Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 21 Dec 2010 17:25:11 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/21/t1292952204y5mxk0gwe0gxv22.htm/, Retrieved Fri, 17 May 2024 04:43:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113768, Retrieved Fri, 17 May 2024 04:43:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-12-21 17:25:11] [3bbb4c38423daa916cf90d93c467bd86] [Current]
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Dataseries X:
57.7
63.6
78
77.4
74.1
85.9
82
78.4
68.1
70.9
85.2
149.6
57.9
63.7
85
66.1
80.2
83.4
85.7
81.8
69.4
76.4
90.3
157.3
65.3
68.4
72.7
86.6
82.6
84.8
93.4
82.2
75.2
83.9
85.4
166.3
70.4
73.9
82.4
92.3
82.7
95.8
105.8
84.2
82.7
88.4
90.2
176.6
69.5
77.3
98.6
86.4
90.8
101.5
112.2
93.6
93.8
90.8
98.1
187.6
75
83.7
99.7
104.9
98.9
117.3
115.7
102.2
101.9
96.6
110
203.7
82.3
93.3
121.9
100.9
107.7
130
123.2
116.1
105.3
107.7
123.9
205.2
90.3
106.9
122.4
111.3
122.6
124.8
139.5
118.8
111
121.2
120.6
219.1
101.3
105
113.4
133.6
123.9
136.2
151.7
121.9
120.2
132.2
125.2
233.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113768&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113768&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113768&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.111001096231486
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.111001096231486 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113768&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]0.111001096231486[/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=113768&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113768&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
alpha0.111001096231486
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
263.657.75.9
37858.354906467765819.6450935322342
477.460.535533385413816.8644666145862
574.162.407507666992211.6924923330078
685.963.705387133634322.1946128663657
78266.169013492234315.8309865077657
878.467.926270349022210.4737296509778
968.169.088865821913-0.988865821912952
1070.968.97910063165481.92089936834525
1185.269.192322567291516.0076774327085
12149.670.969192310442178.6308076895579
1357.979.6972981615502-21.7972981615502
1463.777.2777741707336-13.5777741707336
158575.77062635339869.22937364660142
1666.176.7950969457013-10.6950969457013
1780.275.60792946042654.59207053957354
1883.476.11765432429147.28234567570857
1985.776.92600267743178.77399732256829
2081.877.89992599856893.90007400143108
2169.478.3328384881117-8.93283848811167
2276.477.3412836234725-0.941283623472458
2390.377.236800109402313.0631998905977
24157.378.686829617549678.6131703824504
2565.387.4129777082342-22.1129777082342
2668.484.9584129416778-16.5584129416778
2772.783.1204109532979-10.4204109532979
2886.681.96373391429934.63626608570071
2982.682.4783645322330.121635467767078
3084.882.49186620249572.30813379750431
3193.482.748071584267610.6519284157324
3282.283.9304473153932-1.73044731539321
