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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 computationFri, 28 Nov 2014 14:19:07 +0000
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/Nov/28/t14171843790qaoz0ehzn1z3gp.htm/, Retrieved Sun, 19 May 2024 12:56:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260906, Retrieved Sun, 19 May 2024 12:56:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-28 14:19:07] [702db51622d5a06f9c7dbf229ec3eabf] [Current]
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Dataseries X:
0,52
0,53
0,53
0,53
0,53
0,51
0,5
0,49
0,49
0,5
0,5
0,51
0,52
0,52
0,52
0,52
0,51
0,51
0,47
0,44
0,44
0,47
0,49
0,48
0,52
0,51
0,52
0,51
0,51
0,5
0,51
0,47
0,49
0,48
0,51
0,51
0,51
0,52
0,52
0,51
0,52
0,52
0,5
0,45
0,42
0,43
0,47
0,48
0,5
0,52
0,5
0,51
0,5
0,5
0,49
0,47
0,46
0,46
0,49
0,5
0,53
0,5
0,51
0,51
0,5
0,49
0,5
0,51
0,5
0,47
0,49
0,49




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260906&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]3 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=260906&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260906&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0512906931937651
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0512906931937651 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260906&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]0.0512906931937651[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260906&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260906&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
beta0.0512906931937651
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
30.530.54-0.01
40.530.539487093068062-0.00948709306806239
50.530.539000493488208-0.00900049348820764
60.510.538538851938112-0.0285388519381116
70.50.517075074439252-0.0170750744392516
80.490.506199282034927-0.0161992820349273
90.490.495368409630114-0.00536840963011448
100.50.4950930601788380.00490693982116219
110.50.505344740523725-0.00534474052372536
120.510.5050706050773230.00492939492267741
130.520.5153234371599330.00467656284006746
140.520.525563301309764-0.0055633013097639
150.520.52527795572914-0.00527795572914025
160.520.525007245721147-0.00500724572114664
170.510.524750420617118-0.0147504206171175
180.510.513993861318766-0.003993861318766
190.470.513789013403207-0.0437890134032067
200.440.471543044551485-0.0315430445514852
210.440.4399251799309987.48200690023348e-05
220.470.4399290175042020.0300709824957984
230.490.4714713790414290.0185286209585713
240.480.492421724854318-0.0124217248543184
250.520.4817846059758780.0382153940241219
260.510.523744700026048-0.0137447000260482
270.520.5130397248339720.00696027516602815
280.510.523396722172057-0.0133967221720568
290.510.512709595005328-0.00270959500532775
300.50.51257061799923-0.0125706179992301
310.510.5019258622881760.00807413771182441
320.470.512339990408357-0.042339990408357
330.490.4701683429504950.0198316570495051
340.480.491185522387745-0.0111855223877451
350.510.4806118091907430.0293881908092568
360.510.512119149869061-0.0021191498690607
370.510.512010457203295-0.00201045720329507
