Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 May 2008 10:48:13 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/26/t1211820525j164k043yvz8tbt.htm/, Retrieved Mon, 20 May 2024 05:49:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13278, Retrieved Mon, 20 May 2024 05:49:14 +0000
QR Codes:

Original text written by user:Additief Double
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact183
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Inschrijvingen ni...] [2008-05-25 16:13:28] [74be16979710d4c4e7c6647856088456]
-   PD    [Exponential Smoothing] [Gemiddelde consum...] [2008-05-26 16:48:13] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
4.07
4.07
4.08
4.09
4.08
4.09
4.12
4.14
4.14
4.14
4.14
4.14
4.23
4.29
4.32
4.33
4.35
4.35
4.35
4.35
4.36
4.36
4.38
4.4
4.4
4.4
4.43
4.44
4.46
4.47
4.49
4.49
4.57
4.62
4.64
4.66
4.67
4.68
4.72
4.74
4.75
4.76
4.77
4.76
4.77
4.77
4.78
4.81
4.81
4.85
4.92
4.96
4.95
4.96
4.97
5
5
5.01
5.01
5.02
5.04
5.04
5.19
5.22
5.22
5.22
5.24
5.28
5.34
5.36
5.38
5.39
5.41
5.44
5.51
5.55
5.56
5.57
5.58
5.58
5.59
5.61
5.63
5.64
5.64




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13278&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13278&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13278&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0708297900210963
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0708297900210963 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13278&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]0.0708297900210963[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13278&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13278&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
beta0.0708297900210963
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
34.084.070.00999999999999979
44.094.080708297900210.00929170209978913
54.084.09136642720888-0.0113664272088769
64.094.080561345556380.00943865444361691
74.124.091229883468710.0287701165312946
84.144.12326766478150.0167323352184994
94.144.14445281257159-0.00445281257158836
104.144.14413742079214-0.00413742079213986
114.144.1438443681462-0.00384436814620326
124.144.14357207235764-0.00357207235764445
134.234.143319063222610.0866809367773884
144.294.239458655773390.0505413442266134
154.324.303038488572340.0169615114276587
164.334.3342398688652-0.004239868865203
174.354.343939559843760.00606044015623564
184.354.36436881954747-0.0143688195474656
194.354.36335107907607-0.0133510790760676
204.354.36240542494855-0.0124054249485548
214.364.36152675130433-0.00152675130432556
224.364.37141861183003-0.0114186118300257
234.384.370609833951770.00939016604822651
244.44.391274937441230.00872506255876804
254.44.41189293179019-0.0118929317901904
264.44.41105055792876-0.0110505579287556
274.434.410267849231050.0197321507689532
284.444.44166547332668-0.00166547332667477
294.464.451547508200660.00845249179933827
304.474.47214619641996-0.00214619641996450
314.494.481994181778190.00800581822180657
324.494.50256123220179-0.0125612322017918
334.574.501671522762530.0683284772374675
344.624.586511214457720.0334887855422767
