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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 10 Mar 2008 11:56:43 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Mar/10/t1205171842e0ry9c7xankjola.htm/, Retrieved Sun, 28 Apr 2024 15:53:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10053, Retrieved Sun, 28 Apr 2024 15:53:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact705

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:56:43] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- R PD    [Exponential Smoothing] [steve] [2008-04-15 17:48:35] [74be16979710d4c4e7c6647856088456]
-    D    [Exponential Smoothing] [Triple Exponentia...] [2008-05-03 21:48:57] [74be16979710d4c4e7c6647856088456]
-    D    [Exponential Smoothing] [Triple Exponentia...] [2008-05-03 21:48:57] [74be16979710d4c4e7c6647856088456]
-    D    [Exponential Smoothing] [triple exponentia...] [2008-05-08 21:51:52] [74be16979710d4c4e7c6647856088456]
-   PD    [Exponential Smoothing] [multiplicative ho...] [2008-05-08 22:00:10] [74be16979710d4c4e7c6647856088456]
-  MPD      [Exponential Smoothing] [Workshop 8 - Expo...] [2010-11-30 08:26:52] [1429a1a14191a86916b95357f6de790b]
- RM          [Exponential Smoothing] [] [2011-11-29 20:31:39] [74be16979710d4c4e7c6647856088456]
- R           [Exponential Smoothing] [Exponential Smoot...] [2011-12-01 20:56:13] [3dd791303389e75e672968b227170a72]
-  M D    [Exponential Smoothing] [Holt-Winters mode...] [2010-11-29 14:39:25] [2843717cd92615903379c14ebee3c5df]
-  M D    [Exponential Smoothing] [] [2010-11-29 20:50:26] [de55ccbf69577500a5f46ed42a101114]
-  M D    [Exponential Smoothing] [ws 8] [2010-11-30 16:11:48] [0e7b3997dca5cf9d94982fb4db7bd3d5]
-  M D    [Exponential Smoothing] [Holt-Winters model] [2010-11-30 19:51:51] [1afa3497b02a8d7c9f6727c1b17b89b2]
-  M D    [Exponential Smoothing] [Workshop 8 - blog 2] [2010-11-30 19:48:44] [1aa8d85d6b335d32b1f6be940e33a166]
-  M D    [Exponential Smoothing] [Paper Triple Expo...] [2010-12-07 17:44:26] [56d90b683fcd93137645f9226b43c62b]
-  M D    [Exponential Smoothing] [WS5 - monthly bir...] [2010-12-08 15:43:57] [8ed0bd3560b9ca2814a2ed0a29182575]
-  M D    [Exponential Smoothing] [Exponential Smoot...] [2010-12-08 17:32:26] [6a528ed37664d761abf4790b0717b23b]
- R PD      [Exponential Smoothing] [Paper ES] [2010-12-13 14:25:18] [6a528ed37664d761abf4790b0717b23b]
-  M D    [Exponential Smoothing] [] [2010-12-09 19:54:22] [897115520fe7b6114489bc0eeed64548]
-    D      [Exponential Smoothing] [] [2010-12-27 06:47:49] [bfba28641a1925a39268a5d6ad3b00f2]
- RM          [Exponential Smoothing] [] [2012-08-21 21:50:05] [897115520fe7b6114489bc0eeed64548]
-  M D    [Exponential Smoothing] [Workshop 5 Expone...] [2010-12-09 21:05:42] [9856f62fe16b3bb5126cae5dd74e4807]
-    D      [Exponential Smoothing] [exponential smoot...] [2010-12-29 18:25:49] [f1aa04283d83c25edc8ae3bb0d0fb93e]
-   P         [Exponential Smoothing] [] [2010-12-29 21:12:18] [99820e5c3330fe494c612533a1ea567a]
- R PD          [Exponential Smoothing] [exponential smoot...] [2011-12-22 08:04:13] [74be16979710d4c4e7c6647856088456]
-  MP             [Exponential Smoothing] [exponential smoot...] [2011-12-22 10:27:03] [f1aa04283d83c25edc8ae3bb0d0fb93e]
- RMPD    [Exponential Smoothing] [Workshop 8 (Smoot...] [2010-12-10 15:44:28] [845827b7f02503df17c96f445745fee7]
- RMPD    [Exponential Smoothing] [Workshop 8 (Doubl...] [2010-12-10 15:49:13] [845827b7f02503df17c96f445745fee7]
- RM D    [Exponential Smoothing] [Workshop 8 (Tripl...] [2010-12-10 15:51:42] [845827b7f02503df17c96f445745fee7]
-  MPD    [Exponential Smoothing] [Aantal openstaand...] [2010-12-27 18:28:16] [4f1a20f787b3465111b61213cdeef1a9]
- RM      [Exponential Smoothing] [Triple exponentia...] [2011-11-28 18:23:03] [74be16979710d4c4e7c6647856088456]
- RM D    [Exponential Smoothing] [triple exponentia...] [2011-11-28 21:13:02] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [Tutorial3.5] [2011-11-29 08:57:26] [9e469a83342941fcd5c6dffbf184cd3a]
