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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 17:29:49 +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/2016/Apr/26/t14616882240ka5tmxno4ogumq.htm/, Retrieved Fri, 03 May 2024 18:40:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294917, Retrieved Fri, 03 May 2024 18:40:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Moerman Nicolaï] [2016-04-26 16:29:49] [ab100cc47aff291ae023e643a55282f8] [Current]
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Dataseries X:
96,4
96,9
98,1
99,2
100
100,3
100,3
100,8
101,3
101,4
101,9
103,4
105,6
107,5
109
110,5
109,8
109,6
109,6
108,8
109,4
109,1
109
109,2
110,5
112,2
113,2
113,6
113,2
112,2
112,2
113,2
113,8
113,8
113,7
113,9
114
114,3
114,3
112,8
112,3
112,2
112,6
111,9
111,7
111
110,8
111,1
110,5
110,5
109,8
109
109
109,4
108,8
108,4
108,3
108,2
106,8
103,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294917&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294917&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294917&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 Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999932422965254
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999932422965254 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294917&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]0.999932422965254[/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=294917&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294917&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
alpha0.999932422965254
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
296.996.40.5
398.196.89996621148261.20003378851736
499.298.0999189052751.10008109472503
510099.19992565978160.800074340218359
6100.399.99994593334850.300054066651484
7100.3100.2999797232362.02767640899992e-05
8100.8100.299999998630.500000001370239
9101.3100.7999662114830.500033788517456
10101.4101.2999662091990.100033790800708
11101.9101.3999932400130.500006759986945
12103.4101.8999662110261.50003378897419
13105.6103.3998986321652.20010136783546
14107.5105.5998513236731.90014867632658
15109107.4998715935871.50012840641313
16110.5108.9998986257711.50010137422944
17109.8110.499898627597-0.699898627597307
18109.6109.800047297074-0.20004729707388
19109.6109.600013518603-1.35186031542389e-05
20108.8109.600000000914-0.800000000913556
21109.4108.8000540616280.599945938372144
22109.1109.399959457432-0.299959457432493
23109109.100020270371-0.100020270370678
24109.2109.0000067590730.199993240926716
25110.5109.199986485051.30001351495018
26112.2110.4999121489421.70008785105848
27113.2112.1998851131041.00011488689577
28113.6113.1999324152020.400067584798464
29113.2113.599972964619-0.399972964618911
30112.2113.200027028987-1.00002702898692
31112.2112.200067578861-6.757886129094e-05
32113.2112.2000000045670.999999995433214
33113.8113.1999324229660.600067577034437
34113.8113.7999594492124.05507875029798e-05
35113.7113.79999999726-0.0999999972596868
36113.9113.7000067577030.199993242296713
37114113.899986485050.100013514950277
38114.3113.9999932413830.300006758616775
39114.3114.2999797264332.02735671450682e-05
