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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 24 May 2015 15:15:02 +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/May/24/t14324770197huzrmkoai8dbc8.htm/, Retrieved Thu, 02 May 2024 18:43:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279302, Retrieved Thu, 02 May 2024 18:43:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [opgave 8 oef 2] [2015-05-24 12:09:30] [6514c6841f87d5984b117bf64f5432d7]
- RMPD  [Classical Decomposition] [Opgave 9 OEF1 stap 2] [2015-05-24 12:56:05] [6514c6841f87d5984b117bf64f5432d7]
- RMPD      [Exponential Smoothing] [Opgave 10 OEF2] [2015-05-24 14:15:02] [1738856fac0304df70af8aee7fa46d3f] [Current]
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Dataseries X:
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0
-2
-3
1
-2
-1
1
-3
-4
-9
-9
-7
-14
-12
-16
-20
-12
-12
-10
-10
-13
-16
-14
-17
-24
-25
-23
-17
-24
-20
-19
-18
-16
-12
-7
-6
-6
-5
-4
-4
-8
-9
-6
-7
-10
-11
-11
-12
-14
-12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279302&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]1 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=279302&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279302&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.86692886944907
beta0.242998645828878
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.86692886944907 \tabularnewline
beta & 0.242998645828878 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279302&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]0.86692886944907[/C][/ROW]
[ROW][C]beta[/C][C]0.242998645828878[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279302&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279302&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
alpha0.86692886944907
beta0.242998645828878
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3-24-284
4-22-27.68963435697945.68963435697938
5-19-24.71588307833665.71588307833664
6-18-20.51525357027232.51525357027232
7-17-18.55947247401681.55947247401677
8-11-17.10376316850566.10376316850558
9-11-10.4226428081654-0.57735719183459
10-12-9.65520610174133-2.34479389825867
11-10-10.91397154248640.913971542486435
12-15-9.15507957606505-5.84492042393495
13-15-14.4869719710597-0.513028028940269
14-15-15.30456870837540.304568708375388
15-13-15.34920601243612.34920601243606
16-8-13.12639850142275.12639850142271
17-13-7.4160225096323-5.5839774903677
18-9-12.1671155564963.16711555649604
19-7-8.66444079005711.6644407900571
20-4-6.113842833349772.11384283334977
21-4-2.72833776812751-1.27166223187249
22-2-2.545716379061710.545716379061711
230-0.672595006212310.67259500621231
24-21.45221168470848-3.45221168470848
25-3-0.7261473122539-2.2738526877461
261-2.361968461930813.36196846193081
27-21.5963072660801-3.5963072660801
28-1-1.235354344098370.235354344098367
291-0.6956575422182231.69565754221822
30-31.46722978728935-4.46722978728935
31-4-2.65374580790369-1.34625419209631
32-9-4.35266288812887-4.64733711187113