- RM D    [Exponential Smoothing] [WS 8 Exponential ...] [2011-11-29 14:12:16] [d0cddc92c01af61bef0226b9e5ade9b3]
-           [Exponential Smoothing] [WS8 - Mini-tutori...] [2011-11-29 14:34:49] [95a4a8598e82ac3272c4dca488d0ba38]
-             [Exponential Smoothing] [Paper - Deel 2 - ...] [2011-12-20 12:19:03] [95a4a8598e82ac3272c4dca488d0ba38]
- R             [Exponential Smoothing] [Paper Deel 4 Trip...] [2012-12-19 20:09:06] [d5c5f9d2d41487720068c665b8e94d36]
-  M          [Exponential Smoothing] [WS 8 05] [2012-11-26 12:57:49] [527264e3173c1bca10b2a11a99a7175d]
- RM D    [Exponential Smoothing] [] [2011-11-29 16:23:28] [a1957df0bc37aec4aa3c994e6a08412c]
- RM D    [Exponential Smoothing] [Triple exponentia...] [2011-12-21 19:35:15] [65d03b877b3f337979d6af245efa927d]
- RM D    [Exponential Smoothing] [Workshop 8: tripl...] [2012-11-09 16:27:59] [40b341cf5fb1ddfd74e4c5704837f48c]
- RM D    [Exponential Smoothing] [triple exponentio...] [2012-11-09 17:37:15] [74be16979710d4c4e7c6647856088456]
- R P       [Exponential Smoothing] [double exponentia...] [2012-11-27 22:55:27] [93b3e8d0ee7e4ccb504c2c04707a9358]
- RMPD    [Exponential Smoothing] [Triple smoothing] [2012-11-10 14:36:53] [86dcce9422b96d4554cb918e531c1d5d]
- RM D    [Exponential Smoothing] [WS8 0299787] [2012-11-11 14:52:32] [74be16979710d4c4e7c6647856088456]
-           [Exponential Smoothing] [Paper 0299787] [2012-12-05 13:00:23] [a2dcdd13e1df6929c5c71aa45a46cc8e]
- RM D    [Exponential Smoothing] [Single Exponentia...] [2012-11-22 15:26:08] [9d6050326bbbd058eed49c2dec5f39c1]
- RMPD    [Exponential Smoothing] [] [2012-11-24 20:04:44] [f6b89b7e4a7442873f7514a83779c1e1]
- RMPD    [Exponential Smoothing] [WS-Blog7] [2012-11-26 13:24:33] [74be16979710d4c4e7c6647856088456]

[Truncated]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13328
12873
14000
13477
14237
13674
13529
14058
12975
14326
14008
16193
14483
14011
15057
14884
15414
14440
14900
15074
14442
15307
14938
17193
15528
14765
15838
15723
16150
15486
15986
15983
15692
16490
15686
18897
16316
15636
17163
16534
16518
16375
16290
16352
15943
16362
16393
19051
16747
16320
17910
16961
17480
17049
16879
17473
16998
17307
17418
20169
17871
17226
19062
17804
19100
18522
18060
18869
18127
18871
18890
21263
19547
18450
20254
19240
20216
19420
19415
20018
18652
19978
19509
21971

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10053&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10053&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10053&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.422989536624582
beta0.000514955626444454
gamma0.94620902518207

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.422989536624582 \tabularnewline
beta & 0.000514955626444454 \tabularnewline
gamma & 0.94620902518207 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10053&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]0.422989536624582[/C][/ROW]
[ROW][C]beta[/C][C]0.000514955626444454[/C][/ROW]
[ROW][C]gamma[/C][C]0.94620902518207[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10053&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10053&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.422989536624582
beta0.000514955626444454
gamma0.94620902518207






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131448313944.8804166667538.119583333326
141401113686.0979965736324.902003426432
151505714851.1975415833205.802458416676
161488414748.4223866353135.577613364725
171541415341.347388649072.6526113509572
181444014402.879931805237.1200681947994
191490014878.598999854521.4010001455226
201507415071.92372817732.07627182270880
211444214462.0747508767-20.0747508767181
221530715336.3100833830-29.3100833829540
231493814974.5075825248-36.5075825247623
241719317225.0276627274-32.027662727367
251552815776.9425577243-248.942557724304
261476515068.9243948347-303.924394834674
271583815902.9691486429-64.9691486428728
281572315647.217895527675.7821044724187
291615016180.3799702807-30.3799702807264
301548615178.7938436343307.206156365735
311598615760.0959782035225.904021796508
