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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 25 Nov 2017 13:15:01 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Nov/25/t1511612131pbmma9mqkop0nmv.htm/, Retrieved Fri, 17 May 2024 10:44:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308211, Retrieved Fri, 17 May 2024 10:44:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-11-25 12:15:01] [7b600e37b7623e0607d4fc29480a062d] [Current]
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Dataseries X:
1028
869
2698
2367
1928
1846
1404
1316
1008
865
586
343
1143
1807
2380
2334
2116
1788
1571
1306
952
806
473
278
993
1038
2259
2283
1746
1515
1230
882
1028
704
390
238
594
692
2125
1849
1468
1531
1203
878
818
605
316
136
528
654
1892
1597
1515
1241
1026
758
733
481
280
117
651
611
1898
1385
1047
1007
842
827
711
443
313
202
473
566
1609
1296
1153
1155
859
798
557
402
223
153
548
647
1757
1326
1308
1175
992
808
758
551
310
146
649
602
1801
1481
1400
1319
1153
950
829
636
310
191
679
842
1975
1677
1418
1540
1173
941
989
614
352
405




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308211&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308211&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308211&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.151846481484424
beta0.0257056065272407
gamma0.770506217209368

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.151846481484424 \tabularnewline
beta & 0.0257056065272407 \tabularnewline
gamma & 0.770506217209368 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308211&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]0.151846481484424[/C][/ROW]
[ROW][C]beta[/C][C]0.0257056065272407[/C][/ROW]
[ROW][C]gamma[/C][C]0.770506217209368[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308211&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308211&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
alpha0.151846481484424
beta0.0257056065272407
gamma0.770506217209368







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311431115.3056914226527.6943085773532
1418071766.1485734142540.8514265857502
1523802344.7711718368335.2288281631741
1623342318.3927705692115.6072294307946
1721162120.0934532182-4.09345321820319
1817881804.97348358887-16.9734835888696
1915711477.2633676363393.7366323636729
2013061358.04888708436-52.0488870843649
219521018.12273857243-66.1227385724317
22806876.09576887565-70.0957688756502
23473584.861504590111-111.861504590111
24278331.585969717353-53.5859697173528
259931092.63379182817-99.6337918281722
2610381694.56598426099-656.565984260985
2722592091.26466679695167.735333203052
2822832069.88709028978213.112909710224
2917461903.87186457765-157.87186457765
3015151587.77439013648-72.7743901364829
3112301348.97694312716-118.976943127163
328821130.07994408807-248.079944088066
331028804.903813932609223.096186067391
34704718.768343759976-14.7683437599765
35390443.995375895568-53.9953758955682
36238259.633833222896-21.633833222896
37594909.829921546607-315.829921546607
386921050.24950689341-358.249506893412
3921251871.24674772185253.753252278148
4018491885.98879660477-36.9887966047709
4114681502.94852936236-34.9485293623648
4215311292.64859814717238.35140185283
4312031100.32442355947102.675576440531
44878854.94583076187523.0541692381249
45818870.694281911607-52.694281911607
46605619.610345647909-14.6103456479088
47316355.404397310783-39.4043973107834
48136213.42616527269-77.4261652726896
49528573.698318561931-45.6983185619308
50654692.457989114121-38.4579891141215
5118921829.8762362906362.1237637093659
5215971646.02158400381-49.0215840038068
5315151303.41139239896211.588607601043
5412411305.84387593823-64.8438759382263
5510261015.6506141164710.3493858835276