33-9-9.892403898244920.892403898244918
34-7-10.44158742434473.44158742434468
35-14-8.05579660520507-5.94420339479493
36-12-15.05903980297543.05903980297538
37-16-13.6126864550764-2.38731354492361
38-20-17.3908515959597-2.60914840404033
39-12-21.91098161390129.91098161390125
40-12-13.48917689641111.48917689641106
41-10-12.05476403192322.05476403192322
42-10-9.69716553872161-0.302834461278394
43-13-9.44723311905406-3.55276688094594
44-16-12.7631958375629-3.23680416243706
45-14-16.4871147442962.48711474429597
46-17-14.7248611918436-2.27513880815644
47-24-17.5704292507989-6.42957074920114
48-25-25.37206400914110.37206400914113
49-23-27.1987852863344.19878528633403
50-17-24.82348463417577.82348463417567
51-24-17.6577123193956-6.34228768060437
52-20-24.10873942283124.10873942283117
53-19-20.63391192652561.63391192652564
54-18-18.96037979496150.960379794961526
55-16-17.66843606452631.6684360645263
56-12-15.41118093145113.41118093145112
57-7-10.92448191728033.92448191728029
58-6-5.16604612577345-0.833953874226554
59-6-3.70851853782024-2.29148146217976
60-5-3.99729300206071-1.00270699793929
61-4-3.38002448141364-0.619975518586358
62-4-2.56156061036153-1.43843938963847
63-8-2.75567199506154-5.24432800493846
64-9-7.35400155923566-1.64599844076434
65-6-9.179585556952423.17958555695242
66-7-6.15191190136934-0.848088098630655
67-10-6.79460520863969-3.20539479136031
68-11-10.1561723546201-0.843827645379873
69-11-11.64819164080770.648191640807731
70-12-11.7101866357186-0.289813364281411
71-14-12.6464180690529-1.35358193094707
72-12-14.79001019268152.7900101926815

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & -24 & -28 & 4 \tabularnewline
4 & -22 & -27.6896343569794 & 5.68963435697938 \tabularnewline
5 & -19 & -24.7158830783366 & 5.71588307833664 \tabularnewline
6 & -18 & -20.5152535702723 & 2.51525357027232 \tabularnewline
7 & -17 & -18.5594724740168 & 1.55947247401677 \tabularnewline
8 & -11 & -17.1037631685056 & 6.10376316850558 \tabularnewline
9 & -11 & -10.4226428081654 & -0.57735719183459 \tabularnewline
10 & -12 & -9.65520610174133 & -2.34479389825867 \tabularnewline
11 & -10 & -10.9139715424864 & 0.913971542486435 \tabularnewline
12 & -15 & -9.15507957606505 & -5.84492042393495 \tabularnewline
13 & -15 & -14.4869719710597 & -0.513028028940269 \tabularnewline
14 & -15 & -15.3045687083754 & 0.304568708375388 \tabularnewline
15 & -13 & -15.3492060124361 & 2.34920601243606 \tabularnewline
16 & -8 & -13.1263985014227 & 5.12639850142271 \tabularnewline
17 & -13 & -7.4160225096323 & -5.5839774903677 \tabularnewline
18 & -9 & -12.167115556496 & 3.16711555649604 \tabularnewline
19 & -7 & -8.6644407900571 & 1.6644407900571 \tabularnewline
20 & -4 & -6.11384283334977 & 2.11384283334977 \tabularnewline
21 & -4 & -2.72833776812751 & -1.27166223187249 \tabularnewline
22 & -2 & -2.54571637906171 & 0.545716379061711 \tabularnewline
23 & 0 & -0.67259500621231 & 0.67259500621231 \tabularnewline
24 & -2 & 1.45221168470848 & -3.45221168470848 \tabularnewline
25 & -3 & -0.7261473122539 & -2.2738526877461 \tabularnewline
