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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 computationSun, 06 Dec 2009 08:52:59 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/06/t1260114884l797xirkc1d9tb9.htm/, Retrieved Mon, 06 May 2024 01:28:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64438, Retrieved Mon, 06 May 2024 01:28:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [] [2009-12-06 15:52:59] [9f6463b67b1eb7bae5c03a796abf0348] [Current]
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Dataseries X:
62
64
62
64
64
69
69
65
56
58
53
62
55
60
59
58
53
57
57
53
54
53
57
57
55
49
50
49
54
58
58
52
56
52
59
53
52
53
51
50
56
52
46
48
46
48
48
49
53
48
51
48
50
55
52
53
52
55
53
53
56
54
52
55
54
59
56
56
51
53
52
51
46
49
46
55
57
53
52
53
50
54
53
50
51
52
47
51
49
53
52
45
53
51
48
48
48
48
40
43
40
39
39
36
41
39
40
39
46
40
37
37
44
41
40
36
38
43
42
45
46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64438&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64438&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64438&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.423371990682941
beta0.0195569935214878
gamma0.730774983925955

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.423371990682941 \tabularnewline
beta & 0.0195569935214878 \tabularnewline
gamma & 0.730774983925955 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64438&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]0.423371990682941[/C][/ROW]
[ROW][C]beta[/C][C]0.0195569935214878[/C][/ROW]
[ROW][C]gamma[/C][C]0.730774983925955[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64438&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64438&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
alpha0.423371990682941
beta0.0195569935214878
gamma0.730774983925955







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135558.9023392751817-3.90233927518170
146062.8634077747937-2.86340777479365
155960.546313553452-1.54631355345199
165858.475457358636-0.47545735863595
175352.64098541744080.359014582559205
185756.12416287586270.875837124137291
195761.2947882409337-4.29478824093374
205355.6947116162030-2.69471161620295
215446.5546054961237.44539450387703
225351.16572132873511.83427867126492
235747.45152837746539.54847162253474
245760.6274256909451-3.62742569094512
255551.24920268211453.7507973178855
264958.6305811592515-9.63058115925155
275054.0261322304602-4.0261322304602
284951.4089408524789-2.40894085247891
295445.72574689048798.27425310951212
305852.55446522796845.44553477203164
315857.43090981050220.569090189497842
325254.6943984799615-2.69439847996153
335649.76456079609456.23543920390546
345251.61945786800720.380542131992812
355950.35663405989458.64336594010547
365357.555527799128-4.55552779912804
375251.08148272007310.91851727992691
385351.37073310957371.62926689042625
395154.0787039994874-3.07870399948737
405052.7136347268283-2.71363472682827
415651.33802822135264.66197177864736
425255.5220162897591-3.5220162897591
434654.5521144379234-8.55211443792344
444847.00633666985340.993663330146553
454647.249880566214-1.24988056621404
464843.84211495343544.15788504656458
474847.11880144585650.88119855414353
484945.61743718220743.38256281779258
495345.01743386227367.98256613772642
504848.5925208556935-0.5925208556935
515148.33590866504292.66409133495714
524849.5868036537874-1.58680365378743
535051.7158859689251-1.71588596892507
545549.80875956933275.19124043066726
555250.27202467485891.72797532514111
565351.33863241668191.66136758331808
575251.05628155923710.943718440762858
585550.98756329332254.01243670667746
595353.1057351936292-0.105735193629229
605352.36217088597260.637829114027426