380.520.5119073394597020.00809266054029834
390.520.522322417628595-0.00232241762859542
400.510.522203299218539-0.0122032992185394
410.520.5115773835423690.00842261645763054
420.520.522009385378987-0.00200938537898654
430.50.521906322610005-0.021906322610005
440.450.500782732138011-0.0507827321380115
450.420.44817805060438-0.0281780506043797
460.430.4167327788560320.013267221143968
470.470.4274132638252610.0425867361747388
480.480.4695975670445230.0104024329554765
490.50.4801311150417120.0198688849582885
500.520.5011502039242090.0188497960757907
510.50.522117023031498-0.0221170230314978
520.510.500982625588830.00901737441117023
530.50.511445132973166-0.0114451329731664
540.50.500858104169278-0.000858104169277896
550.490.500814091411603-0.0108140914116032
560.470.490259429166841-0.0202594291668413
570.460.469220309001164-0.00922030900116394
580.460.4587473929610340.0012526070389664
590.490.4588116400443620.0311883599556384
600.50.4904113126460630.00958868735393709
610.530.5009031230672650.0290968769327353
620.50.532395522054918-0.0323955220549184
630.510.5007339332723480.0092660667276524
640.510.511209196257989-0.00120919625798865
650.50.511147175743709-0.011147175743709
660.490.500575429372662-0.0105754293726615
670.50.4900330082693160.00996699173068399
680.510.5005442221842390.00945577781576068
690.50.511029215583096-0.0110292155830959
700.470.500463519470455-0.0304635194704554
710.490.4689010244396940.021098975560306
720.490.489983205521861.67944781395701e-05

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.53 & 0.54 & -0.01 \tabularnewline
4 & 0.53 & 0.539487093068062 & -0.00948709306806239 \tabularnewline
5 & 0.53 & 0.539000493488208 & -0.00900049348820764 \tabularnewline
6 & 0.51 & 0.538538851938112 & -0.0285388519381116 \tabularnewline
7 & 0.5 & 0.517075074439252 & -0.0170750744392516 \tabularnewline
8 & 0.49 & 0.506199282034927 & -0.0161992820349273 \tabularnewline
9 & 0.49 & 0.495368409630114 & -0.00536840963011448 \tabularnewline
10 & 0.5 & 0.495093060178838 & 0.00490693982116219 \tabularnewline
11 & 0.5 & 0.505344740523725 & -0.00534474052372536 \tabularnewline
12 & 0.51 & 0.505070605077323 & 0.00492939492267741 \tabularnewline
13 & 0.52 & 0.515323437159933 & 0.00467656284006746 \tabularnewline
14 & 0.52 & 0.525563301309764 & -0.0055633013097639 \tabularnewline
15 & 0.52 & 0.52527795572914 & -0.00527795572914025 \tabularnewline
16 & 0.52 & 0.525007245721147 & -0.00500724572114664 \tabularnewline
17 & 0.51 & 0.524750420617118 & -0.0147504206171175 \tabularnewline
18 & 0.51 & 0.513993861318766 & -0.003993861318766 \tabularnewline
19 & 0.47 & 0.513789013403207 & -0.0437890134032067 \tabularnewline
20 & 0.44 & 0.471543044551485 & -0.0315430445514852 \tabularnewline
21 & 0.44 & 0.439925179930998 & 7.48200690023348e-05 \tabularnewline
22 & 0.47 & 0.439929017504202 & 0.0300709824957984 \tabularnewline
23 & 0.49 & 0.471471379041429 & 0.0185286209585713 \tabularnewline
24 & 0.48 & 0.492421724854318 & -0.0124217248543184 \tabularnewline
25 & 0.52 & 0.481784605975878 & 0.0382153940241219 \tabularnewline
26 & 0.51 & 0.523744700026048 & -0.0137447000260482 \tabularnewline
