Free Statistics

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 computationThu, 22 Dec 2016 22:23:54 +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/2016/Dec/22/t1482442082jx5hrwaitvu7aqb.htm/, Retrieved Mon, 29 Apr 2024 05:51:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302693, Retrieved Mon, 29 Apr 2024 05:51:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact48
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-22 21:23:54] [d4ebbcc95b180bc93fc42d05f31a3dde] [Current]
Feedback Forum

Post a new message
Dataseries X:
5572.3
5565.55
5576.85
5577.3
5598.85
5752.55
5782.2
5763
5694.6
5686.85
5691.6
5674.15
5635.55
5652.6
5675.7
5692.25
5747.05
5854.15
5894.8
5839.4
5778.15
5797.75
5790.7
5786.3
5758.6
5764.75
5804.75
5801.35
5829.75
5913.7
5962
5920.25
5879.1
5902.3
5889.95
5873.9
5856.1
5870.8
5900.1
5900.6
5944.3
6066.2
6098.75
6058.4
5998
6022.4
6018.7
5989.95
5972.55
5985.35
6004.45
6004.1
6071.05
6143.55
6191.25
6167.5
6081.35
6124.25
6118.3
6097.8
6074.55
6083.9
6084.65
6099.8
6124.45
6235.65
6278.05
6254.4
6177.3
6205.95
6217.2
6190.8
6189.55
6179.5
6195.35
6213
6243.45
6361.75
6395.2
6356.6
6276.5
6306.25
6318.4
6284.9
6249.5
6256
6272.9
6273.65
6313.95
6396.85
6426.35
6382.6
6319
6329.5
6321.8
6312.35
6260
6283.6
6295.15
6309.15
6315.75
6427.95
6446.55
6385.65
6351.45
6359.1
6350.05
6335.6
6333.55
6348.55
6369.1
6372.75
6413.95
6528.6
6558.4
6501.95
6430.5




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302693&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302693&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302693&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.500918719430804
beta0.0370687846507679
gamma0.904759859508393

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.500918719430804 \tabularnewline
beta & 0.0370687846507679 \tabularnewline
gamma & 0.904759859508393 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302693&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]0.500918719430804[/C][/ROW]
[ROW][C]beta[/C][C]0.0370687846507679[/C][/ROW]
[ROW][C]gamma[/C][C]0.904759859508393[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302693&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302693&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
alpha0.500918719430804
beta0.0370687846507679
gamma0.904759859508393







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135635.555578.9964743589756.5535256410267
145652.65626.22253714526.3774628550009
155675.75666.083050420499.61694957950931
165692.255689.738980678532.51101932146685
175747.055747.48412651673-0.43412651673134
185854.155855.99384928407-1.84384928407508
195894.85886.923594774917.876405225089
205839.45875.94781699562-36.5478169956232
215778.155791.35714513205-13.2071451320498
225797.755777.7005165395920.0494834604078
235790.75791.51879354809-0.818793548085523
245786.35773.2248062352213.0751937647774
255758.65768.00336815462-9.40336815462433
265764.755768.88475795723-4.13475795723025
275804.755785.6467079269819.1032920730195
285801.355810.77576514835-9.42576514834946
295829.755860.91994189626-31.1699418962562
305913.75952.53451099548-38.8345109954798
3159625967.77480089346-5.7748008934559
325920.255928.09838743365-7.84838743364617
335879.15867.1533604101411.9466395898626
345902.35880.310900994321.9890990056956
355889.955884.910919668875.03908033113294
365873.95875.16703018277-1.26703018277385
375856.15851.686792292174.41320770782659
385870.85861.200404354489.59959564552446
395900.15894.922492910685.1775070893209
405900.65899.522256839041.07774316095583
415944.35944.63296847667-0.332968476673159
426066.26048.3297091730217.8702908269834
436098.756108.05176602809-9.30176602809388
446058.46066.75601493106-8.35601493105969
4559986015.56941138691-17.5694113869085
466022.46019.002686531123.39731346887675
476018.76006.8169695728211.8830304271842