26 & 1 & -2.36196846193081 & 3.36196846193081 \tabularnewline
27 & -2 & 1.5963072660801 & -3.5963072660801 \tabularnewline
28 & -1 & -1.23535434409837 & 0.235354344098367 \tabularnewline
29 & 1 & -0.695657542218223 & 1.69565754221822 \tabularnewline
30 & -3 & 1.46722978728935 & -4.46722978728935 \tabularnewline
31 & -4 & -2.65374580790369 & -1.34625419209631 \tabularnewline
32 & -9 & -4.35266288812887 & -4.64733711187113 \tabularnewline
33 & -9 & -9.89240389824492 & 0.892403898244918 \tabularnewline
34 & -7 & -10.4415874243447 & 3.44158742434468 \tabularnewline
35 & -14 & -8.05579660520507 & -5.94420339479493 \tabularnewline
36 & -12 & -15.0590398029754 & 3.05903980297538 \tabularnewline
37 & -16 & -13.6126864550764 & -2.38731354492361 \tabularnewline
38 & -20 & -17.3908515959597 & -2.60914840404033 \tabularnewline
39 & -12 & -21.9109816139012 & 9.91098161390125 \tabularnewline
40 & -12 & -13.4891768964111 & 1.48917689641106 \tabularnewline
41 & -10 & -12.0547640319232 & 2.05476403192322 \tabularnewline
42 & -10 & -9.69716553872161 & -0.302834461278394 \tabularnewline
43 & -13 & -9.44723311905406 & -3.55276688094594 \tabularnewline
44 & -16 & -12.7631958375629 & -3.23680416243706 \tabularnewline
45 & -14 & -16.487114744296 & 2.48711474429597 \tabularnewline
46 & -17 & -14.7248611918436 & -2.27513880815644 \tabularnewline
47 & -24 & -17.5704292507989 & -6.42957074920114 \tabularnewline
48 & -25 & -25.3720640091411 & 0.37206400914113 \tabularnewline
49 & -23 & -27.198785286334 & 4.19878528633403 \tabularnewline
50 & -17 & -24.8234846341757 & 7.82348463417567 \tabularnewline
51 & -24 & -17.6577123193956 & -6.34228768060437 \tabularnewline
52 & -20 & -24.1087394228312 & 4.10873942283117 \tabularnewline
53 & -19 & -20.6339119265256 & 1.63391192652564 \tabularnewline
54 & -18 & -18.9603797949615 & 0.960379794961526 \tabularnewline
55 & -16 & -17.6684360645263 & 1.6684360645263 \tabularnewline
56 & -12 & -15.4111809314511 & 3.41118093145112 \tabularnewline
57 & -7 & -10.9244819172803 & 3.92448191728029 \tabularnewline
58 & -6 & -5.16604612577345 & -0.833953874226554 \tabularnewline
59 & -6 & -3.70851853782024 & -2.29148146217976 \tabularnewline
60 & -5 & -3.99729300206071 & -1.00270699793929 \tabularnewline
61 & -4 & -3.38002448141364 & -0.619975518586358 \tabularnewline
62 & -4 & -2.56156061036153 & -1.43843938963847 \tabularnewline
63 & -8 & -2.75567199506154 & -5.24432800493846 \tabularnewline
64 & -9 & -7.35400155923566 & -1.64599844076434 \tabularnewline
65 & -6 & -9.17958555695242 & 3.17958555695242 \tabularnewline
66 & -7 & -6.15191190136934 & -0.848088098630655 \tabularnewline
67 & -10 & -6.79460520863969 & -3.20539479136031 \tabularnewline
68 & -11 & -10.1561723546201 & -0.843827645379873 \tabularnewline
69 & -11 & -11.6481916408077 & 0.648191640807731 \tabularnewline
70 & -12 & -11.7101866357186 & -0.289813364281411 \tabularnewline
71 & -14 & -12.6464180690529 & -1.35358193094707 \tabularnewline