615652.49674458657583.50325541342418
625450.55989165834233.44010834165772
635253.6694461616626-1.66944616166263
645551.35290957402683.64709042597318
655456.1215125883556-2.12151258835559
665957.25500605584151.74499394415845
675654.7409330054831.25906699451698
685655.7645886202560.235411379743958
695154.6501131039374-3.65011310393743
705353.9979510761349-0.997951076134868
715252.3255943171342-0.325594317134190
725151.8514706285443-0.851470628544305
734652.5242473405578-6.52424734055778
744946.56002514887062.43997485112942
754647.0591717230597-1.05917172305969
765547.05528769349297.9447123065071
775751.10874163722155.89125836277847
785357.2586583767913-4.25865837679129
795252.1779199812679-0.177919981267898
805352.13553677816450.8644632218355
815049.76947734132060.230522658679448
825451.83153301252222.16846698747776
835351.84569968176211.15430031823792
845051.8421779770833-1.84217797708325
855149.61410428967841.38589571032156
865250.93943424403121.06056575596885
874749.3879241678224-2.38792416782242
885152.7086080942778-1.70860809427776
894951.7175238785488-2.71752387854877
905349.88161898638343.11838101361658
915249.71273369840292.28726630159712
924551.1621189657747-6.16211896577473
935345.7525110491427.24748895085803
945151.5505192219968-0.550519221996836
954850.0404845254472-2.04048452544724
964847.50144917991120.498550820088795
974847.61451050295830.385489497041654
984848.3219208580364-0.321920858036364
994044.9262089909116-4.92620899091164
1004346.9442843611873-3.94428436118725
1014044.5513370720774-4.55133707207737
1023944.0083697566031-5.00836975660307
1033940.2145498272243-1.21454982722427
1043637.0151467322396-1.01514673223964
1054138.51536696938932.48463303061067
1063938.92019377461570.0798062253843028
1074037.27939764296232.7206023570377
1083937.78256505320491.21743494679509
1094638.02200273917257.97799726082753
1104041.5297337835317-1.52973378353173
1113736.28688206563460.713117934365442
1123740.5493501836833-3.54935018368331
1134438.05243304668645.94756695331359
1144141.7288759229973-0.728875922997325
1154041.4643457946619-1.46434579466186
1163638.2481997700295-2.24819977002948
1173840.8968713160479-2.89687131604788
1184338.09649231067844.90350768932164
1194239.66634272363642.33365727636360
1204539.43026187041175.56973812958829
1214644.42624795072521.57375204927482

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 55 & 58.9023392751817 & -3.90233927518170 \tabularnewline
14 & 60 & 62.8634077747937 & -2.86340777479365 \tabularnewline
15 & 59 & 60.546313553452 & -1.54631355345199 \tabularnewline
16 & 58 & 58.475457358636 & -0.47545735863595 \tabularnewline
17 & 53 & 52.6409854174408 & 0.359014582559205 \tabularnewline
18 & 57 & 56.1241628758627 & 0.875837124137291 \tabularnewline
19 & 57 & 61.2947882409337 & -4.29478824093374 \tabularnewline
20 & 53 & 55.6947116162030 & -2.69471161620295 \tabularnewline
21 & 54 & 46.554605496123 & 7.44539450387703 \tabularnewline
22 & 53 & 51.1657213287351 & 1.83427867126492 \tabularnewline
23 & 57 & 47.4515283774653 & 9.54847162253474 \tabularnewline
24 & 57 & 60.6274256909451 & -3.62742569094512 \tabularnewline
25 & 55 & 51.2492026821145 & 3.7507973178855 \tabularnewline
26 & 49 & 58.6305811592515 & -9.63058115925155 \tabularnewline
27 & 50 & 54.0261322304602 & -4.0261322304602 \tabularnewline
28 & 49 & 51.4089408524789 & -2.40894085247891 \tabularnewline
29 & 54 & 45.7257468904879 & 8.27425310951212 \tabularnewline
30 & 58 & 52.5544652279684 & 5.44553477203164 \tabularnewline
31 & 58 & 57.4309098105022 & 0.569090189497842 \tabularnewline
32 & 52 & 54.6943984799615 & -2.69439847996153 \tabularnewline
33 & 56 & 49.7645607960945 & 6.23543920390546 \tabularnewline
