Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 20 Aug 2013 04:33:32 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/20/t1376987626jfsfca829ghnxfg.htm/, Retrieved Sat, 27 Apr 2024 10:34:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211238, Retrieved Sat, 27 Apr 2024 10:34:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-08-20 08:33:32] [38a0db91cd47487c7649642dcb33e029] [Current]
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Dataseries X:
57
56
55
53
73
72
57
47
48
48
49
51
45
39
34
34
53
55
40
22
31
31
39
43
42
31
37
35
52
48
31
19
30
34
37
41
32
25
28
29
56
56
41
39
45
42
50
60
62
48
44
40
67
69
64
69
68
60
69
79
83
71
63
69
95
103
101
105
104
94
111
116
122
103
96
104
124
141
137
137
139
132
150
150
147
130
133
135
148
165
153
159
154
151
174
169
162
152
162
167
173
181
173
178
172
171
196
199
190
176
188
193
200
209
200
207
204
192
216
216




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211238&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211238&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211238&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999919100758338
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999919100758338 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211238&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]0.999919100758338[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211238&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211238&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
alpha0.999919100758338
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
25657-1
35556.0000808992417-1.00008089924166
45355.0000809057863-2.00008090578635
57353.000161805028519.9998381949715
67272.9983820282567-0.998382028256657
75772.000080768349-15.000080768349
84757.001213495159-10.001213495159
94847.00080909058750.99919090941254
104847.99991916621328.08337868463127e-05
114947.99999999346061.00000000653939
125148.99991910075782.00008089924219
134550.999838194972-5.99983819497199
143945.0004853823601-6.00048538236007
153439.000485434717-5.00048543471704
163434.0004045354796-0.000404535479610502
175334.000000032726618.9999999672734
185552.99846291441112.00153708558894
194054.9998380771676-14.9998380771676
202240.0012134755255-18.0012134755255
213122.00145628451928.99854371548083
223130.99927202463740.000727975362647015
233930.99999994110738.00000005889266
244338.99935280606194.00064719393806
254242.9996763506759-0.999676350675855
263142.0000808730587-11.0000808730587
273731.00088989820095.99911010179915
283536.9995146765421-1.99951467654212
295235.00016175922116.999838240779
304851.9986247259779-3.99862472597794
313148.000323485708-17.000323485708
321931.001375313278-12.001375313278
333019.000970902161710.9990290978383
343429.9991101868874.00088981311304
353733.99967633104813.00032366895186
364136.99975727609044.00024272390956
373240.9996763833972-8.99967638339717
382532.0007280669946-7.00072806699463
392825.00056635359172.9994336464083
402927.99975734809261.00024265190741
415628.99991908112827.000080918872
425655.99781571392880.00218428607115584
434155.9999998232929-14.9999998232929
443941.0012134886106-2.00121348861064
454539.00016189665365.99983810334637
464244.9995146176473-2.99951461764734
475042.00024265845797.99975734154208
486049.999352825697610.0006471743024
496259.99919095522752.00080904477253
504861.9998381360656-13.9998381360656
514448.0011325762886-4.0011325762886
524044.0003236885912-4.00032368859121
536740.000323623152826.9996763768472
546966.9978157466562.00218425334401
556468.9998380248122-4.99983802481223
566964.00040448310464.99959551689535
576868.9995955365141-0.999595536514065
586068.0000808665209-8.00008086652088
596960.00064720047538.99935279952467
607968.999271959183110.0007280408169
618378.99919094868544.00080905131458
627182.9996763375817-11.9996763375817
636371.0009707647159-8.0009707647159