321598316029.3387757661-46.3387757660985
331569215386.8725459578305.127454042171
341649016393.649262055896.3507379441799
351568616081.1241999454-395.124199945367
361889718182.3748650146714.625134985403
371631616931.8248968647-615.824896864662
381563616038.6592424093-402.659242409331
391716316961.440147934201.559852066006
401653416895.3692076351-361.369207635129
411651817185.6590761955-667.65907619552
421637516098.6842863866276.315713613410
431629016622.3856142795-332.385614279458
441635216506.5733049799-154.573304979949
451594316009.9249756602-66.9249756602021
461636216744.9690936872-382.969093687232
471639315960.8885818412432.111418158844
481905119017.647702806233.3522971937673
491674716752.0927339026-5.09273390255112
501632016233.331433221686.6685667783695
511791017692.7749344060217.225065593975
521696117325.7848750970-364.784875097022
531748017447.201810491732.7981895083321
541704917171.8476788322-122.847678832197
551687917194.2362119124-315.236211912375
561747317182.6256225956290.374377404431
571699816922.003074083475.9969259165773
581730717544.9453812475-237.945381247519
591741817267.2466428405150.753357159461
602016919987.2481541018181.751845898201
611787117763.4724595371107.527540462852
621722617342.4697830918-116.469783091849
631906218787.2461782215274.753821778475
641780418126.8193160791-322.819316079116
651910018483.0563700456616.94362995437
661852218369.9382247645152.061775235463
671806018403.7585538249-343.758553824875
681886918710.9106552419158.089344758126
691812718277.4405233282-150.440523328172
701887118633.3007632566237.699236743370
711889018769.2196251411120.780374858885
722126321493.6667510483-230.666751048338
731954719055.0275915991491.97240840091
741845018674.5381477947-224.538147794676
752025420287.3700052764-33.370005276367
761924019170.454284776269.5457152238196
772021620205.930640742810.0693592572279
781942019582.3543934525-162.354393452457
791941519212.4632947279202.536705272050
802001820024.794315328-6.79431532801027
811865219353.2019642645-701.201964264452
821997819687.9602181886290.039781811422
831950919782.1462019758-273.146201975789
842197122147.9623367409-176.962336740871

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 14483 & 13944.8804166667 & 538.119583333326 \tabularnewline
14 & 14011 & 13686.0979965736 & 324.902003426432 \tabularnewline
15 & 15057 & 14851.1975415833 & 205.802458416676 \tabularnewline
16 & 14884 & 14748.4223866353 & 135.577613364725 \tabularnewline
17 & 15414 & 15341.3473886490 & 72.6526113509572 \tabularnewline
18 & 14440 & 14402.8799318052 & 37.1200681947994 \tabularnewline
19 & 14900 & 14878.5989998545 & 21.4010001455226 \tabularnewline
20 & 15074 & 15071.9237281773 & 2.07627182270880 \tabularnewline
21 & 14442 & 14462.0747508767 & -20.0747508767181 \tabularnewline
22 & 15307 & 15336.3100833830 & -29.3100833829540 \tabularnewline
23 & 14938 & 14974.5075825248 & -36.5075825247623 \tabularnewline
24 & 17193 & 17225.0276627274 & -32.027662727367 \tabularnewline
25 & 15528 & 15776.9425577243 & -248.942557724304 \tabularnewline
26 & 14765 & 15068.9243948347 & -303.924394834674 \tabularnewline
27 & 15838 & 15902.9691486429 & -64.9691486428728 \tabularnewline
28 & 15723 & 15647.2178955276 & 75.7821044724187 \tabularnewline
29 & 16150 & 16180.3799702807 & -30.3799702807264 \tabularnewline
30 & 15486 & 15178.7938436343 & 307.206156365735 \tabularnewline
31 & 15986 & 15760.0959782035 & 225.904021796508 \tabularnewline
32 & 15983 & 16029.3387757661 & -46.3387757660985 \tabularnewline
33 & 15692 & 15386.8725459578 & 305.127454042171 \tabularnewline
34 & 16490 & 16393.6492620558 & 96.3507379441799 \tabularnewline
35 & 15686 & 16081.1241999454 & -395.124199945367 \tabularnewline
36 & 18897 & 18182.3748650146 & 714.625134985403 \tabularnewline
37 & 16316 & 16931.8248968647 & -615.824896864662 \tabularnewline
38 & 15636 & 16038.6592424093 & -402.659242409331 \tabularnewline
39 & 17163 & 16961.440147934 & 201.559852066006 \tabularnewline
40 & 16534 & 16895.3692076351 & -361.369207635129 \tabularnewline
41 & 16518 & 17185.6590761955 & -667.65907619552 \tabularnewline