40112.8114.29999999863-1.49999999862997
41112.3112.800101365552-0.500101365552027
42112.2112.300033795367-0.100033795367352
43112.6112.2000067599870.399993240012719
44111.9112.599972969643-0.699972969642914
45111.7111.900047302098-0.200047302097701
46111111.700013518603-0.700013518603484
47110.8111.000047304838-0.200047304837867
48111.1110.8000135186040.299986481396331
49110.5111.099979727803-0.599979727803117
50110.5110.500040544851-4.05448509042117e-05
51109.8110.50000000274-0.700000002739898
52109109.800047303925-0.800047303924515
53109109.000054064824-5.40648244538033e-05
54109.4109.0000000036540.399999996346466
55108.8109.399972969186-0.599972969186368
56108.4108.800040544394-0.400040544394173
57108.3108.400027033554-0.100027033553772
58108.2108.30000675953-0.100006759530316
59106.8108.20000675816-1.40000675816027
60103.6106.800094608305-3.20009460830535

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 96.9 & 96.4 & 0.5 \tabularnewline
3 & 98.1 & 96.8999662114826 & 1.20003378851736 \tabularnewline
4 & 99.2 & 98.099918905275 & 1.10008109472503 \tabularnewline
5 & 100 & 99.1999256597816 & 0.800074340218359 \tabularnewline
6 & 100.3 & 99.9999459333485 & 0.300054066651484 \tabularnewline
7 & 100.3 & 100.299979723236 & 2.02767640899992e-05 \tabularnewline
8 & 100.8 & 100.29999999863 & 0.500000001370239 \tabularnewline
9 & 101.3 & 100.799966211483 & 0.500033788517456 \tabularnewline
10 & 101.4 & 101.299966209199 & 0.100033790800708 \tabularnewline
11 & 101.9 & 101.399993240013 & 0.500006759986945 \tabularnewline
12 & 103.4 & 101.899966211026 & 1.50003378897419 \tabularnewline
13 & 105.6 & 103.399898632165 & 2.20010136783546 \tabularnewline
14 & 107.5 & 105.599851323673 & 1.90014867632658 \tabularnewline
15 & 109 & 107.499871593587 & 1.50012840641313 \tabularnewline
16 & 110.5 & 108.999898625771 & 1.50010137422944 \tabularnewline
17 & 109.8 & 110.499898627597 & -0.699898627597307 \tabularnewline
18 & 109.6 & 109.800047297074 & -0.20004729707388 \tabularnewline
19 & 109.6 & 109.600013518603 & -1.35186031542389e-05 \tabularnewline
20 & 108.8 & 109.600000000914 & -0.800000000913556 \tabularnewline
21 & 109.4 & 108.800054061628 & 0.599945938372144 \tabularnewline
22 & 109.1 & 109.399959457432 & -0.299959457432493 \tabularnewline
23 & 109 & 109.100020270371 & -0.100020270370678 \tabularnewline
24 & 109.2 & 109.000006759073 & 0.199993240926716 \tabularnewline
25 & 110.5 & 109.19998648505 & 1.30001351495018 \tabularnewline
26 & 112.2 & 110.499912148942 & 1.70008785105848 \tabularnewline
27 & 113.2 & 112.199885113104 & 1.00011488689577 \tabularnewline
28 & 113.6 & 113.199932415202 & 0.400067584798464 \tabularnewline
29 & 113.2 & 113.599972964619 & -0.399972964618911 \tabularnewline
30 & 112.2 & 113.200027028987 & -1.00002702898692 \tabularnewline
31 & 112.2 & 112.200067578861 & -6.757886129094e-05 \tabularnewline
32 & 113.2 & 112.200000004567 & 0.999999995433214 \tabularnewline
33 & 113.8 & 113.199932422966 & 0.600067577034437 \tabularnewline
34 & 113.8 & 113.799959449212 & 4.05507875029798e-05 \tabularnewline
35 & 113.7 & 113.79999999726 & -0.0999999972596868 \tabularnewline