56758745.79596966640312.2040303335967
57733713.29997815534719.7000218446534
58481526.147442360018-45.147442360018
59280280.398948422348-0.398948422348496
60117138.118892910677-21.1188929106765
61651484.55697780346166.44302219654
62611633.762098452243-22.762098452243
6318981783.08420480272114.915795197282
6413851546.78180950193-161.781809501931
6510471363.32363047068-316.323630470679
6610071125.42378112727-118.423781127265
67842901.397573510192-59.3975735101922
68827655.29289164173171.70710835827
69711653.98402216600457.0159778339964
70443450.573744487588-7.57374448758759
71313256.90549752902356.0945024709771
72202117.56164866109984.4383513389013
73473635.800853908312-162.800853908312
74566612.308396364918-46.3083963649182
7516091829.59013326753-220.59013326753
7612961379.20742242115-83.2074224211533
7711531109.5426116418943.4573883581079
7811551056.3314347652598.6685652347487
79859899.69936822758-40.6993682275798
80798801.732783403839-3.73278340383911
81557698.881345390376-141.881345390376
82402431.57249198399-29.5724919839898
83223281.090167828478-58.0901678284778
84153150.5587016079652.44129839203455
85548425.067351583881122.932648416119
86647510.317535304388136.682464695612
8717571553.2402525256203.759747474402
8813261270.7675527635855.2324472364178
8913081110.34251941479197.657480585212
9011751117.7454682907157.254531709295
91992867.056366823701124.943633176299
92808818.869147274161-10.8691472741613
93758618.649739616438139.350260383562
94551452.91891794679998.0810820532008
95310279.09728448996230.902715510038
96146185.617011766209-39.6170117662091
97649594.88363973376854.1163602662317
98602689.698268265715-87.6982682657153
9918011842.24780367082-41.2478036708178
10014811400.8852659948980.1147340051104
10114001331.900238361968.0997616380973
10213191223.8750770424695.1249229575351
10311531010.00632102809142.993678971908
104950867.54059286776682.4594071322343
105829769.90016732258859.0998326774118
106636549.99441451096386.0055854890367
107310317.063712182913-7.06371218291304
108191165.35911713258825.6408828674123
109679695.413293740919-16.4132937409194
110842686.728645900917155.271354099083
11119752090.5181512874-115.518151287401
11216771670.818833415876.18116658412646
11314181575.19032799785-157.190327997846
11415401441.9205314947498.0794685052622
11511731237.3012059032-64.3012059031983
1169411006.42909875573-65.4290987557305
117989863.374197848613125.625802151387
118614654.005039769252-40.0050397692515
119352327.1503479170324.8496520829698
120405193.359345848511211.640654151489

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1143 & 1115.30569142265 & 27.6943085773532 \tabularnewline
14 & 1807 & 1766.14857341425 & 40.8514265857502 \tabularnewline
15 & 2380 & 2344.77117183683 & 35.2288281631741 \tabularnewline
16 & 2334 & 2318.39277056921 & 15.6072294307946 \tabularnewline
17 & 2116 & 2120.0934532182 & -4.09345321820319 \tabularnewline
18 & 1788 & 1804.97348358887 & -16.9734835888696 \tabularnewline
19 & 1571 & 1477.26336763633 & 93.7366323636729 \tabularnewline
20 & 1306 & 1358.04888708436 & -52.0488870843649 \tabularnewline
21 & 952 & 1018.12273857243 & -66.1227385724317 \tabularnewline
22 & 806 & 876.09576887565 & -70.0957688756502 \tabularnewline
23 & 473 & 584.861504590111 & -111.861504590111 \tabularnewline
24 & 278 & 331.585969717353 & -53.5859697173528 \tabularnewline
25 & 993 & 1092.63379182817 & -99.6337918281722 \tabularnewline
26 & 1038 & 1694.56598426099 & -656.565984260985 \tabularnewline
27 & 2259 & 2091.26466679695 & 167.735333203052 \tabularnewline
28 & 2283 & 2069.88709028978 & 213.112909710224 \tabularnewline
29 & 1746 & 1903.87186457765 & -157.87186457765 \tabularnewline
30 & 1515 & 1587.77439013648 & -72.7743901364829 \tabularnewline