42 & 16375 & 16098.6842863866 & 276.315713613410 \tabularnewline
43 & 16290 & 16622.3856142795 & -332.385614279458 \tabularnewline
44 & 16352 & 16506.5733049799 & -154.573304979949 \tabularnewline
45 & 15943 & 16009.9249756602 & -66.9249756602021 \tabularnewline
46 & 16362 & 16744.9690936872 & -382.969093687232 \tabularnewline
47 & 16393 & 15960.8885818412 & 432.111418158844 \tabularnewline
48 & 19051 & 19017.6477028062 & 33.3522971937673 \tabularnewline
49 & 16747 & 16752.0927339026 & -5.09273390255112 \tabularnewline
50 & 16320 & 16233.3314332216 & 86.6685667783695 \tabularnewline
51 & 17910 & 17692.7749344060 & 217.225065593975 \tabularnewline
52 & 16961 & 17325.7848750970 & -364.784875097022 \tabularnewline
53 & 17480 & 17447.2018104917 & 32.7981895083321 \tabularnewline
54 & 17049 & 17171.8476788322 & -122.847678832197 \tabularnewline
55 & 16879 & 17194.2362119124 & -315.236211912375 \tabularnewline
56 & 17473 & 17182.6256225956 & 290.374377404431 \tabularnewline
57 & 16998 & 16922.0030740834 & 75.9969259165773 \tabularnewline
58 & 17307 & 17544.9453812475 & -237.945381247519 \tabularnewline
59 & 17418 & 17267.2466428405 & 150.753357159461 \tabularnewline
60 & 20169 & 19987.2481541018 & 181.751845898201 \tabularnewline
61 & 17871 & 17763.4724595371 & 107.527540462852 \tabularnewline
62 & 17226 & 17342.4697830918 & -116.469783091849 \tabularnewline
63 & 19062 & 18787.2461782215 & 274.753821778475 \tabularnewline
64 & 17804 & 18126.8193160791 & -322.819316079116 \tabularnewline
65 & 19100 & 18483.0563700456 & 616.94362995437 \tabularnewline
66 & 18522 & 18369.9382247645 & 152.061775235463 \tabularnewline
67 & 18060 & 18403.7585538249 & -343.758553824875 \tabularnewline
68 & 18869 & 18710.9106552419 & 158.089344758126 \tabularnewline
69 & 18127 & 18277.4405233282 & -150.440523328172 \tabularnewline
70 & 18871 & 18633.3007632566 & 237.699236743370 \tabularnewline
71 & 18890 & 18769.2196251411 & 120.780374858885 \tabularnewline
72 & 21263 & 21493.6667510483 & -230.666751048338 \tabularnewline
73 & 19547 & 19055.0275915991 & 491.97240840091 \tabularnewline
74 & 18450 & 18674.5381477947 & -224.538147794676 \tabularnewline
75 & 20254 & 20287.3700052764 & -33.370005276367 \tabularnewline
76 & 19240 & 19170.4542847762 & 69.5457152238196 \tabularnewline
77 & 20216 & 20205.9306407428 & 10.0693592572279 \tabularnewline
78 & 19420 & 19582.3543934525 & -162.354393452457 \tabularnewline
79 & 19415 & 19212.4632947279 & 202.536705272050 \tabularnewline
80 & 20018 & 20024.794315328 & -6.79431532801027 \tabularnewline
81 & 18652 & 19353.2019642645 & -701.201964264452 \tabularnewline
82 & 19978 & 19687.9602181886 & 290.039781811422 \tabularnewline
83 & 19509 & 19782.1462019758 & -273.146201975789 \tabularnewline
84 & 21971 & 22147.9623367409 & -176.962336740871 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10053&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]14483[/C][C]13944.8804166667[/C][C]538.119583333326[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]13686.0979965736[/C][C]324.902003426432[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]14851.1975415833[/C][C]205.802458416676[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]14748.4223866353[/C][C]135.577613364725[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]15341.3473886490[/C][C]72.6526113509572[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]14402.8799318052[/C][C]37.1200681947994[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]14878.5989998545[/C][C]21.4010001455226[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]15071.9237281773[/C][C]2.07627182270880[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]14462.0747508767[/C][C]-20.0747508767181[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]15336.3100833830[/C][C]-29.3100833829540[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]14974.5075825248[/C][C]-36.5075825247623[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]17225.0276627274[/C][C]-32.027662727367[