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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 Dec 2014 08:42:20 +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/15/t1418632963kn0z6z4vbe5ewxg.htm/, Retrieved Thu, 16 May 2024 21:12:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267958, Retrieved Thu, 16 May 2024 21:12:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-15 08:42:20] [6baf0af87d9d8aa2cb91b54f39a0a5b0] [Current]
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Dataseries X:
50
62
54
71
54
65
73
52
84
42
66
65
78
73
75
72
66
70
61
81
71
69
71
72
68
70
68
61
67
76
70
60
72
69
71
62
70
64
58
76
52
59
68
76
65
67
59
69
76
63
75
63
60
73
63
70
75
66
63
63
64
70
75
61
60
62
73
61
66
64
59
64
60
56
78
53
67
59
66
68
71
66
73
72
71
59
64
66
78
68
73
62
65
68
65
60
71
65
68
64
74
69
76
68
72
67
63
59
73
66
62
69
66




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267958&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267958&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267958&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.11960952754393
beta0.0574918797225096
gamma0.516294162328426

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.11960952754393 \tabularnewline
beta & 0.0574918797225096 \tabularnewline
gamma & 0.516294162328426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267958&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]0.11960952754393[/C][/ROW]
[ROW][C]beta[/C][C]0.0574918797225096[/C][/ROW]
[ROW][C]gamma[/C][C]0.516294162328426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267958&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267958&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
alpha0.11960952754393
beta0.0574918797225096
gamma0.516294162328426







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137873.112490491124.88750950887999
147369.01171067527033.98828932472972
157571.49766976546743.50233023453258
167269.24091591632842.75908408367158
176663.2915373625922.70846263740803
187067.77496856295732.22503143704273
196181.6633997237933-20.6633997237933
208155.538984763032125.4610152369679
217193.8675703291087-22.8675703291087
226945.430020992009723.5699790079903
237176.2268034462631-5.22680344626311
247274.6360527156691-2.63605271566905
256893.4370438408999-25.4370438408999
267084.3067380965298-14.3067380965298
276884.5409727389871-16.5409727389871
286178.95520041799-17.95520041799
296769.6691851492113-2.66918514921133
307673.21879371279922.78120628720085
317076.3230903033597-6.32309030335971
326071.7542862133225-11.7542862133225
337282.8143390799528-10.8143390799528
346955.70599472538713.294005274613
357171.2156896957026-0.215689695702636
366270.8992187550796-8.89921875507959
377077.2498364079392-7.24983640793923
386474.7796598160452-10.7796598160452
395873.7546366242609-15.7546366242609
407667.14964670131038.85035329868965
415267.7335714164456-15.7335714164456
425971.5915405555095-12.5915405555095
436868.312813738321-0.312813738321012
447661.886278711524914.1137212884751
456575.8266002264093-10.8266002264093
466759.68578660779327.31421339220682
475967.697224725398-8.69722472539802
486962.29750212843196.70249787156808
497670.63091137031555.36908862968448
506367.8846564224294-4.88465642242937
517565.0174574964269.98254250357395
526372.7819429553048-9.7819429553048
536059.77238460296080.227615397039223
547366.98451105153576.01548894846431
556371.8475031883197-8.84750318831973
