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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 04 Dec 2014 09:28:56 +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/Dec/04/t1417685382jfr9c4zp0cw937h.htm/, Retrieved Thu, 16 May 2024 16:31:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=263060, Retrieved Thu, 16 May 2024 16:31:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-04 09:28:56] [fd8705890551d8de989fba3c4c1c4b9e] [Current]
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Dataseries X:
1.4
1.5
1.8
1.8
1.8
1.7
1.5
1.1
1.3
1.6
1.9
1.9
2
2.2
2.2
2
2.3
2.6
3.2
3.2
3.1
2.8
2.3
1.9
1.9
2
2
1.8
1.6
1.4
0.2
0.3
0.4
0.7
1
1.1
0.8
0.8
1
1.1
1
0.8
1.6
1.5
1.6
1.6
1.6
1.9
2
1.9
2
2.1
2.3
2.3
2.6
2.6
2.7
2.6
2.6
2.4
2.5
2.5
2.5
2.4
2.1
2.1
2.3
2.3
2.3
2.9
2.8
2.9
3
3
2.9
2.6
2.8
2.9
3.1
2.8
2.4
1.6
1.5
1.7




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=263060&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=263060&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263060&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
alpha1
beta0.0389458936681285
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0389458936681285 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263060&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]0.0389458936681285[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263060&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263060&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
beta0.0389458936681285
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31.81.60.2
41.81.90778917873363-0.107789178733626
51.81.90359123284009-0.103591232840091
61.71.89955677970095-0.199556779700951
71.51.79178486257796-0.291784862577963
81.11.58042104034603-0.480421040346032
91.31.161710613592780.138289386407216
101.61.367096417331230.23290358266877
111.91.676167055496770.223832944503225
121.91.98488442955282-0.0848844295528211
1321.981578529585380.0184214704146228
142.22.082295970213360.117704029786645
152.22.28688005884174-0.0868800588417367
1622.28349643730821-0.283496437308206
172.32.072455415205510.227544584794493
182.62.381317342409670.218682657590329
193.22.689834133939250.510165866060752
203.23.30970299951196-0.109702999511959
213.13.30543051815789-0.205430518157892
222.83.19742984304153-0.397429843041526
232.32.88195158263389-0.58195158263389
241.92.35928695817663-0.459286958176631
251.91.94139961714033-0.0413996171403257
2621.939787272053280.0602127279467228
2722.04213231055336-0.0421323105533582
281.82.04049143006655-0.240491430066555
291.61.83112527640309-0.231125276403086
301.41.62212389596428-0.222123895964275
310.21.4134730823309-1.2134730823309
320.30.1662132886973050.133786711302695
330.40.2714237317299080.128576268270092
340.70.37643124940220.3235687505978
3510.6890329235573110.310967076442689
361.11.001143814250740.0988561857492636
370.81.10499385674936-0.304993856749364
380.80.7931155984349710.00688440156502901