3375.283.7383657664137-8.53836576641373
3483.982.79059780631641.10940219368358
3585.482.91374266597692.48625733402309
36166.383.18971995556783.110280044433
3770.492.4150521486049-22.0150521486049
3873.989.9713572265164-16.0713572265164
3982.488.1874189564453-5.78741895644529
4092.387.5450091079294.75499089207101
4182.788.0728183095196-5.3728183095196
4295.887.47642958731038.32357041268968
43105.888.400355027678817.3996449723212
4484.290.3317346936452-6.13173469364516
4582.789.65110542085-6.95110542084991
4688.488.879525099115-0.479525099114937
4790.288.82629728744271.37370271255733
48176.688.978779794432787.6212202055673
4969.598.704831290391-29.2048312903911
5077.395.463063001902-18.1630630019021
5198.693.44694309776945.15305690223059
5286.494.0189380628602-7.6189380628602
5390.893.173227585763-2.37322758576293
54101.592.90979672213648.59020327786357
55112.293.863318702830618.3366812971694
5693.695.8987104280638-2.2987104280638
5793.895.64355105063-1.84355105062997
5890.895.4389148630513-4.63891486305134
5998.194.92399022792813.17600977207189
60187.695.2765307942792.32346920573
6175105.524537084000-30.5245370839998
6283.7102.136280005717-18.4362800057172
6399.7100.089832714652-0.389832714651973
64104.9100.0465608559794.85343914402129
6598.9100.585297921458-1.68529792145787
66117.3100.39822800469916.9017719953006
67115.7102.27434322443213.4256567755676
68102.2103.764605844148-1.56460584414809
69101.9103.590932880277-1.69093288027746
7096.6103.403237476913-6.80323747691281
71110102.6480706590527.35192934094765
72203.7103.464142875314100.235857124686
7382.3114.590432897857-32.2904328978567
7493.3111.006159448405-17.7061594484054
75121.9109.04075633958312.8592436604171
76100.9110.468146482597-9.56814648259696
77107.7109.406071734125-1.70607173412526
78130109.21669590138820.7833040986122
79123.2111.52366543964611.6763345603539
80116.1112.8197513758113.28024862418903
81105.3113.183862569008-7.88386256900777
82107.7112.308745181310-4.60874518130953
83123.9111.79716941393312.1028305860674
84205.2113.1405968764992.05940312351
8590.3123.359291541616-33.0592915416159
86106.9119.689673939860-12.7896739398603
87122.4118.2700061120934.12999388790749
88111.3118.728439961080-7.42843996107958
89122.6117.903874982114.69612501789004
90124.8118.4251500071366.37484999286414
91139.5119.13276534465520.3672346553449
92118.8121.393550718602-2.59355071860224
93111121.105663745705-10.1056637457054
94121.2119.9839239917851.21607600821466
95120.6120.1189097617980.481090238202015
96219.1120.17231130562598.9276886943753
97101.3131.153393198348-29.8533931983475
98105127.839633827101-22.8396338271014
99113.4125.304409434767-11.9044094347674
100133.6123.9830069375209.61699306248023
101123.9125.050503709906-1.15050370990565
102136.2124.92279653688811.2772034631122
103151.7126.17457848371925.5254215162813
104121.9129.007928253797-7.10792825379667
105120.2128.218940425691-8.0189404256905