646963.00064727246745.99935272753257
659568.999514656913926.0004853430861
6610394.99789658045298.00210341954711
67101102.999352635902-1.99935263590166
68105101.0001617461123.99983825388794
69104104.999676416118-0.99967641611849
7094104.000080873064-10.000080873064
7111194.000808998959216.9991910010408
72116110.9986247783395.00137522166085
73122115.9995953925376.0004046074627
74103121.999514571818-18.9995145718176
7596103.001537046321-7.00153704632081
7610496.00056641903757.99943358096249
77124103.9993528518920.0006471481104
78141123.99838196281317.001618037187
79137140.998624581994-3.99862458199377
80137137.000323485696-0.000323485696384296
81139137.000000026171.99999997383026
82132138.999838201519-6.9998382015188
83150132.00056628160217.9994337183977
84150149.9985438594620.00145614053818122
85147149.999999882199-2.99999988219935
86130147.000242697715-17.0002426977155
87133130.0013753067422.99862469325768
88135132.9997574135362.00024258646371
89148134.99983818189213.0001618181084
90165147.99894829676717.0010517032326
91153164.99862462781-11.9986246278098
92159153.0009706796335.99902932036662
93154158.999514683077-4.99951468307728
94151154.000404456947-3.00040445694654
95174151.00024273044522.9997572695547
96169173.998139337078-4.99813933707847
97162169.000404345682-7.00040434568209
98152162.000566327403-10.0005663274029
99162152.0008090382329.99919096176791
100167161.9991910730345.00080892696604
101173166.999595438356.0004045616499
102181172.9995145718218.00048542817871
103173180.999352766796-7.99935276679594
104178173.0006471415734.99935285842739
105172177.999595556145-5.99959555614495
106171172.000485362731-1.00048536273079
107196171.00008093850724.9999190614929
108199195.9979775255063.00202247449369
109190198.999757138658-8.99975713865837
110176190.000728073528-14.0007280735277
111188176.00113264828411.9988673517161
112193187.999029300735.00097069926957
113200192.9995954252637.00040457473713
114209199.9994336725799.00056632742144
115200208.99927186101-8.99927186100959
116207200.0007280342696.99927196573094
117204206.999433764206-2.99943376420578
118192204.000242651917-12.0002426519169
119216192.0009708105323.9990291894697
120216215.9980584967380.00194150326206

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 56 & 57 & -1 \tabularnewline
3 & 55 & 56.0000808992417 & -1.00008089924166 \tabularnewline
4 & 53 & 55.0000809057863 & -2.00008090578635 \tabularnewline
5 & 73 & 53.0001618050285 & 19.9998381949715 \tabularnewline
6 & 72 & 72.9983820282567 & -0.998382028256657 \tabularnewline
7 & 57 & 72.000080768349 & -15.000080768349 \tabularnewline
8 & 47 & 57.001213495159 & -10.001213495159 \tabularnewline
9 & 48 & 47.0008090905875 & 0.99919090941254 \tabularnewline
10 & 48 & 47.9999191662132 & 8.08337868463127e-05 \tabularnewline
11 & 49 & 47.9999999934606 & 1.00000000653939 \tabularnewline
12 & 51 & 48.9999191007578 & 2.00008089924219 \tabularnewline
13 & 45 & 50.999838194972 & -5.99983819497199 \tabularnewline
14 & 39 & 45.0004853823601 & -6.00048538236007 \tabularnewline
15 & 34 & 39.000485434717 & -5.00048543471704 \tabularnewline
16 & 34 & 34.0004045354796 & -0.000404535479610502 \tabularnewline
17 & 53 & 34.0000000327266 & 18.9999999672734 \tabularnewline
18 & 55 & 52.9984629144111 & 2.00153708558894 \tabularnewline
19 & 40 & 54.9998380771676 & -14.9998380771676 \tabularnewline
20 & 22 & 40.0012134755255 & -18.0012134755255 \tabularnewline
21 & 31 & 22.0014562845192 & 8.99854371548083 \tabularnewline
22 & 31 & 30.9992720246374 & 0.000727975362647015 \tabularnewline
23 & 39 & 30.9999999411073 & 8.00000005889266 \tabularnewline
24 & 43 & 38.9993528060619 & 4.00064719393806 \tabularnewline
25 & 42 & 42.9996763506759 & -0.999676350675855 \tabularnewline
26 & 31 & 42.0000808730587 & -11.0000808730587 \tabularnewline
27 & 37 & 31.0008898982009 & 5.99911010179915 \tabularnewline
28 & 35 & 36.9995146765421 & -1.99951467654212 \tabularnewline