3910.7933837176062910.206616282393709
401.11.00143057337050.0985694266294994
4111.10526944777894-0.105269447778942
420.81.00116963505924-0.20116963505924
431.60.7933349038429670.806665096157033
441.51.62475119690369-0.124751196903689
451.61.519892650054110.0801073499458935
461.61.62301250238713-0.0230125023871348
471.61.62211625991613-0.022116259916128
481.91.62125492240910.278745077590902
4921.932110898561470.0678891014385328
501.92.03475490028732-0.134754900287317
5121.929506750269470.0704932497305319
522.12.032252172877790.0677478271222061
532.32.134890672549140.165109327450857
542.32.34132100285966-0.0413210028596596
552.62.339711719476030.260288280523973
562.62.64984887917237-0.0498488791723735
572.72.647907470024650.052092529975349
582.62.74993626015798-0.149936260157975
592.62.64409685851287-0.0440968585128654
602.42.64237946695012-0.242379466950125
612.52.432939782002950.0670602179970525
622.52.53555150212242-0.0355515021224222
632.52.53416691710102-0.0341669171010204
642.42.53283625598064-0.132836255980636
652.12.42766282927994-0.327662829279942
662.12.11490170757181-0.014901707571807
672.32.114321347253240.185678652746758
682.32.32155276831956-0.0215527683195584
692.32.32071337649633-0.0207133764963312
702.92.31990667553780.580093324462203
712.82.94249892846989-0.142498928469894
722.92.836949180353880.0630508196461173
7332.939404750871510.0605952491284913
7433.04176468700086-0.0417646870008608
752.93.04013812394184-0.140138123941842
762.62.93468031946795-0.334680319467952
772.82.621645895333140.178354104666862
782.92.828592055328770.0714079446712321
793.12.931373101548990.168626898451007
802.83.13794042680565-0.337940426805653
812.42.82477903487712-0.424779034877118
821.62.40823563575234-0.808235635752343
831.51.57675817662354-0.0767581766235403
841.71.47376876083860.226231239161399

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.8 & 1.6 & 0.2 \tabularnewline
4 & 1.8 & 1.90778917873363 & -0.107789178733626 \tabularnewline
5 & 1.8 & 1.90359123284009 & -0.103591232840091 \tabularnewline
6 & 1.7 & 1.89955677970095 & -0.199556779700951 \tabularnewline
7 & 1.5 & 1.79178486257796 & -0.291784862577963 \tabularnewline
8 & 1.1 & 1.58042104034603 & -0.480421040346032 \tabularnewline
9 & 1.3 & 1.16171061359278 & 0.138289386407216 \tabularnewline
10 & 1.6 & 1.36709641733123 & 0.23290358266877 \tabularnewline
11 & 1.9 & 1.67616705549677 & 0.223832944503225 \tabularnewline
12 & 1.9 & 1.98488442955282 & -0.0848844295528211 \tabularnewline
13 & 2 & 1.98157852958538 & 0.0184214704146228 \tabularnewline
14 & 2.2 & 2.08229597021336 & 0.117704029786645 \tabularnewline
15 & 2.2 & 2.28688005884174 & -0.0868800588417367 \tabularnewline
16 & 2 & 2.28349643730821 & -0.283496437308206 \tabularnewline
17 & 2.3 & 2.07245541520551 & 0.227544584794493 \tabularnewline
18 & 2.6 & 2.38131734240967 & 0.218682657590329 \tabularnewline
19 & 3.2 & 2.68983413393925 & 0.510165866060752 \tabularnewline