31 & 1230 & 1348.97694312716 & -118.976943127163 \tabularnewline
32 & 882 & 1130.07994408807 & -248.079944088066 \tabularnewline
33 & 1028 & 804.903813932609 & 223.096186067391 \tabularnewline
34 & 704 & 718.768343759976 & -14.7683437599765 \tabularnewline
35 & 390 & 443.995375895568 & -53.9953758955682 \tabularnewline
36 & 238 & 259.633833222896 & -21.633833222896 \tabularnewline
37 & 594 & 909.829921546607 & -315.829921546607 \tabularnewline
38 & 692 & 1050.24950689341 & -358.249506893412 \tabularnewline
39 & 2125 & 1871.24674772185 & 253.753252278148 \tabularnewline
40 & 1849 & 1885.98879660477 & -36.9887966047709 \tabularnewline
41 & 1468 & 1502.94852936236 & -34.9485293623648 \tabularnewline
42 & 1531 & 1292.64859814717 & 238.35140185283 \tabularnewline
43 & 1203 & 1100.32442355947 & 102.675576440531 \tabularnewline
44 & 878 & 854.945830761875 & 23.0541692381249 \tabularnewline
45 & 818 & 870.694281911607 & -52.694281911607 \tabularnewline
46 & 605 & 619.610345647909 & -14.6103456479088 \tabularnewline
47 & 316 & 355.404397310783 & -39.4043973107834 \tabularnewline
48 & 136 & 213.42616527269 & -77.4261652726896 \tabularnewline
49 & 528 & 573.698318561931 & -45.6983185619308 \tabularnewline
50 & 654 & 692.457989114121 & -38.4579891141215 \tabularnewline
51 & 1892 & 1829.87623629063 & 62.1237637093659 \tabularnewline
52 & 1597 & 1646.02158400381 & -49.0215840038068 \tabularnewline
53 & 1515 & 1303.41139239896 & 211.588607601043 \tabularnewline
54 & 1241 & 1305.84387593823 & -64.8438759382263 \tabularnewline
55 & 1026 & 1015.65061411647 & 10.3493858835276 \tabularnewline
56 & 758 & 745.795969666403 & 12.2040303335967 \tabularnewline
57 & 733 & 713.299978155347 & 19.7000218446534 \tabularnewline
58 & 481 & 526.147442360018 & -45.147442360018 \tabularnewline
59 & 280 & 280.398948422348 & -0.398948422348496 \tabularnewline
60 & 117 & 138.118892910677 & -21.1188929106765 \tabularnewline
61 & 651 & 484.55697780346 & 166.44302219654 \tabularnewline
62 & 611 & 633.762098452243 & -22.762098452243 \tabularnewline
63 & 1898 & 1783.08420480272 & 114.915795197282 \tabularnewline
64 & 1385 & 1546.78180950193 & -161.781809501931 \tabularnewline
65 & 1047 & 1363.32363047068 & -316.323630470679 \tabularnewline
66 & 1007 & 1125.42378112727 & -118.423781127265 \tabularnewline
67 & 842 & 901.397573510192 & -59.3975735101922 \tabularnewline
68 & 827 & 655.29289164173 & 171.70710835827 \tabularnewline
69 & 711 & 653.984022166004 & 57.0159778339964 \tabularnewline
70 & 443 & 450.573744487588 & -7.57374448758759 \tabularnewline
71 & 313 & 256.905497529023 & 56.0945024709771 \tabularnewline
72 & 202 & 117.561648661099 & 84.4383513389013 \tabularnewline
73 & 473 & 635.800853908312 & -162.800853908312 \tabularnewline
74 & 566 & 612.308396364918 & -46.3083963649182 \tabularnewline
75 & 1609 & 1829.59013326753 & -220.59013326753 \tabularnewline
76 & 1296 & 1379.20742242115 & -83.2074224211533 \tabularnewline
77 & 1153 & 1109.54261164189 & 43.4573883581079 \tabularnewline
78 & 1155 & 1056.33143476525 & 98.6685652347487 \tabularnewline
79 & 859 & 899.69936822758 & -40.6993682275798 \tabularnewline
80 & 798 & 801.732783403839 & -3.73278340383911 \tabularnewline
81 & 557 & 698.881345390376 & -141.881345390376 \tabularnewline
82 & 402 & 431.57249198399 & -29.5724919839898 \tabularnewline
83 & 223 & 281.090167828478 & -58.0901678284778 \tabularnewline
84 & 153 & 150.558701607965 & 2.44129839203455 \tabularnewline
85 & 548 & 425.067351583881 & 122.932648416119 \tabularnewline
86 & 647 & 510.317535304388 & 136.682464695612 \tabularnewline
87 & 1757 & 1553.2402525256 & 203.759747474402 \tabularnewline
88 & 1326 & 1270.76755276358 & 55.2324472364178 \tabularnewline