354.644.638883218105740.00111678189425479
364.664.658962319532810.00103768046718677
374.674.67903581822241-0.00903581822241417
384.684.68839581311505-0.00839581311505189
394.724.697801139435060.0221988605649441
404.744.739373480067580.00062651993242202
414.754.75941785634284-0.00941785634283576
424.764.76875079155562-0.00875079155562375
434.774.77813097482722-0.00813097482722114
444.764.78755505958754-0.0275550595875416
454.774.77560334050294-0.00560334050293765
464.774.7852064570717-0.0152064570716979
474.784.78412938691034-0.00412938691034359
484.814.793836903302570.0161630966974302
494.814.82498173204774-0.0149817320477386
504.854.823920579112640.0260794208873554
514.924.865767779017970.0542322209820325
524.964.93960903584250.0203909641574969
534.954.98105332355211-0.031053323552106
544.964.96885382316545-0.00885382316545336
554.974.97822670872976-0.00822670872976072
5654.987644012677870.0123559873221337
5755.0185191846654-0.0185191846653971
585.015.01720747470419-0.00720747470418548
595.015.0266969707843-0.016696970784305
605.025.02551432784966-0.00551432784966455
615.045.035123749165960.00487625083403564
625.045.05546913298863-0.0154691329886303
635.195.054373457547240.135626542452763
645.225.213979857070450.00602014292954589
655.225.24440626253005-0.0244062625300501
665.225.24267757207985-0.0226775720798473
675.245.24107132441124-0.00107132441124236
685.285.260995442728150.0190045572718498
695.345.302341531529160.0376584684708403
705.365.36500887294346-0.0050088729434643
715.385.38465409552464-0.00465409552463747
725.395.40432444691589-0.0143244469158894
735.415.41330984934867-0.00330984934866763
745.445.43307541341430.00692458658569972
755.515.463565880428150.0464341195718507
765.555.536854799367240.0131452006327626
775.565.57778587116784-0.0177858711678409
785.575.58652610164768-0.0165261016476803
795.585.59535556133811-0.015355561338108
805.585.60426793015287-0.0242679301528739
815.595.6025490377559-0.0125490377558997
825.615.61166019204668-0.00166019204668189
835.635.63154260099262-0.0015426009926216
845.645.65143333888823-0.0114333388882271
855.645.66062351789553-0.0206235178955341

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4.08 & 4.07 & 0.00999999999999979 \tabularnewline
4 & 4.09 & 4.08070829790021 & 0.00929170209978913 \tabularnewline
5 & 4.08 & 4.09136642720888 & -0.0113664272088769 \tabularnewline
6 & 4.09 & 4.08056134555638 & 0.00943865444361691 \tabularnewline
7 & 4.12 & 4.09122988346871 & 0.0287701165312946 \tabularnewline
8 & 4.14 & 4.1232676647815 & 0.0167323352184994 \tabularnewline
9 & 4.14 & 4.14445281257159 & -0.00445281257158836 \tabularnewline
10 & 4.14 & 4.14413742079214 & -0.00413742079213986 \tabularnewline
11 & 4.14 & 4.1438443681462 & -0.00384436814620326 \tabularnewline
12 & 4.14 & 4.14357207235764 & -0.00357207235764445 \tabularnewline
13 & 4.23 & 4.14331906322261 & 0.0866809367773884 \tabularnewline
14 & 4.29 & 4.23945865577339 & 0.0505413442266134 \tabularnewline
15 & 4.32 & 4.30303848857234 & 0.0169615114276587 \tabularnewline
16 & 4.33 & 4.3342398688652 & -0.004239868865203 \tabularnewline
