5672544517209-0.0472544517209386
1948.5248.554712798844-0.0347127988439766
2048.4948.552845717927-0.0628457179270185
2148.4548.5194654649782-0.069465464978208
2248.6548.47572915882120.174270841178803
2348.7448.68510258224950.0548974177505031
2448.7448.7780553237306-0.0380553237306103
2548.7448.7760084600062-0.0360084600062152
2648.7948.77407168997430.0159283100257426
2748.8248.8249284184628-0.0049284184628462
2848.8248.8546633359466-0.0346633359466253
2949.248.85279891546720.347201084532834
3049.349.25147365622170.0485263437782564
3149.349.3540837197561-0.0540837197560933
3249.3449.3511747442647-0.0111747442647001
3349.4749.39057369357270.0794263064273437
3449.6549.52484575880430.125154241195702
3549.749.7115773708665-0.0115773708665401
3649.7549.7609546642876-0.0109546642876097
3749.7549.8103654509333-0.0603654509333325
3849.749.8071186029339-0.107118602933909
3950.0949.75135706522880.338642934771173
4050.1950.15957149282410.0304285071759125
4150.5350.26120813656850.268791863431495
4250.5550.6156655175795-0.0656655175795109
4350.5550.6321335973985-0.0821335973985455
4450.5550.6277159163861-0.0777159163860546
4550.5850.6235358470958-0.0435358470957539
4650.6150.6511942050495-0.0411942050495071
4750.9450.67897851179810.261021488201919
4851.0151.0230179513065-0.013017951306459
4951.0151.0923177609078-0.0823177609077703
5051.0451.0878901743796-0.0478901743795817
5151.1551.11531432818820.0346856718117792
5251.3151.22717995003630.0828200499636935
5351.3151.3916345529487-0.0816345529487208
5451.3451.3872437138044-0.047243713804356
5551.3451.4147026384826-0.0747026384826412
5651.3451.4106846429478-0.0706846429477963
5751.4751.40688276144110.063117238558867
5851.9551.54027761854190.409722381458074
5951.9752.0423151627661-0.0723151627661096
6051.9252.0584255812601-0.138425581260051
6151.9252.0009801498977-0.0809801498976768
6251.9151.9966245088211-0.0866245088211528
6351.9751.981965277277-0.0119652772769712
6452.1452.04132170655910.0986782934408552
6552.3352.21662926932380.113370730676209
6652.452.4127270872709-0.0127270872709389
6752.452.4820425414388-0.08204254143876
6852.4152.4776297580102-0.0676297580101703
6952.7152.48399218815690.226007811843147
7053.1752.79614836359150.373851636408503
7153.3353.2762565449930.053743455006952
7253.3253.4391472188251-0.11914721882507
7353.3253.422738703638-0.102738703638032
7453.353.4172127455078-0.1172127455078
7553.3153.3909082789234-0.080908278923431
7653.7253.39655650353710.323443496462936
7753.8753.82395340612260.0460465938774419
7853.9153.9764300925201-0.0664300925201502
7953.9154.012857048508-0.102857048507964
8053.9654.0073247250181-0.0473247250180933
8154.0254.0547792923845-0.0347792923844921
8254.3354.11290863501090.217091364989116
8354.4854.43458522572970.0454147742702773
8454.5454.5870279287445-0.0470279287445052

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 47.51 & 47.43 & 0.0799999999999983 \tabularnewline
4 & 47.96 & 47.5143029222169 & 0.445697077783109 \tabularnewline
5 & 47.99 & 47.9882754204419 & 0.00172457955814309 \tabularnewline
6 & 48.05 & 48.0183681795881 & 0.0316318204119383 \tabularnewline
7 & 48.05 & 48.0800695453732 & -0.0300695453731947 \tabularnewline