89 & 1308 & 1110.34251941479 & 197.657480585212 \tabularnewline
90 & 1175 & 1117.74546829071 & 57.254531709295 \tabularnewline
91 & 992 & 867.056366823701 & 124.943633176299 \tabularnewline
92 & 808 & 818.869147274161 & -10.8691472741613 \tabularnewline
93 & 758 & 618.649739616438 & 139.350260383562 \tabularnewline
94 & 551 & 452.918917946799 & 98.0810820532008 \tabularnewline
95 & 310 & 279.097284489962 & 30.902715510038 \tabularnewline
96 & 146 & 185.617011766209 & -39.6170117662091 \tabularnewline
97 & 649 & 594.883639733768 & 54.1163602662317 \tabularnewline
98 & 602 & 689.698268265715 & -87.6982682657153 \tabularnewline
99 & 1801 & 1842.24780367082 & -41.2478036708178 \tabularnewline
100 & 1481 & 1400.88526599489 & 80.1147340051104 \tabularnewline
101 & 1400 & 1331.9002383619 & 68.0997616380973 \tabularnewline
102 & 1319 & 1223.87507704246 & 95.1249229575351 \tabularnewline
103 & 1153 & 1010.00632102809 & 142.993678971908 \tabularnewline
104 & 950 & 867.540592867766 & 82.4594071322343 \tabularnewline
105 & 829 & 769.900167322588 & 59.0998326774118 \tabularnewline
106 & 636 & 549.994414510963 & 86.0055854890367 \tabularnewline
107 & 310 & 317.063712182913 & -7.06371218291304 \tabularnewline
108 & 191 & 165.359117132588 & 25.6408828674123 \tabularnewline
109 & 679 & 695.413293740919 & -16.4132937409194 \tabularnewline
110 & 842 & 686.728645900917 & 155.271354099083 \tabularnewline
111 & 1975 & 2090.5181512874 & -115.518151287401 \tabularnewline
112 & 1677 & 1670.81883341587 & 6.18116658412646 \tabularnewline
113 & 1418 & 1575.19032799785 & -157.190327997846 \tabularnewline
114 & 1540 & 1441.92053149474 & 98.0794685052622 \tabularnewline
115 & 1173 & 1237.3012059032 & -64.3012059031983 \tabularnewline
116 & 941 & 1006.42909875573 & -65.4290987557305 \tabularnewline
117 & 989 & 863.374197848613 & 125.625802151387 \tabularnewline
118 & 614 & 654.005039769252 & -40.0050397692515 \tabularnewline
119 & 352 & 327.15034791703 & 24.8496520829698 \tabularnewline
120 & 405 & 193.359345848511 & 211.640654151489 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308211&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]1143[/C][C]1115.30569142265[/C][C]27.6943085773532[/C][/ROW]
[ROW][C]14[/C][C]1807[/C][C]1766.14857341425[/C][C]40.8514265857502[/C][/ROW]
[ROW][C]15[/C][C]2380[/C][C]2344.77117183683[/C][C]35.2288281631741[/C][/ROW]
[ROW][C]16[/C][C]2334[/C][C]2318.39277056921[/C][C]15.6072294307946[/C][/ROW]
[ROW][C]17[/C][C]2116[/C][C]2120.0934532182[/C][C]-4.09345321820319[/C][/ROW]
[ROW][C]18[/C][C]1788[/C][C]1804.97348358887[/C][C]-16.9734835888696[/C][/ROW]
[ROW][C]19[/C][C]1571[/C][C]1477.26336763633[/C][C]93.7366323636729[/C][/ROW]
[ROW][C]20[/C][C]1306[/C][C]1358.04888708436[/C][C]-52.0488870843649[/C][/ROW]
[ROW][C]21[/C][C]952[/C][C]1018.12273857243[/C][C]-66.1227385724317[/C][/ROW]
[ROW][C]22[/C][C]806[/C][C]876.09576887565[/C][C]-70.0957688756502[/C][/ROW]
[ROW][C]23[/C][C]473[/C][C]584.861504590111[/C][C]-111.861504590111[/C][/ROW]
[ROW][C]24[/C][C]278[/C][C]331.585969717353[/C][C]-53.5859697173528[/C][/ROW]
[ROW][C]25[/C][C]993[/C][C]1092.63379182817[/C][C]-99.6337918281722[/C][/ROW]
[ROW][C]26[/C][C]1038[/C][C]1694.56598426099[/C][C]-656.565984260985[/C][/ROW]
[ROW][C]27[/C][C]2259[/C][C]2091.26466679695[/C][C]167.735333203052[/C][/ROW]
[ROW][C]28[/C][C]2283[/C][C]2069.88709028978[/C][C]213.112909710224[/C][/ROW]
[ROW][C]29[/C][C]1746[/C][C]1903.87186457765[/C][C]-157.87186457765[/C][/ROW]
[ROW][C]30[/C][C]1515[/C][C]1587.77439013648[/C][C]-72.7743901364829[/C][/ROW]
[ROW][C]31[/C][C]1230[/C][C]1348.97694312716[/C][C]-118.976943127163[/C][/ROW]
[ROW][C]32[/C][C]882[/C][C]1130.07994408807[/C][C]-248.079944088066[/C][/ROW]