567070.8660669719956-0.866066971995636
577571.56700992428523.43299007571476
586665.15555455988690.844445440113105
596365.0536113311195-2.05361133111946
606367.5459879444431-4.54598794444311
616473.9620550992669-9.96205509926693
627064.68378150762995.31621849237014
637569.67075596840785.32924403159215
646167.7479870795136-6.74798707951361
656059.60975532855840.390244671441558
666269.3279258104799-7.32792581047988
677365.69654298384447.30345701615565
686170.2062078678939-9.20620786789385
696671.6880339638018-5.68803396380184
706463.12508738503060.874912614969432
715961.6079029960094-2.60790299600944
726462.65830339611791.34169660388209
736066.965958791438-6.96595879143796
745664.8869789428769-8.88697894287687
757867.682392619270810.3176073807292
765361.0837470635949-8.0837470635949
776756.098928207955610.9010717920444
785963.1647950010214-4.16479500102137
796666.2755306355002-0.275530635500246
806862.37143686606995.62856313393013
817167.03295001871483.9670499812852
826662.68758986962533.31241013037469
837359.930511777663713.0694882223363
847264.86953340186817.13046659813192
857166.2540982176514.74590178234901
865964.7638500005175-5.76385000051749
876477.8208536702204-13.8208536702204
886659.47473389955726.52526610044276
897865.309483473706512.6905165262935
906865.89532673584932.1046732641507
917372.31955254216230.680447457837701
926271.3931342255163-9.39313422551632
936573.9418010255385-8.94180102553848
946867.60270120820820.39729879179184
956568.9351469402133-3.93514694021327
966069.0810144206661-9.08101442066608
977167.29554688086053.70445311913946
986560.86957395508994.13042604491012
996871.2209660403973-3.2209660403973
1006463.2404803834080.75951961659203
1017471.01240996617722.9875900338228
1026965.60100308653883.39899691346122
1037671.323804593194.67619540680995
1046866.2081470602371.79185293976302
1057270.2494187976561.75058120234399
1066769.4626105583446-2.46261055834455
1076368.4909881709429-5.49098817094294
1085966.0366674579093-7.03666745790929
1097370.43817615986432.56182384013567
1106663.95091373765682.04908626234317
1116270.8117801872224-8.81178018722238
1126963.91287295908795.08712704091214
1136673.327231829808-7.32723182980796

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 78 & 73.11249049112 & 4.88750950887999 \tabularnewline
14 & 73 & 69.0117106752703 & 3.98828932472972 \tabularnewline
15 & 75 & 71.4976697654674 & 3.50233023453258 \tabularnewline
16 & 72 & 69.2409159163284 & 2.75908408367158 \tabularnewline
17 & 66 & 63.291537362592 & 2.70846263740803 \tabularnewline
18 & 70 & 67.7749685629573 & 2.22503143704273 \tabularnewline
19 & 61 & 81.6633997237933 & -20.6633997237933 \tabularnewline
20 & 81 & 55.5389847630321 & 25.4610152369679 \tabularnewline
21 & 71 & 93.8675703291087 & -22.8675703291087 \tabularnewline
22 & 69 & 45.4300209920097 & 23.5699790079903 \tabularnewline
23 & 71 & 76.2268034462631 & -5.22680344626311 \tabularnewline
24 & 72 & 74.6360527156691 & -2.63605271566905 \tabularnewline
25 & 68 & 93.4370438408999 & -25.4370438408999 \tabularnewline
26 & 70 & 84.3067380965298 & -14.3067380965298 \tabularnewline
27 & 68 & 84.5409727389871 & -16.5409727389871 \tabularnewline
28 & 61 & 78.95520041799 & -17.95520041799 \tabularnewline
29 & 67 & 69.6691851492113 & -2.66918514921133 \tabularnewline
30 & 76 & 73.2187937127992 & 2.78120628720085 \tabularnewline
31 & 70 & 76.3230903033597 & -6.32309030335971 \tabularnewline