20 & 3.2 & 3.30970299951196 & -0.109702999511959 \tabularnewline
21 & 3.1 & 3.30543051815789 & -0.205430518157892 \tabularnewline
22 & 2.8 & 3.19742984304153 & -0.397429843041526 \tabularnewline
23 & 2.3 & 2.88195158263389 & -0.58195158263389 \tabularnewline
24 & 1.9 & 2.35928695817663 & -0.459286958176631 \tabularnewline
25 & 1.9 & 1.94139961714033 & -0.0413996171403257 \tabularnewline
26 & 2 & 1.93978727205328 & 0.0602127279467228 \tabularnewline
27 & 2 & 2.04213231055336 & -0.0421323105533582 \tabularnewline
28 & 1.8 & 2.04049143006655 & -0.240491430066555 \tabularnewline
29 & 1.6 & 1.83112527640309 & -0.231125276403086 \tabularnewline
30 & 1.4 & 1.62212389596428 & -0.222123895964275 \tabularnewline
31 & 0.2 & 1.4134730823309 & -1.2134730823309 \tabularnewline
32 & 0.3 & 0.166213288697305 & 0.133786711302695 \tabularnewline
33 & 0.4 & 0.271423731729908 & 0.128576268270092 \tabularnewline
34 & 0.7 & 0.3764312494022 & 0.3235687505978 \tabularnewline
35 & 1 & 0.689032923557311 & 0.310967076442689 \tabularnewline
36 & 1.1 & 1.00114381425074 & 0.0988561857492636 \tabularnewline
37 & 0.8 & 1.10499385674936 & -0.304993856749364 \tabularnewline
38 & 0.8 & 0.793115598434971 & 0.00688440156502901 \tabularnewline
39 & 1 & 0.793383717606291 & 0.206616282393709 \tabularnewline
40 & 1.1 & 1.0014305733705 & 0.0985694266294994 \tabularnewline
41 & 1 & 1.10526944777894 & -0.105269447778942 \tabularnewline
42 & 0.8 & 1.00116963505924 & -0.20116963505924 \tabularnewline
43 & 1.6 & 0.793334903842967 & 0.806665096157033 \tabularnewline
44 & 1.5 & 1.62475119690369 & -0.124751196903689 \tabularnewline
45 & 1.6 & 1.51989265005411 & 0.0801073499458935 \tabularnewline
46 & 1.6 & 1.62301250238713 & -0.0230125023871348 \tabularnewline
47 & 1.6 & 1.62211625991613 & -0.022116259916128 \tabularnewline
48 & 1.9 & 1.6212549224091 & 0.278745077590902 \tabularnewline
49 & 2 & 1.93211089856147 & 0.0678891014385328 \tabularnewline
50 & 1.9 & 2.03475490028732 & -0.134754900287317 \tabularnewline
51 & 2 & 1.92950675026947 & 0.0704932497305319 \tabularnewline
52 & 2.1 & 2.03225217287779 & 0.0677478271222061 \tabularnewline
53 & 2.3 & 2.13489067254914 & 0.165109327450857 \tabularnewline
54 & 2.3 & 2.34132100285966 & -0.0413210028596596 \tabularnewline
55 & 2.6 & 2.33971171947603 & 0.260288280523973 \tabularnewline
56 & 2.6 & 2.64984887917237 & -0.0498488791723735 \tabularnewline
57 & 2.7 & 2.64790747002465 & 0.052092529975349 \tabularnewline
58 & 2.6 & 2.74993626015798 & -0.149936260157975 \tabularnewline
59 & 2.6 & 2.64409685851287 & -0.0440968585128654 \tabularnewline
60 & 2.4 & 2.64237946695012 & -0.242379466950125 \tabularnewline
61 & 2.5 & 2.43293978200295 & 0.0670602179970525 \tabularnewline
62 & 2.5 & 2.53555150212242 & -0.0355515021224222 \tabularnewline
63 & 2.5 & 2.53416691710102 & -0.0341669171010204 \tabularnewline
64 & 2.4 & 2.53283625598064 & -0.132836255980636 \tabularnewline
65 & 2.1 & 2.42766282927994 & -0.327662829279942 \tabularnewline