[ROW][C]33[/C][C]1028[/C][C]804.903813932609[/C][C]223.096186067391[/C][/ROW]
[ROW][C]34[/C][C]704[/C][C]718.768343759976[/C][C]-14.7683437599765[/C][/ROW]
[ROW][C]35[/C][C]390[/C][C]443.995375895568[/C][C]-53.9953758955682[/C][/ROW]
[ROW][C]36[/C][C]238[/C][C]259.633833222896[/C][C]-21.633833222896[/C][/ROW]
[ROW][C]37[/C][C]594[/C][C]909.829921546607[/C][C]-315.829921546607[/C][/ROW]
[ROW][C]38[/C][C]692[/C][C]1050.24950689341[/C][C]-358.249506893412[/C][/ROW]
[ROW][C]39[/C][C]2125[/C][C]1871.24674772185[/C][C]253.753252278148[/C][/ROW]
[ROW][C]40[/C][C]1849[/C][C]1885.98879660477[/C][C]-36.9887966047709[/C][/ROW]
[ROW][C]41[/C][C]1468[/C][C]1502.94852936236[/C][C]-34.9485293623648[/C][/ROW]
[ROW][C]42[/C][C]1531[/C][C]1292.64859814717[/C][C]238.35140185283[/C][/ROW]
[ROW][C]43[/C][C]1203[/C][C]1100.32442355947[/C][C]102.675576440531[/C][/ROW]
[ROW][C]44[/C][C]878[/C][C]854.945830761875[/C][C]23.0541692381249[/C][/ROW]
[ROW][C]45[/C][C]818[/C][C]870.694281911607[/C][C]-52.694281911607[/C][/ROW]
[ROW][C]46[/C][C]605[/C][C]619.610345647909[/C][C]-14.6103456479088[/C][/ROW]
[ROW][C]47[/C][C]316[/C][C]355.404397310783[/C][C]-39.4043973107834[/C][/ROW]
[ROW][C]48[/C][C]136[/C][C]213.42616527269[/C][C]-77.4261652726896[/C][/ROW]
[ROW][C]49[/C][C]528[/C][C]573.698318561931[/C][C]-45.6983185619308[/C][/ROW]
[ROW][C]50[/C][C]654[/C][C]692.457989114121[/C][C]-38.4579891141215[/C][/ROW]
[ROW][C]51[/C][C]1892[/C][C]1829.87623629063[/C][C]62.1237637093659[/C][/ROW]
[ROW][C]52[/C][C]1597[/C][C]1646.02158400381[/C][C]-49.0215840038068[/C][/ROW]
[ROW][C]53[/C][C]1515[/C][C]1303.41139239896[/C][C]211.588607601043[/C][/ROW]
[ROW][C]54[/C][C]1241[/C][C]1305.84387593823[/C][C]-64.8438759382263[/C][/ROW]
[ROW][C]55[/C][C]1026[/C][C]1015.65061411647[/C][C]10.3493858835276[/C][/ROW]
[ROW][C]56[/C][C]758[/C][C]745.795969666403[/C][C]12.2040303335967[/C][/ROW]
[ROW][C]57[/C][C]733[/C][C]713.299978155347[/C][C]19.7000218446534[/C][/ROW]
[ROW][C]58[/C][C]481[/C][C]526.147442360018[/C][C]-45.147442360018[/C][/ROW]
[ROW][C]59[/C][C]280[/C][C]280.398948422348[/C][C]-0.398948422348496[/C][/ROW]
[ROW][C]60[/C][C]117[/C][C]138.118892910677[/C][C]-21.1188929106765[/C][/ROW]
[ROW][C]61[/C][C]651[/C][C]484.55697780346[/C][C]166.44302219654[/C][/ROW]
[ROW][C]62[/C][C]611[/C][C]633.762098452243[/C][C]-22.762098452243[/C][/ROW]
[ROW][C]63[/C][C]1898[/C][C]1783.08420480272[/C][C]114.915795197282[/C][/ROW]
[ROW][C]64[/C][C]1385[/C][C]1546.78180950193[/C][C]-161.781809501931[/C][/ROW]
[ROW][C]65[/C][C]1047[/C][C]1363.32363047068[/C][C]-316.323630470679[/C][/ROW]
[ROW][C]66[/C][C]1007[/C][C]1125.42378112727[/C][C]-118.423781127265[/C][/ROW]
[ROW][C]67[/C][C]842[/C][C]901.397573510192[/C][C]-59.3975735101922[/C][/ROW]
[ROW][C]68[/C][C]827[/C][C]655.29289164173[/C][C]171.70710835827[/C][/ROW]
[ROW][C]69[/C][C]711[/C][C]653.984022166004[/C][C]57.0159778339964[/C][/ROW]
[ROW][C]70[/C][C]443[/C][C]450.573744487588[/C][C]-7.57374448758759[/C][/ROW]
[ROW][C]71[/C][C]313[/C][C]256.905497529023[/C][C]56.0945024709771[/C][/ROW]
[ROW][C]72[/C][C]202[/C][C]117.561648661099[/C][C]84.4383513389013[/C][/ROW]
[ROW][C]73[/C][C]473[/C][C]635.800853908312[/C][C]-162.800853908312[/C][/ROW]
[ROW][C]74[/C][C]566[/C][C]612.308396364918[/C][C]-46.3083963649182[/C][/ROW]
[ROW][C]75[/C][C]1609[/C][C]1829.59013326753[/C][C]-220.59013326753[/C][/ROW]
[ROW][C]76[/C][C]1296[/C][C]1379.20742242115[/C][C]-83.2074224211533[/C][/ROW]
[ROW][C]77[/C][C]1153[/C][C]1109.54261164189[/C][C]43.4573883581079[/C][/ROW]
[ROW][C]78[/C][C]1155[/C][C]1056.33143476525[/C][C]98.6685652347487[/C][/ROW]
[ROW][C]79[/C][C]859[/C][C]899.69936822758[/C][C]-40.6993682275798[/C][/ROW]
[ROW][C]80[/C][C]798[/C][C]801.732783403839[/C][C]-3.73278340383911[/C][/ROW]