106132.2127.3288292478244.87117075217611
107125.2127.869534541246-2.66953454124616
108233.8127.57321328074106.22678671926

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 63.6 & 57.7 & 5.9 \tabularnewline
3 & 78 & 58.3549064677658 & 19.6450935322342 \tabularnewline
4 & 77.4 & 60.5355333854138 & 16.8644666145862 \tabularnewline
5 & 74.1 & 62.4075076669922 & 11.6924923330078 \tabularnewline
6 & 85.9 & 63.7053871336343 & 22.1946128663657 \tabularnewline
7 & 82 & 66.1690134922343 & 15.8309865077657 \tabularnewline
8 & 78.4 & 67.9262703490222 & 10.4737296509778 \tabularnewline
9 & 68.1 & 69.088865821913 & -0.988865821912952 \tabularnewline
10 & 70.9 & 68.9791006316548 & 1.92089936834525 \tabularnewline
11 & 85.2 & 69.1923225672915 & 16.0076774327085 \tabularnewline
12 & 149.6 & 70.9691923104421 & 78.6308076895579 \tabularnewline
13 & 57.9 & 79.6972981615502 & -21.7972981615502 \tabularnewline
14 & 63.7 & 77.2777741707336 & -13.5777741707336 \tabularnewline
15 & 85 & 75.7706263533986 & 9.22937364660142 \tabularnewline
16 & 66.1 & 76.7950969457013 & -10.6950969457013 \tabularnewline
17 & 80.2 & 75.6079294604265 & 4.59207053957354 \tabularnewline
18 & 83.4 & 76.1176543242914 & 7.28234567570857 \tabularnewline
19 & 85.7 & 76.9260026774317 & 8.77399732256829 \tabularnewline
20 & 81.8 & 77.8999259985689 & 3.90007400143108 \tabularnewline
21 & 69.4 & 78.3328384881117 & -8.93283848811167 \tabularnewline
22 & 76.4 & 77.3412836234725 & -0.941283623472458 \tabularnewline
23 & 90.3 & 77.2368001094023 & 13.0631998905977 \tabularnewline
24 & 157.3 & 78.6868296175496 & 78.6131703824504 \tabularnewline
25 & 65.3 & 87.4129777082342 & -22.1129777082342 \tabularnewline
26 & 68.4 & 84.9584129416778 & -16.5584129416778 \tabularnewline
27 & 72.7 & 83.1204109532979 & -10.4204109532979 \tabularnewline
28 & 86.6 & 81.9637339142993 & 4.63626608570071 \tabularnewline
29 & 82.6 & 82.478364532233 & 0.121635467767078 \tabularnewline
30 & 84.8 & 82.4918662024957 & 2.30813379750431 \tabularnewline
31 & 93.4 & 82.7480715842676 & 10.6519284157324 \tabularnewline
32 & 82.2 & 83.9304473153932 & -1.73044731539321 \tabularnewline
33 & 75.2 & 83.7383657664137 & -8.53836576641373 \tabularnewline
34 & 83.9 & 82.7905978063164 & 1.10940219368358 \tabularnewline
35 & 85.4 & 82.9137426659769 & 2.48625733402309 \tabularnewline
36 & 166.3 & 83.189719955567 & 83.110280044433 \tabularnewline
37 & 70.4 & 92.4150521486049 & -22.0150521486049 \tabularnewline
38 & 73.9 & 89.9713572265164 & -16.0713572265164 \tabularnewline
39 & 82.4 & 88.1874189564453 & -5.78741895644529 \tabularnewline
40 & 92.3 & 87.545009107929 & 4.75499089207101 \tabularnewline
41 & 82.7 & 88.0728183095196 & -5.3728183095196 \tabularnewline
42 & 95.8 & 87.4764295873103 & 8.32357041268968 \tabularnewline
43 & 105.8 & 88.4003550276788 & 17.3996449723212 \tabularnewline
44 & 84.2 & 90.3317346936452 & -6.13173469364516 \tabularnewline
45 & 82.7 & 89.65110542085 & -6.95110542084991 \tabularnewline