32 & 60 & 71.7542862133225 & -11.7542862133225 \tabularnewline
33 & 72 & 82.8143390799528 & -10.8143390799528 \tabularnewline
34 & 69 & 55.705994725387 & 13.294005274613 \tabularnewline
35 & 71 & 71.2156896957026 & -0.215689695702636 \tabularnewline
36 & 62 & 70.8992187550796 & -8.89921875507959 \tabularnewline
37 & 70 & 77.2498364079392 & -7.24983640793923 \tabularnewline
38 & 64 & 74.7796598160452 & -10.7796598160452 \tabularnewline
39 & 58 & 73.7546366242609 & -15.7546366242609 \tabularnewline
40 & 76 & 67.1496467013103 & 8.85035329868965 \tabularnewline
41 & 52 & 67.7335714164456 & -15.7335714164456 \tabularnewline
42 & 59 & 71.5915405555095 & -12.5915405555095 \tabularnewline
43 & 68 & 68.312813738321 & -0.312813738321012 \tabularnewline
44 & 76 & 61.8862787115249 & 14.1137212884751 \tabularnewline
45 & 65 & 75.8266002264093 & -10.8266002264093 \tabularnewline
46 & 67 & 59.6857866077932 & 7.31421339220682 \tabularnewline
47 & 59 & 67.697224725398 & -8.69722472539802 \tabularnewline
48 & 69 & 62.2975021284319 & 6.70249787156808 \tabularnewline
49 & 76 & 70.6309113703155 & 5.36908862968448 \tabularnewline
50 & 63 & 67.8846564224294 & -4.88465642242937 \tabularnewline
51 & 75 & 65.017457496426 & 9.98254250357395 \tabularnewline
52 & 63 & 72.7819429553048 & -9.7819429553048 \tabularnewline
53 & 60 & 59.7723846029608 & 0.227615397039223 \tabularnewline
54 & 73 & 66.9845110515357 & 6.01548894846431 \tabularnewline
55 & 63 & 71.8475031883197 & -8.84750318831973 \tabularnewline
56 & 70 & 70.8660669719956 & -0.866066971995636 \tabularnewline
57 & 75 & 71.5670099242852 & 3.43299007571476 \tabularnewline
58 & 66 & 65.1555545598869 & 0.844445440113105 \tabularnewline
59 & 63 & 65.0536113311195 & -2.05361133111946 \tabularnewline
60 & 63 & 67.5459879444431 & -4.54598794444311 \tabularnewline
61 & 64 & 73.9620550992669 & -9.96205509926693 \tabularnewline
62 & 70 & 64.6837815076299 & 5.31621849237014 \tabularnewline
63 & 75 & 69.6707559684078 & 5.32924403159215 \tabularnewline
64 & 61 & 67.7479870795136 & -6.74798707951361 \tabularnewline
65 & 60 & 59.6097553285584 & 0.390244671441558 \tabularnewline
66 & 62 & 69.3279258104799 & -7.32792581047988 \tabularnewline
67 & 73 & 65.6965429838444 & 7.30345701615565 \tabularnewline
68 & 61 & 70.2062078678939 & -9.20620786789385 \tabularnewline
69 & 66 & 71.6880339638018 & -5.68803396380184 \tabularnewline
70 & 64 & 63.1250873850306 & 0.874912614969432 \tabularnewline
71 & 59 & 61.6079029960094 & -2.60790299600944 \tabularnewline
72 & 64 & 62.6583033961179 & 1.34169660388209 \tabularnewline
73 & 60 & 66.965958791438 & -6.96595879143796 \tabularnewline
74 & 56 & 64.8869789428769 & -8.88697894287687 \tabularnewline
75 & 78 & 67.6823926192708 & 10.3176073807292 \tabularnewline
76 & 53 & 61.0837470635949 & -8.0837470635949 \tabularnewline
77 & 67 & 56.0989282079556 & 10.9010717920444 \tabularnewline
78 & 59 & 63.1647950010214 & -4.16479500102137 \tabularnewline
79 & 66 & 66.2755306355002 & -0.275530635500246 \tabularnewline
80 & 68 & 62.3714368660699 & 5.62856313393013 \tabularnewline
81 & 71 & 67.0329500187148 & 3.9670499812852 \tabularnewline
82 & 66 & 62.6875898696253 & 3.31241013037469 \tabularnewline
83 & 73 & 59.9305117776637 & 13.0694882223363 \tabularnewline
84 & 72 & 64.8695334018681 & 7.13046659813192 \tabularnewline
85 & 71 & 66.254098217651 & 4.74590178234901 \tabularnewline
86 & 59 & 64.7638500005175 & -5.76385000051749 \tabularnewline