27 & 0.52 & 0.513039724833972 & 0.00696027516602815 \tabularnewline
28 & 0.51 & 0.523396722172057 & -0.0133967221720568 \tabularnewline
29 & 0.51 & 0.512709595005328 & -0.00270959500532775 \tabularnewline
30 & 0.5 & 0.51257061799923 & -0.0125706179992301 \tabularnewline
31 & 0.51 & 0.501925862288176 & 0.00807413771182441 \tabularnewline
32 & 0.47 & 0.512339990408357 & -0.042339990408357 \tabularnewline
33 & 0.49 & 0.470168342950495 & 0.0198316570495051 \tabularnewline
34 & 0.48 & 0.491185522387745 & -0.0111855223877451 \tabularnewline
35 & 0.51 & 0.480611809190743 & 0.0293881908092568 \tabularnewline
36 & 0.51 & 0.512119149869061 & -0.0021191498690607 \tabularnewline
37 & 0.51 & 0.512010457203295 & -0.00201045720329507 \tabularnewline
38 & 0.52 & 0.511907339459702 & 0.00809266054029834 \tabularnewline
39 & 0.52 & 0.522322417628595 & -0.00232241762859542 \tabularnewline
40 & 0.51 & 0.522203299218539 & -0.0122032992185394 \tabularnewline
41 & 0.52 & 0.511577383542369 & 0.00842261645763054 \tabularnewline
42 & 0.52 & 0.522009385378987 & -0.00200938537898654 \tabularnewline
43 & 0.5 & 0.521906322610005 & -0.021906322610005 \tabularnewline
44 & 0.45 & 0.500782732138011 & -0.0507827321380115 \tabularnewline
45 & 0.42 & 0.44817805060438 & -0.0281780506043797 \tabularnewline
46 & 0.43 & 0.416732778856032 & 0.013267221143968 \tabularnewline
47 & 0.47 & 0.427413263825261 & 0.0425867361747388 \tabularnewline
48 & 0.48 & 0.469597567044523 & 0.0104024329554765 \tabularnewline
49 & 0.5 & 0.480131115041712 & 0.0198688849582885 \tabularnewline
50 & 0.52 & 0.501150203924209 & 0.0188497960757907 \tabularnewline
51 & 0.5 & 0.522117023031498 & -0.0221170230314978 \tabularnewline
52 & 0.51 & 0.50098262558883 & 0.00901737441117023 \tabularnewline
53 & 0.5 & 0.511445132973166 & -0.0114451329731664 \tabularnewline
54 & 0.5 & 0.500858104169278 & -0.000858104169277896 \tabularnewline
55 & 0.49 & 0.500814091411603 & -0.0108140914116032 \tabularnewline
56 & 0.47 & 0.490259429166841 & -0.0202594291668413 \tabularnewline
57 & 0.46 & 0.469220309001164 & -0.00922030900116394 \tabularnewline
58 & 0.46 & 0.458747392961034 & 0.0012526070389664 \tabularnewline
59 & 0.49 & 0.458811640044362 & 0.0311883599556384 \tabularnewline
60 & 0.5 & 0.490411312646063 & 0.00958868735393709 \tabularnewline
61 & 0.53 & 0.500903123067265 & 0.0290968769327353 \tabularnewline
62 & 0.5 & 0.532395522054918 & -0.0323955220549184 \tabularnewline
63 & 0.51 & 0.500733933272348 & 0.0092660667276524 \tabularnewline
64 & 0.51 & 0.511209196257989 & -0.00120919625798865 \tabularnewline
65 & 0.5 & 0.511147175743709 & -0.011147175743709 \tabularnewline
66 & 0.49 & 0.500575429372662 & -0.0105754293726615 \tabularnewline
67 & 0.5 & 0.490033008269316 & 0.00996699173068399 \tabularnewline
68 & 0.51 & 0.500544222184239 & 0.00945577781576068 \tabularnewline
69 & 0.5 & 0.511029215583096 & -0.0110292155830959 \tabularnewline
70 & 0.47 & 0.500463519470455 & -0.0304635194704554 \tabularnewline
71 & 0.49 & 0.468901024439694 & 0.021098975560306 \tabularnewline
72 & 0.49 & 0.48998320552186 & 1.67944781395701e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260906&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]0.53[/C][C]0.54[/C][C]-0.01[/C][/ROW]