17 & 4.35 & 4.34393955984376 & 0.00606044015623564 \tabularnewline
18 & 4.35 & 4.36436881954747 & -0.0143688195474656 \tabularnewline
19 & 4.35 & 4.36335107907607 & -0.0133510790760676 \tabularnewline
20 & 4.35 & 4.36240542494855 & -0.0124054249485548 \tabularnewline
21 & 4.36 & 4.36152675130433 & -0.00152675130432556 \tabularnewline
22 & 4.36 & 4.37141861183003 & -0.0114186118300257 \tabularnewline
23 & 4.38 & 4.37060983395177 & 0.00939016604822651 \tabularnewline
24 & 4.4 & 4.39127493744123 & 0.00872506255876804 \tabularnewline
25 & 4.4 & 4.41189293179019 & -0.0118929317901904 \tabularnewline
26 & 4.4 & 4.41105055792876 & -0.0110505579287556 \tabularnewline
27 & 4.43 & 4.41026784923105 & 0.0197321507689532 \tabularnewline
28 & 4.44 & 4.44166547332668 & -0.00166547332667477 \tabularnewline
29 & 4.46 & 4.45154750820066 & 0.00845249179933827 \tabularnewline
30 & 4.47 & 4.47214619641996 & -0.00214619641996450 \tabularnewline
31 & 4.49 & 4.48199418177819 & 0.00800581822180657 \tabularnewline
32 & 4.49 & 4.50256123220179 & -0.0125612322017918 \tabularnewline
33 & 4.57 & 4.50167152276253 & 0.0683284772374675 \tabularnewline
34 & 4.62 & 4.58651121445772 & 0.0334887855422767 \tabularnewline
35 & 4.64 & 4.63888321810574 & 0.00111678189425479 \tabularnewline
36 & 4.66 & 4.65896231953281 & 0.00103768046718677 \tabularnewline
37 & 4.67 & 4.67903581822241 & -0.00903581822241417 \tabularnewline
38 & 4.68 & 4.68839581311505 & -0.00839581311505189 \tabularnewline
39 & 4.72 & 4.69780113943506 & 0.0221988605649441 \tabularnewline
40 & 4.74 & 4.73937348006758 & 0.00062651993242202 \tabularnewline
41 & 4.75 & 4.75941785634284 & -0.00941785634283576 \tabularnewline
42 & 4.76 & 4.76875079155562 & -0.00875079155562375 \tabularnewline
43 & 4.77 & 4.77813097482722 & -0.00813097482722114 \tabularnewline
44 & 4.76 & 4.78755505958754 & -0.0275550595875416 \tabularnewline
45 & 4.77 & 4.77560334050294 & -0.00560334050293765 \tabularnewline
46 & 4.77 & 4.7852064570717 & -0.0152064570716979 \tabularnewline
47 & 4.78 & 4.78412938691034 & -0.00412938691034359 \tabularnewline
48 & 4.81 & 4.79383690330257 & 0.0161630966974302 \tabularnewline
49 & 4.81 & 4.82498173204774 & -0.0149817320477386 \tabularnewline
50 & 4.85 & 4.82392057911264 & 0.0260794208873554 \tabularnewline
51 & 4.92 & 4.86576777901797 & 0.0542322209820325 \tabularnewline
52 & 4.96 & 4.9396090358425 & 0.0203909641574969 \tabularnewline
53 & 4.95 & 4.98105332355211 & -0.031053323552106 \tabularnewline
54 & 4.96 & 4.96885382316545 & -0.00885382316545336 \tabularnewline
55 & 4.97 & 4.97822670872976 & -0.00822670872976072 \tabularnewline
56 & 5 & 4.98764401267787 & 0.0123559873221337 \tabularnewline
57 & 5 & 5.0185191846654 & -0.0185191846653971 \tabularnewline
58 & 5.01 & 5.01720747470419 & -0.00720747470418548 \tabularnewline
59 & 5.01 & 5.0266969707843 & -0.016696970784305 \tabularnewline
60 & 5.02 & 5.02551432784966 & -0.00551432784966455 \tabularnewline
61 & 5.04 & 5.03512374916596 & 0.00487625083403564 \tabularnewline
62 & 5.04 & 5.05546913298863 & -0.0154691329886303 \tabularnewline