36 & 113.9 & 113.700006757703 & 0.199993242296713 \tabularnewline
37 & 114 & 113.89998648505 & 0.100013514950277 \tabularnewline
38 & 114.3 & 113.999993241383 & 0.300006758616775 \tabularnewline
39 & 114.3 & 114.299979726433 & 2.02735671450682e-05 \tabularnewline
40 & 112.8 & 114.29999999863 & -1.49999999862997 \tabularnewline
41 & 112.3 & 112.800101365552 & -0.500101365552027 \tabularnewline
42 & 112.2 & 112.300033795367 & -0.100033795367352 \tabularnewline
43 & 112.6 & 112.200006759987 & 0.399993240012719 \tabularnewline
44 & 111.9 & 112.599972969643 & -0.699972969642914 \tabularnewline
45 & 111.7 & 111.900047302098 & -0.200047302097701 \tabularnewline
46 & 111 & 111.700013518603 & -0.700013518603484 \tabularnewline
47 & 110.8 & 111.000047304838 & -0.200047304837867 \tabularnewline
48 & 111.1 & 110.800013518604 & 0.299986481396331 \tabularnewline
49 & 110.5 & 111.099979727803 & -0.599979727803117 \tabularnewline
50 & 110.5 & 110.500040544851 & -4.05448509042117e-05 \tabularnewline
51 & 109.8 & 110.50000000274 & -0.700000002739898 \tabularnewline
52 & 109 & 109.800047303925 & -0.800047303924515 \tabularnewline
53 & 109 & 109.000054064824 & -5.40648244538033e-05 \tabularnewline
54 & 109.4 & 109.000000003654 & 0.399999996346466 \tabularnewline
55 & 108.8 & 109.399972969186 & -0.599972969186368 \tabularnewline
56 & 108.4 & 108.800040544394 & -0.400040544394173 \tabularnewline
57 & 108.3 & 108.400027033554 & -0.100027033553772 \tabularnewline
58 & 108.2 & 108.30000675953 & -0.100006759530316 \tabularnewline
59 & 106.8 & 108.20000675816 & -1.40000675816027 \tabularnewline
60 & 103.6 & 106.800094608305 & -3.20009460830535 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294917&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]96.9[/C][C]96.4[/C][C]0.5[/C][/ROW]
[ROW][C]3[/C][C]98.1[/C][C]96.8999662114826[/C][C]1.20003378851736[/C][/ROW]
[ROW][C]4[/C][C]99.2[/C][C]98.099918905275[/C][C]1.10008109472503[/C][/ROW]
[ROW][C]5[/C][C]100[/C][C]99.1999256597816[/C][C]0.800074340218359[/C][/ROW]
[ROW][C]6[/C][C]100.3[/C][C]99.9999459333485[/C][C]0.300054066651484[/C][/ROW]
[ROW][C]7[/C][C]100.3[/C][C]100.299979723236[/C][C]2.02767640899992e-05[/C][/ROW]
[ROW][C]8[/C][C]100.8[/C][C]100.29999999863[/C][C]0.500000001370239[/C][/ROW]
[ROW][C]9[/C][C]101.3[/C][C]100.799966211483[/C][C]0.500033788517456[/C][/ROW]
[ROW][C]10[/C][C]101.4[/C][C]101.299966209199[/C][C]0.100033790800708[/C][/ROW]
[ROW][C]11[/C][C]101.9[/C][C]101.399993240013[/C][C]0.500006759986945[/C][/ROW]
[ROW][C]12[/C][C]103.4[/C][C]101.899966211026[/C][C]1.50003378897419[/C][/ROW]
[ROW][C]13[/C][C]105.6[/C][C]103.399898632165[/C][C]2.20010136783546[/C][/ROW]
[ROW][C]14[/C][C]107.5[/C][C]105.599851323673[/C][C]1.90014867632658[/C][/ROW]
[ROW][C]15[/C][C]109[/C][C]107.499871593587[/C][C]1.50012840641313[/C][/ROW]
[ROW][C]16[/C][C]110.5[/C][C]108.999898625771[/C][C]1.50010137422944[/C][/ROW]
[ROW][C]17[/C][C]109.8[/C][C]110.499898627597[/C][C]-0.699898627597307[/C][/ROW]
[ROW][C]18[/C][C]109.6[/C][C]109.800047297074[/C][C]-0.20004729707388[/C][/ROW]
[ROW][C]19[/C][C]109.6[/C][C]109.600013518603[/C][C]-1.35186031542389e-05[/C][/ROW]