[ROW][C]4[/C][C]0.53[/C][C]0.539487093068062[/C][C]-0.00948709306806239[/C][/ROW]
[ROW][C]5[/C][C]0.53[/C][C]0.539000493488208[/C][C]-0.00900049348820764[/C][/ROW]
[ROW][C]6[/C][C]0.51[/C][C]0.538538851938112[/C][C]-0.0285388519381116[/C][/ROW]
[ROW][C]7[/C][C]0.5[/C][C]0.517075074439252[/C][C]-0.0170750744392516[/C][/ROW]
[ROW][C]8[/C][C]0.49[/C][C]0.506199282034927[/C][C]-0.0161992820349273[/C][/ROW]
[ROW][C]9[/C][C]0.49[/C][C]0.495368409630114[/C][C]-0.00536840963011448[/C][/ROW]
[ROW][C]10[/C][C]0.5[/C][C]0.495093060178838[/C][C]0.00490693982116219[/C][/ROW]
[ROW][C]11[/C][C]0.5[/C][C]0.505344740523725[/C][C]-0.00534474052372536[/C][/ROW]
[ROW][C]12[/C][C]0.51[/C][C]0.505070605077323[/C][C]0.00492939492267741[/C][/ROW]
[ROW][C]13[/C][C]0.52[/C][C]0.515323437159933[/C][C]0.00467656284006746[/C][/ROW]
[ROW][C]14[/C][C]0.52[/C][C]0.525563301309764[/C][C]-0.0055633013097639[/C][/ROW]
[ROW][C]15[/C][C]0.52[/C][C]0.52527795572914[/C][C]-0.00527795572914025[/C][/ROW]
[ROW][C]16[/C][C]0.52[/C][C]0.525007245721147[/C][C]-0.00500724572114664[/C][/ROW]
[ROW][C]17[/C][C]0.51[/C][C]0.524750420617118[/C][C]-0.0147504206171175[/C][/ROW]
[ROW][C]18[/C][C]0.51[/C][C]0.513993861318766[/C][C]-0.003993861318766[/C][/ROW]
[ROW][C]19[/C][C]0.47[/C][C]0.513789013403207[/C][C]-0.0437890134032067[/C][/ROW]
[ROW][C]20[/C][C]0.44[/C][C]0.471543044551485[/C][C]-0.0315430445514852[/C][/ROW]
[ROW][C]21[/C][C]0.44[/C][C]0.439925179930998[/C][C]7.48200690023348e-05[/C][/ROW]
[ROW][C]22[/C][C]0.47[/C][C]0.439929017504202[/C][C]0.0300709824957984[/C][/ROW]
[ROW][C]23[/C][C]0.49[/C][C]0.471471379041429[/C][C]0.0185286209585713[/C][/ROW]
[ROW][C]24[/C][C]0.48[/C][C]0.492421724854318[/C][C]-0.0124217248543184[/C][/ROW]
[ROW][C]25[/C][C]0.52[/C][C]0.481784605975878[/C][C]0.0382153940241219[/C][/ROW]
[ROW][C]26[/C][C]0.51[/C][C]0.523744700026048[/C][C]-0.0137447000260482[/C][/ROW]
[ROW][C]27[/C][C]0.52[/C][C]0.513039724833972[/C][C]0.00696027516602815[/C][/ROW]
[ROW][C]28[/C][C]0.51[/C][C]0.523396722172057[/C][C]-0.0133967221720568[/C][/ROW]
[ROW][C]29[/C][C]0.51[/C][C]0.512709595005328[/C][C]-0.00270959500532775[/C][/ROW]
[ROW][C]30[/C][C]0.5[/C][C]0.51257061799923[/C][C]-0.0125706179992301[/C][/ROW]
[ROW][C]31[/C][C]0.51[/C][C]0.501925862288176[/C][C]0.00807413771182441[/C][/ROW]
[ROW][C]32[/C][C]0.47[/C][C]0.512339990408357[/C][C]-0.042339990408357[/C][/ROW]
[ROW][C]33[/C][C]0.49[/C][C]0.470168342950495[/C][C]0.0198316570495051[/C][/ROW]
[ROW][C]34[/C][C]0.48[/C][C]0.491185522387745[/C][C]-0.0111855223877451[/C][/ROW]
[ROW][C]35[/C][C]0.51[/C][C]0.480611809190743[/C][C]0.0293881908092568[/C][/ROW]
[ROW][C]36[/C][C]0.51[/C][C]0.512119149869061[/C][C]-0.0021191498690607[/C][/ROW]
[ROW][C]37[/C][C]0.51[/C][C]0.512010457203295[/C][C]-0.00201045720329507[/C][/ROW]
[ROW][C]38[/C][C]0.52[/C][C]0.511907339459702[/C][C]0.00809266054029834[/C][/ROW]
[ROW][C]39[/C][C]0.52[/C][C]0.522322417628595[/C][C]-0.00232241762859542[/C][/ROW]
[ROW][C]40[/C][C]0.51[/C][C]0.522203299218539[/C][C]-0.0122032992185394[/C][/ROW]
[ROW][C]41[/C][C]0.52[/C][C]0.511577383542369[/C][C]0.00842261645763054[/C][/ROW]