8 & 48.01 & 48.0784522089377 & -0.068452208937714 \tabularnewline
9 & 48 & 48.0347704023048 & -0.0347704023047939 \tabularnewline
10 & 48.06 & 48.0229002230977 & 0.037099776902302 \tabularnewline
11 & 48.23 & 48.0848956912761 & 0.145104308723859 \tabularnewline
12 & 48.4 & 48.2627003481983 & 0.137299651801683 \tabularnewline
13 & 48.4 & 48.4400852197247 & -0.0400852197246877 \tabularnewline
14 & 48.5 & 48.4379291749432 & 0.0620708250568427 \tabularnewline
15 & 48.41 & 48.5412677490951 & -0.131267749095137 \tabularnewline
16 & 48.35 & 48.4442073126708 & -0.0942073126708394 \tabularnewline
17 & 48.53 & 48.3791402284373 & 0.150859771562722 \tabularnewline
18 & 48.52 & 48.5672544517209 & -0.0472544517209386 \tabularnewline
19 & 48.52 & 48.554712798844 & -0.0347127988439766 \tabularnewline
20 & 48.49 & 48.552845717927 & -0.0628457179270185 \tabularnewline
21 & 48.45 & 48.5194654649782 & -0.069465464978208 \tabularnewline
22 & 48.65 & 48.4757291588212 & 0.174270841178803 \tabularnewline
23 & 48.74 & 48.6851025822495 & 0.0548974177505031 \tabularnewline
24 & 48.74 & 48.7780553237306 & -0.0380553237306103 \tabularnewline
25 & 48.74 & 48.7760084600062 & -0.0360084600062152 \tabularnewline
26 & 48.79 & 48.7740716899743 & 0.0159283100257426 \tabularnewline
27 & 48.82 & 48.8249284184628 & -0.0049284184628462 \tabularnewline
28 & 48.82 & 48.8546633359466 & -0.0346633359466253 \tabularnewline
29 & 49.2 & 48.8527989154672 & 0.347201084532834 \tabularnewline
30 & 49.3 & 49.2514736562217 & 0.0485263437782564 \tabularnewline
31 & 49.3 & 49.3540837197561 & -0.0540837197560933 \tabularnewline
32 & 49.34 & 49.3511747442647 & -0.0111747442647001 \tabularnewline
33 & 49.47 & 49.3905736935727 & 0.0794263064273437 \tabularnewline
34 & 49.65 & 49.5248457588043 & 0.125154241195702 \tabularnewline
35 & 49.7 & 49.7115773708665 & -0.0115773708665401 \tabularnewline
36 & 49.75 & 49.7609546642876 & -0.0109546642876097 \tabularnewline
37 & 49.75 & 49.8103654509333 & -0.0603654509333325 \tabularnewline
38 & 49.7 & 49.8071186029339 & -0.107118602933909 \tabularnewline
39 & 50.09 & 49.7513570652288 & 0.338642934771173 \tabularnewline
40 & 50.19 & 50.1595714928241 & 0.0304285071759125 \tabularnewline
41 & 50.53 & 50.2612081365685 & 0.268791863431495 \tabularnewline
42 & 50.55 & 50.6156655175795 & -0.0656655175795109 \tabularnewline
43 & 50.55 & 50.6321335973985 & -0.0821335973985455 \tabularnewline
44 & 50.55 & 50.6277159163861 & -0.0777159163860546 \tabularnewline
45 & 50.58 & 50.6235358470958 & -0.0435358470957539 \tabularnewline
46 & 50.61 & 50.6511942050495 & -0.0411942050495071 \tabularnewline
47 & 50.94 & 50.6789785117981 & 0.261021488201919 \tabularnewline
48 & 51.01 & 51.0230179513065 & -0.013017951306459 \tabularnewline
49 & 51.01 & 51.0923177609078 & -0.0823177609077703 \tabularnewline
50 & 51.04 & 51.0878901743796 & -0.0478901743795817 \tabularnewline
51 & 51.15 & 51.1153143281882 & 0.0346856718117792 \tabularnewline
52 & 51.31 & 51.2271799500363 & 0.0828200499636935 \tabularnewline
53 & 51.31 & 51.3916345529487 & -0.0816345529487208 \tabularnewline
54 & 51.34 & 51.3872437138044 & -0.047243713804356 \tabularnewline