34 & 52 & 51.6194578680072 & 0.380542131992812 \tabularnewline
35 & 59 & 50.3566340598945 & 8.64336594010547 \tabularnewline
36 & 53 & 57.555527799128 & -4.55552779912804 \tabularnewline
37 & 52 & 51.0814827200731 & 0.91851727992691 \tabularnewline
38 & 53 & 51.3707331095737 & 1.62926689042625 \tabularnewline
39 & 51 & 54.0787039994874 & -3.07870399948737 \tabularnewline
40 & 50 & 52.7136347268283 & -2.71363472682827 \tabularnewline
41 & 56 & 51.3380282213526 & 4.66197177864736 \tabularnewline
42 & 52 & 55.5220162897591 & -3.5220162897591 \tabularnewline
43 & 46 & 54.5521144379234 & -8.55211443792344 \tabularnewline
44 & 48 & 47.0063366698534 & 0.993663330146553 \tabularnewline
45 & 46 & 47.249880566214 & -1.24988056621404 \tabularnewline
46 & 48 & 43.8421149534354 & 4.15788504656458 \tabularnewline
47 & 48 & 47.1188014458565 & 0.88119855414353 \tabularnewline
48 & 49 & 45.6174371822074 & 3.38256281779258 \tabularnewline
49 & 53 & 45.0174338622736 & 7.98256613772642 \tabularnewline
50 & 48 & 48.5925208556935 & -0.5925208556935 \tabularnewline
51 & 51 & 48.3359086650429 & 2.66409133495714 \tabularnewline
52 & 48 & 49.5868036537874 & -1.58680365378743 \tabularnewline
53 & 50 & 51.7158859689251 & -1.71588596892507 \tabularnewline
54 & 55 & 49.8087595693327 & 5.19124043066726 \tabularnewline
55 & 52 & 50.2720246748589 & 1.72797532514111 \tabularnewline
56 & 53 & 51.3386324166819 & 1.66136758331808 \tabularnewline
57 & 52 & 51.0562815592371 & 0.943718440762858 \tabularnewline
58 & 55 & 50.9875632933225 & 4.01243670667746 \tabularnewline
59 & 53 & 53.1057351936292 & -0.105735193629229 \tabularnewline
60 & 53 & 52.3621708859726 & 0.637829114027426 \tabularnewline
61 & 56 & 52.4967445865758 & 3.50325541342418 \tabularnewline
62 & 54 & 50.5598916583423 & 3.44010834165772 \tabularnewline
63 & 52 & 53.6694461616626 & -1.66944616166263 \tabularnewline
64 & 55 & 51.3529095740268 & 3.64709042597318 \tabularnewline
65 & 54 & 56.1215125883556 & -2.12151258835559 \tabularnewline
66 & 59 & 57.2550060558415 & 1.74499394415845 \tabularnewline
67 & 56 & 54.740933005483 & 1.25906699451698 \tabularnewline
68 & 56 & 55.764588620256 & 0.235411379743958 \tabularnewline
69 & 51 & 54.6501131039374 & -3.65011310393743 \tabularnewline
70 & 53 & 53.9979510761349 & -0.997951076134868 \tabularnewline
71 & 52 & 52.3255943171342 & -0.325594317134190 \tabularnewline
72 & 51 & 51.8514706285443 & -0.851470628544305 \tabularnewline
73 & 46 & 52.5242473405578 & -6.52424734055778 \tabularnewline
74 & 49 & 46.5600251488706 & 2.43997485112942 \tabularnewline
75 & 46 & 47.0591717230597 & -1.05917172305969 \tabularnewline
76 & 55 & 47.0552876934929 & 7.9447123065071 \tabularnewline
77 & 57 & 51.1087416372215 & 5.89125836277847 \tabularnewline
78 & 53 & 57.2586583767913 & -4.25865837679129 \tabularnewline
79 & 52 & 52.1779199812679 & -0.177919981267898 \tabularnewline
80 & 53 & 52.1355367781645 & 0.8644632218355 \tabularnewline
81 & 50 & 49.7694773413206 & 0.230522658679448 \tabularnewline
82 & 54 & 51.8315330125222 & 2.16846698747776 \tabularnewline
83 & 53 & 51.8456996817621 & 1.15430031823792 \tabularnewline
84 & 50 & 51.8421779770833 & -1.84217797708325 \tabularnewline
85 & 51 & 49.6141042896784 & 1.38589571032156 \tabularnewline
86 & 52 & 50.9394342440312 & 1.06056575596885 \tabularnewline
87 & 47 & 49.3879241678224 & -2.38792416782242 \tabularnewline
88 & 51 & 52.7086080942778 & -1.70860809427776 \tabularnewline
89 & 49 & 51.7175238785488 & -2.71752387854877 \tabularnewline
90 & 53 & 49.8816189863834 & 3.11838101361658 \tabularnewline
91 & 52 & 49.7127336984029 & 2.28726630159712 \tabularnewline