72 & -12 & -14.7900101926815 & 2.7900101926815 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279302&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]-24[/C][C]-28[/C][C]4[/C][/ROW]
[ROW][C]4[/C][C]-22[/C][C]-27.6896343569794[/C][C]5.68963435697938[/C][/ROW]
[ROW][C]5[/C][C]-19[/C][C]-24.7158830783366[/C][C]5.71588307833664[/C][/ROW]
[ROW][C]6[/C][C]-18[/C][C]-20.5152535702723[/C][C]2.51525357027232[/C][/ROW]
[ROW][C]7[/C][C]-17[/C][C]-18.5594724740168[/C][C]1.55947247401677[/C][/ROW]
[ROW][C]8[/C][C]-11[/C][C]-17.1037631685056[/C][C]6.10376316850558[/C][/ROW]
[ROW][C]9[/C][C]-11[/C][C]-10.4226428081654[/C][C]-0.57735719183459[/C][/ROW]
[ROW][C]10[/C][C]-12[/C][C]-9.65520610174133[/C][C]-2.34479389825867[/C][/ROW]
[ROW][C]11[/C][C]-10[/C][C]-10.9139715424864[/C][C]0.913971542486435[/C][/ROW]
[ROW][C]12[/C][C]-15[/C][C]-9.15507957606505[/C][C]-5.84492042393495[/C][/ROW]
[ROW][C]13[/C][C]-15[/C][C]-14.4869719710597[/C][C]-0.513028028940269[/C][/ROW]
[ROW][C]14[/C][C]-15[/C][C]-15.3045687083754[/C][C]0.304568708375388[/C][/ROW]
[ROW][C]15[/C][C]-13[/C][C]-15.3492060124361[/C][C]2.34920601243606[/C][/ROW]
[ROW][C]16[/C][C]-8[/C][C]-13.1263985014227[/C][C]5.12639850142271[/C][/ROW]
[ROW][C]17[/C][C]-13[/C][C]-7.4160225096323[/C][C]-5.5839774903677[/C][/ROW]
[ROW][C]18[/C][C]-9[/C][C]-12.167115556496[/C][C]3.16711555649604[/C][/ROW]
[ROW][C]19[/C][C]-7[/C][C]-8.6644407900571[/C][C]1.6644407900571[/C][/ROW]
[ROW][C]20[/C][C]-4[/C][C]-6.11384283334977[/C][C]2.11384283334977[/C][/ROW]
[ROW][C]21[/C][C]-4[/C][C]-2.72833776812751[/C][C]-1.27166223187249[/C][/ROW]
[ROW][C]22[/C][C]-2[/C][C]-2.54571637906171[/C][C]0.545716379061711[/C][/ROW]
[ROW][C]23[/C][C]0[/C][C]-0.67259500621231[/C][C]0.67259500621231[/C][/ROW]
[ROW][C]24[/C][C]-2[/C][C]1.45221168470848[/C][C]-3.45221168470848[/C][/ROW]
[ROW][C]25[/C][C]-3[/C][C]-0.7261473122539[/C][C]-2.2738526877461[/C][/ROW]
[ROW][C]26[/C][C]1[/C][C]-2.36196846193081[/C][C]3.36196846193081[/C][/ROW]
[ROW][C]27[/C][C]-2[/C][C]1.5963072660801[/C][C]-3.5963072660801[/C][/ROW]
[ROW][C]28[/C][C]-1[/C][C]-1.23535434409837[/C][C]0.235354344098367[/C][/ROW]
[ROW][C]29[/C][C]1[/C][C]-0.695657542218223[/C][C]1.69565754221822[/C][/ROW]
[ROW][C]30[/C][C]-3[/C][C]1.46722978728935[/C][C]-4.46722978728935[/C][/ROW]
[ROW][C]31[/C][C]-4[/C][C]-2.65374580790369[/C][C]-1.34625419209631[/C][/ROW]
[ROW][C]32[/C][C]-9[/C][C]-4.35266288812887[/C][C]-4.64733711187113[/C][/ROW]
[ROW][C]33[/C][C]-9[/C][C]-9.89240389824492[/C][C]0.892403898244918[/C][/ROW]
[ROW][C]34[/C][C]-7[/C][C]-10.4415874243447[/C][C]3.44158742434468[/C][/ROW]
[ROW][C]35[/C][C]-14[/C][C]-8.05579660520507[/C][C]-5.94420339479493[/C][/ROW]
[ROW][C]36[/C][C]-12[/C][C]-15.0590398029754[/C][C]3.05903980297538[/C][/ROW]
[ROW][C]37[/C][C]-16[/C][C]-13.6126864550764[/C][C]-2.38731354492361[/C][/ROW]
[ROW][C]38[/C][C]-20[/C][C]-17.3908515959597[/C][C]-2.60914840404033[/C][/ROW]
[ROW][C]39[/C][C]-12[/C][C]-21.9109816139012[/C][C]9.91098161390125[/C][/ROW]
[ROW][C]40[/C][C]-12[/C][C]-13.4891768964111[/C][C]1.48917689641106[/C][/ROW]