46 & 88.4 & 88.879525099115 & -0.479525099114937 \tabularnewline
47 & 90.2 & 88.8262972874427 & 1.37370271255733 \tabularnewline
48 & 176.6 & 88.9787797944327 & 87.6212202055673 \tabularnewline
49 & 69.5 & 98.704831290391 & -29.2048312903911 \tabularnewline
50 & 77.3 & 95.463063001902 & -18.1630630019021 \tabularnewline
51 & 98.6 & 93.4469430977694 & 5.15305690223059 \tabularnewline
52 & 86.4 & 94.0189380628602 & -7.6189380628602 \tabularnewline
53 & 90.8 & 93.173227585763 & -2.37322758576293 \tabularnewline
54 & 101.5 & 92.9097967221364 & 8.59020327786357 \tabularnewline
55 & 112.2 & 93.8633187028306 & 18.3366812971694 \tabularnewline
56 & 93.6 & 95.8987104280638 & -2.2987104280638 \tabularnewline
57 & 93.8 & 95.64355105063 & -1.84355105062997 \tabularnewline
58 & 90.8 & 95.4389148630513 & -4.63891486305134 \tabularnewline
59 & 98.1 & 94.9239902279281 & 3.17600977207189 \tabularnewline
60 & 187.6 & 95.27653079427 & 92.32346920573 \tabularnewline
61 & 75 & 105.524537084000 & -30.5245370839998 \tabularnewline
62 & 83.7 & 102.136280005717 & -18.4362800057172 \tabularnewline
63 & 99.7 & 100.089832714652 & -0.389832714651973 \tabularnewline
64 & 104.9 & 100.046560855979 & 4.85343914402129 \tabularnewline
65 & 98.9 & 100.585297921458 & -1.68529792145787 \tabularnewline
66 & 117.3 & 100.398228004699 & 16.9017719953006 \tabularnewline
67 & 115.7 & 102.274343224432 & 13.4256567755676 \tabularnewline
68 & 102.2 & 103.764605844148 & -1.56460584414809 \tabularnewline
69 & 101.9 & 103.590932880277 & -1.69093288027746 \tabularnewline
70 & 96.6 & 103.403237476913 & -6.80323747691281 \tabularnewline
71 & 110 & 102.648070659052 & 7.35192934094765 \tabularnewline
72 & 203.7 & 103.464142875314 & 100.235857124686 \tabularnewline
73 & 82.3 & 114.590432897857 & -32.2904328978567 \tabularnewline
74 & 93.3 & 111.006159448405 & -17.7061594484054 \tabularnewline
75 & 121.9 & 109.040756339583 & 12.8592436604171 \tabularnewline
76 & 100.9 & 110.468146482597 & -9.56814648259696 \tabularnewline
77 & 107.7 & 109.406071734125 & -1.70607173412526 \tabularnewline
78 & 130 & 109.216695901388 & 20.7833040986122 \tabularnewline
79 & 123.2 & 111.523665439646 & 11.6763345603539 \tabularnewline
80 & 116.1 & 112.819751375811 & 3.28024862418903 \tabularnewline
81 & 105.3 & 113.183862569008 & -7.88386256900777 \tabularnewline
82 & 107.7 & 112.308745181310 & -4.60874518130953 \tabularnewline
83 & 123.9 & 111.797169413933 & 12.1028305860674 \tabularnewline
84 & 205.2 & 113.14059687649 & 92.05940312351 \tabularnewline
85 & 90.3 & 123.359291541616 & -33.0592915416159 \tabularnewline
86 & 106.9 & 119.689673939860 & -12.7896739398603 \tabularnewline
87 & 122.4 & 118.270006112093 & 4.12999388790749 \tabularnewline
88 & 111.3 & 118.728439961080 & -7.42843996107958 \tabularnewline
89 & 122.6 & 117.90387498211 & 4.69612501789004 \tabularnewline
90 & 124.8 & 118.425150007136 & 6.37484999286414 \tabularnewline