92 & 45 & 51.1621189657747 & -6.16211896577473 \tabularnewline
93 & 53 & 45.752511049142 & 7.24748895085803 \tabularnewline
94 & 51 & 51.5505192219968 & -0.550519221996836 \tabularnewline
95 & 48 & 50.0404845254472 & -2.04048452544724 \tabularnewline
96 & 48 & 47.5014491799112 & 0.498550820088795 \tabularnewline
97 & 48 & 47.6145105029583 & 0.385489497041654 \tabularnewline
98 & 48 & 48.3219208580364 & -0.321920858036364 \tabularnewline
99 & 40 & 44.9262089909116 & -4.92620899091164 \tabularnewline
100 & 43 & 46.9442843611873 & -3.94428436118725 \tabularnewline
101 & 40 & 44.5513370720774 & -4.55133707207737 \tabularnewline
102 & 39 & 44.0083697566031 & -5.00836975660307 \tabularnewline
103 & 39 & 40.2145498272243 & -1.21454982722427 \tabularnewline
104 & 36 & 37.0151467322396 & -1.01514673223964 \tabularnewline
105 & 41 & 38.5153669693893 & 2.48463303061067 \tabularnewline
106 & 39 & 38.9201937746157 & 0.0798062253843028 \tabularnewline
107 & 40 & 37.2793976429623 & 2.7206023570377 \tabularnewline
108 & 39 & 37.7825650532049 & 1.21743494679509 \tabularnewline
109 & 46 & 38.0220027391725 & 7.97799726082753 \tabularnewline
110 & 40 & 41.5297337835317 & -1.52973378353173 \tabularnewline
111 & 37 & 36.2868820656346 & 0.713117934365442 \tabularnewline
112 & 37 & 40.5493501836833 & -3.54935018368331 \tabularnewline
113 & 44 & 38.0524330466864 & 5.94756695331359 \tabularnewline
114 & 41 & 41.7288759229973 & -0.728875922997325 \tabularnewline
115 & 40 & 41.4643457946619 & -1.46434579466186 \tabularnewline
116 & 36 & 38.2481997700295 & -2.24819977002948 \tabularnewline
117 & 38 & 40.8968713160479 & -2.89687131604788 \tabularnewline
118 & 43 & 38.0964923106784 & 4.90350768932164 \tabularnewline
119 & 42 & 39.6663427236364 & 2.33365727636360 \tabularnewline
120 & 45 & 39.4302618704117 & 5.56973812958829 \tabularnewline
121 & 46 & 44.4262479507252 & 1.57375204927482 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64438&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]55[/C][C]58.9023392751817[/C][C]-3.90233927518170[/C][/ROW]
[ROW][C]14[/C][C]60[/C][C]62.8634077747937[/C][C]-2.86340777479365[/C][/ROW]
[ROW][C]15[/C][C]59[/C][C]60.546313553452[/C][C]-1.54631355345199[/C][/ROW]
[ROW][C]16[/C][C]58[/C][C]58.475457358636[/C][C]-0.47545735863595[/C][/ROW]
[ROW][C]17[/C][C]53[/C][C]52.6409854174408[/C][C]0.359014582559205[/C][/ROW]
[ROW][C]18[/C][C]57[/C][C]56.1241628758627[/C][C]0.875837124137291[/C][/ROW]
[ROW][C]19[/C][C]57[/C][C]61.2947882409337[/C][C]-4.29478824093374[/C][/ROW]
[ROW][C]20[/C][C]53[/C][C]55.6947116162030[/C][C]-2.69471161620295[/C][/ROW]
[ROW][C]21[/C][C]54[/C][C]46.554605496123[/C][C]7.44539450387703[/C][/ROW]
[ROW][C]22[/C][C]53[/C][C]51.1657213287351[/C][C]1.83427867126492[/C][/ROW]
[ROW][C]23[/C][C]57[/C][C]47.4515283774653[/C][C]9.54847162253474[/C][/ROW]
[ROW][C]24[/C][C]57[/C][C]60.6274256909451[/C][C]-3.62742569094512[/C][/ROW]
[ROW][C]25[/C][C]55[/C][C]51.2492026821145[/C][C]3.7507973178855[/C][/ROW]
[ROW][C]26[/C][C]49[/C][C]58.6305811592515[/C][C]-9.63058115925155[/C][/ROW]
[ROW][C]27[/C][C]50[/C][C]54.0261322304602[/C][C]-4.0261322304602[/C][/ROW]
[ROW][C]28[/C][C]49[/C][C]51.4089408524789[/C][C]-2.40894085247891[/C][/ROW]
[ROW][C]29[/C][C]54[/C][C]45.7257468904879[/C][C]8.27425310951212[/C][/ROW]
[ROW][C]30[/C][C]58[/C][C]52.5544652279684[/C][C]5.44553477203164[/C][/ROW]
[ROW][C]31[/C][C]58[/C][C]57.4309098105022[/C][C]0.569090189497842[/C][/ROW]
[ROW][C]32[/C][C]52[/C][C]54.6943984799615[/C][C]-2.69439847996153[/C][/ROW]
[ROW][C]33[/C][C]56[/C][C]49.7645607960945[/C][C]6.23543920390546[/C][/ROW]
[ROW][C]34[/C][C]52[/C][C]51.6194578680072[/C][C]0.380542131992812[/C][/ROW]