55 & 51.34 & 51.4147026384826 & -0.0747026384826412 \tabularnewline
56 & 51.34 & 51.4106846429478 & -0.0706846429477963 \tabularnewline
57 & 51.47 & 51.4068827614411 & 0.063117238558867 \tabularnewline
58 & 51.95 & 51.5402776185419 & 0.409722381458074 \tabularnewline
59 & 51.97 & 52.0423151627661 & -0.0723151627661096 \tabularnewline
60 & 51.92 & 52.0584255812601 & -0.138425581260051 \tabularnewline
61 & 51.92 & 52.0009801498977 & -0.0809801498976768 \tabularnewline
62 & 51.91 & 51.9966245088211 & -0.0866245088211528 \tabularnewline
63 & 51.97 & 51.981965277277 & -0.0119652772769712 \tabularnewline
64 & 52.14 & 52.0413217065591 & 0.0986782934408552 \tabularnewline
65 & 52.33 & 52.2166292693238 & 0.113370730676209 \tabularnewline
66 & 52.4 & 52.4127270872709 & -0.0127270872709389 \tabularnewline
67 & 52.4 & 52.4820425414388 & -0.08204254143876 \tabularnewline
68 & 52.41 & 52.4776297580102 & -0.0676297580101703 \tabularnewline
69 & 52.71 & 52.4839921881569 & 0.226007811843147 \tabularnewline
70 & 53.17 & 52.7961483635915 & 0.373851636408503 \tabularnewline
71 & 53.33 & 53.276256544993 & 0.053743455006952 \tabularnewline
72 & 53.32 & 53.4391472188251 & -0.11914721882507 \tabularnewline
73 & 53.32 & 53.422738703638 & -0.102738703638032 \tabularnewline
74 & 53.3 & 53.4172127455078 & -0.1172127455078 \tabularnewline
75 & 53.31 & 53.3909082789234 & -0.080908278923431 \tabularnewline
76 & 53.72 & 53.3965565035371 & 0.323443496462936 \tabularnewline
77 & 53.87 & 53.8239534061226 & 0.0460465938774419 \tabularnewline
78 & 53.91 & 53.9764300925201 & -0.0664300925201502 \tabularnewline
79 & 53.91 & 54.012857048508 & -0.102857048507964 \tabularnewline
80 & 53.96 & 54.0073247250181 & -0.0473247250180933 \tabularnewline
81 & 54.02 & 54.0547792923845 & -0.0347792923844921 \tabularnewline
82 & 54.33 & 54.1129086350109 & 0.217091364989116 \tabularnewline
83 & 54.48 & 54.4345852257297 & 0.0454147742702773 \tabularnewline
84 & 54.54 & 54.5870279287445 & -0.0470279287445052 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232945&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]47.51[/C][C]47.43[/C][C]0.0799999999999983[/C][/ROW]
[ROW][C]4[/C][C]47.96[/C][C]47.5143029222169[/C][C]0.445697077783109[/C][/ROW]
[ROW][C]5[/C][C]47.99[/C][C]47.9882754204419[/C][C]0.00172457955814309[/C][/ROW]
[ROW][C]6[/C][C]48.05[/C][C]48.0183681795881[/C][C]0.0316318204119383[/C][/ROW]
[ROW][C]7[/C][C]48.05[/C][C]48.0800695453732[/C][C]-0.0300695453731947[/C][/ROW]
[ROW][C]8[/C][C]48.01[/C][C]48.0784522089377[/C][C]-0.068452208937714[/C][/ROW]
[ROW][C]9[/C][C]48[/C][C]48.0347704023048[/C][C]-0.0347704023047939[/C][/ROW]
[ROW][C]10[/C][C]48.06[/C][C]48.0229002230977[/C][C]0.037099776902302[/C][/ROW]
[ROW][C]11[/C][C]48.23[/C][C]48.0848956912761[/C][C]0.145104308723859[/C][/ROW]
[ROW][C]12[/C][C]48.4[/C][C]48.2627003481983[/C][C]0.137299651801683[/C][/ROW]
[ROW][C]13[/C][C]48.4[/C][C]48.4400852197247[/C][C]-0.0400852197246877[/C][/ROW]
[ROW][C]14[/C][C]48.5[/C][C]48.4379291749432[/C][C]0.0620708250568427[/C][/ROW]
[ROW][C]15[/C][C]48.41[/C][C]48.5412677490951[/C][C]-0.131267749095137[/C][/ROW]
[ROW][C]16[/C][C]48.35[/C][C]48.4442073126708[/C][C]-0.0942073126708394[/C][/ROW]