29 & 52 & 35.000161759221 & 16.999838240779 \tabularnewline
30 & 48 & 51.9986247259779 & -3.99862472597794 \tabularnewline
31 & 31 & 48.000323485708 & -17.000323485708 \tabularnewline
32 & 19 & 31.001375313278 & -12.001375313278 \tabularnewline
33 & 30 & 19.0009709021617 & 10.9990290978383 \tabularnewline
34 & 34 & 29.999110186887 & 4.00088981311304 \tabularnewline
35 & 37 & 33.9996763310481 & 3.00032366895186 \tabularnewline
36 & 41 & 36.9997572760904 & 4.00024272390956 \tabularnewline
37 & 32 & 40.9996763833972 & -8.99967638339717 \tabularnewline
38 & 25 & 32.0007280669946 & -7.00072806699463 \tabularnewline
39 & 28 & 25.0005663535917 & 2.9994336464083 \tabularnewline
40 & 29 & 27.9997573480926 & 1.00024265190741 \tabularnewline
41 & 56 & 28.999919081128 & 27.000080918872 \tabularnewline
42 & 56 & 55.9978157139288 & 0.00218428607115584 \tabularnewline
43 & 41 & 55.9999998232929 & -14.9999998232929 \tabularnewline
44 & 39 & 41.0012134886106 & -2.00121348861064 \tabularnewline
45 & 45 & 39.0001618966536 & 5.99983810334637 \tabularnewline
46 & 42 & 44.9995146176473 & -2.99951461764734 \tabularnewline
47 & 50 & 42.0002426584579 & 7.99975734154208 \tabularnewline
48 & 60 & 49.9993528256976 & 10.0006471743024 \tabularnewline
49 & 62 & 59.9991909552275 & 2.00080904477253 \tabularnewline
50 & 48 & 61.9998381360656 & -13.9998381360656 \tabularnewline
51 & 44 & 48.0011325762886 & -4.0011325762886 \tabularnewline
52 & 40 & 44.0003236885912 & -4.00032368859121 \tabularnewline
53 & 67 & 40.0003236231528 & 26.9996763768472 \tabularnewline
54 & 69 & 66.997815746656 & 2.00218425334401 \tabularnewline
55 & 64 & 68.9998380248122 & -4.99983802481223 \tabularnewline
56 & 69 & 64.0004044831046 & 4.99959551689535 \tabularnewline
57 & 68 & 68.9995955365141 & -0.999595536514065 \tabularnewline
58 & 60 & 68.0000808665209 & -8.00008086652088 \tabularnewline
59 & 69 & 60.0006472004753 & 8.99935279952467 \tabularnewline
60 & 79 & 68.9992719591831 & 10.0007280408169 \tabularnewline
61 & 83 & 78.9991909486854 & 4.00080905131458 \tabularnewline
62 & 71 & 82.9996763375817 & -11.9996763375817 \tabularnewline
63 & 63 & 71.0009707647159 & -8.0009707647159 \tabularnewline
64 & 69 & 63.0006472724674 & 5.99935272753257 \tabularnewline
65 & 95 & 68.9995146569139 & 26.0004853430861 \tabularnewline
66 & 103 & 94.9978965804529 & 8.00210341954711 \tabularnewline
67 & 101 & 102.999352635902 & -1.99935263590166 \tabularnewline
68 & 105 & 101.000161746112 & 3.99983825388794 \tabularnewline
69 & 104 & 104.999676416118 & -0.99967641611849 \tabularnewline
70 & 94 & 104.000080873064 & -10.000080873064 \tabularnewline
71 & 111 & 94.0008089989592 & 16.9991910010408 \tabularnewline
72 & 116 & 110.998624778339 & 5.00137522166085 \tabularnewline
73 & 122 & 115.999595392537 & 6.0004046074627 \tabularnewline
74 & 103 & 121.999514571818 & -18.9995145718176 \tabularnewline
75 & 96 & 103.001537046321 & -7.00153704632081 \tabularnewline
76 & 104 & 96.0005664190375 & 7.99943358096249 \tabularnewline
77 & 124 & 103.99935285189 & 20.0006471481104 \tabularnewline
78 & 141 & 123.998381962813 & 17.001618037187 \tabularnewline
79 & 137 & 140.998624581994 & -3.99862458199377 \tabularnewline
80 & 137 & 137.000323485696 & -0.000323485696384296 \tabularnewline
81 & 139 & 137.00000002617 & 1.99999997383026 \tabularnewline
82 & 132 & 138.999838201519 & -6.9998382015188 \tabularnewline
83 & 150 & 132.000566281602 & 17.9994337183977 \tabularnewline
84 & 150 & 149.998543859462 & 0.00145614053818122 \tabularnewline
85 & 147 & 149.999999882199 & -2.99999988219935 \tabularnewline
86 & 130 & 147.000242697715 & -17.0002426977155 \tabularnewline
87 & 133 & 130.001375306742 & 2.99862469325768 \tabularnewline
88 & 135 & 132.999757413536 & 2.00024258646371 \tabularnewline
89 & 148 & 134.999838181892 & 13.0001618181084 \tabularnewline
90 & 165 & 147.998948296767 & 17.0010517032326 \tabularnewline