[ROW][C]35[/C][C]59[/C][C]50.3566340598945[/C][C]8.64336594010547[/C][/ROW]
[ROW][C]36[/C][C]53[/C][C]57.555527799128[/C][C]-4.55552779912804[/C][/ROW]
[ROW][C]37[/C][C]52[/C][C]51.0814827200731[/C][C]0.91851727992691[/C][/ROW]
[ROW][C]38[/C][C]53[/C][C]51.3707331095737[/C][C]1.62926689042625[/C][/ROW]
[ROW][C]39[/C][C]51[/C][C]54.0787039994874[/C][C]-3.07870399948737[/C][/ROW]
[ROW][C]40[/C][C]50[/C][C]52.7136347268283[/C][C]-2.71363472682827[/C][/ROW]
[ROW][C]41[/C][C]56[/C][C]51.3380282213526[/C][C]4.66197177864736[/C][/ROW]
[ROW][C]42[/C][C]52[/C][C]55.5220162897591[/C][C]-3.5220162897591[/C][/ROW]
[ROW][C]43[/C][C]46[/C][C]54.5521144379234[/C][C]-8.55211443792344[/C][/ROW]
[ROW][C]44[/C][C]48[/C][C]47.0063366698534[/C][C]0.993663330146553[/C][/ROW]
[ROW][C]45[/C][C]46[/C][C]47.249880566214[/C][C]-1.24988056621404[/C][/ROW]
[ROW][C]46[/C][C]48[/C][C]43.8421149534354[/C][C]4.15788504656458[/C][/ROW]
[ROW][C]47[/C][C]48[/C][C]47.1188014458565[/C][C]0.88119855414353[/C][/ROW]
[ROW][C]48[/C][C]49[/C][C]45.6174371822074[/C][C]3.38256281779258[/C][/ROW]
[ROW][C]49[/C][C]53[/C][C]45.0174338622736[/C][C]7.98256613772642[/C][/ROW]
[ROW][C]50[/C][C]48[/C][C]48.5925208556935[/C][C]-0.5925208556935[/C][/ROW]
[ROW][C]51[/C][C]51[/C][C]48.3359086650429[/C][C]2.66409133495714[/C][/ROW]
[ROW][C]52[/C][C]48[/C][C]49.5868036537874[/C][C]-1.58680365378743[/C][/ROW]
[ROW][C]53[/C][C]50[/C][C]51.7158859689251[/C][C]-1.71588596892507[/C][/ROW]
[ROW][C]54[/C][C]55[/C][C]49.8087595693327[/C][C]5.19124043066726[/C][/ROW]
[ROW][C]55[/C][C]52[/C][C]50.2720246748589[/C][C]1.72797532514111[/C][/ROW]
[ROW][C]56[/C][C]53[/C][C]51.3386324166819[/C][C]1.66136758331808[/C][/ROW]
[ROW][C]57[/C][C]52[/C][C]51.0562815592371[/C][C]0.943718440762858[/C][/ROW]
[ROW][C]58[/C][C]55[/C][C]50.9875632933225[/C][C]4.01243670667746[/C][/ROW]
[ROW][C]59[/C][C]53[/C][C]53.1057351936292[/C][C]-0.105735193629229[/C][/ROW]
[ROW][C]60[/C][C]53[/C][C]52.3621708859726[/C][C]0.637829114027426[/C][/ROW]
[ROW][C]61[/C][C]56[/C][C]52.4967445865758[/C][C]3.50325541342418[/C][/ROW]
[ROW][C]62[/C][C]54[/C][C]50.5598916583423[/C][C]3.44010834165772[/C][/ROW]
[ROW][C]63[/C][C]52[/C][C]53.6694461616626[/C][C]-1.66944616166263[/C][/ROW]
[ROW][C]64[/C][C]55[/C][C]51.3529095740268[/C][C]3.64709042597318[/C][/ROW]
[ROW][C]65[/C][C]54[/C][C]56.1215125883556[/C][C]-2.12151258835559[/C][/ROW]
[ROW][C]66[/C][C]59[/C][C]57.2550060558415[/C][C]1.74499394415845[/C][/ROW]
[ROW][C]67[/C][C]56[/C][C]54.740933005483[/C][C]1.25906699451698[/C][/ROW]
[ROW][C]68[/C][C]56[/C][C]55.764588620256[/C][C]0.235411379743958[/C][/ROW]
[ROW][C]69[/C][C]51[/C][C]54.6501131039374[/C][C]-3.65011310393743[/C][/ROW]
[ROW][C]70[/C][C]53[/C][C]53.9979510761349[/C][C]-0.997951076134868[/C][/ROW]
[ROW][C]71[/C][C]52[/C][C]52.3255943171342[/C][C]-0.325594317134190[/C][/ROW]
[ROW][C]72[/C][C]51[/C][C]51.8514706285443[/C][C]-0.851470628544305[/C][/ROW]
[ROW][C]73[/C][C]46[/C][C]52.5242473405578[/C][C]-6.52424734055778[/C][/ROW]
[ROW][C]74[/C][C]49[/C][C]46.5600251488706[/C][C]2.43997485112942[/C][/ROW]
[ROW][C]75[/C][C]46[/C][C]47.0591717230597[/C][C]-1.05917172305969[/C][/ROW]
[ROW][C]76[/C][C]55[/C][C]47.0552876934929[/C][C]7.9447123065071[/C][/ROW]
[ROW][C]77[/C][C]57[/C][C]51.1087416372215[/C][C]5.89125836277847[/C][/ROW]
[ROW][C]78[/C][C]53[/C][C]57.2586583767913[/C][C]-4.25865837679129[/C][/ROW]
[ROW][C]79[/C][C]52[/C][C]52.1779199812679[/C][C]-0.177919981267898[/C][/ROW]
[ROW][C]80[/C][C]53[/C][C]52.1355367781645[/C][C]0.8644632218355[/C][/ROW]
[ROW][C]81[/C][C]50[/C][C]49.7694773413206[/C][C]0.230522658679448[/C][/ROW]
[ROW][C]82[/C][C]54[/C][C]51.8315330125222[/C][C]2.16846698747776[/C][/ROW]