[ROW][C]17[/C][C]48.53[/C][C]48.3791402284373[/C][C]0.150859771562722[/C][/ROW]
[ROW][C]18[/C][C]48.52[/C][C]48.5672544517209[/C][C]-0.0472544517209386[/C][/ROW]
[ROW][C]19[/C][C]48.52[/C][C]48.554712798844[/C][C]-0.0347127988439766[/C][/ROW]
[ROW][C]20[/C][C]48.49[/C][C]48.552845717927[/C][C]-0.0628457179270185[/C][/ROW]
[ROW][C]21[/C][C]48.45[/C][C]48.5194654649782[/C][C]-0.069465464978208[/C][/ROW]
[ROW][C]22[/C][C]48.65[/C][C]48.4757291588212[/C][C]0.174270841178803[/C][/ROW]
[ROW][C]23[/C][C]48.74[/C][C]48.6851025822495[/C][C]0.0548974177505031[/C][/ROW]
[ROW][C]24[/C][C]48.74[/C][C]48.7780553237306[/C][C]-0.0380553237306103[/C][/ROW]
[ROW][C]25[/C][C]48.74[/C][C]48.7760084600062[/C][C]-0.0360084600062152[/C][/ROW]
[ROW][C]26[/C][C]48.79[/C][C]48.7740716899743[/C][C]0.0159283100257426[/C][/ROW]
[ROW][C]27[/C][C]48.82[/C][C]48.8249284184628[/C][C]-0.0049284184628462[/C][/ROW]
[ROW][C]28[/C][C]48.82[/C][C]48.8546633359466[/C][C]-0.0346633359466253[/C][/ROW]
[ROW][C]29[/C][C]49.2[/C][C]48.8527989154672[/C][C]0.347201084532834[/C][/ROW]
[ROW][C]30[/C][C]49.3[/C][C]49.2514736562217[/C][C]0.0485263437782564[/C][/ROW]
[ROW][C]31[/C][C]49.3[/C][C]49.3540837197561[/C][C]-0.0540837197560933[/C][/ROW]
[ROW][C]32[/C][C]49.34[/C][C]49.3511747442647[/C][C]-0.0111747442647001[/C][/ROW]
[ROW][C]33[/C][C]49.47[/C][C]49.3905736935727[/C][C]0.0794263064273437[/C][/ROW]
[ROW][C]34[/C][C]49.65[/C][C]49.5248457588043[/C][C]0.125154241195702[/C][/ROW]
[ROW][C]35[/C][C]49.7[/C][C]49.7115773708665[/C][C]-0.0115773708665401[/C][/ROW]
[ROW][C]36[/C][C]49.75[/C][C]49.7609546642876[/C][C]-0.0109546642876097[/C][/ROW]
[ROW][C]37[/C][C]49.75[/C][C]49.8103654509333[/C][C]-0.0603654509333325[/C][/ROW]
[ROW][C]38[/C][C]49.7[/C][C]49.8071186029339[/C][C]-0.107118602933909[/C][/ROW]
[ROW][C]39[/C][C]50.09[/C][C]49.7513570652288[/C][C]0.338642934771173[/C][/ROW]
[ROW][C]40[/C][C]50.19[/C][C]50.1595714928241[/C][C]0.0304285071759125[/C][/ROW]
[ROW][C]41[/C][C]50.53[/C][C]50.2612081365685[/C][C]0.268791863431495[/C][/ROW]
[ROW][C]42[/C][C]50.55[/C][C]50.6156655175795[/C][C]-0.0656655175795109[/C][/ROW]
[ROW][C]43[/C][C]50.55[/C][C]50.6321335973985[/C][C]-0.0821335973985455[/C][/ROW]
[ROW][C]44[/C][C]50.55[/C][C]50.6277159163861[/C][C]-0.0777159163860546[/C][/ROW]
[ROW][C]45[/C][C]50.58[/C][C]50.6235358470958[/C][C]-0.0435358470957539[/C][/ROW]
[ROW][C]46[/C][C]50.61[/C][C]50.6511942050495[/C][C]-0.0411942050495071[/C][/ROW]
[ROW][C]47[/C][C]50.94[/C][C]50.6789785117981[/C][C]0.261021488201919[/C][/ROW]
[ROW][C]48[/C][C]51.01[/C][C]51.0230179513065[/C][C]-0.013017951306459[/C][/ROW]
[ROW][C]49[/C][C]51.01[/C][C]51.0923177609078[/C][C]-0.0823177609077703[/C][/ROW]
[ROW][C]50[/C][C]51.04[/C][C]51.0878901743796[/C][C]-0.0478901743795817[/C][/ROW]
[ROW][C]51[/C][C]51.15[/C][C]51.1153143281882[/C][C]0.0346856718117792[/C][/ROW]
[ROW][C]52[/C][C]51.31[/C][C]51.2271799500363[/C][C]0.0828200499636935[/C][/ROW]
[ROW][C]53[/C][C]51.31[/C][C]51.3916345529487[/C][C]-0.0816345529487208[/C][/ROW]
[ROW][C]54[/C][C]51.34[/C][C]51.3872437138044[/C][C]-0.047243713804356[/C][/ROW]
[ROW][C]55[/C][C]51.34[/C][C]51.4147026384826[/C][C]-0.0747026384826412[/C][/ROW]