91 & 153 & 164.99862462781 & -11.9986246278098 \tabularnewline
92 & 159 & 153.000970679633 & 5.99902932036662 \tabularnewline
93 & 154 & 158.999514683077 & -4.99951468307728 \tabularnewline
94 & 151 & 154.000404456947 & -3.00040445694654 \tabularnewline
95 & 174 & 151.000242730445 & 22.9997572695547 \tabularnewline
96 & 169 & 173.998139337078 & -4.99813933707847 \tabularnewline
97 & 162 & 169.000404345682 & -7.00040434568209 \tabularnewline
98 & 152 & 162.000566327403 & -10.0005663274029 \tabularnewline
99 & 162 & 152.000809038232 & 9.99919096176791 \tabularnewline
100 & 167 & 161.999191073034 & 5.00080892696604 \tabularnewline
101 & 173 & 166.99959543835 & 6.0004045616499 \tabularnewline
102 & 181 & 172.999514571821 & 8.00048542817871 \tabularnewline
103 & 173 & 180.999352766796 & -7.99935276679594 \tabularnewline
104 & 178 & 173.000647141573 & 4.99935285842739 \tabularnewline
105 & 172 & 177.999595556145 & -5.99959555614495 \tabularnewline
106 & 171 & 172.000485362731 & -1.00048536273079 \tabularnewline
107 & 196 & 171.000080938507 & 24.9999190614929 \tabularnewline
108 & 199 & 195.997977525506 & 3.00202247449369 \tabularnewline
109 & 190 & 198.999757138658 & -8.99975713865837 \tabularnewline
110 & 176 & 190.000728073528 & -14.0007280735277 \tabularnewline
111 & 188 & 176.001132648284 & 11.9988673517161 \tabularnewline
112 & 193 & 187.99902930073 & 5.00097069926957 \tabularnewline
113 & 200 & 192.999595425263 & 7.00040457473713 \tabularnewline
114 & 209 & 199.999433672579 & 9.00056632742144 \tabularnewline
115 & 200 & 208.99927186101 & -8.99927186100959 \tabularnewline
116 & 207 & 200.000728034269 & 6.99927196573094 \tabularnewline
117 & 204 & 206.999433764206 & -2.99943376420578 \tabularnewline
118 & 192 & 204.000242651917 & -12.0002426519169 \tabularnewline
119 & 216 & 192.00097081053 & 23.9990291894697 \tabularnewline
120 & 216 & 215.998058496738 & 0.00194150326206 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211238&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]2[/C][C]56[/C][C]57[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]55[/C][C]56.0000808992417[/C][C]-1.00008089924166[/C][/ROW]
[ROW][C]4[/C][C]53[/C][C]55.0000809057863[/C][C]-2.00008090578635[/C][/ROW]
[ROW][C]5[/C][C]73[/C][C]53.0001618050285[/C][C]19.9998381949715[/C][/ROW]
[ROW][C]6[/C][C]72[/C][C]72.9983820282567[/C][C]-0.998382028256657[/C][/ROW]
[ROW][C]7[/C][C]57[/C][C]72.000080768349[/C][C]-15.000080768349[/C][/ROW]
[ROW][C]8[/C][C]47[/C][C]57.001213495159[/C][C]-10.001213495159[/C][/ROW]
[ROW][C]9[/C][C]48[/C][C]47.0008090905875[/C][C]0.99919090941254[/C][/ROW]
[ROW][C]10[/C][C]48[/C][C]47.9999191662132[/C][C]8.08337868463127e-05[/C][/ROW]
[ROW][C]11[/C][C]49[/C][C]47.9999999934606[/C][C]1.00000000653939[/C][/ROW]
[ROW][C]12[/C][C]51[/C][C]48.9999191007578[/C][C]2.00008089924219[/C][/ROW]
[ROW][C]13[/C][C]45[/C][C]50.999838194972[/C][C]-5.99983819497199[/C][/ROW]
[ROW][C]14[/C][C]39[/C][C]45.0004853823601[/C][C]-6.00048538236007[/C][/ROW]
[ROW][C]15[/C][C]34[/C][C]39.000485434717[/C][C]-5.00048543471704[/C][/ROW]
[ROW][C]16[/C][C]34[/C][C]34.0004045354796[/C][C]-0.000404535479610502[/C][/ROW]
[ROW][C]17[/C][C]53[/C][C]34.0000000327266[/C][C]18.9999999672734[/C][/ROW]
[ROW][C]18[/C][C]55[/C][C]52.9984629144111[/C][C]2.00153708558894[/C][/ROW]
[ROW][C]19[/C][C]40[/C][C]54.9998380771676[/C][C]-14.9998380771676[/C][/ROW]
[ROW][C]20[/C][C]22[/C][C]40.0012134755255[/C][C]-18.0012134755255[/C][/ROW]
[ROW][C]21[/C][C]31[/C][C]22.0014562845192[/C][C]8.99854371548083[/C][/ROW]
[ROW][C]22[/C][C]31[/C][C]30.9992720246374[/C][C]0.000727975362647015[/C][/ROW]
[ROW][C]23[/C][C]39[/C][C]30.9999999411073[/C][C]8.00000005889266[/C][/ROW]
[ROW][C]24[/C][C]43[/C][C]38.9993528060619[/C][C]4.00064719393806[/C][/ROW]
[ROW][C]25[/C][C]42[/C][C]42.9996763506759[/C][C]-0.999676350675855[/C][/ROW]
[ROW][C]26[/C][C]31[/C][C]42.0000808730587[/C][C]-11.0000808730587[/C][/ROW]