63 & 5.19 & 5.05437345754724 & 0.135626542452763 \tabularnewline
64 & 5.22 & 5.21397985707045 & 0.00602014292954589 \tabularnewline
65 & 5.22 & 5.24440626253005 & -0.0244062625300501 \tabularnewline
66 & 5.22 & 5.24267757207985 & -0.0226775720798473 \tabularnewline
67 & 5.24 & 5.24107132441124 & -0.00107132441124236 \tabularnewline
68 & 5.28 & 5.26099544272815 & 0.0190045572718498 \tabularnewline
69 & 5.34 & 5.30234153152916 & 0.0376584684708403 \tabularnewline
70 & 5.36 & 5.36500887294346 & -0.0050088729434643 \tabularnewline
71 & 5.38 & 5.38465409552464 & -0.00465409552463747 \tabularnewline
72 & 5.39 & 5.40432444691589 & -0.0143244469158894 \tabularnewline
73 & 5.41 & 5.41330984934867 & -0.00330984934866763 \tabularnewline
74 & 5.44 & 5.4330754134143 & 0.00692458658569972 \tabularnewline
75 & 5.51 & 5.46356588042815 & 0.0464341195718507 \tabularnewline
76 & 5.55 & 5.53685479936724 & 0.0131452006327626 \tabularnewline
77 & 5.56 & 5.57778587116784 & -0.0177858711678409 \tabularnewline
78 & 5.57 & 5.58652610164768 & -0.0165261016476803 \tabularnewline
79 & 5.58 & 5.59535556133811 & -0.015355561338108 \tabularnewline
80 & 5.58 & 5.60426793015287 & -0.0242679301528739 \tabularnewline
81 & 5.59 & 5.6025490377559 & -0.0125490377558997 \tabularnewline
82 & 5.61 & 5.61166019204668 & -0.00166019204668189 \tabularnewline
83 & 5.63 & 5.63154260099262 & -0.0015426009926216 \tabularnewline
84 & 5.64 & 5.65143333888823 & -0.0114333388882271 \tabularnewline
85 & 5.64 & 5.66062351789553 & -0.0206235178955341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13278&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]4.08[/C][C]4.07[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]4.09[/C][C]4.08070829790021[/C][C]0.00929170209978913[/C][/ROW]
[ROW][C]5[/C][C]4.08[/C][C]4.09136642720888[/C][C]-0.0113664272088769[/C][/ROW]
[ROW][C]6[/C][C]4.09[/C][C]4.08056134555638[/C][C]0.00943865444361691[/C][/ROW]
[ROW][C]7[/C][C]4.12[/C][C]4.09122988346871[/C][C]0.0287701165312946[/C][/ROW]
[ROW][C]8[/C][C]4.14[/C][C]4.1232676647815[/C][C]0.0167323352184994[/C][/ROW]
[ROW][C]9[/C][C]4.14[/C][C]4.14445281257159[/C][C]-0.00445281257158836[/C][/ROW]
[ROW][C]10[/C][C]4.14[/C][C]4.14413742079214[/C][C]-0.00413742079213986[/C][/ROW]
[ROW][C]11[/C][C]4.14[/C][C]4.1438443681462[/C][C]-0.00384436814620326[/C][/ROW]
[ROW][C]12[/C][C]4.14[/C][C]4.14357207235764[/C][C]-0.00357207235764445[/C][/ROW]
[ROW][C]13[/C][C]4.23[/C][C]4.14331906322261[/C][C]0.0866809367773884[/C][/ROW]
[ROW][C]14[/C][C]4.29[/C][C]4.23945865577339[/C][C]0.0505413442266134[/C][/ROW]
[ROW][C]15[/C][C]4.32[/C][C]4.30303848857234[/C][C]0.0169615114276587[/C][/ROW]
[ROW][C]16[/C][C]4.33[/C][C]4.3342398688652[/C][C]-0.004239868865203[/C][/ROW]
[ROW][C]17[/C][C]4.35[/C][C]4.34393955984376[/C][C]0.00606044015623564[/C][/ROW]
[ROW][C]18[/C][C]4.35[/C][C]4.36436881954747[/C][C]-0.0143688195474656[/C][/ROW]
[ROW][C]19[/C][C]4.35[/C][C]4.36335107907607[/C][C]-0.0133510790760676[/C][/ROW]
[ROW][C]20[/C][C]4.35[/C][C]4.36240542494855[/C][C]-0.0124054249485548[/C][/ROW]
[ROW][C]21[/C][C]4.36[/C][C]4.36152675130433[/C][C]-0.00152675130432556[/C][/ROW]