[ROW][C]41[/C][C]-10[/C][C]-12.0547640319232[/C][C]2.05476403192322[/C][/ROW]
[ROW][C]42[/C][C]-10[/C][C]-9.69716553872161[/C][C]-0.302834461278394[/C][/ROW]
[ROW][C]43[/C][C]-13[/C][C]-9.44723311905406[/C][C]-3.55276688094594[/C][/ROW]
[ROW][C]44[/C][C]-16[/C][C]-12.7631958375629[/C][C]-3.23680416243706[/C][/ROW]
[ROW][C]45[/C][C]-14[/C][C]-16.487114744296[/C][C]2.48711474429597[/C][/ROW]
[ROW][C]46[/C][C]-17[/C][C]-14.7248611918436[/C][C]-2.27513880815644[/C][/ROW]
[ROW][C]47[/C][C]-24[/C][C]-17.5704292507989[/C][C]-6.42957074920114[/C][/ROW]
[ROW][C]48[/C][C]-25[/C][C]-25.3720640091411[/C][C]0.37206400914113[/C][/ROW]
[ROW][C]49[/C][C]-23[/C][C]-27.198785286334[/C][C]4.19878528633403[/C][/ROW]
[ROW][C]50[/C][C]-17[/C][C]-24.8234846341757[/C][C]7.82348463417567[/C][/ROW]
[ROW][C]51[/C][C]-24[/C][C]-17.6577123193956[/C][C]-6.34228768060437[/C][/ROW]
[ROW][C]52[/C][C]-20[/C][C]-24.1087394228312[/C][C]4.10873942283117[/C][/ROW]
[ROW][C]53[/C][C]-19[/C][C]-20.6339119265256[/C][C]1.63391192652564[/C][/ROW]
[ROW][C]54[/C][C]-18[/C][C]-18.9603797949615[/C][C]0.960379794961526[/C][/ROW]
[ROW][C]55[/C][C]-16[/C][C]-17.6684360645263[/C][C]1.6684360645263[/C][/ROW]
[ROW][C]56[/C][C]-12[/C][C]-15.4111809314511[/C][C]3.41118093145112[/C][/ROW]
[ROW][C]57[/C][C]-7[/C][C]-10.9244819172803[/C][C]3.92448191728029[/C][/ROW]
[ROW][C]58[/C][C]-6[/C][C]-5.16604612577345[/C][C]-0.833953874226554[/C][/ROW]
[ROW][C]59[/C][C]-6[/C][C]-3.70851853782024[/C][C]-2.29148146217976[/C][/ROW]
[ROW][C]60[/C][C]-5[/C][C]-3.99729300206071[/C][C]-1.00270699793929[/C][/ROW]
[ROW][C]61[/C][C]-4[/C][C]-3.38002448141364[/C][C]-0.619975518586358[/C][/ROW]
[ROW][C]62[/C][C]-4[/C][C]-2.56156061036153[/C][C]-1.43843938963847[/C][/ROW]
[ROW][C]63[/C][C]-8[/C][C]-2.75567199506154[/C][C]-5.24432800493846[/C][/ROW]
[ROW][C]64[/C][C]-9[/C][C]-7.35400155923566[/C][C]-1.64599844076434[/C][/ROW]
[ROW][C]65[/C][C]-6[/C][C]-9.17958555695242[/C][C]3.17958555695242[/C][/ROW]
[ROW][C]66[/C][C]-7[/C][C]-6.15191190136934[/C][C]-0.848088098630655[/C][/ROW]
[ROW][C]67[/C][C]-10[/C][C]-6.79460520863969[/C][C]-3.20539479136031[/C][/ROW]
[ROW][C]68[/C][C]-11[/C][C]-10.1561723546201[/C][C]-0.843827645379873[/C][/ROW]
[ROW][C]69[/C][C]-11[/C][C]-11.6481916408077[/C][C]0.648191640807731[/C][/ROW]
[ROW][C]70[/C][C]-12[/C][C]-11.7101866357186[/C][C]-0.289813364281411[/C][/ROW]
[ROW][C]71[/C][C]-14[/C][C]-12.6464180690529[/C][C]-1.35358193094707[/C][/ROW]
[ROW][C]72[/C][C]-12[/C][C]-14.7900101926815[/C][C]2.7900101926815[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279302&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279302&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
3-24-284
4-22-27.68963435697945.68963435697938
5-19-24.71588307833665.71588307833664
6-18-20.51525357027232.51525357027232
7-17-18.55947247401681.55947247401677
8-11-17.10376316850566.10376316850558
9-11-10.4226428081654-0.57735719183459
10-12-9.65520610174133-2.34479389825867
11-10-10.91397154248640.913971542486435
12-15-9.15507957606505-5.84492042393495