66 & 2.1 & 2.11490170757181 & -0.014901707571807 \tabularnewline
67 & 2.3 & 2.11432134725324 & 0.185678652746758 \tabularnewline
68 & 2.3 & 2.32155276831956 & -0.0215527683195584 \tabularnewline
69 & 2.3 & 2.32071337649633 & -0.0207133764963312 \tabularnewline
70 & 2.9 & 2.3199066755378 & 0.580093324462203 \tabularnewline
71 & 2.8 & 2.94249892846989 & -0.142498928469894 \tabularnewline
72 & 2.9 & 2.83694918035388 & 0.0630508196461173 \tabularnewline
73 & 3 & 2.93940475087151 & 0.0605952491284913 \tabularnewline
74 & 3 & 3.04176468700086 & -0.0417646870008608 \tabularnewline
75 & 2.9 & 3.04013812394184 & -0.140138123941842 \tabularnewline
76 & 2.6 & 2.93468031946795 & -0.334680319467952 \tabularnewline
77 & 2.8 & 2.62164589533314 & 0.178354104666862 \tabularnewline
78 & 2.9 & 2.82859205532877 & 0.0714079446712321 \tabularnewline
79 & 3.1 & 2.93137310154899 & 0.168626898451007 \tabularnewline
80 & 2.8 & 3.13794042680565 & -0.337940426805653 \tabularnewline
81 & 2.4 & 2.82477903487712 & -0.424779034877118 \tabularnewline
82 & 1.6 & 2.40823563575234 & -0.808235635752343 \tabularnewline
83 & 1.5 & 1.57675817662354 & -0.0767581766235403 \tabularnewline
84 & 1.7 & 1.4737687608386 & 0.226231239161399 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263060&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]1.8[/C][C]1.6[/C][C]0.2[/C][/ROW]
[ROW][C]4[/C][C]1.8[/C][C]1.90778917873363[/C][C]-0.107789178733626[/C][/ROW]
[ROW][C]5[/C][C]1.8[/C][C]1.90359123284009[/C][C]-0.103591232840091[/C][/ROW]
[ROW][C]6[/C][C]1.7[/C][C]1.89955677970095[/C][C]-0.199556779700951[/C][/ROW]
[ROW][C]7[/C][C]1.5[/C][C]1.79178486257796[/C][C]-0.291784862577963[/C][/ROW]
[ROW][C]8[/C][C]1.1[/C][C]1.58042104034603[/C][C]-0.480421040346032[/C][/ROW]
[ROW][C]9[/C][C]1.3[/C][C]1.16171061359278[/C][C]0.138289386407216[/C][/ROW]
[ROW][C]10[/C][C]1.6[/C][C]1.36709641733123[/C][C]0.23290358266877[/C][/ROW]
[ROW][C]11[/C][C]1.9[/C][C]1.67616705549677[/C][C]0.223832944503225[/C][/ROW]
[ROW][C]12[/C][C]1.9[/C][C]1.98488442955282[/C][C]-0.0848844295528211[/C][/ROW]
[ROW][C]13[/C][C]2[/C][C]1.98157852958538[/C][C]0.0184214704146228[/C][/ROW]
[ROW][C]14[/C][C]2.2[/C][C]2.08229597021336[/C][C]0.117704029786645[/C][/ROW]
[ROW][C]15[/C][C]2.2[/C][C]2.28688005884174[/C][C]-0.0868800588417367[/C][/ROW]
[ROW][C]16[/C][C]2[/C][C]2.28349643730821[/C][C]-0.283496437308206[/C][/ROW]
[ROW][C]17[/C][C]2.3[/C][C]2.07245541520551[/C][C]0.227544584794493[/C][/ROW]
[ROW][C]18[/C][C]2.6[/C][C]2.38131734240967[/C][C]0.218682657590329[/C][/ROW]
[ROW][C]19[/C][C]3.2[/C][C]2.68983413393925[/C][C]0.510165866060752[/C][/ROW]
[ROW][C]20[/C][C]3.2[/C][C]3.30970299951196[/C][C]-0.109702999511959[/C][/ROW]
[ROW][C]21[/C][C]3.1[/C][C]3.30543051815789[/C][C]-0.205430518157892[/C][/ROW]
[ROW][C]22[/C][C]2.8[/C][C]3.19742984304153[/C][C]-0.397429843041526[/C][/ROW]
[ROW][C]23[/C][C]2.3[/C][C]2.88195158263389[/C][C]-0.58195158263389[/C][/ROW]