[ROW][C]27[/C][C]37[/C][C]31.0008898982009[/C][C]5.99911010179915[/C][/ROW]
[ROW][C]28[/C][C]35[/C][C]36.9995146765421[/C][C]-1.99951467654212[/C][/ROW]
[ROW][C]29[/C][C]52[/C][C]35.000161759221[/C][C]16.999838240779[/C][/ROW]
[ROW][C]30[/C][C]48[/C][C]51.9986247259779[/C][C]-3.99862472597794[/C][/ROW]
[ROW][C]31[/C][C]31[/C][C]48.000323485708[/C][C]-17.000323485708[/C][/ROW]
[ROW][C]32[/C][C]19[/C][C]31.001375313278[/C][C]-12.001375313278[/C][/ROW]
[ROW][C]33[/C][C]30[/C][C]19.0009709021617[/C][C]10.9990290978383[/C][/ROW]
[ROW][C]34[/C][C]34[/C][C]29.999110186887[/C][C]4.00088981311304[/C][/ROW]
[ROW][C]35[/C][C]37[/C][C]33.9996763310481[/C][C]3.00032366895186[/C][/ROW]
[ROW][C]36[/C][C]41[/C][C]36.9997572760904[/C][C]4.00024272390956[/C][/ROW]
[ROW][C]37[/C][C]32[/C][C]40.9996763833972[/C][C]-8.99967638339717[/C][/ROW]
[ROW][C]38[/C][C]25[/C][C]32.0007280669946[/C][C]-7.00072806699463[/C][/ROW]
[ROW][C]39[/C][C]28[/C][C]25.0005663535917[/C][C]2.9994336464083[/C][/ROW]
[ROW][C]40[/C][C]29[/C][C]27.9997573480926[/C][C]1.00024265190741[/C][/ROW]
[ROW][C]41[/C][C]56[/C][C]28.999919081128[/C][C]27.000080918872[/C][/ROW]
[ROW][C]42[/C][C]56[/C][C]55.9978157139288[/C][C]0.00218428607115584[/C][/ROW]
[ROW][C]43[/C][C]41[/C][C]55.9999998232929[/C][C]-14.9999998232929[/C][/ROW]
[ROW][C]44[/C][C]39[/C][C]41.0012134886106[/C][C]-2.00121348861064[/C][/ROW]
[ROW][C]45[/C][C]45[/C][C]39.0001618966536[/C][C]5.99983810334637[/C][/ROW]
[ROW][C]46[/C][C]42[/C][C]44.9995146176473[/C][C]-2.99951461764734[/C][/ROW]
[ROW][C]47[/C][C]50[/C][C]42.0002426584579[/C][C]7.99975734154208[/C][/ROW]
[ROW][C]48[/C][C]60[/C][C]49.9993528256976[/C][C]10.0006471743024[/C][/ROW]
[ROW][C]49[/C][C]62[/C][C]59.9991909552275[/C][C]2.00080904477253[/C][/ROW]
[ROW][C]50[/C][C]48[/C][C]61.9998381360656[/C][C]-13.9998381360656[/C][/ROW]
[ROW][C]51[/C][C]44[/C][C]48.0011325762886[/C][C]-4.0011325762886[/C][/ROW]
[ROW][C]52[/C][C]40[/C][C]44.0003236885912[/C][C]-4.00032368859121[/C][/ROW]
[ROW][C]53[/C][C]67[/C][C]40.0003236231528[/C][C]26.9996763768472[/C][/ROW]
[ROW][C]54[/C][C]69[/C][C]66.997815746656[/C][C]2.00218425334401[/C][/ROW]
[ROW][C]55[/C][C]64[/C][C]68.9998380248122[/C][C]-4.99983802481223[/C][/ROW]
[ROW][C]56[/C][C]69[/C][C]64.0004044831046[/C][C]4.99959551689535[/C][/ROW]
[ROW][C]57[/C][C]68[/C][C]68.9995955365141[/C][C]-0.999595536514065[/C][/ROW]
[ROW][C]58[/C][C]60[/C][C]68.0000808665209[/C][C]-8.00008086652088[/C][/ROW]
[ROW][C]59[/C][C]69[/C][C]60.0006472004753[/C][C]8.99935279952467[/C][/ROW]
[ROW][C]60[/C][C]79[/C][C]68.9992719591831[/C][C]10.0007280408169[/C][/ROW]
[ROW][C]61[/C][C]83[/C][C]78.9991909486854[/C][C]4.00080905131458[/C][/ROW]
[ROW][C]62[/C][C]71[/C][C]82.9996763375817[/C][C]-11.9996763375817[/C][/ROW]
[ROW][C]63[/C][C]63[/C][C]71.0009707647159[/C][C]-8.0009707647159[/C][/ROW]
[ROW][C]64[/C][C]69[/C][C]63.0006472724674[/C][C]5.99935272753257[/C][/ROW]
[ROW][C]65[/C][C]95[/C][C]68.9995146569139[/C][C]26.0004853430861[/C][/ROW]
[ROW][C]66[/C][C]103[/C][C]94.9978965804529[/C][C]8.00210341954711[/C][/ROW]
[ROW][C]67[/C][C]101[/C][C]102.999352635902[/C][C]-1.99935263590166[/C][/ROW]
[ROW][C]68[/C][C]105[/C][C]101.000161746112[/C][C]3.99983825388794[/C][/ROW]
[ROW][C]69[/C][C]104[/C][C]104.999676416118[/C][C]-0.99967641611849[/C][/ROW]
[ROW][C]70[/C][C]94[/C][C]104.000080873064[/C][C]-10.000080873064[/C][/ROW]
[ROW][C]71[/C][C]111[/C][C]94.0008089989592[/C][C]16.9991910010408[/C][/ROW]
[ROW][C]72[/C][C]116[/C][C]110.998624778339[/C][C]5.00137522166085[/C][/ROW]
[ROW][C]73[/C][C]122[/C][C]115.999595392537[/C][C]6.0004046074627[/C][/ROW]
[ROW][C]74[/C][C]103[/C][C]121.999514571818[/C][C]-18.9995145718176[/C][/ROW]
[ROW][C]75[/C][C]96[/C][C]103.001537046321[/C][C]-7.00153704632081[/C][/ROW]
[ROW][C]76[/C][C]104[/C][C]96.0005664190375[/C][C]7.99943358096249[/C][/ROW]
[ROW][C]77[/C][C]124[/C][C]103.99935285189[/C][C]20.0006471481104[/C][/ROW]