485989.955997.96190509902-8.01190509902517
495972.555973.85077368808-1.30077368808361
505985.355982.920789016092.42921098390616
516004.456010.99790310438-6.54790310437875
526004.16007.59881760691-3.49881760691369
536071.056049.4209307783321.629069221668
546143.556172.38721798826-28.8372179882645
556191.256195.62450865321-4.37450865320534
566167.56156.49686373611.0031362639957
576081.356110.47969157301-29.1296915730072
586124.256117.007414486827.24258551318235
596118.36110.068692521268.23130747874166
606097.86089.822184082467.97781591753574
616074.556076.46921515546-1.91921515546255
626083.96086.62043702336-2.72043702336487
636084.656107.67549645811-23.0254964581118
646099.86096.704427993373.09557200662948
656124.456152.60384818551-28.1538481855114
666235.656226.348150741339.30184925866524
676278.056278.94749968549-0.897499685491312
686254.46247.781252750436.61874724956942
696177.36180.6404635351-3.34046353509621
706205.956216.18374633661-10.2337463366093
716217.26200.286148397916.9138516020985
726190.86183.784536095767.01546390423664
736189.556164.972757080624.5772429193958
746179.56188.01899986093-8.51899986092849
756195.356196.8772966958-1.52729669579912
7662136208.745771335064.25422866493591
776243.456251.4122210974-7.96222109740029
786361.756352.856158768868.89384123113814
796395.26401.31024922203-6.11024922203433
806356.66371.49462061625-14.89462061625
816276.56289.24867463766-12.748674637658
826306.256316.96022024391-10.7102202439128
836318.46313.067227848435.33277215156977
846284.96286.06460662925-1.16460662925147
856249.56270.70315934926-21.203159349262
8662566254.640388459551.35961154045344
876272.96270.555404210042.34459578996302
886273.656285.99716062696-12.3471606269604
896313.956313.546217603580.403782396419047
906396.856425.66239592356-28.8123959235554
916426.356446.62372206279-20.2737220627914
926382.66403.65385289739-21.0538528973939
9363196317.084343606981.91565639302189
946329.56351.12699475338-21.6269947533783
956321.86346.87207676683-25.0720767668345
966312.356299.0029423076113.3470576923919
9762606279.4294635529-19.4294635529004
986283.66272.043481775111.5565182248984
996295.156291.300549675263.84945032474025
1006309.156298.6794774093810.4705225906191
1016315.756341.65710503362-25.9071050336242
1026427.956425.153681480982.79631851901649
1036446.556464.1434980941-17.5934980941029
1046385.656420.55317036678-34.9031703667797
1056351.456335.550204795915.8997952041027
1066359.16364.35885668386-5.25885668386218
1076350.056365.44309161928-15.3930916192749
1086335.66338.64584481372-3.04584481372331
1096333.556294.6316599355538.9183400644542
1106348.556330.1192949416918.4307050583147
1116369.16349.1217277629919.9782722370101
1126372.756367.651180762485.09881923752073
1136413.956391.4935664373722.456433562631
1146528.66513.0571900373815.5428099626233
1156558.46550.341501487088.05849851291714
1166501.956513.3774306864-11.4274306864036
1176430.56465.10267596875-34.6026759687475

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5635.55 & 5578.99647435897 & 56.5535256410267 \tabularnewline
14 & 5652.6 & 5626.222537145 & 26.3774628550009 \tabularnewline
15 & 5675.7 & 5666.08305042049 & 9.61694957950931 \tabularnewline
16 & 5692.25 & 5689.73898067853 & 2.51101932146685 \tabularnewline
17 & 5747.05 & 5747.48412651673 & -0.43412651673134 \tabularnewline
18 & 5854.15 & 5855.99384928407 & -1.84384928407508 \tabularnewline
19 & 5894.8 & 5886.92359477491 & 7.876405225089 \tabularnewline
20 & 5839.4 & 5875.94781699562 & -36.5478169956232 \tabularnewline
21 & 5778.15 & 5791.35714513205 & -13.2071451320498 \tabularnewline
22 & 5797.75 & 5777.70051653959 & 20.0494834604078 \tabularnewline
23 & 5790.7 & 5791.51879354809 & -0.818793548085523 \tabularnewline
24 & 5786.3 & 5773.22480623522 & 13.0751937647774 \tabularnewline
25 & 5758.6 & 5768.00336815462 & -9.40336815462433 \tabularnewline