91 & 139.5 & 119.132765344655 & 20.3672346553449 \tabularnewline
92 & 118.8 & 121.393550718602 & -2.59355071860224 \tabularnewline
93 & 111 & 121.105663745705 & -10.1056637457054 \tabularnewline
94 & 121.2 & 119.983923991785 & 1.21607600821466 \tabularnewline
95 & 120.6 & 120.118909761798 & 0.481090238202015 \tabularnewline
96 & 219.1 & 120.172311305625 & 98.9276886943753 \tabularnewline
97 & 101.3 & 131.153393198348 & -29.8533931983475 \tabularnewline
98 & 105 & 127.839633827101 & -22.8396338271014 \tabularnewline
99 & 113.4 & 125.304409434767 & -11.9044094347674 \tabularnewline
100 & 133.6 & 123.983006937520 & 9.61699306248023 \tabularnewline
101 & 123.9 & 125.050503709906 & -1.15050370990565 \tabularnewline
102 & 136.2 & 124.922796536888 & 11.2772034631122 \tabularnewline
103 & 151.7 & 126.174578483719 & 25.5254215162813 \tabularnewline
104 & 121.9 & 129.007928253797 & -7.10792825379667 \tabularnewline
105 & 120.2 & 128.218940425691 & -8.0189404256905 \tabularnewline
106 & 132.2 & 127.328829247824 & 4.87117075217611 \tabularnewline
107 & 125.2 & 127.869534541246 & -2.66953454124616 \tabularnewline
108 & 233.8 & 127.57321328074 & 106.22678671926 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113768&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]63.6[/C][C]57.7[/C][C]5.9[/C][/ROW]
[ROW][C]3[/C][C]78[/C][C]58.3549064677658[/C][C]19.6450935322342[/C][/ROW]
[ROW][C]4[/C][C]77.4[/C][C]60.5355333854138[/C][C]16.8644666145862[/C][/ROW]
[ROW][C]5[/C][C]74.1[/C][C]62.4075076669922[/C][C]11.6924923330078[/C][/ROW]
[ROW][C]6[/C][C]85.9[/C][C]63.7053871336343[/C][C]22.1946128663657[/C][/ROW]
[ROW][C]7[/C][C]82[/C][C]66.1690134922343[/C][C]15.8309865077657[/C][/ROW]
[ROW][C]8[/C][C]78.4[/C][C]67.9262703490222[/C][C]10.4737296509778[/C][/ROW]
[ROW][C]9[/C][C]68.1[/C][C]69.088865821913[/C][C]-0.988865821912952[/C][/ROW]
[ROW][C]10[/C][C]70.9[/C][C]68.9791006316548[/C][C]1.92089936834525[/C][/ROW]
[ROW][C]11[/C][C]85.2[/C][C]69.1923225672915[/C][C]16.0076774327085[/C][/ROW]
[ROW][C]12[/C][C]149.6[/C][C]70.9691923104421[/C][C]78.6308076895579[/C][/ROW]
[ROW][C]13[/C][C]57.9[/C][C]79.6972981615502[/C][C]-21.7972981615502[/C][/ROW]
[ROW][C]14[/C][C]63.7[/C][C]77.2777741707336[/C][C]-13.5777741707336[/C][/ROW]
[ROW][C]15[/C][C]85[/C][C]75.7706263533986[/C][C]9.22937364660142[/C][/ROW]
[ROW][C]16[/C][C]66.1[/C][C]76.7950969457013[/C][C]-10.6950969457013[/C][/ROW]
[ROW][C]17[/C][C]80.2[/C][C]75.6079294604265[/C][C]4.59207053957354[/C][/ROW]
[ROW][C]18[/C][C]83.4[/C][C]76.1176543242914[/C][C]7.28234567570857[/C][/ROW]
[ROW][C]19[/C][C]85.7[/C][C]76.9260026774317[/C][C]8.77399732256829[/C][/ROW]
[ROW][C]20[/C][C]81.8[/C][C]77.8999259985689[/C][C]3.90007400143108[/C][/ROW]
[ROW][C]21[/C][C]69.4[/C][C]78.3328384881117[/C][C]-8.93283848811167[/C][/ROW]
[ROW][C]22[/C][C]76.4[/C][C]77.3412836234725[/C][C]-0.941283623472458[/C][/ROW]
[ROW][C]23[/C][C]90.3[/C][C]77.2368001094023[/C][C]13.0631998905977[/C][/ROW]