[ROW][C]56[/C][C]51.34[/C][C]51.4106846429478[/C][C]-0.0706846429477963[/C][/ROW]
[ROW][C]57[/C][C]51.47[/C][C]51.4068827614411[/C][C]0.063117238558867[/C][/ROW]
[ROW][C]58[/C][C]51.95[/C][C]51.5402776185419[/C][C]0.409722381458074[/C][/ROW]
[ROW][C]59[/C][C]51.97[/C][C]52.0423151627661[/C][C]-0.0723151627661096[/C][/ROW]
[ROW][C]60[/C][C]51.92[/C][C]52.0584255812601[/C][C]-0.138425581260051[/C][/ROW]
[ROW][C]61[/C][C]51.92[/C][C]52.0009801498977[/C][C]-0.0809801498976768[/C][/ROW]
[ROW][C]62[/C][C]51.91[/C][C]51.9966245088211[/C][C]-0.0866245088211528[/C][/ROW]
[ROW][C]63[/C][C]51.97[/C][C]51.981965277277[/C][C]-0.0119652772769712[/C][/ROW]
[ROW][C]64[/C][C]52.14[/C][C]52.0413217065591[/C][C]0.0986782934408552[/C][/ROW]
[ROW][C]65[/C][C]52.33[/C][C]52.2166292693238[/C][C]0.113370730676209[/C][/ROW]
[ROW][C]66[/C][C]52.4[/C][C]52.4127270872709[/C][C]-0.0127270872709389[/C][/ROW]
[ROW][C]67[/C][C]52.4[/C][C]52.4820425414388[/C][C]-0.08204254143876[/C][/ROW]
[ROW][C]68[/C][C]52.41[/C][C]52.4776297580102[/C][C]-0.0676297580101703[/C][/ROW]
[ROW][C]69[/C][C]52.71[/C][C]52.4839921881569[/C][C]0.226007811843147[/C][/ROW]
[ROW][C]70[/C][C]53.17[/C][C]52.7961483635915[/C][C]0.373851636408503[/C][/ROW]
[ROW][C]71[/C][C]53.33[/C][C]53.276256544993[/C][C]0.053743455006952[/C][/ROW]
[ROW][C]72[/C][C]53.32[/C][C]53.4391472188251[/C][C]-0.11914721882507[/C][/ROW]
[ROW][C]73[/C][C]53.32[/C][C]53.422738703638[/C][C]-0.102738703638032[/C][/ROW]
[ROW][C]74[/C][C]53.3[/C][C]53.4172127455078[/C][C]-0.1172127455078[/C][/ROW]
[ROW][C]75[/C][C]53.31[/C][C]53.3909082789234[/C][C]-0.080908278923431[/C][/ROW]
[ROW][C]76[/C][C]53.72[/C][C]53.3965565035371[/C][C]0.323443496462936[/C][/ROW]
[ROW][C]77[/C][C]53.87[/C][C]53.8239534061226[/C][C]0.0460465938774419[/C][/ROW]
[ROW][C]78[/C][C]53.91[/C][C]53.9764300925201[/C][C]-0.0664300925201502[/C][/ROW]
[ROW][C]79[/C][C]53.91[/C][C]54.012857048508[/C][C]-0.102857048507964[/C][/ROW]
[ROW][C]80[/C][C]53.96[/C][C]54.0073247250181[/C][C]-0.0473247250180933[/C][/ROW]
[ROW][C]81[/C][C]54.02[/C][C]54.0547792923845[/C][C]-0.0347792923844921[/C][/ROW]
[ROW][C]82[/C][C]54.33[/C][C]54.1129086350109[/C][C]0.217091364989116[/C][/ROW]
[ROW][C]83[/C][C]54.48[/C][C]54.4345852257297[/C][C]0.0454147742702773[/C][/ROW]
[ROW][C]84[/C][C]54.54[/C][C]54.5870279287445[/C][C]-0.0470279287445052[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232945&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232945&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
347.5147.430.0799999999999983
447.9647.51430292221690.445697077783109
547.9947.98827542044190.00172457955814309
648.0548.01836817958810.0316318204119383
748.0548.0800695453732-0.0300695453731947
848.0148.0784522089377-0.068452208937714
94848.0347704023048-0.0347704023047939
1048.0648.02290022309770.037099776902302
1148.2348.08489569127610.145104308723859
1248.448.26270034819830.137299651801683
1348.448.4400852197247-0.0400852197246877
1448.548.43792917494320.0620708250568427
1548.4148.5412677490951-0.131267749095137
1648.3548.4442073126708-0.0942073126708394
1748.5348.37914022843730.150859771562722
1848.5248.5672544517209-0.0472544517209386
1948.5248.554712798844-0.0347127988439766