[ROW][C]24[/C][C]1.9[/C][C]2.35928695817663[/C][C]-0.459286958176631[/C][/ROW]
[ROW][C]25[/C][C]1.9[/C][C]1.94139961714033[/C][C]-0.0413996171403257[/C][/ROW]
[ROW][C]26[/C][C]2[/C][C]1.93978727205328[/C][C]0.0602127279467228[/C][/ROW]
[ROW][C]27[/C][C]2[/C][C]2.04213231055336[/C][C]-0.0421323105533582[/C][/ROW]
[ROW][C]28[/C][C]1.8[/C][C]2.04049143006655[/C][C]-0.240491430066555[/C][/ROW]
[ROW][C]29[/C][C]1.6[/C][C]1.83112527640309[/C][C]-0.231125276403086[/C][/ROW]
[ROW][C]30[/C][C]1.4[/C][C]1.62212389596428[/C][C]-0.222123895964275[/C][/ROW]
[ROW][C]31[/C][C]0.2[/C][C]1.4134730823309[/C][C]-1.2134730823309[/C][/ROW]
[ROW][C]32[/C][C]0.3[/C][C]0.166213288697305[/C][C]0.133786711302695[/C][/ROW]
[ROW][C]33[/C][C]0.4[/C][C]0.271423731729908[/C][C]0.128576268270092[/C][/ROW]
[ROW][C]34[/C][C]0.7[/C][C]0.3764312494022[/C][C]0.3235687505978[/C][/ROW]
[ROW][C]35[/C][C]1[/C][C]0.689032923557311[/C][C]0.310967076442689[/C][/ROW]
[ROW][C]36[/C][C]1.1[/C][C]1.00114381425074[/C][C]0.0988561857492636[/C][/ROW]
[ROW][C]37[/C][C]0.8[/C][C]1.10499385674936[/C][C]-0.304993856749364[/C][/ROW]
[ROW][C]38[/C][C]0.8[/C][C]0.793115598434971[/C][C]0.00688440156502901[/C][/ROW]
[ROW][C]39[/C][C]1[/C][C]0.793383717606291[/C][C]0.206616282393709[/C][/ROW]
[ROW][C]40[/C][C]1.1[/C][C]1.0014305733705[/C][C]0.0985694266294994[/C][/ROW]
[ROW][C]41[/C][C]1[/C][C]1.10526944777894[/C][C]-0.105269447778942[/C][/ROW]
[ROW][C]42[/C][C]0.8[/C][C]1.00116963505924[/C][C]-0.20116963505924[/C][/ROW]
[ROW][C]43[/C][C]1.6[/C][C]0.793334903842967[/C][C]0.806665096157033[/C][/ROW]
[ROW][C]44[/C][C]1.5[/C][C]1.62475119690369[/C][C]-0.124751196903689[/C][/ROW]
[ROW][C]45[/C][C]1.6[/C][C]1.51989265005411[/C][C]0.0801073499458935[/C][/ROW]
[ROW][C]46[/C][C]1.6[/C][C]1.62301250238713[/C][C]-0.0230125023871348[/C][/ROW]
[ROW][C]47[/C][C]1.6[/C][C]1.62211625991613[/C][C]-0.022116259916128[/C][/ROW]
[ROW][C]48[/C][C]1.9[/C][C]1.6212549224091[/C][C]0.278745077590902[/C][/ROW]
[ROW][C]49[/C][C]2[/C][C]1.93211089856147[/C][C]0.0678891014385328[/C][/ROW]
[ROW][C]50[/C][C]1.9[/C][C]2.03475490028732[/C][C]-0.134754900287317[/C][/ROW]
[ROW][C]51[/C][C]2[/C][C]1.92950675026947[/C][C]0.0704932497305319[/C][/ROW]
[ROW][C]52[/C][C]2.1[/C][C]2.03225217287779[/C][C]0.0677478271222061[/C][/ROW]
[ROW][C]53[/C][C]2.3[/C][C]2.13489067254914[/C][C]0.165109327450857[/C][/ROW]
[ROW][C]54[/C][C]2.3[/C][C]2.34132100285966[/C][C]-0.0413210028596596[/C][/ROW]
[ROW][C]55[/C][C]2.6[/C][C]2.33971171947603[/C][C]0.260288280523973[/C][/ROW]
[ROW][C]56[/C][C]2.6[/C][C]2.64984887917237[/C][C]-0.0498488791723735[/C][/ROW]
[ROW][C]57[/C][C]2.7[/C][C]2.64790747002465[/C][C]0.052092529975349[/C][/ROW]
[ROW][C]58[/C][C]2.6[/C][C]2.74993626015798[/C][C]-0.149936260157975[/C][/ROW]
[ROW][C]59[/C][C]2.6[/C][C]2.64409685851287[/C][C]-0.0440968585128654[/C][/ROW]
[ROW][C]60[/C][C]2.4[/C][C]2.64237946695012[/C][C]-0.242379466950125[/C][/ROW]
[ROW][C]61[/C][C]2.5[/C][C]2.43293978200295[/C][C]0.0670602179970525[/C][/ROW]