[ROW][C]42[/C][C]0.52[/C][C]0.522009385378987[/C][C]-0.00200938537898654[/C][/ROW]
[ROW][C]43[/C][C]0.5[/C][C]0.521906322610005[/C][C]-0.021906322610005[/C][/ROW]
[ROW][C]44[/C][C]0.45[/C][C]0.500782732138011[/C][C]-0.0507827321380115[/C][/ROW]
[ROW][C]45[/C][C]0.42[/C][C]0.44817805060438[/C][C]-0.0281780506043797[/C][/ROW]
[ROW][C]46[/C][C]0.43[/C][C]0.416732778856032[/C][C]0.013267221143968[/C][/ROW]
[ROW][C]47[/C][C]0.47[/C][C]0.427413263825261[/C][C]0.0425867361747388[/C][/ROW]
[ROW][C]48[/C][C]0.48[/C][C]0.469597567044523[/C][C]0.0104024329554765[/C][/ROW]
[ROW][C]49[/C][C]0.5[/C][C]0.480131115041712[/C][C]0.0198688849582885[/C][/ROW]
[ROW][C]50[/C][C]0.52[/C][C]0.501150203924209[/C][C]0.0188497960757907[/C][/ROW]
[ROW][C]51[/C][C]0.5[/C][C]0.522117023031498[/C][C]-0.0221170230314978[/C][/ROW]
[ROW][C]52[/C][C]0.51[/C][C]0.50098262558883[/C][C]0.00901737441117023[/C][/ROW]
[ROW][C]53[/C][C]0.5[/C][C]0.511445132973166[/C][C]-0.0114451329731664[/C][/ROW]
[ROW][C]54[/C][C]0.5[/C][C]0.500858104169278[/C][C]-0.000858104169277896[/C][/ROW]
[ROW][C]55[/C][C]0.49[/C][C]0.500814091411603[/C][C]-0.0108140914116032[/C][/ROW]
[ROW][C]56[/C][C]0.47[/C][C]0.490259429166841[/C][C]-0.0202594291668413[/C][/ROW]
[ROW][C]57[/C][C]0.46[/C][C]0.469220309001164[/C][C]-0.00922030900116394[/C][/ROW]
[ROW][C]58[/C][C]0.46[/C][C]0.458747392961034[/C][C]0.0012526070389664[/C][/ROW]
[ROW][C]59[/C][C]0.49[/C][C]0.458811640044362[/C][C]0.0311883599556384[/C][/ROW]
[ROW][C]60[/C][C]0.5[/C][C]0.490411312646063[/C][C]0.00958868735393709[/C][/ROW]
[ROW][C]61[/C][C]0.53[/C][C]0.500903123067265[/C][C]0.0290968769327353[/C][/ROW]
[ROW][C]62[/C][C]0.5[/C][C]0.532395522054918[/C][C]-0.0323955220549184[/C][/ROW]
[ROW][C]63[/C][C]0.51[/C][C]0.500733933272348[/C][C]0.0092660667276524[/C][/ROW]
[ROW][C]64[/C][C]0.51[/C][C]0.511209196257989[/C][C]-0.00120919625798865[/C][/ROW]
[ROW][C]65[/C][C]0.5[/C][C]0.511147175743709[/C][C]-0.011147175743709[/C][/ROW]
[ROW][C]66[/C][C]0.49[/C][C]0.500575429372662[/C][C]-0.0105754293726615[/C][/ROW]
[ROW][C]67[/C][C]0.5[/C][C]0.490033008269316[/C][C]0.00996699173068399[/C][/ROW]
[ROW][C]68[/C][C]0.51[/C][C]0.500544222184239[/C][C]0.00945577781576068[/C][/ROW]
[ROW][C]69[/C][C]0.5[/C][C]0.511029215583096[/C][C]-0.0110292155830959[/C][/ROW]
[ROW][C]70[/C][C]0.47[/C][C]0.500463519470455[/C][C]-0.0304635194704554[/C][/ROW]
[ROW][C]71[/C][C]0.49[/C][C]0.468901024439694[/C][C]0.021098975560306[/C][/ROW]
[ROW][C]72[/C][C]0.49[/C][C]0.48998320552186[/C][C]1.67944781395701e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260906&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260906&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
30.530.54-0.01
40.530.539487093068062-0.00948709306806239
50.530.539000493488208-0.00900049348820764
60.510.538538851938112-0.0285388519381116
70.50.517075074439252-0.0170750744392516
80.490.506199282034927-0.0161992820349273
90.490.495368409630114-0.00536840963011448
100.50.4950930601788380.00490693982116219
110.50.505344740523725-0.00534474052372536
120.510.5050706050773230.00492939492267741
130.520.5153234371599330.00467656284006746