26 & 5764.75 & 5768.88475795723 & -4.13475795723025 \tabularnewline
27 & 5804.75 & 5785.64670792698 & 19.1032920730195 \tabularnewline
28 & 5801.35 & 5810.77576514835 & -9.42576514834946 \tabularnewline
29 & 5829.75 & 5860.91994189626 & -31.1699418962562 \tabularnewline
30 & 5913.7 & 5952.53451099548 & -38.8345109954798 \tabularnewline
31 & 5962 & 5967.77480089346 & -5.7748008934559 \tabularnewline
32 & 5920.25 & 5928.09838743365 & -7.84838743364617 \tabularnewline
33 & 5879.1 & 5867.15336041014 & 11.9466395898626 \tabularnewline
34 & 5902.3 & 5880.3109009943 & 21.9890990056956 \tabularnewline
35 & 5889.95 & 5884.91091966887 & 5.03908033113294 \tabularnewline
36 & 5873.9 & 5875.16703018277 & -1.26703018277385 \tabularnewline
37 & 5856.1 & 5851.68679229217 & 4.41320770782659 \tabularnewline
38 & 5870.8 & 5861.20040435448 & 9.59959564552446 \tabularnewline
39 & 5900.1 & 5894.92249291068 & 5.1775070893209 \tabularnewline
40 & 5900.6 & 5899.52225683904 & 1.07774316095583 \tabularnewline
41 & 5944.3 & 5944.63296847667 & -0.332968476673159 \tabularnewline
42 & 6066.2 & 6048.32970917302 & 17.8702908269834 \tabularnewline
43 & 6098.75 & 6108.05176602809 & -9.30176602809388 \tabularnewline
44 & 6058.4 & 6066.75601493106 & -8.35601493105969 \tabularnewline
45 & 5998 & 6015.56941138691 & -17.5694113869085 \tabularnewline
46 & 6022.4 & 6019.00268653112 & 3.39731346887675 \tabularnewline
47 & 6018.7 & 6006.81696957282 & 11.8830304271842 \tabularnewline
48 & 5989.95 & 5997.96190509902 & -8.01190509902517 \tabularnewline
49 & 5972.55 & 5973.85077368808 & -1.30077368808361 \tabularnewline
50 & 5985.35 & 5982.92078901609 & 2.42921098390616 \tabularnewline
51 & 6004.45 & 6010.99790310438 & -6.54790310437875 \tabularnewline
52 & 6004.1 & 6007.59881760691 & -3.49881760691369 \tabularnewline
53 & 6071.05 & 6049.42093077833 & 21.629069221668 \tabularnewline
54 & 6143.55 & 6172.38721798826 & -28.8372179882645 \tabularnewline
55 & 6191.25 & 6195.62450865321 & -4.37450865320534 \tabularnewline
56 & 6167.5 & 6156.496863736 & 11.0031362639957 \tabularnewline
57 & 6081.35 & 6110.47969157301 & -29.1296915730072 \tabularnewline
58 & 6124.25 & 6117.00741448682 & 7.24258551318235 \tabularnewline
59 & 6118.3 & 6110.06869252126 & 8.23130747874166 \tabularnewline
60 & 6097.8 & 6089.82218408246 & 7.97781591753574 \tabularnewline
61 & 6074.55 & 6076.46921515546 & -1.91921515546255 \tabularnewline
62 & 6083.9 & 6086.62043702336 & -2.72043702336487 \tabularnewline
63 & 6084.65 & 6107.67549645811 & -23.0254964581118 \tabularnewline
64 & 6099.8 & 6096.70442799337 & 3.09557200662948 \tabularnewline
65 & 6124.45 & 6152.60384818551 & -28.1538481855114 \tabularnewline
66 & 6235.65 & 6226.34815074133 & 9.30184925866524 \tabularnewline
67 & 6278.05 & 6278.94749968549 & -0.897499685491312 \tabularnewline
68 & 6254.4 & 6247.78125275043 & 6.61874724956942 \tabularnewline
69 & 6177.3 & 6180.6404635351 & -3.34046353509621 \tabularnewline
70 & 6205.95 & 6216.18374633661 & -10.2337463366093 \tabularnewline
71 & 6217.2 & 6200.2861483979 & 16.9138516020985 \tabularnewline
72 & 6190.8 & 6183.78453609576 & 7.01546390423664 \tabularnewline
73 & 6189.55 & 6164.9727570806 & 24.5772429193958 \tabularnewline
74 & 6179.5 & 6188.01899986093 & -8.51899986092849 \tabularnewline
75 & 6195.35 & 6196.8772966958 & -1.52729669579912 \tabularnewline
76 & 6213 & 6208.74577133506 & 4.25422866493591 \tabularnewline
77 & 6243.45 & 6251.4122210974 & -7.96222109740029 \tabularnewline
78 & 6361.75 & 6352.85615876886 & 8.89384123113814 \tabularnewline
79 & 6395.2 & 6401.31024922203 & -6.11024922203433 \tabularnewline
80 & 6356.6 & 6371.49462061625 & -14.89462061625 \tabularnewline
81 & 6276.5 & 6289.24867463766 & -12.748674637658 \tabularnewline
82 & 6306.25 & 6316.96022024391 & -10.7102202439128 \tabularnewline