2048.4948.552845717927-0.0628457179270185
2148.4548.5194654649782-0.069465464978208
2248.6548.47572915882120.174270841178803
2348.7448.68510258224950.0548974177505031
2448.7448.7780553237306-0.0380553237306103
2548.7448.7760084600062-0.0360084600062152
2648.7948.77407168997430.0159283100257426
2748.8248.8249284184628-0.0049284184628462
2848.8248.8546633359466-0.0346633359466253
2949.248.85279891546720.347201084532834
3049.349.25147365622170.0485263437782564
3149.349.3540837197561-0.0540837197560933
3249.3449.3511747442647-0.0111747442647001
3349.4749.39057369357270.0794263064273437
3449.6549.52484575880430.125154241195702
3549.749.7115773708665-0.0115773708665401
3649.7549.7609546642876-0.0109546642876097
3749.7549.8103654509333-0.0603654509333325
3849.749.8071186029339-0.107118602933909
3950.0949.75135706522880.338642934771173
4050.1950.15957149282410.0304285071759125
4150.5350.26120813656850.268791863431495
4250.5550.6156655175795-0.0656655175795109
4350.5550.6321335973985-0.0821335973985455
4450.5550.6277159163861-0.0777159163860546
4550.5850.6235358470958-0.0435358470957539
4650.6150.6511942050495-0.0411942050495071
4750.9450.67897851179810.261021488201919
4851.0151.0230179513065-0.013017951306459
4951.0151.0923177609078-0.0823177609077703
5051.0451.0878901743796-0.0478901743795817
5151.1551.11531432818820.0346856718117792
5251.3151.22717995003630.0828200499636935
5351.3151.3916345529487-0.0816345529487208
5451.3451.3872437138044-0.047243713804356
5551.3451.4147026384826-0.0747026384826412
5651.3451.4106846429478-0.0706846429477963
5751.4751.40688276144110.063117238558867
5851.9551.54027761854190.409722381458074
5951.9752.0423151627661-0.0723151627661096
6051.9252.0584255812601-0.138425581260051
6151.9252.0009801498977-0.0809801498976768
6251.9151.9966245088211-0.0866245088211528
6351.9751.981965277277-0.0119652772769712
6452.1452.04132170655910.0986782934408552
6552.3352.21662926932380.113370730676209
6652.452.4127270872709-0.0127270872709389
6752.452.4820425414388-0.08204254143876
6852.4152.4776297580102-0.0676297580101703
6952.7152.48399218815690.226007811843147
7053.1752.79614836359150.373851636408503
7153.3353.2762565449930.053743455006952
7253.3253.4391472188251-0.11914721882507
7353.3253.422738703638-0.102738703638032
7453.353.4172127455078-0.1172127455078
7553.3153.3909082789234-0.080908278923431
7653.7253.39655650353710.323443496462936
7753.8753.82395340612260.0460465938774419
7853.9153.9764300925201-0.0664300925201502
7953.9154.012857048508-0.102857048507964
8053.9654.0073247250181-0.0473247250180933
8154.0254.0547792923845-0.0347792923844921
8254.3354.11290863501090.217091364989116
8354.4854.43458522572970.0454147742702773
8454.5454.5870279287445-0.0470279287445052







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8554.644498459751954.382367888362154.9066290311417
8654.748996919503854.368188222019455.1298056169882
8754.853495379255754.374636264558855.3323544939526
8854.957993839007654.390558936782455.5254287412327
8955.062492298759454.4117682539155.7132163436089
9055.166990758511354.436181711335155.8977998056875
9155.271489218263254.462600981365356.0803774551612