[ROW][C]83[/C][C]53[/C][C]51.8456996817621[/C][C]1.15430031823792[/C][/ROW]
[ROW][C]84[/C][C]50[/C][C]51.8421779770833[/C][C]-1.84217797708325[/C][/ROW]
[ROW][C]85[/C][C]51[/C][C]49.6141042896784[/C][C]1.38589571032156[/C][/ROW]
[ROW][C]86[/C][C]52[/C][C]50.9394342440312[/C][C]1.06056575596885[/C][/ROW]
[ROW][C]87[/C][C]47[/C][C]49.3879241678224[/C][C]-2.38792416782242[/C][/ROW]
[ROW][C]88[/C][C]51[/C][C]52.7086080942778[/C][C]-1.70860809427776[/C][/ROW]
[ROW][C]89[/C][C]49[/C][C]51.7175238785488[/C][C]-2.71752387854877[/C][/ROW]
[ROW][C]90[/C][C]53[/C][C]49.8816189863834[/C][C]3.11838101361658[/C][/ROW]
[ROW][C]91[/C][C]52[/C][C]49.7127336984029[/C][C]2.28726630159712[/C][/ROW]
[ROW][C]92[/C][C]45[/C][C]51.1621189657747[/C][C]-6.16211896577473[/C][/ROW]
[ROW][C]93[/C][C]53[/C][C]45.752511049142[/C][C]7.24748895085803[/C][/ROW]
[ROW][C]94[/C][C]51[/C][C]51.5505192219968[/C][C]-0.550519221996836[/C][/ROW]
[ROW][C]95[/C][C]48[/C][C]50.0404845254472[/C][C]-2.04048452544724[/C][/ROW]
[ROW][C]96[/C][C]48[/C][C]47.5014491799112[/C][C]0.498550820088795[/C][/ROW]
[ROW][C]97[/C][C]48[/C][C]47.6145105029583[/C][C]0.385489497041654[/C][/ROW]
[ROW][C]98[/C][C]48[/C][C]48.3219208580364[/C][C]-0.321920858036364[/C][/ROW]
[ROW][C]99[/C][C]40[/C][C]44.9262089909116[/C][C]-4.92620899091164[/C][/ROW]
[ROW][C]100[/C][C]43[/C][C]46.9442843611873[/C][C]-3.94428436118725[/C][/ROW]
[ROW][C]101[/C][C]40[/C][C]44.5513370720774[/C][C]-4.55133707207737[/C][/ROW]
[ROW][C]102[/C][C]39[/C][C]44.0083697566031[/C][C]-5.00836975660307[/C][/ROW]
[ROW][C]103[/C][C]39[/C][C]40.2145498272243[/C][C]-1.21454982722427[/C][/ROW]
[ROW][C]104[/C][C]36[/C][C]37.0151467322396[/C][C]-1.01514673223964[/C][/ROW]
[ROW][C]105[/C][C]41[/C][C]38.5153669693893[/C][C]2.48463303061067[/C][/ROW]
[ROW][C]106[/C][C]39[/C][C]38.9201937746157[/C][C]0.0798062253843028[/C][/ROW]
[ROW][C]107[/C][C]40[/C][C]37.2793976429623[/C][C]2.7206023570377[/C][/ROW]
[ROW][C]108[/C][C]39[/C][C]37.7825650532049[/C][C]1.21743494679509[/C][/ROW]
[ROW][C]109[/C][C]46[/C][C]38.0220027391725[/C][C]7.97799726082753[/C][/ROW]
[ROW][C]110[/C][C]40[/C][C]41.5297337835317[/C][C]-1.52973378353173[/C][/ROW]
[ROW][C]111[/C][C]37[/C][C]36.2868820656346[/C][C]0.713117934365442[/C][/ROW]
[ROW][C]112[/C][C]37[/C][C]40.5493501836833[/C][C]-3.54935018368331[/C][/ROW]
[ROW][C]113[/C][C]44[/C][C]38.0524330466864[/C][C]5.94756695331359[/C][/ROW]
[ROW][C]114[/C][C]41[/C][C]41.7288759229973[/C][C]-0.728875922997325[/C][/ROW]
[ROW][C]115[/C][C]40[/C][C]41.4643457946619[/C][C]-1.46434579466186[/C][/ROW]
[ROW][C]116[/C][C]36[/C][C]38.2481997700295[/C][C]-2.24819977002948[/C][/ROW]
[ROW][C]117[/C][C]38[/C][C]40.8968713160479[/C][C]-2.89687131604788[/C][/ROW]
[ROW][C]118[/C][C]43[/C][C]38.0964923106784[/C][C]4.90350768932164[/C][/ROW]
[ROW][C]119[/C][C]42[/C][C]39.6663427236364[/C][C]2.33365727636360[/C][/ROW]
[ROW][C]120[/C][C]45[/C][C]39.4302618704117[/C][C]5.56973812958829[/C][/ROW]
[ROW][C]121[/C][C]46[/C][C]44.4262479507252[/C][C]1.57375204927482[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64438&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64438&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
135558.9023392751817-3.90233927518170
146062.8634077747937-2.86340777479365
155960.546313553452-1.54631355345199
165858.475457358636-0.47545735863595
175352.64098541744080.359014582559205
185756.12416287586270.875837124137291
195761.2947882409337-4.29478824093374
205355.6947116162030-2.69471161620295
215446.5546054961237.44539450387703
225351.16572132873511.83427867126492
235747.45152837746539.54847162253474
245760.6274256909451-3.62742569094512
255551.24920268211453.7507973178855
264958.6305811592515-9.63058115925155