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15776.9425577243[/C][C]-248.942557724304[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]15068.9243948347[/C][C]-303.924394834674[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15902.9691486429[/C][C]-64.9691486428728[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15647.2178955276[/C][C]75.7821044724187[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]16180.3799702807[/C][C]-30.3799702807264[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15178.7938436343[/C][C]307.206156365735[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]15760.0959782035[/C][C]225.904021796508[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]16029.3387757661[/C][C]-46.3387757660985[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]15386.8725459578[/C][C]305.127454042171[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]16393.6492620558[/C][C]96.3507379441799[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]16081.1241999454[/C][C]-395.124199945367[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]18182.3748650146[/C][C]714.625134985403[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]16931.8248968647[/C][C]-615.824896864662[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]16038.6592424093[/C][C]-402.659242409331[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]16961.440147934[/C][C]201.559852066006[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16895.3692076351[/C][C]-361.369207635129[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]17185.6590761955[/C][C]-667.65907619552[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16098.6842863866[/C][C]276.315713613410[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16622.3856142795[/C][C]-332.385614279458[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16506.5733049799[/C][C]-154.573304979949[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]16009.9249756602[/C][C]-66.9249756602021[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16744.9690936872[/C][C]-382.969093687232[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]15960.8885818412[/C][C]432.111418158844[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]19017.6477028062[/C][C]33.3522971937673[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]16752.0927339026[/C][C]-5.09273390255112[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]16233.3314332216[/C][C]86.6685667783695[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]17692.7749344060[/C][C]217.225065593975[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17325.7848750970[/C][C]-364.784875097022[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17447.2018104917[/C][C]32.7981895083321[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17171.8476788322[/C][C]-122.847678832197[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]17194.2362119124[/C][C]-315.236211912375[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17182.6256225956[/C][C]290.374377404431[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]16922.0030740834[/C][C]75.9969259165773[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17544.9453812475[/C][C]-237.945381247519[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17267.2466428405[/C][C]150.753357159461[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]19987.2481541018[/C][C]181.751845898201[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]17763.4724595371[/C][C]107.527540462852[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]17342.4697830918[/C][C]-116.469783091849[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]18787.2461782215[/C][C]274.753821778475[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]18126.8193160791[/C][C]-322.819316079116[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]18483.0563700456[/C][C]616.94362995437[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18369.9382247645[/C][C]152.061775235463[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18403.7585538249[/C][C]-343.758553824875[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18710.9106552419[/C][C]158.089344758126[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18277.4405233282[/C][C]-150.440523328172[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18633.3007632566[/C][C]237.699236743370[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18769.2196251411[/C][C]120.780374858885[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]21493.6667510483[/C][C]-230.666751048338[/C][/ROW]