83 & 6318.4 & 6313.06722784843 & 5.33277215156977 \tabularnewline
84 & 6284.9 & 6286.06460662925 & -1.16460662925147 \tabularnewline
85 & 6249.5 & 6270.70315934926 & -21.203159349262 \tabularnewline
86 & 6256 & 6254.64038845955 & 1.35961154045344 \tabularnewline
87 & 6272.9 & 6270.55540421004 & 2.34459578996302 \tabularnewline
88 & 6273.65 & 6285.99716062696 & -12.3471606269604 \tabularnewline
89 & 6313.95 & 6313.54621760358 & 0.403782396419047 \tabularnewline
90 & 6396.85 & 6425.66239592356 & -28.8123959235554 \tabularnewline
91 & 6426.35 & 6446.62372206279 & -20.2737220627914 \tabularnewline
92 & 6382.6 & 6403.65385289739 & -21.0538528973939 \tabularnewline
93 & 6319 & 6317.08434360698 & 1.91565639302189 \tabularnewline
94 & 6329.5 & 6351.12699475338 & -21.6269947533783 \tabularnewline
95 & 6321.8 & 6346.87207676683 & -25.0720767668345 \tabularnewline
96 & 6312.35 & 6299.00294230761 & 13.3470576923919 \tabularnewline
97 & 6260 & 6279.4294635529 & -19.4294635529004 \tabularnewline
98 & 6283.6 & 6272.0434817751 & 11.5565182248984 \tabularnewline
99 & 6295.15 & 6291.30054967526 & 3.84945032474025 \tabularnewline
100 & 6309.15 & 6298.67947740938 & 10.4705225906191 \tabularnewline
101 & 6315.75 & 6341.65710503362 & -25.9071050336242 \tabularnewline
102 & 6427.95 & 6425.15368148098 & 2.79631851901649 \tabularnewline
103 & 6446.55 & 6464.1434980941 & -17.5934980941029 \tabularnewline
104 & 6385.65 & 6420.55317036678 & -34.9031703667797 \tabularnewline
105 & 6351.45 & 6335.5502047959 & 15.8997952041027 \tabularnewline
106 & 6359.1 & 6364.35885668386 & -5.25885668386218 \tabularnewline
107 & 6350.05 & 6365.44309161928 & -15.3930916192749 \tabularnewline
108 & 6335.6 & 6338.64584481372 & -3.04584481372331 \tabularnewline
109 & 6333.55 & 6294.63165993555 & 38.9183400644542 \tabularnewline
110 & 6348.55 & 6330.11929494169 & 18.4307050583147 \tabularnewline
111 & 6369.1 & 6349.12172776299 & 19.9782722370101 \tabularnewline
112 & 6372.75 & 6367.65118076248 & 5.09881923752073 \tabularnewline
113 & 6413.95 & 6391.49356643737 & 22.456433562631 \tabularnewline
114 & 6528.6 & 6513.05719003738 & 15.5428099626233 \tabularnewline
115 & 6558.4 & 6550.34150148708 & 8.05849851291714 \tabularnewline
116 & 6501.95 & 6513.3774306864 & -11.4274306864036 \tabularnewline
117 & 6430.5 & 6465.10267596875 & -34.6026759687475 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302693&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]5635.55[/C][C]5578.99647435897[/C][C]56.5535256410267[/C][/ROW]
[ROW][C]14[/C][C]5652.6[/C][C]5626.222537145[/C][C]26.3774628550009[/C][/ROW]
[ROW][C]15[/C][C]5675.7[/C][C]5666.08305042049[/C][C]9.61694957950931[/C][/ROW]
[ROW][C]16[/C][C]5692.25[/C][C]5689.73898067853[/C][C]2.51101932146685[/C][/ROW]
[ROW][C]17[/C][C]5747.05[/C][C]5747.48412651673[/C][C]-0.43412651673134[/C][/ROW]
[ROW][C]18[/C][C]5854.15[/C][C]5855.99384928407[/C][C]-1.84384928407508[/C][/ROW]
[ROW][C]19[/C][C]5894.8[/C][C]5886.92359477491[/C][C]7.876405225089[/C][/ROW]
[ROW][C]20[/C][C]5839.4[/C][C]5875.94781699562[/C][C]-36.5478169956232[/C][/ROW]
[ROW][C]21[/C][C]5778.15[/C][C]5791.35714513205[/C][C]-13.2071451320498[/C][/ROW]
[ROW][C]22[/C][C]5797.75[/C][C]5777.70051653959[/C][C]20.0494834604078[/C][/ROW]
[ROW][C]23[/C][C]5790.7[/C][C]5791.51879354809[/C][C]-0.818793548085523[/C][/ROW]
[ROW][C]24[/C][C]5786.3[/C][C]5773.22480623522[/C][C]13.0751937647774[/C][/ROW]
[ROW][C]25[/C][C]5758.6[/C][C]5768.00336815462[/C][C]-9.40336815462433[/C][/ROW]
[ROW][C]26[/C][C]5764.75[/C][C]5768.88475795723[/C][C]-4.13475795723025[/C][/ROW]
[ROW][C]27[/C][C]5804.75[/C][C]5785.64670792698[/C][C]19.1032920730195[/C][/ROW]
[ROW][C]28[/C][C]5801.35[/C][C]5810.77576514835[/C][C]-9.42576514834946[/C][/ROW]
[ROW][C]29[/C][C]5829.75[/C][C]5860.91994189626[/C][C]-31.1699418962562[/C][/ROW]
[ROW][C]30[/C][C]5913.7[/C][C]5952.53451099548[/C][C]-38.8345109954798[/C][/ROW]