275054.0261322304602-4.0261322304602
284951.4089408524789-2.40894085247891
295445.72574689048798.27425310951212
305852.55446522796845.44553477203164
315857.43090981050220.569090189497842
325254.6943984799615-2.69439847996153
335649.76456079609456.23543920390546
345251.61945786800720.380542131992812
355950.35663405989458.64336594010547
365357.555527799128-4.55552779912804
375251.08148272007310.91851727992691
385351.37073310957371.62926689042625
395154.0787039994874-3.07870399948737
405052.7136347268283-2.71363472682827
415651.33802822135264.66197177864736
425255.5220162897591-3.5220162897591
434654.5521144379234-8.55211443792344
444847.00633666985340.993663330146553
454647.249880566214-1.24988056621404
464843.84211495343544.15788504656458
474847.11880144585650.88119855414353
484945.61743718220743.38256281779258
495345.01743386227367.98256613772642
504848.5925208556935-0.5925208556935
515148.33590866504292.66409133495714
524849.5868036537874-1.58680365378743
535051.7158859689251-1.71588596892507
545549.80875956933275.19124043066726
555250.27202467485891.72797532514111
565351.33863241668191.66136758331808
575251.05628155923710.943718440762858
585550.98756329332254.01243670667746
595353.1057351936292-0.105735193629229
605352.36217088597260.637829114027426
615652.49674458657583.50325541342418
625450.55989165834233.44010834165772
635253.6694461616626-1.66944616166263
645551.35290957402683.64709042597318
655456.1215125883556-2.12151258835559
665957.25500605584151.74499394415845
675654.7409330054831.25906699451698
685655.7645886202560.235411379743958
695154.6501131039374-3.65011310393743
705353.9979510761349-0.997951076134868
715252.3255943171342-0.325594317134190
725151.8514706285443-0.851470628544305
734652.5242473405578-6.52424734055778
744946.56002514887062.43997485112942
754647.0591717230597-1.05917172305969
765547.05528769349297.9447123065071
775751.10874163722155.89125836277847
785357.2586583767913-4.25865837679129
795252.1779199812679-0.177919981267898
805352.13553677816450.8644632218355
815049.76947734132060.230522658679448
825451.83153301252222.16846698747776
835351.84569968176211.15430031823792
845051.8421779770833-1.84217797708325
855149.61410428967841.38589571032156
865250.93943424403121.06056575596885
874749.3879241678224-2.38792416782242
885152.7086080942778-1.70860809427776
894951.7175238785488-2.71752387854877
905349.88161898638343.11838101361658
915249.71273369840292.28726630159712
924551.1621189657747-6.16211896577473
935345.7525110491427.24748895085803
945151.5505192219968-0.550519221996836
954850.0404845254472-2.04048452544724
964847.50144917991120.498550820088795
974847.61451050295830.385489497041654
984848.3219208580364-0.321920858036364
994044.9262089909116-4.92620899091164
1004346.9442843611873-3.94428436118725
1014044.5513370720774-4.55133707207737
1023944.0083697566031-5.00836975660307
1033940.2145498272243-1.21454982722427
1043637.0151467322396-1.01514673223964
1054138.51536696938932.48463303061067
1063938.92019377461570.0798062253843028
1074037.27939764296232.7206023570377
1083937.78256505320491.21743494679509
1094638.02200273917257.97799726082753
1104041.5297337835317-1.52973378353173
1113736.28688206563460.713117934365442
1123740.5493501836833-3.54935018368331
1134438.05243304668645.94756695331359
1144141.7288759229973-0.728875922997325
1154041.4643457946619-1.46434579466186
1163638.2481997700295-2.24819977002948
1173840.8968713160479-2.89687131604788
1184338.09649231067844.90350768932164
1194239.66634272363642.33365727636360
1204539.43026187041175.56973812958829
1214644.42624795072521.57375204927482







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12241.249575391141535.035659898981347.4634908833018