[ROW][C]73[/C][C]19547[/C][C]19055.0275915991[/C][C]491.97240840091[/C][/ROW]
[ROW][C]74[/C][C]18450[/C][C]18674.5381477947[/C][C]-224.538147794676[/C][/ROW]
[ROW][C]75[/C][C]20254[/C][C]20287.3700052764[/C][C]-33.370005276367[/C][/ROW]
[ROW][C]76[/C][C]19240[/C][C]19170.4542847762[/C][C]69.5457152238196[/C][/ROW]
[ROW][C]77[/C][C]20216[/C][C]20205.9306407428[/C][C]10.0693592572279[/C][/ROW]
[ROW][C]78[/C][C]19420[/C][C]19582.3543934525[/C][C]-162.354393452457[/C][/ROW]
[ROW][C]79[/C][C]19415[/C][C]19212.4632947279[/C][C]202.536705272050[/C][/ROW]
[ROW][C]80[/C][C]20018[/C][C]20024.794315328[/C][C]-6.79431532801027[/C][/ROW]
[ROW][C]81[/C][C]18652[/C][C]19353.2019642645[/C][C]-701.201964264452[/C][/ROW]
[ROW][C]82[/C][C]19978[/C][C]19687.9602181886[/C][C]290.039781811422[/C][/ROW]
[ROW][C]83[/C][C]19509[/C][C]19782.1462019758[/C][C]-273.146201975789[/C][/ROW]
[ROW][C]84[/C][C]21971[/C][C]22147.9623367409[/C][C]-176.962336740871[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10053&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10053&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131448313944.8804166667538.119583333326
141401113686.0979965736324.902003426432
151505714851.1975415833205.802458416676
161488414748.4223866353135.577613364725
171541415341.347388649072.6526113509572
181444014402.879931805237.1200681947994
191490014878.598999854521.4010001455226
201507415071.92372817732.07627182270880
211444214462.0747508767-20.0747508767181
221530715336.3100833830-29.3100833829540
231493814974.5075825248-36.5075825247623
241719317225.0276627274-32.027662727367
251552815776.9425577243-248.942557724304
261476515068.9243948347-303.924394834674
271583815902.9691486429-64.9691486428728
281572315647.217895527675.7821044724187
291615016180.3799702807-30.3799702807264
301548615178.7938436343307.206156365735
311598615760.0959782035225.904021796508
321598316029.3387757661-46.3387757660985
331569215386.8725459578305.127454042171
341649016393.649262055896.3507379441799
351568616081.1241999454-395.124199945367
361889718182.3748650146714.625134985403
371631616931.8248968647-615.824896864662
381563616038.6592424093-402.659242409331
391716316961.440147934201.559852066006
401653416895.3692076351-361.369207635129
411651817185.6590761955-667.65907619552
421637516098.6842863866276.315713613410
431629016622.3856142795-332.385614279458
441635216506.5733049799-154.573304979949
451594316009.9249756602-66.9249756602021
461636216744.9690936872-382.969093687232
471639315960.8885818412432.111418158844
481905119017.647702806233.3522971937673
491674716752.0927339026-5.09273390255112
501632016233.331433221686.6685667783695
511791017692.7749344060217.225065593975
521696117325.7848750970-364.784875097022
531748017447.201810491732.7981895083321
541704917171.8476788322-122.847678832197
551687917194.2362119124-315.236211912375
561747317182.6256225956290.374377404431
571699816922.003074083475.9969259165773
581730717544.9453812475-237.945381247519
591741817267.2466428405150.753357159461
602016919987.2481541018181.751845898201
611787117763.4724595371107.527540462852
621722617342.4697830918-116.469783091849
631906218787.2461782215274.753821778475
641780418126.8193160791-322.819316079116
651910018483.0563700456616.94362995437
661852218369.9382247645152.061775235463
671806018403.7585538249-343.758553824875
681886918710.9106552419158.089344758126
691812718277.4405233282-150.440523328172
701887118633.3007632566237.699236743370
711889018769.2196251411120.780374858885
722126321493.6667510483-230.666751048338
731954719055.0275915991491.97240840091