[ROW][C]22[/C][C]4.36[/C][C]4.37141861183003[/C][C]-0.0114186118300257[/C][/ROW]
[ROW][C]23[/C][C]4.38[/C][C]4.37060983395177[/C][C]0.00939016604822651[/C][/ROW]
[ROW][C]24[/C][C]4.4[/C][C]4.39127493744123[/C][C]0.00872506255876804[/C][/ROW]
[ROW][C]25[/C][C]4.4[/C][C]4.41189293179019[/C][C]-0.0118929317901904[/C][/ROW]
[ROW][C]26[/C][C]4.4[/C][C]4.41105055792876[/C][C]-0.0110505579287556[/C][/ROW]
[ROW][C]27[/C][C]4.43[/C][C]4.41026784923105[/C][C]0.0197321507689532[/C][/ROW]
[ROW][C]28[/C][C]4.44[/C][C]4.44166547332668[/C][C]-0.00166547332667477[/C][/ROW]
[ROW][C]29[/C][C]4.46[/C][C]4.45154750820066[/C][C]0.00845249179933827[/C][/ROW]
[ROW][C]30[/C][C]4.47[/C][C]4.47214619641996[/C][C]-0.00214619641996450[/C][/ROW]
[ROW][C]31[/C][C]4.49[/C][C]4.48199418177819[/C][C]0.00800581822180657[/C][/ROW]
[ROW][C]32[/C][C]4.49[/C][C]4.50256123220179[/C][C]-0.0125612322017918[/C][/ROW]
[ROW][C]33[/C][C]4.57[/C][C]4.50167152276253[/C][C]0.0683284772374675[/C][/ROW]
[ROW][C]34[/C][C]4.62[/C][C]4.58651121445772[/C][C]0.0334887855422767[/C][/ROW]
[ROW][C]35[/C][C]4.64[/C][C]4.63888321810574[/C][C]0.00111678189425479[/C][/ROW]
[ROW][C]36[/C][C]4.66[/C][C]4.65896231953281[/C][C]0.00103768046718677[/C][/ROW]
[ROW][C]37[/C][C]4.67[/C][C]4.67903581822241[/C][C]-0.00903581822241417[/C][/ROW]
[ROW][C]38[/C][C]4.68[/C][C]4.68839581311505[/C][C]-0.00839581311505189[/C][/ROW]
[ROW][C]39[/C][C]4.72[/C][C]4.69780113943506[/C][C]0.0221988605649441[/C][/ROW]
[ROW][C]40[/C][C]4.74[/C][C]4.73937348006758[/C][C]0.00062651993242202[/C][/ROW]
[ROW][C]41[/C][C]4.75[/C][C]4.75941785634284[/C][C]-0.00941785634283576[/C][/ROW]
[ROW][C]42[/C][C]4.76[/C][C]4.76875079155562[/C][C]-0.00875079155562375[/C][/ROW]
[ROW][C]43[/C][C]4.77[/C][C]4.77813097482722[/C][C]-0.00813097482722114[/C][/ROW]
[ROW][C]44[/C][C]4.76[/C][C]4.78755505958754[/C][C]-0.0275550595875416[/C][/ROW]
[ROW][C]45[/C][C]4.77[/C][C]4.77560334050294[/C][C]-0.00560334050293765[/C][/ROW]
[ROW][C]46[/C][C]4.77[/C][C]4.7852064570717[/C][C]-0.0152064570716979[/C][/ROW]
[ROW][C]47[/C][C]4.78[/C][C]4.78412938691034[/C][C]-0.00412938691034359[/C][/ROW]
[ROW][C]48[/C][C]4.81[/C][C]4.79383690330257[/C][C]0.0161630966974302[/C][/ROW]
[ROW][C]49[/C][C]4.81[/C][C]4.82498173204774[/C][C]-0.0149817320477386[/C][/ROW]
[ROW][C]50[/C][C]4.85[/C][C]4.82392057911264[/C][C]0.0260794208873554[/C][/ROW]
[ROW][C]51[/C][C]4.92[/C][C]4.86576777901797[/C][C]0.0542322209820325[/C][/ROW]
[ROW][C]52[/C][C]4.96[/C][C]4.9396090358425[/C][C]0.0203909641574969[/C][/ROW]
[ROW][C]53[/C][C]4.95[/C][C]4.98105332355211[/C][C]-0.031053323552106[/C][/ROW]
[ROW][C]54[/C][C]4.96[/C][C]4.96885382316545[/C][C]-0.00885382316545336[/C][/ROW]
[ROW][C]55[/C][C]4.97[/C][C]4.97822670872976[/C][C]-0.00822670872976072[/C][/ROW]
[ROW][C]56[/C][C]5[/C][C]4.98764401267787[/C][C]0.0123559873221337[/C][/ROW]
[ROW][C]57[/C][C]5[/C][C]5.0185191846654[/C][C]-0.0185191846653971[/C][/ROW]
[ROW][C]58[/C][C]5.01[/C][C]5.01720747470419[/C][C]-0.00720747470418548[/C][/ROW]
[ROW][C]59[/C][C]5.01[/C][C]5.0266969707843[/C][C]-0.016696970784305[/C][/ROW]