87 & 64 & 77.8208536702204 & -13.8208536702204 \tabularnewline
88 & 66 & 59.4747338995572 & 6.52526610044276 \tabularnewline
89 & 78 & 65.3094834737065 & 12.6905165262935 \tabularnewline
90 & 68 & 65.8953267358493 & 2.1046732641507 \tabularnewline
91 & 73 & 72.3195525421623 & 0.680447457837701 \tabularnewline
92 & 62 & 71.3931342255163 & -9.39313422551632 \tabularnewline
93 & 65 & 73.9418010255385 & -8.94180102553848 \tabularnewline
94 & 68 & 67.6027012082082 & 0.39729879179184 \tabularnewline
95 & 65 & 68.9351469402133 & -3.93514694021327 \tabularnewline
96 & 60 & 69.0810144206661 & -9.08101442066608 \tabularnewline
97 & 71 & 67.2955468808605 & 3.70445311913946 \tabularnewline
98 & 65 & 60.8695739550899 & 4.13042604491012 \tabularnewline
99 & 68 & 71.2209660403973 & -3.2209660403973 \tabularnewline
100 & 64 & 63.240480383408 & 0.75951961659203 \tabularnewline
101 & 74 & 71.0124099661772 & 2.9875900338228 \tabularnewline
102 & 69 & 65.6010030865388 & 3.39899691346122 \tabularnewline
103 & 76 & 71.32380459319 & 4.67619540680995 \tabularnewline
104 & 68 & 66.208147060237 & 1.79185293976302 \tabularnewline
105 & 72 & 70.249418797656 & 1.75058120234399 \tabularnewline
106 & 67 & 69.4626105583446 & -2.46261055834455 \tabularnewline
107 & 63 & 68.4909881709429 & -5.49098817094294 \tabularnewline
108 & 59 & 66.0366674579093 & -7.03666745790929 \tabularnewline
109 & 73 & 70.4381761598643 & 2.56182384013567 \tabularnewline
110 & 66 & 63.9509137376568 & 2.04908626234317 \tabularnewline
111 & 62 & 70.8117801872224 & -8.81178018722238 \tabularnewline
112 & 69 & 63.9128729590879 & 5.08712704091214 \tabularnewline
113 & 66 & 73.327231829808 & -7.32723182980796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267958&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]13[/C][C]78[/C][C]73.11249049112[/C][C]4.88750950887999[/C][/ROW]
[ROW][C]14[/C][C]73[/C][C]69.0117106752703[/C][C]3.98828932472972[/C][/ROW]
[ROW][C]15[/C][C]75[/C][C]71.4976697654674[/C][C]3.50233023453258[/C][/ROW]
[ROW][C]16[/C][C]72[/C][C]69.2409159163284[/C][C]2.75908408367158[/C][/ROW]
[ROW][C]17[/C][C]66[/C][C]63.291537362592[/C][C]2.70846263740803[/C][/ROW]
[ROW][C]18[/C][C]70[/C][C]67.7749685629573[/C][C]2.22503143704273[/C][/ROW]
[ROW][C]19[/C][C]61[/C][C]81.6633997237933[/C][C]-20.6633997237933[/C][/ROW]
[ROW][C]20[/C][C]81[/C][C]55.5389847630321[/C][C]25.4610152369679[/C][/ROW]
[ROW][C]21[/C][C]71[/C][C]93.8675703291087[/C][C]-22.8675703291087[/C][/ROW]
[ROW][C]22[/C][C]69[/C][C]45.4300209920097[/C][C]23.5699790079903[/C][/ROW]
[ROW][C]23[/C][C]71[/C][C]76.2268034462631[/C][C]-5.22680344626311[/C][/ROW]
[ROW][C]24[/C][C]72[/C][C]74.6360527156691[/C][C]-2.63605271566905[/C][/ROW]
[ROW][C]25[/C][C]68[/C][C]93.4370438408999[/C][C]-25.4370438408999[/C][/ROW]
[ROW][C]26[/C][C]70[/C][C]84.3067380965298[/C][C]-14.3067380965298[/C][/ROW]
[ROW][C]27[/C][C]68[/C][C]84.5409727389871[/C][C]-16.5409727389871[/C][/ROW]
[ROW][C]28[/C][C]61[/C][C]78.95520041799[/C][C]-17.95520041799[/C][/ROW]
[ROW][C]29[/C][C]67[/C][C]69.6691851492113[/C][C]-2.66918514921133[/C][/ROW]
[ROW][C]30[/C][C]76[/C][C]73.2187937127992[/C][C]2.78120628720085[/C][/ROW]
[ROW][C]31[/C][C]70[/C][C]76.3230903033597[/C][C]-6.32309030335971[/C][/ROW]
[ROW][C]32[/C][C]60[/C][C]71.7542862133225[/C][C]-11.7542862133225[/C][/ROW]
[ROW][C]33[/C][C]72[/C][C]82.8143390799528[/C][C]-10.8143390799528[/C][/ROW]
[ROW][C]34[/C][C]69[/C][C]55.705994725387[/C][C]13.294005274613[/C][/ROW]