12337.587489490319230.727015422353344.4479635582851
12439.813714222428432.068729761142047.5586986837148
12542.968507246999834.217652285926851.7193622080729
12641.371896547315432.155064328052450.5887287665783
12741.159732195254631.323300484278950.9961639062304
12838.216778612230728.221464160553548.212093063908
12941.787938943820830.494473061912553.0814048257292
13043.690123719449331.380288027240755.9999594116578
13142.112869122834029.547261700123954.678476545544
13242.184818659475128.990922503200455.3787148157497
13343.09017516148086.8418621588705679.3384881640911

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
122 & 41.2495753911415 & 35.0356598989813 & 47.4634908833018 \tabularnewline
123 & 37.5874894903192 & 30.7270154223533 & 44.4479635582851 \tabularnewline
124 & 39.8137142224284 & 32.0687297611420 & 47.5586986837148 \tabularnewline
125 & 42.9685072469998 & 34.2176522859268 & 51.7193622080729 \tabularnewline
126 & 41.3718965473154 & 32.1550643280524 & 50.5887287665783 \tabularnewline
127 & 41.1597321952546 & 31.3233004842789 & 50.9961639062304 \tabularnewline
128 & 38.2167786122307 & 28.2214641605535 & 48.212093063908 \tabularnewline
129 & 41.7879389438208 & 30.4944730619125 & 53.0814048257292 \tabularnewline
130 & 43.6901237194493 & 31.3802880272407 & 55.9999594116578 \tabularnewline
131 & 42.1128691228340 & 29.5472617001239 & 54.678476545544 \tabularnewline
132 & 42.1848186594751 & 28.9909225032004 & 55.3787148157497 \tabularnewline
133 & 43.0901751614808 & 6.84186215887056 & 79.3384881640911 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64438&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]122[/C][C]41.2495753911415[/C][C]35.0356598989813[/C][C]47.4634908833018[/C][/ROW]
[ROW][C]123[/C][C]37.5874894903192[/C][C]30.7270154223533[/C][C]44.4479635582851[/C][/ROW]
[ROW][C]124[/C][C]39.8137142224284[/C][C]32.0687297611420[/C][C]47.5586986837148[/C][/ROW]
[ROW][C]125[/C][C]42.9685072469998[/C][C]34.2176522859268[/C][C]51.7193622080729[/C][/ROW]
[ROW][C]126[/C][C]41.3718965473154[/C][C]32.1550643280524[/C][C]50.5887287665783[/C][/ROW]
[ROW][C]127[/C][C]41.1597321952546[/C][C]31.3233004842789[/C][C]50.9961639062304[/C][/ROW]
[ROW][C]128[/C][C]38.2167786122307[/C][C]28.2214641605535[/C][C]48.212093063908[/C][/ROW]
[ROW][C]129[/C][C]41.7879389438208[/C][C]30.4944730619125[/C][C]53.0814048257292[/C][/ROW]
[ROW][C]130[/C][C]43.6901237194493[/C][C]31.3802880272407[/C][C]55.9999594116578[/C][/ROW]
[ROW][C]131[/C][C]42.1128691228340[/C][C]29.5472617001239[/C][C]54.678476545544[/C][/ROW]
[ROW][C]132[/C][C]42.1848186594751[/C][C]28.9909225032004[/C][C]55.3787148157497[/C][/ROW]
[ROW][C]133[/C][C]43.0901751614808[/C][C]6.84186215887056[/C][C]79.3384881640911[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64438&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64438&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
12241.249575391141535.035659898981347.4634908833018
12337.587489490319230.727015422353344.4479635582851
12439.813714222428432.068729761142047.5586986837148
12542.968507246999834.217652285926851.7193622080729
12641.371896547315432.155064328052450.5887287665783
12741.159732195254631.323300484278950.9961639062304
12838.216778612230728.221464160553548.212093063908
12941.787938943820830.494473061912553.0814048257292
13043.690123719449331.380288027240755.9999594116578
13142.112869122834029.547261700123954.678476545544
13242.184818659475128.990922503200455.3787148157497
13343.09017516148086.8418621588705679.3384881640911



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=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')