[ROW][C]60[/C][C]5.02[/C][C]5.02551432784966[/C][C]-0.00551432784966455[/C][/ROW]
[ROW][C]61[/C][C]5.04[/C][C]5.03512374916596[/C][C]0.00487625083403564[/C][/ROW]
[ROW][C]62[/C][C]5.04[/C][C]5.05546913298863[/C][C]-0.0154691329886303[/C][/ROW]
[ROW][C]63[/C][C]5.19[/C][C]5.05437345754724[/C][C]0.135626542452763[/C][/ROW]
[ROW][C]64[/C][C]5.22[/C][C]5.21397985707045[/C][C]0.00602014292954589[/C][/ROW]
[ROW][C]65[/C][C]5.22[/C][C]5.24440626253005[/C][C]-0.0244062625300501[/C][/ROW]
[ROW][C]66[/C][C]5.22[/C][C]5.24267757207985[/C][C]-0.0226775720798473[/C][/ROW]
[ROW][C]67[/C][C]5.24[/C][C]5.24107132441124[/C][C]-0.00107132441124236[/C][/ROW]
[ROW][C]68[/C][C]5.28[/C][C]5.26099544272815[/C][C]0.0190045572718498[/C][/ROW]
[ROW][C]69[/C][C]5.34[/C][C]5.30234153152916[/C][C]0.0376584684708403[/C][/ROW]
[ROW][C]70[/C][C]5.36[/C][C]5.36500887294346[/C][C]-0.0050088729434643[/C][/ROW]
[ROW][C]71[/C][C]5.38[/C][C]5.38465409552464[/C][C]-0.00465409552463747[/C][/ROW]
[ROW][C]72[/C][C]5.39[/C][C]5.40432444691589[/C][C]-0.0143244469158894[/C][/ROW]
[ROW][C]73[/C][C]5.41[/C][C]5.41330984934867[/C][C]-0.00330984934866763[/C][/ROW]
[ROW][C]74[/C][C]5.44[/C][C]5.4330754134143[/C][C]0.00692458658569972[/C][/ROW]
[ROW][C]75[/C][C]5.51[/C][C]5.46356588042815[/C][C]0.0464341195718507[/C][/ROW]
[ROW][C]76[/C][C]5.55[/C][C]5.53685479936724[/C][C]0.0131452006327626[/C][/ROW]
[ROW][C]77[/C][C]5.56[/C][C]5.57778587116784[/C][C]-0.0177858711678409[/C][/ROW]
[ROW][C]78[/C][C]5.57[/C][C]5.58652610164768[/C][C]-0.0165261016476803[/C][/ROW]
[ROW][C]79[/C][C]5.58[/C][C]5.59535556133811[/C][C]-0.015355561338108[/C][/ROW]
[ROW][C]80[/C][C]5.58[/C][C]5.60426793015287[/C][C]-0.0242679301528739[/C][/ROW]
[ROW][C]81[/C][C]5.59[/C][C]5.6025490377559[/C][C]-0.0125490377558997[/C][/ROW]
[ROW][C]82[/C][C]5.61[/C][C]5.61166019204668[/C][C]-0.00166019204668189[/C][/ROW]
[ROW][C]83[/C][C]5.63[/C][C]5.63154260099262[/C][C]-0.0015426009926216[/C][/ROW]
[ROW][C]84[/C][C]5.64[/C][C]5.65143333888823[/C][C]-0.0114333388882271[/C][/ROW]
[ROW][C]85[/C][C]5.64[/C][C]5.66062351789553[/C][C]-0.0206235178955341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13278&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13278&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
34.084.070.00999999999999979
44.094.080708297900210.00929170209978913
54.084.09136642720888-0.0113664272088769
64.094.080561345556380.00943865444361691
74.124.091229883468710.0287701165312946
84.144.12326766478150.0167323352184994
94.144.14445281257159-0.00445281257158836
104.144.14413742079214-0.00413742079213986
114.144.1438443681462-0.00384436814620326
124.144.14357207235764-0.00357207235764445
134.234.143319063222610.0866809367773884
144.294.239458655773390.0505413442266134
154.324.303038488572340.0169615114276587
164.334.3342398688652-0.004239868865203
174.354.343939559843760.00606044015623564
184.354.36436881954747-0.0143688195474656
194.354.36335107907607-0.0133510790760676
204.354.36240542494855-0.0124054249485548
214.364.36152675130433-0.00152675130432556
224.364.37141861183003-0.0114186118300257
234.384.370609833951770.00939016604822651