[ROW][C]35[/C][C]71[/C][C]71.2156896957026[/C][C]-0.215689695702636[/C][/ROW]
[ROW][C]36[/C][C]62[/C][C]70.8992187550796[/C][C]-8.89921875507959[/C][/ROW]
[ROW][C]37[/C][C]70[/C][C]77.2498364079392[/C][C]-7.24983640793923[/C][/ROW]
[ROW][C]38[/C][C]64[/C][C]74.7796598160452[/C][C]-10.7796598160452[/C][/ROW]
[ROW][C]39[/C][C]58[/C][C]73.7546366242609[/C][C]-15.7546366242609[/C][/ROW]
[ROW][C]40[/C][C]76[/C][C]67.1496467013103[/C][C]8.85035329868965[/C][/ROW]
[ROW][C]41[/C][C]52[/C][C]67.7335714164456[/C][C]-15.7335714164456[/C][/ROW]
[ROW][C]42[/C][C]59[/C][C]71.5915405555095[/C][C]-12.5915405555095[/C][/ROW]
[ROW][C]43[/C][C]68[/C][C]68.312813738321[/C][C]-0.312813738321012[/C][/ROW]
[ROW][C]44[/C][C]76[/C][C]61.8862787115249[/C][C]14.1137212884751[/C][/ROW]
[ROW][C]45[/C][C]65[/C][C]75.8266002264093[/C][C]-10.8266002264093[/C][/ROW]
[ROW][C]46[/C][C]67[/C][C]59.6857866077932[/C][C]7.31421339220682[/C][/ROW]
[ROW][C]47[/C][C]59[/C][C]67.697224725398[/C][C]-8.69722472539802[/C][/ROW]
[ROW][C]48[/C][C]69[/C][C]62.2975021284319[/C][C]6.70249787156808[/C][/ROW]
[ROW][C]49[/C][C]76[/C][C]70.6309113703155[/C][C]5.36908862968448[/C][/ROW]
[ROW][C]50[/C][C]63[/C][C]67.8846564224294[/C][C]-4.88465642242937[/C][/ROW]
[ROW][C]51[/C][C]75[/C][C]65.017457496426[/C][C]9.98254250357395[/C][/ROW]
[ROW][C]52[/C][C]63[/C][C]72.7819429553048[/C][C]-9.7819429553048[/C][/ROW]
[ROW][C]53[/C][C]60[/C][C]59.7723846029608[/C][C]0.227615397039223[/C][/ROW]
[ROW][C]54[/C][C]73[/C][C]66.9845110515357[/C][C]6.01548894846431[/C][/ROW]
[ROW][C]55[/C][C]63[/C][C]71.8475031883197[/C][C]-8.84750318831973[/C][/ROW]
[ROW][C]56[/C][C]70[/C][C]70.8660669719956[/C][C]-0.866066971995636[/C][/ROW]
[ROW][C]57[/C][C]75[/C][C]71.5670099242852[/C][C]3.43299007571476[/C][/ROW]
[ROW][C]58[/C][C]66[/C][C]65.1555545598869[/C][C]0.844445440113105[/C][/ROW]
[ROW][C]59[/C][C]63[/C][C]65.0536113311195[/C][C]-2.05361133111946[/C][/ROW]
[ROW][C]60[/C][C]63[/C][C]67.5459879444431[/C][C]-4.54598794444311[/C][/ROW]
[ROW][C]61[/C][C]64[/C][C]73.9620550992669[/C][C]-9.96205509926693[/C][/ROW]
[ROW][C]62[/C][C]70[/C][C]64.6837815076299[/C][C]5.31621849237014[/C][/ROW]
[ROW][C]63[/C][C]75[/C][C]69.6707559684078[/C][C]5.32924403159215[/C][/ROW]
[ROW][C]64[/C][C]61[/C][C]67.7479870795136[/C][C]-6.74798707951361[/C][/ROW]
[ROW][C]65[/C][C]60[/C][C]59.6097553285584[/C][C]0.390244671441558[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]69.3279258104799[/C][C]-7.32792581047988[/C][/ROW]
[ROW][C]67[/C][C]73[/C][C]65.6965429838444[/C][C]7.30345701615565[/C][/ROW]
[ROW][C]68[/C][C]61[/C][C]70.2062078678939[/C][C]-9.20620786789385[/C][/ROW]
[ROW][C]69[/C][C]66[/C][C]71.6880339638018[/C][C]-5.68803396380184[/C][/ROW]
[ROW][C]70[/C][C]64[/C][C]63.1250873850306[/C][C]0.874912614969432[/C][/ROW]
[ROW][C]71[/C][C]59[/C][C]61.6079029960094[/C][C]-2.60790299600944[/C][/ROW]
[ROW][C]72[/C][C]64[/C][C]62.6583033961179[/C][C]1.34169660388209[/C][/ROW]
[ROW][C]73[/C][C]60[/C][C]66.965958791438[/C][C]-6.96595879143796[/C][/ROW]
[ROW][C]74[/C][C]56[/C][C]64.8869789428769[/C][C]-8.88697894287687[/C][/ROW]
[ROW][C]75[/C][C]78[/C][C]67.6823926192708[/C][C]10.3176073807292[/C][/ROW]
[ROW][C]76[/C][C]53[/C][C]61.0837470635949[/C][C]-8.0837470635949[/C][/ROW]
[ROW][C]77[/C][C]67[/C][C]56.0989282079556[/C][C]10.9010717920444[/C][/ROW]
[ROW][C]78[/C][C]59[/C][C]63.1647950010214[/C][C]-4.16479500102137[/C][/ROW]