[ROW][C]20[/C][C]108.8[/C][C]109.600000000914[/C][C]-0.800000000913556[/C][/ROW]
[ROW][C]21[/C][C]109.4[/C][C]108.800054061628[/C][C]0.599945938372144[/C][/ROW]
[ROW][C]22[/C][C]109.1[/C][C]109.399959457432[/C][C]-0.299959457432493[/C][/ROW]
[ROW][C]23[/C][C]109[/C][C]109.100020270371[/C][C]-0.100020270370678[/C][/ROW]
[ROW][C]24[/C][C]109.2[/C][C]109.000006759073[/C][C]0.199993240926716[/C][/ROW]
[ROW][C]25[/C][C]110.5[/C][C]109.19998648505[/C][C]1.30001351495018[/C][/ROW]
[ROW][C]26[/C][C]112.2[/C][C]110.499912148942[/C][C]1.70008785105848[/C][/ROW]
[ROW][C]27[/C][C]113.2[/C][C]112.199885113104[/C][C]1.00011488689577[/C][/ROW]
[ROW][C]28[/C][C]113.6[/C][C]113.199932415202[/C][C]0.400067584798464[/C][/ROW]
[ROW][C]29[/C][C]113.2[/C][C]113.599972964619[/C][C]-0.399972964618911[/C][/ROW]
[ROW][C]30[/C][C]112.2[/C][C]113.200027028987[/C][C]-1.00002702898692[/C][/ROW]
[ROW][C]31[/C][C]112.2[/C][C]112.200067578861[/C][C]-6.757886129094e-05[/C][/ROW]
[ROW][C]32[/C][C]113.2[/C][C]112.200000004567[/C][C]0.999999995433214[/C][/ROW]
[ROW][C]33[/C][C]113.8[/C][C]113.199932422966[/C][C]0.600067577034437[/C][/ROW]
[ROW][C]34[/C][C]113.8[/C][C]113.799959449212[/C][C]4.05507875029798e-05[/C][/ROW]
[ROW][C]35[/C][C]113.7[/C][C]113.79999999726[/C][C]-0.0999999972596868[/C][/ROW]
[ROW][C]36[/C][C]113.9[/C][C]113.700006757703[/C][C]0.199993242296713[/C][/ROW]
[ROW][C]37[/C][C]114[/C][C]113.89998648505[/C][C]0.100013514950277[/C][/ROW]
[ROW][C]38[/C][C]114.3[/C][C]113.999993241383[/C][C]0.300006758616775[/C][/ROW]
[ROW][C]39[/C][C]114.3[/C][C]114.299979726433[/C][C]2.02735671450682e-05[/C][/ROW]
[ROW][C]40[/C][C]112.8[/C][C]114.29999999863[/C][C]-1.49999999862997[/C][/ROW]
[ROW][C]41[/C][C]112.3[/C][C]112.800101365552[/C][C]-0.500101365552027[/C][/ROW]
[ROW][C]42[/C][C]112.2[/C][C]112.300033795367[/C][C]-0.100033795367352[/C][/ROW]
[ROW][C]43[/C][C]112.6[/C][C]112.200006759987[/C][C]0.399993240012719[/C][/ROW]
[ROW][C]44[/C][C]111.9[/C][C]112.599972969643[/C][C]-0.699972969642914[/C][/ROW]
[ROW][C]45[/C][C]111.7[/C][C]111.900047302098[/C][C]-0.200047302097701[/C][/ROW]
[ROW][C]46[/C][C]111[/C][C]111.700013518603[/C][C]-0.700013518603484[/C][/ROW]
[ROW][C]47[/C][C]110.8[/C][C]111.000047304838[/C][C]-0.200047304837867[/C][/ROW]
[ROW][C]48[/C][C]111.1[/C][C]110.800013518604[/C][C]0.299986481396331[/C][/ROW]
[ROW][C]49[/C][C]110.5[/C][C]111.099979727803[/C][C]-0.599979727803117[/C][/ROW]
[ROW][C]50[/C][C]110.5[/C][C]110.500040544851[/C][C]-4.05448509042117e-05[/C][/ROW]
[ROW][C]51[/C][C]109.8[/C][C]110.50000000274[/C][C]-0.700000002739898[/C][/ROW]
[ROW][C]52[/C][C]109[/C][C]109.800047303925[/C][C]-0.800047303924515[/C][/ROW]
[ROW][C]53[/C][C]109[/C][C]109.000054064824[/C][C]-5.40648244538033e-05[/C][/ROW]
[ROW][C]54[/C][C]109.4[/C][C]109.000000003654[/C][C]0.399999996346466[/C][/ROW]
[ROW][C]55[/C][C]108.8[/C][C]109.399972969186[/C][C]-0.599972969186368[/C][/ROW]
[ROW][C]56[/C][C]108.4[/C][C]108.800040544394[/C][C]-0.400040544394173[/C][/ROW]
[ROW][C]57[/C][C]108.3[/C][C]108.400027033554[/C][C]-0.100027033553772[/C][/ROW]
[ROW][C]58[/C][C]108.2[/C][C]108.30000675953[/C][C]-0.100006759530316[/C][/ROW]