[ROW][C]62[/C][C]2.5[/C][C]2.53555150212242[/C][C]-0.0355515021224222[/C][/ROW]
[ROW][C]63[/C][C]2.5[/C][C]2.53416691710102[/C][C]-0.0341669171010204[/C][/ROW]
[ROW][C]64[/C][C]2.4[/C][C]2.53283625598064[/C][C]-0.132836255980636[/C][/ROW]
[ROW][C]65[/C][C]2.1[/C][C]2.42766282927994[/C][C]-0.327662829279942[/C][/ROW]
[ROW][C]66[/C][C]2.1[/C][C]2.11490170757181[/C][C]-0.014901707571807[/C][/ROW]
[ROW][C]67[/C][C]2.3[/C][C]2.11432134725324[/C][C]0.185678652746758[/C][/ROW]
[ROW][C]68[/C][C]2.3[/C][C]2.32155276831956[/C][C]-0.0215527683195584[/C][/ROW]
[ROW][C]69[/C][C]2.3[/C][C]2.32071337649633[/C][C]-0.0207133764963312[/C][/ROW]
[ROW][C]70[/C][C]2.9[/C][C]2.3199066755378[/C][C]0.580093324462203[/C][/ROW]
[ROW][C]71[/C][C]2.8[/C][C]2.94249892846989[/C][C]-0.142498928469894[/C][/ROW]
[ROW][C]72[/C][C]2.9[/C][C]2.83694918035388[/C][C]0.0630508196461173[/C][/ROW]
[ROW][C]73[/C][C]3[/C][C]2.93940475087151[/C][C]0.0605952491284913[/C][/ROW]
[ROW][C]74[/C][C]3[/C][C]3.04176468700086[/C][C]-0.0417646870008608[/C][/ROW]
[ROW][C]75[/C][C]2.9[/C][C]3.04013812394184[/C][C]-0.140138123941842[/C][/ROW]
[ROW][C]76[/C][C]2.6[/C][C]2.93468031946795[/C][C]-0.334680319467952[/C][/ROW]
[ROW][C]77[/C][C]2.8[/C][C]2.62164589533314[/C][C]0.178354104666862[/C][/ROW]
[ROW][C]78[/C][C]2.9[/C][C]2.82859205532877[/C][C]0.0714079446712321[/C][/ROW]
[ROW][C]79[/C][C]3.1[/C][C]2.93137310154899[/C][C]0.168626898451007[/C][/ROW]
[ROW][C]80[/C][C]2.8[/C][C]3.13794042680565[/C][C]-0.337940426805653[/C][/ROW]
[ROW][C]81[/C][C]2.4[/C][C]2.82477903487712[/C][C]-0.424779034877118[/C][/ROW]
[ROW][C]82[/C][C]1.6[/C][C]2.40823563575234[/C][C]-0.808235635752343[/C][/ROW]
[ROW][C]83[/C][C]1.5[/C][C]1.57675817662354[/C][C]-0.0767581766235403[/C][/ROW]
[ROW][C]84[/C][C]1.7[/C][C]1.4737687608386[/C][C]0.226231239161399[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263060&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263060&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
31.81.60.2
41.81.90778917873363-0.107789178733626
51.81.90359123284009-0.103591232840091
61.71.89955677970095-0.199556779700951
71.51.79178486257796-0.291784862577963
81.11.58042104034603-0.480421040346032
91.31.161710613592780.138289386407216
101.61.367096417331230.23290358266877
111.91.676167055496770.223832944503225
121.91.98488442955282-0.0848844295528211
1321.981578529585380.0184214704146228
142.22.082295970213360.117704029786645
152.22.28688005884174-0.0868800588417367
1622.28349643730821-0.283496437308206
172.32.072455415205510.227544584794493
182.62.381317342409670.218682657590329
193.22.689834133939250.510165866060752
203.23.30970299951196-0.109702999511959
213.13.30543051815789-0.205430518157892
222.83.19742984304153-0.397429843041526
232.32.88195158263389-0.58195158263389
241.92.35928695817663-0.459286958176631
251.91.94139961714033-0.0413996171403257
2621.939787272053280.0602127279467228
2722.04213231055336-0.0421323105533582
281.82.04049143006655-0.240491430066555