[ROW][C]79[/C][C]66[/C][C]66.2755306355002[/C][C]-0.275530635500246[/C][/ROW]
[ROW][C]80[/C][C]68[/C][C]62.3714368660699[/C][C]5.62856313393013[/C][/ROW]
[ROW][C]81[/C][C]71[/C][C]67.0329500187148[/C][C]3.9670499812852[/C][/ROW]
[ROW][C]82[/C][C]66[/C][C]62.6875898696253[/C][C]3.31241013037469[/C][/ROW]
[ROW][C]83[/C][C]73[/C][C]59.9305117776637[/C][C]13.0694882223363[/C][/ROW]
[ROW][C]84[/C][C]72[/C][C]64.8695334018681[/C][C]7.13046659813192[/C][/ROW]
[ROW][C]85[/C][C]71[/C][C]66.254098217651[/C][C]4.74590178234901[/C][/ROW]
[ROW][C]86[/C][C]59[/C][C]64.7638500005175[/C][C]-5.76385000051749[/C][/ROW]
[ROW][C]87[/C][C]64[/C][C]77.8208536702204[/C][C]-13.8208536702204[/C][/ROW]
[ROW][C]88[/C][C]66[/C][C]59.4747338995572[/C][C]6.52526610044276[/C][/ROW]
[ROW][C]89[/C][C]78[/C][C]65.3094834737065[/C][C]12.6905165262935[/C][/ROW]
[ROW][C]90[/C][C]68[/C][C]65.8953267358493[/C][C]2.1046732641507[/C][/ROW]
[ROW][C]91[/C][C]73[/C][C]72.3195525421623[/C][C]0.680447457837701[/C][/ROW]
[ROW][C]92[/C][C]62[/C][C]71.3931342255163[/C][C]-9.39313422551632[/C][/ROW]
[ROW][C]93[/C][C]65[/C][C]73.9418010255385[/C][C]-8.94180102553848[/C][/ROW]
[ROW][C]94[/C][C]68[/C][C]67.6027012082082[/C][C]0.39729879179184[/C][/ROW]
[ROW][C]95[/C][C]65[/C][C]68.9351469402133[/C][C]-3.93514694021327[/C][/ROW]
[ROW][C]96[/C][C]60[/C][C]69.0810144206661[/C][C]-9.08101442066608[/C][/ROW]
[ROW][C]97[/C][C]71[/C][C]67.2955468808605[/C][C]3.70445311913946[/C][/ROW]
[ROW][C]98[/C][C]65[/C][C]60.8695739550899[/C][C]4.13042604491012[/C][/ROW]
[ROW][C]99[/C][C]68[/C][C]71.2209660403973[/C][C]-3.2209660403973[/C][/ROW]
[ROW][C]100[/C][C]64[/C][C]63.240480383408[/C][C]0.75951961659203[/C][/ROW]
[ROW][C]101[/C][C]74[/C][C]71.0124099661772[/C][C]2.9875900338228[/C][/ROW]
[ROW][C]102[/C][C]69[/C][C]65.6010030865388[/C][C]3.39899691346122[/C][/ROW]
[ROW][C]103[/C][C]76[/C][C]71.32380459319[/C][C]4.67619540680995[/C][/ROW]
[ROW][C]104[/C][C]68[/C][C]66.208147060237[/C][C]1.79185293976302[/C][/ROW]
[ROW][C]105[/C][C]72[/C][C]70.249418797656[/C][C]1.75058120234399[/C][/ROW]
[ROW][C]106[/C][C]67[/C][C]69.4626105583446[/C][C]-2.46261055834455[/C][/ROW]
[ROW][C]107[/C][C]63[/C][C]68.4909881709429[/C][C]-5.49098817094294[/C][/ROW]
[ROW][C]108[/C][C]59[/C][C]66.0366674579093[/C][C]-7.03666745790929[/C][/ROW]
[ROW][C]109[/C][C]73[/C][C]70.4381761598643[/C][C]2.56182384013567[/C][/ROW]
[ROW][C]110[/C][C]66[/C][C]63.9509137376568[/C][C]2.04908626234317[/C][/ROW]
[ROW][C]111[/C][C]62[/C][C]70.8117801872224[/C][C]-8.81178018722238[/C][/ROW]
[ROW][C]112[/C][C]69[/C][C]63.9128729590879[/C][C]5.08712704091214[/C][/ROW]
[ROW][C]113[/C][C]66[/C][C]73.327231829808[/C][C]-7.32723182980796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267958&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267958&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
137873.112490491124.88750950887999
147369.01171067527033.98828932472972
157571.49766976546743.50233023453258
167269.24091591632842.75908408367158
176663.2915373625922.70846263740803
187067.77496856295732.22503143704273
196181.6633997237933-20.6633997237933
208155.538984763032125.4610152369679
217193.8675703291087-22.8675703291087
226945.430020992009723.5699790079903
237176.2268034462631-5.22680344626311
247274.6360527156691-2.63605271566905
256893.4370438408999-25.4370438408999
267084.3067380965298-14.3067380965298
276884.5409727389871-16.5409727389871
286178.95520041799-17.95520041799