[ROW][C]59[/C][C]106.8[/C][C]108.20000675816[/C][C]-1.40000675816027[/C][/ROW]
[ROW][C]60[/C][C]103.6[/C][C]106.800094608305[/C][C]-3.20009460830535[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294917&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294917&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
296.996.40.5
398.196.89996621148261.20003378851736
499.298.0999189052751.10008109472503
510099.19992565978160.800074340218359
6100.399.99994593334850.300054066651484
7100.3100.2999797232362.02767640899992e-05
8100.8100.299999998630.500000001370239
9101.3100.7999662114830.500033788517456
10101.4101.2999662091990.100033790800708
11101.9101.3999932400130.500006759986945
12103.4101.8999662110261.50003378897419
13105.6103.3998986321652.20010136783546
14107.5105.5998513236731.90014867632658
15109107.4998715935871.50012840641313
16110.5108.9998986257711.50010137422944
17109.8110.499898627597-0.699898627597307
18109.6109.800047297074-0.20004729707388
19109.6109.600013518603-1.35186031542389e-05
20108.8109.600000000914-0.800000000913556
21109.4108.8000540616280.599945938372144
22109.1109.399959457432-0.299959457432493
23109109.100020270371-0.100020270370678
24109.2109.0000067590730.199993240926716
25110.5109.199986485051.30001351495018
26112.2110.4999121489421.70008785105848
27113.2112.1998851131041.00011488689577
28113.6113.1999324152020.400067584798464
29113.2113.599972964619-0.399972964618911
30112.2113.200027028987-1.00002702898692
31112.2112.200067578861-6.757886129094e-05
32113.2112.2000000045670.999999995433214
33113.8113.1999324229660.600067577034437
34113.8113.7999594492124.05507875029798e-05
35113.7113.79999999726-0.0999999972596868
36113.9113.7000067577030.199993242296713
37114113.899986485050.100013514950277
38114.3113.9999932413830.300006758616775
39114.3114.2999797264332.02735671450682e-05
40112.8114.29999999863-1.49999999862997
41112.3112.800101365552-0.500101365552027
42112.2112.300033795367-0.100033795367352
43112.6112.2000067599870.399993240012719
44111.9112.599972969643-0.699972969642914
45111.7111.900047302098-0.200047302097701
46111111.700013518603-0.700013518603484
47110.8111.000047304838-0.200047304837867
48111.1110.8000135186040.299986481396331
49110.5111.099979727803-0.599979727803117
50110.5110.500040544851-4.05448509042117e-05
51109.8110.50000000274-0.700000002739898
52109109.800047303925-0.800047303924515
53109109.000054064824-5.40648244538033e-05
54109.4109.0000000036540.399999996346466
55108.8109.399972969186-0.599972969186368
56108.4108.800040544394-0.400040544394173
57108.3108.400027033554-0.100027033553772
58108.2108.30000675953-0.100006759530316
59106.8108.20000675816-1.40000675816027
60103.6106.800094608305-3.20009460830535







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61103.600216252905101.835783801807105.364648704002
62103.600216252905101.105016261204106.095416244605
63103.600216252905100.544267280379106.65616522543
64103.600216252905100.071530201868107.128902303941
65103.60021625290599.6550386433567107.545393862452
66103.60021625290599.2785004483918107.921932057417
67103.60021625290598.9322371806428108.268195325166
68103.60021625290598.6099427390407108.590489766768