291.61.83112527640309-0.231125276403086
301.41.62212389596428-0.222123895964275
310.21.4134730823309-1.2134730823309
320.30.1662132886973050.133786711302695
330.40.2714237317299080.128576268270092
340.70.37643124940220.3235687505978
3510.6890329235573110.310967076442689
361.11.001143814250740.0988561857492636
370.81.10499385674936-0.304993856749364
380.80.7931155984349710.00688440156502901
3910.7933837176062910.206616282393709
401.11.00143057337050.0985694266294994
4111.10526944777894-0.105269447778942
420.81.00116963505924-0.20116963505924
431.60.7933349038429670.806665096157033
441.51.62475119690369-0.124751196903689
451.61.519892650054110.0801073499458935
461.61.62301250238713-0.0230125023871348
471.61.62211625991613-0.022116259916128
481.91.62125492240910.278745077590902
4921.932110898561470.0678891014385328
501.92.03475490028732-0.134754900287317
5121.929506750269470.0704932497305319
522.12.032252172877790.0677478271222061
532.32.134890672549140.165109327450857
542.32.34132100285966-0.0413210028596596
552.62.339711719476030.260288280523973
562.62.64984887917237-0.0498488791723735
572.72.647907470024650.052092529975349
582.62.74993626015798-0.149936260157975
592.62.64409685851287-0.0440968585128654
602.42.64237946695012-0.242379466950125
612.52.432939782002950.0670602179970525
622.52.53555150212242-0.0355515021224222
632.52.53416691710102-0.0341669171010204
642.42.53283625598064-0.132836255980636
652.12.42766282927994-0.327662829279942
662.12.11490170757181-0.014901707571807
672.32.114321347253240.185678652746758
682.32.32155276831956-0.0215527683195584
692.32.32071337649633-0.0207133764963312
702.92.31990667553780.580093324462203
712.82.94249892846989-0.142498928469894
722.92.836949180353880.0630508196461173
7332.939404750871510.0605952491284913
7433.04176468700086-0.0417646870008608
752.93.04013812394184-0.140138123941842
762.62.93468031946795-0.334680319467952
772.82.621645895333140.178354104666862
782.92.828592055328770.0714079446712321
793.12.931373101548990.168626898451007
802.83.13794042680565-0.337940426805653
812.42.82477903487712-0.424779034877118
821.62.40823563575234-0.808235635752343
831.51.57675817662354-0.0767581766235403
841.71.47376876083860.226231239161399







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
851.682579538623391.129542315045782.235616762201
861.665159077246780.8676708541348622.4626473003587
871.647738615870170.6520781805439412.6433990511964
881.630318154493560.4586378668158332.80199844217128
891.612897693116950.2782066185110952.9475887677228
901.595477231740340.1061941078083513.08476035567232
911.57805677036373-0.06006849614537633.21618203687283
921.56063630898711-0.2222822471247253.34355486509895
931.5432158476105-0.3816022234134943.4680339186345
941.52579538623389-0.5388499323784973.59044070484628
951.50837492485728-0.6946306242880583.71138047400262
961.49095446348067-0.8494027521354743.83131167909682