296769.6691851492113-2.66918514921133
307673.21879371279922.78120628720085
317076.3230903033597-6.32309030335971
326071.7542862133225-11.7542862133225
337282.8143390799528-10.8143390799528
346955.70599472538713.294005274613
357171.2156896957026-0.215689695702636
366270.8992187550796-8.89921875507959
377077.2498364079392-7.24983640793923
386474.7796598160452-10.7796598160452
395873.7546366242609-15.7546366242609
407667.14964670131038.85035329868965
415267.7335714164456-15.7335714164456
425971.5915405555095-12.5915405555095
436868.312813738321-0.312813738321012
447661.886278711524914.1137212884751
456575.8266002264093-10.8266002264093
466759.68578660779327.31421339220682
475967.697224725398-8.69722472539802
486962.29750212843196.70249787156808
497670.63091137031555.36908862968448
506367.8846564224294-4.88465642242937
517565.0174574964269.98254250357395
526372.7819429553048-9.7819429553048
536059.77238460296080.227615397039223
547366.98451105153576.01548894846431
556371.8475031883197-8.84750318831973
567070.8660669719956-0.866066971995636
577571.56700992428523.43299007571476
586665.15555455988690.844445440113105
596365.0536113311195-2.05361133111946
606367.5459879444431-4.54598794444311
616473.9620550992669-9.96205509926693
627064.68378150762995.31621849237014
637569.67075596840785.32924403159215
646167.7479870795136-6.74798707951361
656059.60975532855840.390244671441558
666269.3279258104799-7.32792581047988
677365.69654298384447.30345701615565
686170.2062078678939-9.20620786789385
696671.6880339638018-5.68803396380184
706463.12508738503060.874912614969432
715961.6079029960094-2.60790299600944
726462.65830339611791.34169660388209
736066.965958791438-6.96595879143796
745664.8869789428769-8.88697894287687
757867.682392619270810.3176073807292
765361.0837470635949-8.0837470635949
776756.098928207955610.9010717920444
785963.1647950010214-4.16479500102137
796666.2755306355002-0.275530635500246
806862.37143686606995.62856313393013
817167.03295001871483.9670499812852
826662.68758986962533.31241013037469
837359.930511777663713.0694882223363
847264.86953340186817.13046659813192
857166.2540982176514.74590178234901
865964.7638500005175-5.76385000051749
876477.8208536702204-13.8208536702204
886659.47473389955726.52526610044276
897865.309483473706512.6905165262935
906865.89532673584932.1046732641507
917372.31955254216230.680447457837701
926271.3931342255163-9.39313422551632
936573.9418010255385-8.94180102553848
946867.60270120820820.39729879179184
956568.9351469402133-3.93514694021327
966069.0810144206661-9.08101442066608
977167.29554688086053.70445311913946
986560.86957395508994.13042604491012
996871.2209660403973-3.2209660403973
1006463.2404803834080.75951961659203
1017471.01240996617722.9875900338228
1026965.60100308653883.39899691346122
1037671.323804593194.67619540680995
1046866.2081470602371.79185293976302
1057270.2494187976561.75058120234399
1066769.4626105583446-2.46261055834455
1076368.4909881709429-5.49098817094294
1085966.0366674579093-7.03666745790929
1097370.43817615986432.56182384013567
1106663.95091373765682.04908626234317
1116270.8117801872224-8.81178018722238
1126963.91287295908795.08712704091214
1136673.327231829808-7.32723182980796







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
11466.818999165446956.719121714877576.9188766160163
11572.542934723997262.158104017528982.9277654304655
11665.580402181912855.027680390828876.1331239729969
11769.161718108037158.250800540796880.0726356752773