[ROW][C]81[/C][C]557[/C][C]698.881345390376[/C][C]-141.881345390376[/C][/ROW]
[ROW][C]82[/C][C]402[/C][C]431.57249198399[/C][C]-29.5724919839898[/C][/ROW]
[ROW][C]83[/C][C]223[/C][C]281.090167828478[/C][C]-58.0901678284778[/C][/ROW]
[ROW][C]84[/C][C]153[/C][C]150.558701607965[/C][C]2.44129839203455[/C][/ROW]
[ROW][C]85[/C][C]548[/C][C]425.067351583881[/C][C]122.932648416119[/C][/ROW]
[ROW][C]86[/C][C]647[/C][C]510.317535304388[/C][C]136.682464695612[/C][/ROW]
[ROW][C]87[/C][C]1757[/C][C]1553.2402525256[/C][C]203.759747474402[/C][/ROW]
[ROW][C]88[/C][C]1326[/C][C]1270.76755276358[/C][C]55.2324472364178[/C][/ROW]
[ROW][C]89[/C][C]1308[/C][C]1110.34251941479[/C][C]197.657480585212[/C][/ROW]
[ROW][C]90[/C][C]1175[/C][C]1117.74546829071[/C][C]57.254531709295[/C][/ROW]
[ROW][C]91[/C][C]992[/C][C]867.056366823701[/C][C]124.943633176299[/C][/ROW]
[ROW][C]92[/C][C]808[/C][C]818.869147274161[/C][C]-10.8691472741613[/C][/ROW]
[ROW][C]93[/C][C]758[/C][C]618.649739616438[/C][C]139.350260383562[/C][/ROW]
[ROW][C]94[/C][C]551[/C][C]452.918917946799[/C][C]98.0810820532008[/C][/ROW]
[ROW][C]95[/C][C]310[/C][C]279.097284489962[/C][C]30.902715510038[/C][/ROW]
[ROW][C]96[/C][C]146[/C][C]185.617011766209[/C][C]-39.6170117662091[/C][/ROW]
[ROW][C]97[/C][C]649[/C][C]594.883639733768[/C][C]54.1163602662317[/C][/ROW]
[ROW][C]98[/C][C]602[/C][C]689.698268265715[/C][C]-87.6982682657153[/C][/ROW]
[ROW][C]99[/C][C]1801[/C][C]1842.24780367082[/C][C]-41.2478036708178[/C][/ROW]
[ROW][C]100[/C][C]1481[/C][C]1400.88526599489[/C][C]80.1147340051104[/C][/ROW]
[ROW][C]101[/C][C]1400[/C][C]1331.9002383619[/C][C]68.0997616380973[/C][/ROW]
[ROW][C]102[/C][C]1319[/C][C]1223.87507704246[/C][C]95.1249229575351[/C][/ROW]
[ROW][C]103[/C][C]1153[/C][C]1010.00632102809[/C][C]142.993678971908[/C][/ROW]
[ROW][C]104[/C][C]950[/C][C]867.540592867766[/C][C]82.4594071322343[/C][/ROW]
[ROW][C]105[/C][C]829[/C][C]769.900167322588[/C][C]59.0998326774118[/C][/ROW]
[ROW][C]106[/C][C]636[/C][C]549.994414510963[/C][C]86.0055854890367[/C][/ROW]
[ROW][C]107[/C][C]310[/C][C]317.063712182913[/C][C]-7.06371218291304[/C][/ROW]
[ROW][C]108[/C][C]191[/C][C]165.359117132588[/C][C]25.6408828674123[/C][/ROW]
[ROW][C]109[/C][C]679[/C][C]695.413293740919[/C][C]-16.4132937409194[/C][/ROW]
[ROW][C]110[/C][C]842[/C][C]686.728645900917[/C][C]155.271354099083[/C][/ROW]
[ROW][C]111[/C][C]1975[/C][C]2090.5181512874[/C][C]-115.518151287401[/C][/ROW]
[ROW][C]112[/C][C]1677[/C][C]1670.81883341587[/C][C]6.18116658412646[/C][/ROW]
[ROW][C]113[/C][C]1418[/C][C]1575.19032799785[/C][C]-157.190327997846[/C][/ROW]
[ROW][C]114[/C][C]1540[/C][C]1441.92053149474[/C][C]98.0794685052622[/C][/ROW]
[ROW][C]115[/C][C]1173[/C][C]1237.3012059032[/C][C]-64.3012059031983[/C][/ROW]
[ROW][C]116[/C][C]941[/C][C]1006.42909875573[/C][C]-65.4290987557305[/C][/ROW]
[ROW][C]117[/C][C]989[/C][C]863.374197848613[/C][C]125.625802151387[/C][/ROW]
[ROW][C]118[/C][C]614[/C][C]654.005039769252[/C][C]-40.0050397692515[/C][/ROW]
[ROW][C]119[/C][C]352[/C][C]327.15034791703[/C][C]24.8496520829698[/C][/ROW]
[ROW][C]120[/C][C]405[/C][C]193.359345848511[/C][C]211.640654151489[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308211&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308211&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
1311431115.3056914226527.6943085773532
1418071766.1485734142540.8514265857502
1523802344.7711718368335.2288281631741
1623342318.3927705692115.6072294307946
1721162120.0934532182-4.09345321820319
1817881804.97348358887-16.9734835888696
1915711477.2633676363393.7366323636729
2013061358.04888708436-52.0488870843649
219521018.12273857243-66.1227385724317
22806876.09576887565-70.0957688756502
23473584.861504590111-111.861504590111