244.44.391274937441230.00872506255876804
254.44.41189293179019-0.0118929317901904
264.44.41105055792876-0.0110505579287556
274.434.410267849231050.0197321507689532
284.444.44166547332668-0.00166547332667477
294.464.451547508200660.00845249179933827
304.474.47214619641996-0.00214619641996450
314.494.481994181778190.00800581822180657
324.494.50256123220179-0.0125612322017918
334.574.501671522762530.0683284772374675
344.624.586511214457720.0334887855422767
354.644.638883218105740.00111678189425479
364.664.658962319532810.00103768046718677
374.674.67903581822241-0.00903581822241417
384.684.68839581311505-0.00839581311505189
394.724.697801139435060.0221988605649441
404.744.739373480067580.00062651993242202
414.754.75941785634284-0.00941785634283576
424.764.76875079155562-0.00875079155562375
434.774.77813097482722-0.00813097482722114
444.764.78755505958754-0.0275550595875416
454.774.77560334050294-0.00560334050293765
464.774.7852064570717-0.0152064570716979
474.784.78412938691034-0.00412938691034359
484.814.793836903302570.0161630966974302
494.814.82498173204774-0.0149817320477386
504.854.823920579112640.0260794208873554
514.924.865767779017970.0542322209820325
524.964.93960903584250.0203909641574969
534.954.98105332355211-0.031053323552106
544.964.96885382316545-0.00885382316545336
554.974.97822670872976-0.00822670872976072
5654.987644012677870.0123559873221337
5755.0185191846654-0.0185191846653971
585.015.01720747470419-0.00720747470418548
595.015.0266969707843-0.016696970784305
605.025.02551432784966-0.00551432784966455
615.045.035123749165960.00487625083403564
625.045.05546913298863-0.0154691329886303
635.195.054373457547240.135626542452763
645.225.213979857070450.00602014292954589
655.225.24440626253005-0.0244062625300501
665.225.24267757207985-0.0226775720798473
675.245.24107132441124-0.00107132441124236
685.285.260995442728150.0190045572718498
695.345.302341531529160.0376584684708403
705.365.36500887294346-0.0050088729434643
715.385.38465409552464-0.00465409552463747
725.395.40432444691589-0.0143244469158894
735.415.41330984934867-0.00330984934866763
745.445.43307541341430.00692458658569972
755.515.463565880428150.0464341195718507
765.555.536854799367240.0131452006327626
775.565.57778587116784-0.0177858711678409
785.575.58652610164768-0.0165261016476803
795.585.59535556133811-0.015355561338108
805.585.60426793015287-0.0242679301528739
815.595.6025490377559-0.0125490377558997
825.615.61166019204668-0.00166019204668189
835.635.63154260099262-0.0015426009926216
845.645.65143333888823-0.0114333388882271
855.645.66062351789553-0.0206235178955341







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
865.65916275845355.60912318002525.70920233688179
875.678325516906995.605009825076335.75164120873766
885.697488275360495.604543034485275.79043351623571
895.716651033813995.605655696835895.82764637079209
905.735813792267485.607580583695895.86404700083908
915.754976550720985.609940987241635.90001211420034
925.774139309174485.612523203745985.93575541460298
935.793302067627985.615194705668285.97140942958767
945.812464826081475.617868219615066.00706143254788