[ROW][C]31[/C][C]5962[/C][C]5967.77480089346[/C][C]-5.7748008934559[/C][/ROW]
[ROW][C]32[/C][C]5920.25[/C][C]5928.09838743365[/C][C]-7.84838743364617[/C][/ROW]
[ROW][C]33[/C][C]5879.1[/C][C]5867.15336041014[/C][C]11.9466395898626[/C][/ROW]
[ROW][C]34[/C][C]5902.3[/C][C]5880.3109009943[/C][C]21.9890990056956[/C][/ROW]
[ROW][C]35[/C][C]5889.95[/C][C]5884.91091966887[/C][C]5.03908033113294[/C][/ROW]
[ROW][C]36[/C][C]5873.9[/C][C]5875.16703018277[/C][C]-1.26703018277385[/C][/ROW]
[ROW][C]37[/C][C]5856.1[/C][C]5851.68679229217[/C][C]4.41320770782659[/C][/ROW]
[ROW][C]38[/C][C]5870.8[/C][C]5861.20040435448[/C][C]9.59959564552446[/C][/ROW]
[ROW][C]39[/C][C]5900.1[/C][C]5894.92249291068[/C][C]5.1775070893209[/C][/ROW]
[ROW][C]40[/C][C]5900.6[/C][C]5899.52225683904[/C][C]1.07774316095583[/C][/ROW]
[ROW][C]41[/C][C]5944.3[/C][C]5944.63296847667[/C][C]-0.332968476673159[/C][/ROW]
[ROW][C]42[/C][C]6066.2[/C][C]6048.32970917302[/C][C]17.8702908269834[/C][/ROW]
[ROW][C]43[/C][C]6098.75[/C][C]6108.05176602809[/C][C]-9.30176602809388[/C][/ROW]
[ROW][C]44[/C][C]6058.4[/C][C]6066.75601493106[/C][C]-8.35601493105969[/C][/ROW]
[ROW][C]45[/C][C]5998[/C][C]6015.56941138691[/C][C]-17.5694113869085[/C][/ROW]
[ROW][C]46[/C][C]6022.4[/C][C]6019.00268653112[/C][C]3.39731346887675[/C][/ROW]
[ROW][C]47[/C][C]6018.7[/C][C]6006.81696957282[/C][C]11.8830304271842[/C][/ROW]
[ROW][C]48[/C][C]5989.95[/C][C]5997.96190509902[/C][C]-8.01190509902517[/C][/ROW]
[ROW][C]49[/C][C]5972.55[/C][C]5973.85077368808[/C][C]-1.30077368808361[/C][/ROW]
[ROW][C]50[/C][C]5985.35[/C][C]5982.92078901609[/C][C]2.42921098390616[/C][/ROW]
[ROW][C]51[/C][C]6004.45[/C][C]6010.99790310438[/C][C]-6.54790310437875[/C][/ROW]
[ROW][C]52[/C][C]6004.1[/C][C]6007.59881760691[/C][C]-3.49881760691369[/C][/ROW]
[ROW][C]53[/C][C]6071.05[/C][C]6049.42093077833[/C][C]21.629069221668[/C][/ROW]
[ROW][C]54[/C][C]6143.55[/C][C]6172.38721798826[/C][C]-28.8372179882645[/C][/ROW]
[ROW][C]55[/C][C]6191.25[/C][C]6195.62450865321[/C][C]-4.37450865320534[/C][/ROW]
[ROW][C]56[/C][C]6167.5[/C][C]6156.496863736[/C][C]11.0031362639957[/C][/ROW]
[ROW][C]57[/C][C]6081.35[/C][C]6110.47969157301[/C][C]-29.1296915730072[/C][/ROW]
[ROW][C]58[/C][C]6124.25[/C][C]6117.00741448682[/C][C]7.24258551318235[/C][/ROW]
[ROW][C]59[/C][C]6118.3[/C][C]6110.06869252126[/C][C]8.23130747874166[/C][/ROW]
[ROW][C]60[/C][C]6097.8[/C][C]6089.82218408246[/C][C]7.97781591753574[/C][/ROW]
[ROW][C]61[/C][C]6074.55[/C][C]6076.46921515546[/C][C]-1.91921515546255[/C][/ROW]
[ROW][C]62[/C][C]6083.9[/C][C]6086.62043702336[/C][C]-2.72043702336487[/C][/ROW]
[ROW][C]63[/C][C]6084.65[/C][C]6107.67549645811[/C][C]-23.0254964581118[/C][/ROW]
[ROW][C]64[/C][C]6099.8[/C][C]6096.70442799337[/C][C]3.09557200662948[/C][/ROW]
[ROW][C]65[/C][C]6124.45[/C][C]6152.60384818551[/C][C]-28.1538481855114[/C][/ROW]
[ROW][C]66[/C][C]6235.65[/C][C]6226.34815074133[/C][C]9.30184925866524[/C][/ROW]
[ROW][C]67[/C][C]6278.05[/C][C]6278.94749968549[/C][C]-0.897499685491312[/C][/ROW]
[ROW][C]68[/C][C]6254.4[/C][C]6247.78125275043[/C][C]6.61874724956942[/C][/ROW]
[ROW][C]69[/C][C]6177.3[/C][C]6180.6404635351[/C][C]-3.34046353509621[/C][/ROW]
[ROW][C]70[/C][C]6205.95[/C][C]6216.18374633661[/C][C]-10.2337463366093[/C][/ROW]
[ROW][C]71[/C][C]6217.2[/C][C]6200.2861483979[/C][C]16.9138516020985[/C][/ROW]
[ROW][C]72[/C][C]6190.8[/C][C]6183.78453609576[/C][C]7.01546390423664[/C][/ROW]
[ROW][C]73[/C][C]6189.55[/C][C]6164.9727570806[/C][C]24.5772429193958[/C][/ROW]
[ROW][C]74[/C][C]6179.5[/C][C]6188.01899986093[/C][C]-8.51899986092849[/C][/ROW]
[ROW][C]75[/C][C]6195.35[/C][C]6196.8772966958[/C][C]-1.52729669579912[/C][/ROW]
[ROW][C]76[/C][C]6213[/C][C]6208.74577133506[/C][C]4.25422866493591[/C][/ROW]
[ROW][C]77[/C][C]6243.45[/C][C]6251.4122210974[/C][C]-7.96222109740029[/C][/ROW]