69103.60021625290598.3072368587193108.89319564709
70103.60021625290598.0209302778566109.179502227952
71103.60021625290597.7486153509748109.451817154834
72103.60021625290597.488421570525109.712010935284

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 103.600216252905 & 101.835783801807 & 105.364648704002 \tabularnewline
62 & 103.600216252905 & 101.105016261204 & 106.095416244605 \tabularnewline
63 & 103.600216252905 & 100.544267280379 & 106.65616522543 \tabularnewline
64 & 103.600216252905 & 100.071530201868 & 107.128902303941 \tabularnewline
65 & 103.600216252905 & 99.6550386433567 & 107.545393862452 \tabularnewline
66 & 103.600216252905 & 99.2785004483918 & 107.921932057417 \tabularnewline
67 & 103.600216252905 & 98.9322371806428 & 108.268195325166 \tabularnewline
68 & 103.600216252905 & 98.6099427390407 & 108.590489766768 \tabularnewline
69 & 103.600216252905 & 98.3072368587193 & 108.89319564709 \tabularnewline
70 & 103.600216252905 & 98.0209302778566 & 109.179502227952 \tabularnewline
71 & 103.600216252905 & 97.7486153509748 & 109.451817154834 \tabularnewline
72 & 103.600216252905 & 97.488421570525 & 109.712010935284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294917&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]61[/C][C]103.600216252905[/C][C]101.835783801807[/C][C]105.364648704002[/C][/ROW]
[ROW][C]62[/C][C]103.600216252905[/C][C]101.105016261204[/C][C]106.095416244605[/C][/ROW]
[ROW][C]63[/C][C]103.600216252905[/C][C]100.544267280379[/C][C]106.65616522543[/C][/ROW]
[ROW][C]64[/C][C]103.600216252905[/C][C]100.071530201868[/C][C]107.128902303941[/C][/ROW]
[ROW][C]65[/C][C]103.600216252905[/C][C]99.6550386433567[/C][C]107.545393862452[/C][/ROW]
[ROW][C]66[/C][C]103.600216252905[/C][C]99.2785004483918[/C][C]107.921932057417[/C][/ROW]
[ROW][C]67[/C][C]103.600216252905[/C][C]98.9322371806428[/C][C]108.268195325166[/C][/ROW]
[ROW][C]68[/C][C]103.600216252905[/C][C]98.6099427390407[/C][C]108.590489766768[/C][/ROW]
[ROW][C]69[/C][C]103.600216252905[/C][C]98.3072368587193[/C][C]108.89319564709[/C][/ROW]
[ROW][C]70[/C][C]103.600216252905[/C][C]98.0209302778566[/C][C]109.179502227952[/C][/ROW]
[ROW][C]71[/C][C]103.600216252905[/C][C]97.7486153509748[/C][C]109.451817154834[/C][/ROW]
[ROW][C]72[/C][C]103.600216252905[/C][C]97.488421570525[/C][C]109.712010935284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294917&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294917&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
61103.600216252905101.835783801807105.364648704002
62103.600216252905101.105016261204106.095416244605
63103.600216252905100.544267280379106.65616522543
64103.600216252905100.071530201868107.128902303941
65103.60021625290599.6550386433567107.545393862452
66103.60021625290599.2785004483918107.921932057417
67103.60021625290598.9322371806428108.268195325166
68103.60021625290598.6099427390407108.590489766768
69103.60021625290598.3072368587193108.89319564709
70103.60021625290598.0209302778566109.179502227952
71103.60021625290597.7486153509748109.451817154834
72103.60021625290597.488421570525109.712010935284



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')