9255.375987678015154.490270849408256.2617045066221
9355.48048613776754.51868480986656.442287465668
9455.584984597518954.547487498594756.6224816964431
9555.689483057270854.576420984828356.8025451297133
9655.793981517022754.605293078568656.9826699554767

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 54.6444984597519 & 54.3823678883621 & 54.9066290311417 \tabularnewline
86 & 54.7489969195038 & 54.3681882220194 & 55.1298056169882 \tabularnewline
87 & 54.8534953792557 & 54.3746362645588 & 55.3323544939526 \tabularnewline
88 & 54.9579938390076 & 54.3905589367824 & 55.5254287412327 \tabularnewline
89 & 55.0624922987594 & 54.41176825391 & 55.7132163436089 \tabularnewline
90 & 55.1669907585113 & 54.4361817113351 & 55.8977998056875 \tabularnewline
91 & 55.2714892182632 & 54.4626009813653 & 56.0803774551612 \tabularnewline
92 & 55.3759876780151 & 54.4902708494082 & 56.2617045066221 \tabularnewline
93 & 55.480486137767 & 54.518684809866 & 56.442287465668 \tabularnewline
94 & 55.5849845975189 & 54.5474874985947 & 56.6224816964431 \tabularnewline
95 & 55.6894830572708 & 54.5764209848283 & 56.8025451297133 \tabularnewline
96 & 55.7939815170227 & 54.6052930785686 & 56.9826699554767 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232945&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]54.6444984597519[/C][C]54.3823678883621[/C][C]54.9066290311417[/C][/ROW]
[ROW][C]86[/C][C]54.7489969195038[/C][C]54.3681882220194[/C][C]55.1298056169882[/C][/ROW]
[ROW][C]87[/C][C]54.8534953792557[/C][C]54.3746362645588[/C][C]55.3323544939526[/C][/ROW]
[ROW][C]88[/C][C]54.9579938390076[/C][C]54.3905589367824[/C][C]55.5254287412327[/C][/ROW]
[ROW][C]89[/C][C]55.0624922987594[/C][C]54.41176825391[/C][C]55.7132163436089[/C][/ROW]
[ROW][C]90[/C][C]55.1669907585113[/C][C]54.4361817113351[/C][C]55.8977998056875[/C][/ROW]
[ROW][C]91[/C][C]55.2714892182632[/C][C]54.4626009813653[/C][C]56.0803774551612[/C][/ROW]
[ROW][C]92[/C][C]55.3759876780151[/C][C]54.4902708494082[/C][C]56.2617045066221[/C][/ROW]
[ROW][C]93[/C][C]55.480486137767[/C][C]54.518684809866[/C][C]56.442287465668[/C][/ROW]
[ROW][C]94[/C][C]55.5849845975189[/C][C]54.5474874985947[/C][C]56.6224816964431[/C][/ROW]
[ROW][C]95[/C][C]55.6894830572708[/C][C]54.5764209848283[/C][C]56.8025451297133[/C][/ROW]
[ROW][C]96[/C][C]55.7939815170227[/C][C]54.6052930785686[/C][C]56.9826699554767[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232945&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232945&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
8554.644498459751954.382367888362154.9066290311417
8654.748996919503854.368188222019455.1298056169882
8754.853495379255754.374636264558855.3323544939526
8854.957993839007654.390558936782455.5254287412327
8955.062492298759454.4117682539155.7132163436089
9055.166990758511354.436181711335155.8977998056875
9155.271489218263254.462600981365356.0803774551612
9255.375987678015154.490270849408256.2617045066221
9355.48048613776754.51868480986656.442287465668
9455.584984597518954.547487498594756.6224816964431
9555.689483057270854.576420984828356.8025451297133
9655.793981517022754.605293078568656.9826699554767



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')