13-15-14.4869719710597-0.513028028940269
14-15-15.30456870837540.304568708375388
15-13-15.34920601243612.34920601243606
16-8-13.12639850142275.12639850142271
17-13-7.4160225096323-5.5839774903677
18-9-12.1671155564963.16711555649604
19-7-8.66444079005711.6644407900571
20-4-6.113842833349772.11384283334977
21-4-2.72833776812751-1.27166223187249
22-2-2.545716379061710.545716379061711
230-0.672595006212310.67259500621231
24-21.45221168470848-3.45221168470848
25-3-0.7261473122539-2.2738526877461
261-2.361968461930813.36196846193081
27-21.5963072660801-3.5963072660801
28-1-1.235354344098370.235354344098367
291-0.6956575422182231.69565754221822
30-31.46722978728935-4.46722978728935
31-4-2.65374580790369-1.34625419209631
32-9-4.35266288812887-4.64733711187113
33-9-9.892403898244920.892403898244918
34-7-10.44158742434473.44158742434468
35-14-8.05579660520507-5.94420339479493
36-12-15.05903980297543.05903980297538
37-16-13.6126864550764-2.38731354492361
38-20-17.3908515959597-2.60914840404033
39-12-21.91098161390129.91098161390125
40-12-13.48917689641111.48917689641106
41-10-12.05476403192322.05476403192322
42-10-9.69716553872161-0.302834461278394
43-13-9.44723311905406-3.55276688094594
44-16-12.7631958375629-3.23680416243706
45-14-16.4871147442962.48711474429597
46-17-14.7248611918436-2.27513880815644
47-24-17.5704292507989-6.42957074920114
48-25-25.37206400914110.37206400914113
49-23-27.1987852863344.19878528633403
50-17-24.82348463417577.82348463417567
51-24-17.6577123193956-6.34228768060437
52-20-24.10873942283124.10873942283117
53-19-20.63391192652561.63391192652564
54-18-18.96037979496150.960379794961526
55-16-17.66843606452631.6684360645263
56-12-15.41118093145113.41118093145112
57-7-10.92448191728033.92448191728029
58-6-5.16604612577345-0.833953874226554
59-6-3.70851853782024-2.29148146217976
60-5-3.99729300206071-1.00270699793929
61-4-3.38002448141364-0.619975518586358
62-4-2.56156061036153-1.43843938963847
63-8-2.75567199506154-5.24432800493846
64-9-7.35400155923566-1.64599844076434
65-6-9.179585556952423.17958555695242
66-7-6.15191190136934-0.848088098630655
67-10-6.79460520863969-3.20539479136031
68-11-10.1561723546201-0.843827645379873
69-11-11.64819164080770.648191640807731
70-12-11.7101866357186-0.289813364281411
71-14-12.6464180690529-1.35358193094707
72-12-14.79001019268152.7900101926815







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73-12.7536520436545-19.5337923819835-5.97351170532556
74-13.1360342767203-23.1035398922557-3.16852866118492
75-13.5184165097861-26.7714690784984-0.265363941073758
76-13.9007987428518-30.60191279969422.80031531399056
77-14.2831809759176-34.6125390179176.04617706608175
78-14.6655632089834-38.80661477103739.47548835307049
79-15.0479454420492-43.18209075086813.0861998667697
80-15.4303276751149-47.734851952064516.8741966018346
81-15.8127099081807-52.460043306135820.8346234897744
82-16.1950921412465-57.352650458918124.9624661764251
83-16.5774743743123-62.407761067581729.2528123189572
84-16.959856607378-67.620679394590333.7009661798342