955.831627584534975.620483770632586.04277139843735
965.850790342988475.622998839392266.07858184658467
975.869953101441965.625382579596556.11452362328737

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 5.6591627584535 & 5.6091231800252 & 5.70920233688179 \tabularnewline
87 & 5.67832551690699 & 5.60500982507633 & 5.75164120873766 \tabularnewline
88 & 5.69748827536049 & 5.60454303448527 & 5.79043351623571 \tabularnewline
89 & 5.71665103381399 & 5.60565569683589 & 5.82764637079209 \tabularnewline
90 & 5.73581379226748 & 5.60758058369589 & 5.86404700083908 \tabularnewline
91 & 5.75497655072098 & 5.60994098724163 & 5.90001211420034 \tabularnewline
92 & 5.77413930917448 & 5.61252320374598 & 5.93575541460298 \tabularnewline
93 & 5.79330206762798 & 5.61519470566828 & 5.97140942958767 \tabularnewline
94 & 5.81246482608147 & 5.61786821961506 & 6.00706143254788 \tabularnewline
95 & 5.83162758453497 & 5.62048377063258 & 6.04277139843735 \tabularnewline
96 & 5.85079034298847 & 5.62299883939226 & 6.07858184658467 \tabularnewline
97 & 5.86995310144196 & 5.62538257959655 & 6.11452362328737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13278&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]86[/C][C]5.6591627584535[/C][C]5.6091231800252[/C][C]5.70920233688179[/C][/ROW]
[ROW][C]87[/C][C]5.67832551690699[/C][C]5.60500982507633[/C][C]5.75164120873766[/C][/ROW]
[ROW][C]88[/C][C]5.69748827536049[/C][C]5.60454303448527[/C][C]5.79043351623571[/C][/ROW]
[ROW][C]89[/C][C]5.71665103381399[/C][C]5.60565569683589[/C][C]5.82764637079209[/C][/ROW]
[ROW][C]90[/C][C]5.73581379226748[/C][C]5.60758058369589[/C][C]5.86404700083908[/C][/ROW]
[ROW][C]91[/C][C]5.75497655072098[/C][C]5.60994098724163[/C][C]5.90001211420034[/C][/ROW]
[ROW][C]92[/C][C]5.77413930917448[/C][C]5.61252320374598[/C][C]5.93575541460298[/C][/ROW]
[ROW][C]93[/C][C]5.79330206762798[/C][C]5.61519470566828[/C][C]5.97140942958767[/C][/ROW]
[ROW][C]94[/C][C]5.81246482608147[/C][C]5.61786821961506[/C][C]6.00706143254788[/C][/ROW]
[ROW][C]95[/C][C]5.83162758453497[/C][C]5.62048377063258[/C][C]6.04277139843735[/C][/ROW]
[ROW][C]96[/C][C]5.85079034298847[/C][C]5.62299883939226[/C][C]6.07858184658467[/C][/ROW]
[ROW][C]97[/C][C]5.86995310144196[/C][C]5.62538257959655[/C][C]6.11452362328737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13278&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13278&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
865.65916275845355.60912318002525.70920233688179
875.678325516906995.605009825076335.75164120873766
885.697488275360495.604543034485275.79043351623571
895.716651033813995.605655696835895.82764637079209
905.735813792267485.607580583695895.86404700083908
915.754976550720985.609940987241635.90001211420034
925.774139309174485.612523203745985.93575541460298
935.793302067627985.615194705668285.97140942958767
945.812464826081475.617868219615066.00706143254788
955.831627584534975.620483770632586.04277139843735
965.850790342988475.622998839392266.07858184658467
975.869953101441965.625382579596556.11452362328737



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')