24278331.585969717353-53.5859697173528
259931092.63379182817-99.6337918281722
2610381694.56598426099-656.565984260985
2722592091.26466679695167.735333203052
2822832069.88709028978213.112909710224
2917461903.87186457765-157.87186457765
3015151587.77439013648-72.7743901364829
3112301348.97694312716-118.976943127163
328821130.07994408807-248.079944088066
331028804.903813932609223.096186067391
34704718.768343759976-14.7683437599765
35390443.995375895568-53.9953758955682
36238259.633833222896-21.633833222896
37594909.829921546607-315.829921546607
386921050.24950689341-358.249506893412
3921251871.24674772185253.753252278148
4018491885.98879660477-36.9887966047709
4114681502.94852936236-34.9485293623648
4215311292.64859814717238.35140185283
4312031100.32442355947102.675576440531
44878854.94583076187523.0541692381249
45818870.694281911607-52.694281911607
46605619.610345647909-14.6103456479088
47316355.404397310783-39.4043973107834
48136213.42616527269-77.4261652726896
49528573.698318561931-45.6983185619308
50654692.457989114121-38.4579891141215
5118921829.8762362906362.1237637093659
5215971646.02158400381-49.0215840038068
5315151303.41139239896211.588607601043
5412411305.84387593823-64.8438759382263
5510261015.6506141164710.3493858835276
56758745.79596966640312.2040303335967
57733713.29997815534719.7000218446534
58481526.147442360018-45.147442360018
59280280.398948422348-0.398948422348496
60117138.118892910677-21.1188929106765
61651484.55697780346166.44302219654
62611633.762098452243-22.762098452243
6318981783.08420480272114.915795197282
6413851546.78180950193-161.781809501931
6510471363.32363047068-316.323630470679
6610071125.42378112727-118.423781127265
67842901.397573510192-59.3975735101922
68827655.29289164173171.70710835827
69711653.98402216600457.0159778339964
70443450.573744487588-7.57374448758759
71313256.90549752902356.0945024709771
72202117.56164866109984.4383513389013
73473635.800853908312-162.800853908312
74566612.308396364918-46.3083963649182
7516091829.59013326753-220.59013326753
7612961379.20742242115-83.2074224211533
7711531109.5426116418943.4573883581079
7811551056.3314347652598.6685652347487
79859899.69936822758-40.6993682275798
80798801.732783403839-3.73278340383911
81557698.881345390376-141.881345390376
82402431.57249198399-29.5724919839898
83223281.090167828478-58.0901678284778
84153150.5587016079652.44129839203455
85548425.067351583881122.932648416119
86647510.317535304388136.682464695612
8717571553.2402525256203.759747474402
8813261270.7675527635855.2324472364178
8913081110.34251941479197.657480585212
9011751117.7454682907157.254531709295
91992867.056366823701124.943633176299
92808818.869147274161-10.8691472741613
93758618.649739616438139.350260383562
94551452.91891794679998.0810820532008
95310279.09728448996230.902715510038
96146185.617011766209-39.6170117662091
97649594.88363973376854.1163602662317
98602689.698268265715-87.6982682657153
9918011842.24780367082-41.2478036708178
10014811400.8852659948980.1147340051104
10114001331.900238361968.0997616380973
10213191223.8750770424695.1249229575351
10311531010.00632102809142.993678971908
104950867.54059286776682.4594071322343
105829769.90016732258859.0998326774118
106636549.99441451096386.0055854890367
107310317.063712182913-7.06371218291304
108191165.35911713258825.6408828674123
109679695.413293740919-16.4132937409194
110842686.728645900917155.271354099083
11119752090.5181512874-115.518151287401
11216771670.818833415876.18116658412646
11314181575.19032799785-157.190327997846
11415401441.9205314947498.0794685052622
11511731237.3012059032-64.3012059031983
1169411006.42909875573-65.4290987557305
117989863.374197848613125.625802151387
118614654.005039769252-40.0050397692515
119352327.1503479170324.8496520829698