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & -12.7536520436545 & -19.5337923819835 & -5.97351170532556 \tabularnewline
74 & -13.1360342767203 & -23.1035398922557 & -3.16852866118492 \tabularnewline
75 & -13.5184165097861 & -26.7714690784984 & -0.265363941073758 \tabularnewline
76 & -13.9007987428518 & -30.6019127996942 & 2.80031531399056 \tabularnewline
77 & -14.2831809759176 & -34.612539017917 & 6.04617706608175 \tabularnewline
78 & -14.6655632089834 & -38.8066147710373 & 9.47548835307049 \tabularnewline
79 & -15.0479454420492 & -43.182090750868 & 13.0861998667697 \tabularnewline
80 & -15.4303276751149 & -47.7348519520645 & 16.8741966018346 \tabularnewline
81 & -15.8127099081807 & -52.4600433061358 & 20.8346234897744 \tabularnewline
82 & -16.1950921412465 & -57.3526504589181 & 24.9624661764251 \tabularnewline
83 & -16.5774743743123 & -62.4077610675817 & 29.2528123189572 \tabularnewline
84 & -16.959856607378 & -67.6206793945903 & 33.7009661798342 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279302&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]-12.7536520436545[/C][C]-19.5337923819835[/C][C]-5.97351170532556[/C][/ROW]
[ROW][C]74[/C][C]-13.1360342767203[/C][C]-23.1035398922557[/C][C]-3.16852866118492[/C][/ROW]
[ROW][C]75[/C][C]-13.5184165097861[/C][C]-26.7714690784984[/C][C]-0.265363941073758[/C][/ROW]
[ROW][C]76[/C][C]-13.9007987428518[/C][C]-30.6019127996942[/C][C]2.80031531399056[/C][/ROW]
[ROW][C]77[/C][C]-14.2831809759176[/C][C]-34.612539017917[/C][C]6.04617706608175[/C][/ROW]
[ROW][C]78[/C][C]-14.6655632089834[/C][C]-38.8066147710373[/C][C]9.47548835307049[/C][/ROW]
[ROW][C]79[/C][C]-15.0479454420492[/C][C]-43.182090750868[/C][C]13.0861998667697[/C][/ROW]
[ROW][C]80[/C][C]-15.4303276751149[/C][C]-47.7348519520645[/C][C]16.8741966018346[/C][/ROW]
[ROW][C]81[/C][C]-15.8127099081807[/C][C]-52.4600433061358[/C][C]20.8346234897744[/C][/ROW]
[ROW][C]82[/C][C]-16.1950921412465[/C][C]-57.3526504589181[/C][C]24.9624661764251[/C][/ROW]
[ROW][C]83[/C][C]-16.5774743743123[/C][C]-62.4077610675817[/C][C]29.2528123189572[/C][/ROW]
[ROW][C]84[/C][C]-16.959856607378[/C][C]-67.6206793945903[/C][C]33.7009661798342[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279302&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279302&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
73-12.7536520436545-19.5337923819835-5.97351170532556
74-13.1360342767203-23.1035398922557-3.16852866118492
75-13.5184165097861-26.7714690784984-0.265363941073758
76-13.9007987428518-30.60191279969422.80031531399056
77-14.2831809759176-34.6125390179176.04617706608175
78-14.6655632089834-38.80661477103739.47548835307049
79-15.0479454420492-43.18209075086813.0861998667697
80-15.4303276751149-47.734851952064516.8741966018346
81-15.8127099081807-52.460043306135820.8346234897744
82-16.1950921412465-57.352650458918124.9624661764251
83-16.5774743743123-62.407761067581729.2528123189572
84-16.959856607378-67.620679394590333.7009661798342



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')