[ROW][C]78[/C][C]141[/C][C]123.998381962813[/C][C]17.001618037187[/C][/ROW]
[ROW][C]79[/C][C]137[/C][C]140.998624581994[/C][C]-3.99862458199377[/C][/ROW]
[ROW][C]80[/C][C]137[/C][C]137.000323485696[/C][C]-0.000323485696384296[/C][/ROW]
[ROW][C]81[/C][C]139[/C][C]137.00000002617[/C][C]1.99999997383026[/C][/ROW]
[ROW][C]82[/C][C]132[/C][C]138.999838201519[/C][C]-6.9998382015188[/C][/ROW]
[ROW][C]83[/C][C]150[/C][C]132.000566281602[/C][C]17.9994337183977[/C][/ROW]
[ROW][C]84[/C][C]150[/C][C]149.998543859462[/C][C]0.00145614053818122[/C][/ROW]
[ROW][C]85[/C][C]147[/C][C]149.999999882199[/C][C]-2.99999988219935[/C][/ROW]
[ROW][C]86[/C][C]130[/C][C]147.000242697715[/C][C]-17.0002426977155[/C][/ROW]
[ROW][C]87[/C][C]133[/C][C]130.001375306742[/C][C]2.99862469325768[/C][/ROW]
[ROW][C]88[/C][C]135[/C][C]132.999757413536[/C][C]2.00024258646371[/C][/ROW]
[ROW][C]89[/C][C]148[/C][C]134.999838181892[/C][C]13.0001618181084[/C][/ROW]
[ROW][C]90[/C][C]165[/C][C]147.998948296767[/C][C]17.0010517032326[/C][/ROW]
[ROW][C]91[/C][C]153[/C][C]164.99862462781[/C][C]-11.9986246278098[/C][/ROW]
[ROW][C]92[/C][C]159[/C][C]153.000970679633[/C][C]5.99902932036662[/C][/ROW]
[ROW][C]93[/C][C]154[/C][C]158.999514683077[/C][C]-4.99951468307728[/C][/ROW]
[ROW][C]94[/C][C]151[/C][C]154.000404456947[/C][C]-3.00040445694654[/C][/ROW]
[ROW][C]95[/C][C]174[/C][C]151.000242730445[/C][C]22.9997572695547[/C][/ROW]
[ROW][C]96[/C][C]169[/C][C]173.998139337078[/C][C]-4.99813933707847[/C][/ROW]
[ROW][C]97[/C][C]162[/C][C]169.000404345682[/C][C]-7.00040434568209[/C][/ROW]
[ROW][C]98[/C][C]152[/C][C]162.000566327403[/C][C]-10.0005663274029[/C][/ROW]
[ROW][C]99[/C][C]162[/C][C]152.000809038232[/C][C]9.99919096176791[/C][/ROW]
[ROW][C]100[/C][C]167[/C][C]161.999191073034[/C][C]5.00080892696604[/C][/ROW]
[ROW][C]101[/C][C]173[/C][C]166.99959543835[/C][C]6.0004045616499[/C][/ROW]
[ROW][C]102[/C][C]181[/C][C]172.999514571821[/C][C]8.00048542817871[/C][/ROW]
[ROW][C]103[/C][C]173[/C][C]180.999352766796[/C][C]-7.99935276679594[/C][/ROW]
[ROW][C]104[/C][C]178[/C][C]173.000647141573[/C][C]4.99935285842739[/C][/ROW]
[ROW][C]105[/C][C]172[/C][C]177.999595556145[/C][C]-5.99959555614495[/C][/ROW]
[ROW][C]106[/C][C]171[/C][C]172.000485362731[/C][C]-1.00048536273079[/C][/ROW]
[ROW][C]107[/C][C]196[/C][C]171.000080938507[/C][C]24.9999190614929[/C][/ROW]
[ROW][C]108[/C][C]199[/C][C]195.997977525506[/C][C]3.00202247449369[/C][/ROW]
[ROW][C]109[/C][C]190[/C][C]198.999757138658[/C][C]-8.99975713865837[/C][/ROW]
[ROW][C]110[/C][C]176[/C][C]190.000728073528[/C][C]-14.0007280735277[/C][/ROW]
[ROW][C]111[/C][C]188[/C][C]176.001132648284[/C][C]11.9988673517161[/C][/ROW]
[ROW][C]112[/C][C]193[/C][C]187.99902930073[/C][C]5.00097069926957[/C][/ROW]
[ROW][C]113[/C][C]200[/C][C]192.999595425263[/C][C]7.00040457473713[/C][/ROW]
[ROW][C]114[/C][C]209[/C][C]199.999433672579[/C][C]9.00056632742144[/C][/ROW]
[ROW][C]115[/C][C]200[/C][C]208.99927186101[/C][C]-8.99927186100959[/C][/ROW]
[ROW][C]116[/C][C]207[/C][C]200.000728034269[/C][C]6.99927196573094[/C][/ROW]
[ROW][C]117[/C][C]204[/C][C]206.999433764206[/C][C]-2.99943376420578[/C][/ROW]
[ROW][C]118[/C][C]192[/C][C]204.000242651917[/C][C]-12.0002426519169[/C][/ROW]
[ROW][C]119[/C][C]216[/C][C]192.00097081053[/C][C]23.9990291894697[/C][/ROW]
[ROW][C]120[/C][C]216[/C][C]215.998058496738[/C][C]0.00194150326206[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211238&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211238&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
25657-1
35556.0000808992417-1.00008089924166
45355.0000809057863-2.00008090578635
57353.000161805028519.9998381949715
67272.9983820282567-0.998382028256657
75772.000080768349-15.000080768349
84757.001213495159-10.001213495159
94847.00080909058750.99919090941254
104847.99991916621328.08337868463127e-05
114947.99999999346061.00000000653939
125148.99991910075782.00008089924219