[ROW][C]78[/C][C]6361.75[/C][C]6352.85615876886[/C][C]8.89384123113814[/C][/ROW]
[ROW][C]79[/C][C]6395.2[/C][C]6401.31024922203[/C][C]-6.11024922203433[/C][/ROW]
[ROW][C]80[/C][C]6356.6[/C][C]6371.49462061625[/C][C]-14.89462061625[/C][/ROW]
[ROW][C]81[/C][C]6276.5[/C][C]6289.24867463766[/C][C]-12.748674637658[/C][/ROW]
[ROW][C]82[/C][C]6306.25[/C][C]6316.96022024391[/C][C]-10.7102202439128[/C][/ROW]
[ROW][C]83[/C][C]6318.4[/C][C]6313.06722784843[/C][C]5.33277215156977[/C][/ROW]
[ROW][C]84[/C][C]6284.9[/C][C]6286.06460662925[/C][C]-1.16460662925147[/C][/ROW]
[ROW][C]85[/C][C]6249.5[/C][C]6270.70315934926[/C][C]-21.203159349262[/C][/ROW]
[ROW][C]86[/C][C]6256[/C][C]6254.64038845955[/C][C]1.35961154045344[/C][/ROW]
[ROW][C]87[/C][C]6272.9[/C][C]6270.55540421004[/C][C]2.34459578996302[/C][/ROW]
[ROW][C]88[/C][C]6273.65[/C][C]6285.99716062696[/C][C]-12.3471606269604[/C][/ROW]
[ROW][C]89[/C][C]6313.95[/C][C]6313.54621760358[/C][C]0.403782396419047[/C][/ROW]
[ROW][C]90[/C][C]6396.85[/C][C]6425.66239592356[/C][C]-28.8123959235554[/C][/ROW]
[ROW][C]91[/C][C]6426.35[/C][C]6446.62372206279[/C][C]-20.2737220627914[/C][/ROW]
[ROW][C]92[/C][C]6382.6[/C][C]6403.65385289739[/C][C]-21.0538528973939[/C][/ROW]
[ROW][C]93[/C][C]6319[/C][C]6317.08434360698[/C][C]1.91565639302189[/C][/ROW]
[ROW][C]94[/C][C]6329.5[/C][C]6351.12699475338[/C][C]-21.6269947533783[/C][/ROW]
[ROW][C]95[/C][C]6321.8[/C][C]6346.87207676683[/C][C]-25.0720767668345[/C][/ROW]
[ROW][C]96[/C][C]6312.35[/C][C]6299.00294230761[/C][C]13.3470576923919[/C][/ROW]
[ROW][C]97[/C][C]6260[/C][C]6279.4294635529[/C][C]-19.4294635529004[/C][/ROW]
[ROW][C]98[/C][C]6283.6[/C][C]6272.0434817751[/C][C]11.5565182248984[/C][/ROW]
[ROW][C]99[/C][C]6295.15[/C][C]6291.30054967526[/C][C]3.84945032474025[/C][/ROW]
[ROW][C]100[/C][C]6309.15[/C][C]6298.67947740938[/C][C]10.4705225906191[/C][/ROW]
[ROW][C]101[/C][C]6315.75[/C][C]6341.65710503362[/C][C]-25.9071050336242[/C][/ROW]
[ROW][C]102[/C][C]6427.95[/C][C]6425.15368148098[/C][C]2.79631851901649[/C][/ROW]
[ROW][C]103[/C][C]6446.55[/C][C]6464.1434980941[/C][C]-17.5934980941029[/C][/ROW]
[ROW][C]104[/C][C]6385.65[/C][C]6420.55317036678[/C][C]-34.9031703667797[/C][/ROW]
[ROW][C]105[/C][C]6351.45[/C][C]6335.5502047959[/C][C]15.8997952041027[/C][/ROW]
[ROW][C]106[/C][C]6359.1[/C][C]6364.35885668386[/C][C]-5.25885668386218[/C][/ROW]
[ROW][C]107[/C][C]6350.05[/C][C]6365.44309161928[/C][C]-15.3930916192749[/C][/ROW]
[ROW][C]108[/C][C]6335.6[/C][C]6338.64584481372[/C][C]-3.04584481372331[/C][/ROW]
[ROW][C]109[/C][C]6333.55[/C][C]6294.63165993555[/C][C]38.9183400644542[/C][/ROW]
[ROW][C]110[/C][C]6348.55[/C][C]6330.11929494169[/C][C]18.4307050583147[/C][/ROW]
[ROW][C]111[/C][C]6369.1[/C][C]6349.12172776299[/C][C]19.9782722370101[/C][/ROW]
[ROW][C]112[/C][C]6372.75[/C][C]6367.65118076248[/C][C]5.09881923752073[/C][/ROW]
[ROW][C]113[/C][C]6413.95[/C][C]6391.49356643737[/C][C]22.456433562631[/C][/ROW]
[ROW][C]114[/C][C]6528.6[/C][C]6513.05719003738[/C][C]15.5428099626233[/C][/ROW]
[ROW][C]115[/C][C]6558.4[/C][C]6550.34150148708[/C][C]8.05849851291714[/C][/ROW]
[ROW][C]116[/C][C]6501.95[/C][C]6513.3774306864[/C][C]-11.4274306864036[/C][/ROW]
[ROW][C]117[/C][C]6430.5[/C][C]6465.10267596875[/C][C]-34.6026759687475[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302693&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302693&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
135635.555578.9964743589756.5535256410267
145652.65626.22253714526.3774628550009
155675.75666.083050420499.61694957950931
165692.255689.738980678532.51101932146685
175747.055747.48412651673-0.43412651673134
185854.155855.99384928407-1.84384928407508
195894.85886.923594774917.876405225089
205839.45875.94781699562-36.5478169956232
215778.155791.35714513205-13.2071451320498
225797.755777.7005165395920.0494834604078
235790.75791.51879354809-0.818793548085523