140.520.525563301309764-0.0055633013097639
150.520.52527795572914-0.00527795572914025
160.520.525007245721147-0.00500724572114664
170.510.524750420617118-0.0147504206171175
180.510.513993861318766-0.003993861318766
190.470.513789013403207-0.0437890134032067
200.440.471543044551485-0.0315430445514852
210.440.4399251799309987.48200690023348e-05
220.470.4399290175042020.0300709824957984
230.490.4714713790414290.0185286209585713
240.480.492421724854318-0.0124217248543184
250.520.4817846059758780.0382153940241219
260.510.523744700026048-0.0137447000260482
270.520.5130397248339720.00696027516602815
280.510.523396722172057-0.0133967221720568
290.510.512709595005328-0.00270959500532775
300.50.51257061799923-0.0125706179992301
310.510.5019258622881760.00807413771182441
320.470.512339990408357-0.042339990408357
330.490.4701683429504950.0198316570495051
340.480.491185522387745-0.0111855223877451
350.510.4806118091907430.0293881908092568
360.510.512119149869061-0.0021191498690607
370.510.512010457203295-0.00201045720329507
380.520.5119073394597020.00809266054029834
390.520.522322417628595-0.00232241762859542
400.510.522203299218539-0.0122032992185394
410.520.5115773835423690.00842261645763054
420.520.522009385378987-0.00200938537898654
430.50.521906322610005-0.021906322610005
440.450.500782732138011-0.0507827321380115
450.420.44817805060438-0.0281780506043797
460.430.4167327788560320.013267221143968
470.470.4274132638252610.0425867361747388
480.480.4695975670445230.0104024329554765
490.50.4801311150417120.0198688849582885
500.520.5011502039242090.0188497960757907
510.50.522117023031498-0.0221170230314978
520.510.500982625588830.00901737441117023
530.50.511445132973166-0.0114451329731664
540.50.500858104169278-0.000858104169277896
550.490.500814091411603-0.0108140914116032
560.470.490259429166841-0.0202594291668413
570.460.469220309001164-0.00922030900116394
580.460.4587473929610340.0012526070389664
590.490.4588116400443620.0311883599556384
600.50.4904113126460630.00958868735393709
610.530.5009031230672650.0290968769327353
620.50.532395522054918-0.0323955220549184
630.510.5007339332723480.0092660667276524
640.510.511209196257989-0.00120919625798865
650.50.511147175743709-0.011147175743709
660.490.500575429372662-0.0105754293726615
670.50.4900330082693160.00996699173068399
680.510.5005442221842390.00945577781576068
690.50.511029215583096-0.0110292155830959
700.470.500463519470455-0.0304635194704554
710.490.4689010244396940.021098975560306
720.490.489983205521861.67944781395701e-05







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
730.4899840669222860.4531086320235230.526859501821049
740.4899681338445720.4364642779200140.54347198976913
750.4899522007668580.4227528761063030.557151525427413
760.4899362676891440.4103987787769660.569473756601322
770.489920334611430.3988093810601570.581031288162703
780.4899044015337160.3876895057801990.592119297287233
790.4898884684560020.3768689840806910.602907952831313
800.4898725353782880.3662403502642810.613504720492296
810.4898566023005740.3557313642128930.623981840388255
820.489840669222860.3452912130776860.634390125368035