134550.999838194972-5.99983819497199
143945.0004853823601-6.00048538236007
153439.000485434717-5.00048543471704
163434.0004045354796-0.000404535479610502
175334.000000032726618.9999999672734
185552.99846291441112.00153708558894
194054.9998380771676-14.9998380771676
202240.0012134755255-18.0012134755255
213122.00145628451928.99854371548083
223130.99927202463740.000727975362647015
233930.99999994110738.00000005889266
244338.99935280606194.00064719393806
254242.9996763506759-0.999676350675855
263142.0000808730587-11.0000808730587
273731.00088989820095.99911010179915
283536.9995146765421-1.99951467654212
295235.00016175922116.999838240779
304851.9986247259779-3.99862472597794
313148.000323485708-17.000323485708
321931.001375313278-12.001375313278
333019.000970902161710.9990290978383
343429.9991101868874.00088981311304
353733.99967633104813.00032366895186
364136.99975727609044.00024272390956
373240.9996763833972-8.99967638339717
382532.0007280669946-7.00072806699463
392825.00056635359172.9994336464083
402927.99975734809261.00024265190741
415628.99991908112827.000080918872
425655.99781571392880.00218428607115584
434155.9999998232929-14.9999998232929
443941.0012134886106-2.00121348861064
454539.00016189665365.99983810334637
464244.9995146176473-2.99951461764734
475042.00024265845797.99975734154208
486049.999352825697610.0006471743024
496259.99919095522752.00080904477253
504861.9998381360656-13.9998381360656
514448.0011325762886-4.0011325762886
524044.0003236885912-4.00032368859121
536740.000323623152826.9996763768472
546966.9978157466562.00218425334401
556468.9998380248122-4.99983802481223
566964.00040448310464.99959551689535
576868.9995955365141-0.999595536514065
586068.0000808665209-8.00008086652088
596960.00064720047538.99935279952467
607968.999271959183110.0007280408169
618378.99919094868544.00080905131458
627182.9996763375817-11.9996763375817
636371.0009707647159-8.0009707647159
646963.00064727246745.99935272753257
659568.999514656913926.0004853430861
6610394.99789658045298.00210341954711
67101102.999352635902-1.99935263590166
68105101.0001617461123.99983825388794
69104104.999676416118-0.99967641611849
7094104.000080873064-10.000080873064
7111194.000808998959216.9991910010408
72116110.9986247783395.00137522166085
73122115.9995953925376.0004046074627
74103121.999514571818-18.9995145718176
7596103.001537046321-7.00153704632081
7610496.00056641903757.99943358096249
77124103.9993528518920.0006471481104
78141123.99838196281317.001618037187
79137140.998624581994-3.99862458199377
80137137.000323485696-0.000323485696384296
81139137.000000026171.99999997383026
82132138.999838201519-6.9998382015188
83150132.00056628160217.9994337183977
84150149.9985438594620.00145614053818122
85147149.999999882199-2.99999988219935
86130147.000242697715-17.0002426977155
87133130.0013753067422.99862469325768
88135132.9997574135362.00024258646371
89148134.99983818189213.0001618181084
90165147.99894829676717.0010517032326
91153164.99862462781-11.9986246278098
92159153.0009706796335.99902932036662
93154158.999514683077-4.99951468307728
94151154.000404456947-3.00040445694654
95174151.00024273044522.9997572695547
96169173.998139337078-4.99813933707847
97162169.000404345682-7.00040434568209
98152162.000566327403-10.0005663274029
99162152.0008090382329.99919096176791
100167161.9991910730345.00080892696604
101173166.999595438356.0004045616499
102181172.9995145718218.00048542817871
103173180.999352766796-7.99935276679594
104178173.0006471415734.99935285842739
105172177.999595556145-5.99959555614495
106171172.000485362731-1.00048536273079
107196171.00008093850724.9999190614929
108199195.9979775255063.00202247449369
109190198.999757138658-8.99975713865837
110176190.000728073528-14.0007280735277
111188176.00113264828411.9988673517161
112193187.999029300735.00097069926957
113200192.9995954252637.00040457473713
114209199.9994336725799.00056632742144