120405193.359345848511211.640654151489







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121833.308003219777623.9494052459561042.6666011936
122962.575557628405748.1065384543151177.0445768025
1232396.263291755612135.767906356232656.75867715498
1242016.04829411081765.719201201172266.37738702044
1251775.478689359971529.991624094222020.96575462572
1261851.903413898711598.618612550412105.18821524701
1271460.004800310761219.29548223211700.71411838942
1281190.55442862565956.8121593639251424.29669788738
1291182.54195931369944.8942046125311420.18971401485
130771.983804387608548.142337933493995.825270841723
131427.593005745272212.366708208017642.819303282528
132385.453853828904326.118395858664444.789311799144

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 833.308003219777 & 623.949405245956 & 1042.6666011936 \tabularnewline
122 & 962.575557628405 & 748.106538454315 & 1177.0445768025 \tabularnewline
123 & 2396.26329175561 & 2135.76790635623 & 2656.75867715498 \tabularnewline
124 & 2016.0482941108 & 1765.71920120117 & 2266.37738702044 \tabularnewline
125 & 1775.47868935997 & 1529.99162409422 & 2020.96575462572 \tabularnewline
126 & 1851.90341389871 & 1598.61861255041 & 2105.18821524701 \tabularnewline
127 & 1460.00480031076 & 1219.2954822321 & 1700.71411838942 \tabularnewline
128 & 1190.55442862565 & 956.812159363925 & 1424.29669788738 \tabularnewline
129 & 1182.54195931369 & 944.894204612531 & 1420.18971401485 \tabularnewline
130 & 771.983804387608 & 548.142337933493 & 995.825270841723 \tabularnewline
131 & 427.593005745272 & 212.366708208017 & 642.819303282528 \tabularnewline
132 & 385.453853828904 & 326.118395858664 & 444.789311799144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308211&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]121[/C][C]833.308003219777[/C][C]623.949405245956[/C][C]1042.6666011936[/C][/ROW]
[ROW][C]122[/C][C]962.575557628405[/C][C]748.106538454315[/C][C]1177.0445768025[/C][/ROW]
[ROW][C]123[/C][C]2396.26329175561[/C][C]2135.76790635623[/C][C]2656.75867715498[/C][/ROW]
[ROW][C]124[/C][C]2016.0482941108[/C][C]1765.71920120117[/C][C]2266.37738702044[/C][/ROW]
[ROW][C]125[/C][C]1775.47868935997[/C][C]1529.99162409422[/C][C]2020.96575462572[/C][/ROW]
[ROW][C]126[/C][C]1851.90341389871[/C][C]1598.61861255041[/C][C]2105.18821524701[/C][/ROW]
[ROW][C]127[/C][C]1460.00480031076[/C][C]1219.2954822321[/C][C]1700.71411838942[/C][/ROW]
[ROW][C]128[/C][C]1190.55442862565[/C][C]956.812159363925[/C][C]1424.29669788738[/C][/ROW]
[ROW][C]129[/C][C]1182.54195931369[/C][C]944.894204612531[/C][C]1420.18971401485[/C][/ROW]
[ROW][C]130[/C][C]771.983804387608[/C][C]548.142337933493[/C][C]995.825270841723[/C][/ROW]
[ROW][C]131[/C][C]427.593005745272[/C][C]212.366708208017[/C][C]642.819303282528[/C][/ROW]
[ROW][C]132[/C][C]385.453853828904[/C][C]326.118395858664[/C][C]444.789311799144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308211&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308211&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
121833.308003219777623.9494052459561042.6666011936
122962.575557628405748.1065384543151177.0445768025
1232396.263291755612135.767906356232656.75867715498
1242016.04829411081765.719201201172266.37738702044
1251775.478689359971529.991624094222020.96575462572
1261851.903413898711598.618612550412105.18821524701
1271460.004800310761219.29548223211700.71411838942
1281190.55442862565956.8121593639251424.29669788738
1291182.54195931369944.8942046125311420.18971401485
130771.983804387608548.142337933493995.825270841723
131427.593005745272212.366708208017642.819303282528
132385.453853828904326.118395858664444.789311799144



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')