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.68257953862339 & 1.12954231504578 & 2.235616762201 \tabularnewline
86 & 1.66515907724678 & 0.867670854134862 & 2.4626473003587 \tabularnewline
87 & 1.64773861587017 & 0.652078180543941 & 2.6433990511964 \tabularnewline
88 & 1.63031815449356 & 0.458637866815833 & 2.80199844217128 \tabularnewline
89 & 1.61289769311695 & 0.278206618511095 & 2.9475887677228 \tabularnewline
90 & 1.59547723174034 & 0.106194107808351 & 3.08476035567232 \tabularnewline
91 & 1.57805677036373 & -0.0600684961453763 & 3.21618203687283 \tabularnewline
92 & 1.56063630898711 & -0.222282247124725 & 3.34355486509895 \tabularnewline
93 & 1.5432158476105 & -0.381602223413494 & 3.4680339186345 \tabularnewline
94 & 1.52579538623389 & -0.538849932378497 & 3.59044070484628 \tabularnewline
95 & 1.50837492485728 & -0.694630624288058 & 3.71138047400262 \tabularnewline
96 & 1.49095446348067 & -0.849402752135474 & 3.83131167909682 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263060&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]1.68257953862339[/C][C]1.12954231504578[/C][C]2.235616762201[/C][/ROW]
[ROW][C]86[/C][C]1.66515907724678[/C][C]0.867670854134862[/C][C]2.4626473003587[/C][/ROW]
[ROW][C]87[/C][C]1.64773861587017[/C][C]0.652078180543941[/C][C]2.6433990511964[/C][/ROW]
[ROW][C]88[/C][C]1.63031815449356[/C][C]0.458637866815833[/C][C]2.80199844217128[/C][/ROW]
[ROW][C]89[/C][C]1.61289769311695[/C][C]0.278206618511095[/C][C]2.9475887677228[/C][/ROW]
[ROW][C]90[/C][C]1.59547723174034[/C][C]0.106194107808351[/C][C]3.08476035567232[/C][/ROW]
[ROW][C]91[/C][C]1.57805677036373[/C][C]-0.0600684961453763[/C][C]3.21618203687283[/C][/ROW]
[ROW][C]92[/C][C]1.56063630898711[/C][C]-0.222282247124725[/C][C]3.34355486509895[/C][/ROW]
[ROW][C]93[/C][C]1.5432158476105[/C][C]-0.381602223413494[/C][C]3.4680339186345[/C][/ROW]
[ROW][C]94[/C][C]1.52579538623389[/C][C]-0.538849932378497[/C][C]3.59044070484628[/C][/ROW]
[ROW][C]95[/C][C]1.50837492485728[/C][C]-0.694630624288058[/C][C]3.71138047400262[/C][/ROW]
[ROW][C]96[/C][C]1.49095446348067[/C][C]-0.849402752135474[/C][C]3.83131167909682[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263060&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263060&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
851.682579538623391.129542315045782.235616762201
861.665159077246780.8676708541348622.4626473003587
871.647738615870170.6520781805439412.6433990511964
881.630318154493560.4586378668158332.80199844217128
891.612897693116950.2782066185110952.9475887677228
901.595477231740340.1061941078083513.08476035567232
911.57805677036373-0.06006849614537633.21618203687283
921.56063630898711-0.2222822471247253.34355486509895
931.5432158476105-0.3816022234134943.4680339186345
941.52579538623389-0.5388499323784973.59044070484628
951.50837492485728-0.6946306242880583.71138047400262
961.49095446348067-0.8494027521354743.83131167909682



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')