115200208.99927186101-8.99927186100959
116207200.0007280342696.99927196573094
117204206.999433764206-2.99943376420578
118192204.000242651917-12.0002426519169
119216192.0009708105323.9990291894697
120216215.9980584967380.00194150326206







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121215.999999842934195.859203850694236.140795835174
122215.999999842934187.517765112613244.482234573254
123215.999999842934181.116999294456250.883000391412
124215.999999842934175.72085189642256.279147789448
125215.999999842934170.966725574575261.033274111292
126215.999999842934166.66865257407265.331347111798
127215.999999842934162.716157494683269.283842191185
128215.999999842934159.037258621805272.962741064063
129215.999999842934155.581956847009276.418042838858
130215.999999842934152.313847882799279.686151803069
131215.999999842934149.205449290352282.794550395516
132215.999999842934146.235409859523285.764589826345

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 215.999999842934 & 195.859203850694 & 236.140795835174 \tabularnewline
122 & 215.999999842934 & 187.517765112613 & 244.482234573254 \tabularnewline
123 & 215.999999842934 & 181.116999294456 & 250.883000391412 \tabularnewline
124 & 215.999999842934 & 175.72085189642 & 256.279147789448 \tabularnewline
125 & 215.999999842934 & 170.966725574575 & 261.033274111292 \tabularnewline
126 & 215.999999842934 & 166.66865257407 & 265.331347111798 \tabularnewline
127 & 215.999999842934 & 162.716157494683 & 269.283842191185 \tabularnewline
128 & 215.999999842934 & 159.037258621805 & 272.962741064063 \tabularnewline
129 & 215.999999842934 & 155.581956847009 & 276.418042838858 \tabularnewline
130 & 215.999999842934 & 152.313847882799 & 279.686151803069 \tabularnewline
131 & 215.999999842934 & 149.205449290352 & 282.794550395516 \tabularnewline
132 & 215.999999842934 & 146.235409859523 & 285.764589826345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211238&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]215.999999842934[/C][C]195.859203850694[/C][C]236.140795835174[/C][/ROW]
[ROW][C]122[/C][C]215.999999842934[/C][C]187.517765112613[/C][C]244.482234573254[/C][/ROW]
[ROW][C]123[/C][C]215.999999842934[/C][C]181.116999294456[/C][C]250.883000391412[/C][/ROW]
[ROW][C]124[/C][C]215.999999842934[/C][C]175.72085189642[/C][C]256.279147789448[/C][/ROW]
[ROW][C]125[/C][C]215.999999842934[/C][C]170.966725574575[/C][C]261.033274111292[/C][/ROW]
[ROW][C]126[/C][C]215.999999842934[/C][C]166.66865257407[/C][C]265.331347111798[/C][/ROW]
[ROW][C]127[/C][C]215.999999842934[/C][C]162.716157494683[/C][C]269.283842191185[/C][/ROW]
[ROW][C]128[/C][C]215.999999842934[/C][C]159.037258621805[/C][C]272.962741064063[/C][/ROW]
[ROW][C]129[/C][C]215.999999842934[/C][C]155.581956847009[/C][C]276.418042838858[/C][/ROW]
[ROW][C]130[/C][C]215.999999842934[/C][C]152.313847882799[/C][C]279.686151803069[/C][/ROW]
[ROW][C]131[/C][C]215.999999842934[/C][C]149.205449290352[/C][C]282.794550395516[/C][/ROW]
[ROW][C]132[/C][C]215.999999842934[/C][C]146.235409859523[/C][C]285.764589826345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211238&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211238&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
121215.999999842934195.859203850694236.140795835174
122215.999999842934187.517765112613244.482234573254
123215.999999842934181.116999294456250.883000391412
124215.999999842934175.72085189642256.279147789448
125215.999999842934170.966725574575261.033274111292
126215.999999842934166.66865257407265.331347111798
127215.999999842934162.716157494683269.283842191185
128215.999999842934159.037258621805272.962741064063
129215.999999842934155.581956847009276.418042838858
130215.999999842934152.313847882799279.686151803069
131215.999999842934149.205449290352282.794550395516
132215.999999842934146.235409859523285.764589826345



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