11866.195421416856755.068445858661177.3223969750524
11964.058123447221352.692955181807375.4232917126352
12061.488456689087149.90790632685173.0690070513232
12170.972461035689758.499817853030483.445104218349
12263.98335151137151.584429731917376.3822732908247
12365.507693372912852.605513850633978.4098728951916
12465.947172188302152.594635253364979.2997091232392
12568.9809392260479-719.270605494674857.23248394677

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
114 & 66.8189991654469 & 56.7191217148775 & 76.9188766160163 \tabularnewline
115 & 72.5429347239972 & 62.1581040175289 & 82.9277654304655 \tabularnewline
116 & 65.5804021819128 & 55.0276803908288 & 76.1331239729969 \tabularnewline
117 & 69.1617181080371 & 58.2508005407968 & 80.0726356752773 \tabularnewline
118 & 66.1954214168567 & 55.0684458586611 & 77.3223969750524 \tabularnewline
119 & 64.0581234472213 & 52.6929551818073 & 75.4232917126352 \tabularnewline
120 & 61.4884566890871 & 49.907906326851 & 73.0690070513232 \tabularnewline
121 & 70.9724610356897 & 58.4998178530304 & 83.445104218349 \tabularnewline
122 & 63.983351511371 & 51.5844297319173 & 76.3822732908247 \tabularnewline
123 & 65.5076933729128 & 52.6055138506339 & 78.4098728951916 \tabularnewline
124 & 65.9471721883021 & 52.5946352533649 & 79.2997091232392 \tabularnewline
125 & 68.9809392260479 & -719.270605494674 & 857.23248394677 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267958&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]114[/C][C]66.8189991654469[/C][C]56.7191217148775[/C][C]76.9188766160163[/C][/ROW]
[ROW][C]115[/C][C]72.5429347239972[/C][C]62.1581040175289[/C][C]82.9277654304655[/C][/ROW]
[ROW][C]116[/C][C]65.5804021819128[/C][C]55.0276803908288[/C][C]76.1331239729969[/C][/ROW]
[ROW][C]117[/C][C]69.1617181080371[/C][C]58.2508005407968[/C][C]80.0726356752773[/C][/ROW]
[ROW][C]118[/C][C]66.1954214168567[/C][C]55.0684458586611[/C][C]77.3223969750524[/C][/ROW]
[ROW][C]119[/C][C]64.0581234472213[/C][C]52.6929551818073[/C][C]75.4232917126352[/C][/ROW]
[ROW][C]120[/C][C]61.4884566890871[/C][C]49.907906326851[/C][C]73.0690070513232[/C][/ROW]
[ROW][C]121[/C][C]70.9724610356897[/C][C]58.4998178530304[/C][C]83.445104218349[/C][/ROW]
[ROW][C]122[/C][C]63.983351511371[/C][C]51.5844297319173[/C][C]76.3822732908247[/C][/ROW]
[ROW][C]123[/C][C]65.5076933729128[/C][C]52.6055138506339[/C][C]78.4098728951916[/C][/ROW]
[ROW][C]124[/C][C]65.9471721883021[/C][C]52.5946352533649[/C][C]79.2997091232392[/C][/ROW]
[ROW][C]125[/C][C]68.9809392260479[/C][C]-719.270605494674[/C][C]857.23248394677[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267958&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267958&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
11466.818999165446956.719121714877576.9188766160163
11572.542934723997262.158104017528982.9277654304655
11665.580402181912855.027680390828876.1331239729969
11769.161718108037158.250800540796880.0726356752773
11866.195421416856755.068445858661177.3223969750524
11964.058123447221352.692955181807375.4232917126352
12061.488456689087149.90790632685173.0690070513232
12170.972461035689758.499817853030483.445104218349
12263.98335151137151.584429731917376.3822732908247
12365.507693372912852.605513850633978.4098728951916
12465.947172188302152.594635253364979.2997091232392
12568.9809392260479-719.270605494674857.23248394677



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