245786.35773.2248062352213.0751937647774
255758.65768.00336815462-9.40336815462433
265764.755768.88475795723-4.13475795723025
275804.755785.6467079269819.1032920730195
285801.355810.77576514835-9.42576514834946
295829.755860.91994189626-31.1699418962562
305913.75952.53451099548-38.8345109954798
3159625967.77480089346-5.7748008934559
325920.255928.09838743365-7.84838743364617
335879.15867.1533604101411.9466395898626
345902.35880.310900994321.9890990056956
355889.955884.910919668875.03908033113294
365873.95875.16703018277-1.26703018277385
375856.15851.686792292174.41320770782659
385870.85861.200404354489.59959564552446
395900.15894.922492910685.1775070893209
405900.65899.522256839041.07774316095583
415944.35944.63296847667-0.332968476673159
426066.26048.3297091730217.8702908269834
436098.756108.05176602809-9.30176602809388
446058.46066.75601493106-8.35601493105969
4559986015.56941138691-17.5694113869085
466022.46019.002686531123.39731346887675
476018.76006.8169695728211.8830304271842
485989.955997.96190509902-8.01190509902517
495972.555973.85077368808-1.30077368808361
505985.355982.920789016092.42921098390616
516004.456010.99790310438-6.54790310437875
526004.16007.59881760691-3.49881760691369
536071.056049.4209307783321.629069221668
546143.556172.38721798826-28.8372179882645
556191.256195.62450865321-4.37450865320534
566167.56156.49686373611.0031362639957
576081.356110.47969157301-29.1296915730072
586124.256117.007414486827.24258551318235
596118.36110.068692521268.23130747874166
606097.86089.822184082467.97781591753574
616074.556076.46921515546-1.91921515546255
626083.96086.62043702336-2.72043702336487
636084.656107.67549645811-23.0254964581118
646099.86096.704427993373.09557200662948
656124.456152.60384818551-28.1538481855114
666235.656226.348150741339.30184925866524
676278.056278.94749968549-0.897499685491312
686254.46247.781252750436.61874724956942
696177.36180.6404635351-3.34046353509621
706205.956216.18374633661-10.2337463366093
716217.26200.286148397916.9138516020985
726190.86183.784536095767.01546390423664
736189.556164.972757080624.5772429193958
746179.56188.01899986093-8.51899986092849
756195.356196.8772966958-1.52729669579912
7662136208.745771335064.25422866493591
776243.456251.4122210974-7.96222109740029
786361.756352.856158768868.89384123113814
796395.26401.31024922203-6.11024922203433
806356.66371.49462061625-14.89462061625
816276.56289.24867463766-12.748674637658
826306.256316.96022024391-10.7102202439128
836318.46313.067227848435.33277215156977
846284.96286.06460662925-1.16460662925147
856249.56270.70315934926-21.203159349262
8662566254.640388459551.35961154045344
876272.96270.555404210042.34459578996302
886273.656285.99716062696-12.3471606269604
896313.956313.546217603580.403782396419047
906396.856425.66239592356-28.8123959235554
916426.356446.62372206279-20.2737220627914
926382.66403.65385289739-21.0538528973939
9363196317.084343606981.91565639302189
946329.56351.12699475338-21.6269947533783
956321.86346.87207676683-25.0720767668345
966312.356299.0029423076113.3470576923919
9762606279.4294635529-19.4294635529004
986283.66272.043481775111.5565182248984
996295.156291.300549675263.84945032474025
1006309.156298.6794774093810.4705225906191
1016315.756341.65710503362-25.9071050336242
1026427.956425.153681480982.79631851901649
1036446.556464.1434980941-17.5934980941029
1046385.656420.55317036678-34.9031703667797
1056351.456335.550204795915.8997952041027
1066359.16364.35885668386-5.25885668386218
1076350.056365.44309161928-15.3930916192749
1086335.66338.64584481372-3.04584481372331
1096333.556294.6316599355538.9183400644542
1106348.556330.1192949416918.4307050583147
1116369.16349.1217277629919.9782722370101
1126372.756367.651180762485.09881923752073
1136413.956391.4935664373722.456433562631
1146528.66513.0571900373815.5428099626233
1156558.46550.341501487088.05849851291714