741845018674.5381477947-224.538147794676
752025420287.3700052764-33.370005276367
761924019170.454284776269.5457152238196
772021620205.930640742810.0693592572279
781942019582.3543934525-162.354393452457
791941519212.4632947279202.536705272050
802001820024.794315328-6.79431532801027
811865219353.2019642645-701.201964264452
821997819687.9602181886290.039781811422
831950919782.1462019758-273.146201975789
842197122147.9623367409-176.962336740871






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520126.468692712219570.733377025620682.2040083988
8619146.465836360818543.011880655519749.9197920661
8720958.477274194520310.767024918121606.1875234708
8819911.702882515219222.531320789320600.874444241
8920885.111536591320156.796131437121613.4269417456
9020162.957096864919397.459703006320928.4544907235
9120060.815750197619259.824949591320861.8065508039
9220672.997798694219837.986800774621508.0087966138
9319624.964283496418757.232987942920492.6955790499
9420797.479507262719898.185897882821696.7731166425
9520461.399591039619531.583706190021391.2154758892
9622995.228911262222035.831505527323954.6263169972

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 20126.4686927122 & 19570.7333770256 & 20682.2040083988 \tabularnewline
86 & 19146.4658363608 & 18543.0118806555 & 19749.9197920661 \tabularnewline
87 & 20958.4772741945 & 20310.7670249181 & 21606.1875234708 \tabularnewline
88 & 19911.7028825152 & 19222.5313207893 & 20600.874444241 \tabularnewline
89 & 20885.1115365913 & 20156.7961314371 & 21613.4269417456 \tabularnewline
90 & 20162.9570968649 & 19397.4597030063 & 20928.4544907235 \tabularnewline
91 & 20060.8157501976 & 19259.8249495913 & 20861.8065508039 \tabularnewline
92 & 20672.9977986942 & 19837.9868007746 & 21508.0087966138 \tabularnewline
93 & 19624.9642834964 & 18757.2329879429 & 20492.6955790499 \tabularnewline
94 & 20797.4795072627 & 19898.1858978828 & 21696.7731166425 \tabularnewline
95 & 20461.3995910396 & 19531.5837061900 & 21391.2154758892 \tabularnewline
96 & 22995.2289112622 & 22035.8315055273 & 23954.6263169972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10053&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]20126.4686927122[/C][C]19570.7333770256[/C][C]20682.2040083988[/C][/ROW]
[ROW][C]86[/C][C]19146.4658363608[/C][C]18543.0118806555[/C][C]19749.9197920661[/C][/ROW]
[ROW][C]87[/C][C]20958.4772741945[/C][C]20310.7670249181[/C][C]21606.1875234708[/C][/ROW]
[ROW][C]88[/C][C]19911.7028825152[/C][C]19222.5313207893[/C][C]20600.874444241[/C][/ROW]
[ROW][C]89[/C][C]20885.1115365913[/C][C]20156.7961314371[/C][C]21613.4269417456[/C][/ROW]
[ROW][C]90[/C][C]20162.9570968649[/C][C]19397.4597030063[/C][C]20928.4544907235[/C][/ROW]
[ROW][C]91[/C][C]20060.8157501976[/C][C]19259.8249495913[/C][C]20861.8065508039[/C][/ROW]
[ROW][C]92[/C][C]20672.9977986942[/C][C]19837.9868007746[/C][C]21508.0087966138[/C][/ROW]
[ROW][C]93[/C][C]19624.9642834964[/C][C]18757.2329879429[/C][C]20492.6955790499[/C][/ROW]
[ROW][C]94[/C][C]20797.4795072627[/C][C]19898.1858978828[/C][C]21696.7731166425[/C][/ROW]
[ROW][C]95[/C][C]20461.3995910396[/C][C]19531.5837061900[/C][C]21391.2154758892[/C][/ROW]
[ROW][C]96[/C][C]22995.2289112622[/C][C]22035.8315055273[/C][C]23954.6263169972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10053&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10053&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520126.468692712219570.733377025620682.2040083988
8619146.465836360818543.011880655519749.9197920661
8720958.477274194520310.767024918121606.1875234708
8819911.702882515219222.531320789320600.874444241
8920885.111536591320156.796131437121613.4269417456
9020162.957096864919397.459703006320928.4544907235
9120060.815750197619259.824949591320861.8065508039
9220672.997798694219837.986800774621508.0087966138
9319624.964283496418757.232987942920492.6955790499
9420797.479507262719898.185897882821696.7731166425
9520461.399591039619531.583706190021391.2154758892
9622995.228911262222035.831505527323954.6263169972


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')