830.4898247361451460.3348829113501740.644766560940118
840.4898088030674320.3244788135790370.655138792555827

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.489984066922286 & 0.453108632023523 & 0.526859501821049 \tabularnewline
74 & 0.489968133844572 & 0.436464277920014 & 0.54347198976913 \tabularnewline
75 & 0.489952200766858 & 0.422752876106303 & 0.557151525427413 \tabularnewline
76 & 0.489936267689144 & 0.410398778776966 & 0.569473756601322 \tabularnewline
77 & 0.48992033461143 & 0.398809381060157 & 0.581031288162703 \tabularnewline
78 & 0.489904401533716 & 0.387689505780199 & 0.592119297287233 \tabularnewline
79 & 0.489888468456002 & 0.376868984080691 & 0.602907952831313 \tabularnewline
80 & 0.489872535378288 & 0.366240350264281 & 0.613504720492296 \tabularnewline
81 & 0.489856602300574 & 0.355731364212893 & 0.623981840388255 \tabularnewline
82 & 0.48984066922286 & 0.345291213077686 & 0.634390125368035 \tabularnewline
83 & 0.489824736145146 & 0.334882911350174 & 0.644766560940118 \tabularnewline
84 & 0.489808803067432 & 0.324478813579037 & 0.655138792555827 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260906&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]0.489984066922286[/C][C]0.453108632023523[/C][C]0.526859501821049[/C][/ROW]
[ROW][C]74[/C][C]0.489968133844572[/C][C]0.436464277920014[/C][C]0.54347198976913[/C][/ROW]
[ROW][C]75[/C][C]0.489952200766858[/C][C]0.422752876106303[/C][C]0.557151525427413[/C][/ROW]
[ROW][C]76[/C][C]0.489936267689144[/C][C]0.410398778776966[/C][C]0.569473756601322[/C][/ROW]
[ROW][C]77[/C][C]0.48992033461143[/C][C]0.398809381060157[/C][C]0.581031288162703[/C][/ROW]
[ROW][C]78[/C][C]0.489904401533716[/C][C]0.387689505780199[/C][C]0.592119297287233[/C][/ROW]
[ROW][C]79[/C][C]0.489888468456002[/C][C]0.376868984080691[/C][C]0.602907952831313[/C][/ROW]
[ROW][C]80[/C][C]0.489872535378288[/C][C]0.366240350264281[/C][C]0.613504720492296[/C][/ROW]
[ROW][C]81[/C][C]0.489856602300574[/C][C]0.355731364212893[/C][C]0.623981840388255[/C][/ROW]
[ROW][C]82[/C][C]0.48984066922286[/C][C]0.345291213077686[/C][C]0.634390125368035[/C][/ROW]
[ROW][C]83[/C][C]0.489824736145146[/C][C]0.334882911350174[/C][C]0.644766560940118[/C][/ROW]
[ROW][C]84[/C][C]0.489808803067432[/C][C]0.324478813579037[/C][C]0.655138792555827[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260906&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260906&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
730.4899840669222860.4531086320235230.526859501821049
740.4899681338445720.4364642779200140.54347198976913
750.4899522007668580.4227528761063030.557151525427413
760.4899362676891440.4103987787769660.569473756601322
770.489920334611430.3988093810601570.581031288162703
780.4899044015337160.3876895057801990.592119297287233
790.4898884684560020.3768689840806910.602907952831313
800.4898725353782880.3662403502642810.613504720492296
810.4898566023005740.3557313642128930.623981840388255
820.489840669222860.3452912130776860.634390125368035
830.4898247361451460.3348829113501740.644766560940118
840.4898088030674320.3244788135790370.655138792555827



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')