1166501.956513.3774306864-11.4274306864036
1176430.56465.10267596875-34.6026759687475







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1186460.15054006476427.936551686066492.36452844334
1196460.481590205066424.180171161086496.78300924903
1206448.444896477216408.217753296046488.67203965838
1216426.436344389716382.393788619266470.47890016015
1226433.986274594646386.204692000216481.76785718906
1236444.921380020686393.453551257266496.3892087841
1246446.819734984656391.7013568726501.93811309729
1256475.946348147526417.200370757846534.69232553719
1266582.722818015456520.362447919376645.08318811152
1276608.136839990766542.167688846326674.1059911352
1286557.482562606956487.904226238076627.06089897583
1296503.82475174626430.631997147486577.01750634491

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
118 & 6460.1505400647 & 6427.93655168606 & 6492.36452844334 \tabularnewline
119 & 6460.48159020506 & 6424.18017116108 & 6496.78300924903 \tabularnewline
120 & 6448.44489647721 & 6408.21775329604 & 6488.67203965838 \tabularnewline
121 & 6426.43634438971 & 6382.39378861926 & 6470.47890016015 \tabularnewline
122 & 6433.98627459464 & 6386.20469200021 & 6481.76785718906 \tabularnewline
123 & 6444.92138002068 & 6393.45355125726 & 6496.3892087841 \tabularnewline
124 & 6446.81973498465 & 6391.701356872 & 6501.93811309729 \tabularnewline
125 & 6475.94634814752 & 6417.20037075784 & 6534.69232553719 \tabularnewline
126 & 6582.72281801545 & 6520.36244791937 & 6645.08318811152 \tabularnewline
127 & 6608.13683999076 & 6542.16768884632 & 6674.1059911352 \tabularnewline
128 & 6557.48256260695 & 6487.90422623807 & 6627.06089897583 \tabularnewline
129 & 6503.8247517462 & 6430.63199714748 & 6577.01750634491 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302693&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]118[/C][C]6460.1505400647[/C][C]6427.93655168606[/C][C]6492.36452844334[/C][/ROW]
[ROW][C]119[/C][C]6460.48159020506[/C][C]6424.18017116108[/C][C]6496.78300924903[/C][/ROW]
[ROW][C]120[/C][C]6448.44489647721[/C][C]6408.21775329604[/C][C]6488.67203965838[/C][/ROW]
[ROW][C]121[/C][C]6426.43634438971[/C][C]6382.39378861926[/C][C]6470.47890016015[/C][/ROW]
[ROW][C]122[/C][C]6433.98627459464[/C][C]6386.20469200021[/C][C]6481.76785718906[/C][/ROW]
[ROW][C]123[/C][C]6444.92138002068[/C][C]6393.45355125726[/C][C]6496.3892087841[/C][/ROW]
[ROW][C]124[/C][C]6446.81973498465[/C][C]6391.701356872[/C][C]6501.93811309729[/C][/ROW]
[ROW][C]125[/C][C]6475.94634814752[/C][C]6417.20037075784[/C][C]6534.69232553719[/C][/ROW]
[ROW][C]126[/C][C]6582.72281801545[/C][C]6520.36244791937[/C][C]6645.08318811152[/C][/ROW]
[ROW][C]127[/C][C]6608.13683999076[/C][C]6542.16768884632[/C][C]6674.1059911352[/C][/ROW]
[ROW][C]128[/C][C]6557.48256260695[/C][C]6487.90422623807[/C][C]6627.06089897583[/C][/ROW]
[ROW][C]129[/C][C]6503.8247517462[/C][C]6430.63199714748[/C][C]6577.01750634491[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302693&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302693&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
1186460.15054006476427.936551686066492.36452844334
1196460.481590205066424.180171161086496.78300924903
1206448.444896477216408.217753296046488.67203965838
1216426.436344389716382.393788619266470.47890016015
1226433.986274594646386.204692000216481.76785718906
1236444.921380020686393.453551257266496.3892087841
1246446.819734984656391.7013568726501.93811309729
1256475.946348147526417.200370757846534.69232553719
1266582.722818015456520.362447919376645.08318811152
1276608.136839990766542.167688846326674.1059911352
1286557.482562606956487.904226238076627.06089897583
1296503.82475174626430.631997147486577.01750634491



Parameters (Session):
par1 = 1 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; 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')