[ROW][C]24[/C][C]157.3[/C][C]78.6868296175496[/C][C]78.6131703824504[/C][/ROW]
[ROW][C]25[/C][C]65.3[/C][C]87.4129777082342[/C][C]-22.1129777082342[/C][/ROW]
[ROW][C]26[/C][C]68.4[/C][C]84.9584129416778[/C][C]-16.5584129416778[/C][/ROW]
[ROW][C]27[/C][C]72.7[/C][C]83.1204109532979[/C][C]-10.4204109532979[/C][/ROW]
[ROW][C]28[/C][C]86.6[/C][C]81.9637339142993[/C][C]4.63626608570071[/C][/ROW]
[ROW][C]29[/C][C]82.6[/C][C]82.478364532233[/C][C]0.121635467767078[/C][/ROW]
[ROW][C]30[/C][C]84.8[/C][C]82.4918662024957[/C][C]2.30813379750431[/C][/ROW]
[ROW][C]31[/C][C]93.4[/C][C]82.7480715842676[/C][C]10.6519284157324[/C][/ROW]
[ROW][C]32[/C][C]82.2[/C][C]83.9304473153932[/C][C]-1.73044731539321[/C][/ROW]
[ROW][C]33[/C][C]75.2[/C][C]83.7383657664137[/C][C]-8.53836576641373[/C][/ROW]
[ROW][C]34[/C][C]83.9[/C][C]82.7905978063164[/C][C]1.10940219368358[/C][/ROW]
[ROW][C]35[/C][C]85.4[/C][C]82.9137426659769[/C][C]2.48625733402309[/C][/ROW]
[ROW][C]36[/C][C]166.3[/C][C]83.189719955567[/C][C]83.110280044433[/C][/ROW]
[ROW][C]37[/C][C]70.4[/C][C]92.4150521486049[/C][C]-22.0150521486049[/C][/ROW]
[ROW][C]38[/C][C]73.9[/C][C]89.9713572265164[/C][C]-16.0713572265164[/C][/ROW]
[ROW][C]39[/C][C]82.4[/C][C]88.1874189564453[/C][C]-5.78741895644529[/C][/ROW]
[ROW][C]40[/C][C]92.3[/C][C]87.545009107929[/C][C]4.75499089207101[/C][/ROW]
[ROW][C]41[/C][C]82.7[/C][C]88.0728183095196[/C][C]-5.3728183095196[/C][/ROW]
[ROW][C]42[/C][C]95.8[/C][C]87.4764295873103[/C][C]8.32357041268968[/C][/ROW]
[ROW][C]43[/C][C]105.8[/C][C]88.4003550276788[/C][C]17.3996449723212[/C][/ROW]
[ROW][C]44[/C][C]84.2[/C][C]90.3317346936452[/C][C]-6.13173469364516[/C][/ROW]
[ROW][C]45[/C][C]82.7[/C][C]89.65110542085[/C][C]-6.95110542084991[/C][/ROW]
[ROW][C]46[/C][C]88.4[/C][C]88.879525099115[/C][C]-0.479525099114937[/C][/ROW]
[ROW][C]47[/C][C]90.2[/C][C]88.8262972874427[/C][C]1.37370271255733[/C][/ROW]
[ROW][C]48[/C][C]176.6[/C][C]88.9787797944327[/C][C]87.6212202055673[/C][/ROW]
[ROW][C]49[/C][C]69.5[/C][C]98.704831290391[/C][C]-29.2048312903911[/C][/ROW]
[ROW][C]50[/C][C]77.3[/C][C]95.463063001902[/C][C]-18.1630630019021[/C][/ROW]
[ROW][C]51[/C][C]98.6[/C][C]93.4469430977694[/C][C]5.15305690223059[/C][/ROW]
[ROW][C]52[/C][C]86.4[/C][C]94.0189380628602[/C][C]-7.6189380628602[/C][/ROW]
[ROW][C]53[/C][C]90.8[/C][C]93.173227585763[/C][C]-2.37322758576293[/C][/ROW]
[ROW][C]54[/C][C]101.5[/C][C]92.9097967221364[/C][C]8.59020327786357[/C][/ROW]
[ROW][C]55[/C][C]112.2[/C][C]93.8633187028306[/C][C]18.3366812971694[/C][/ROW]
[ROW][C]56[/C][C]93.6[/C][C]95.8987104280638[/C][C]-2.2987104280638[/C][/ROW]
[ROW][C]57[/C][C]93.8[/C][C]95.64355105063[/C][C]-1.84355105062997[/C][/ROW]
[ROW][C]58[/C][C]90.8[/C][C]95.4389148630513[/C][C]-4.63891486305134[/C][/ROW]
[ROW][C]59[/C][C]98.1[/C][C]94.9239902279281[/C][C]3.17600977207189[/C][/ROW]
[ROW][C]60[/C][C]187.6[/C][C]95.27653079427[/C][C]92.32346920573[/C][/ROW]
[ROW][C]61[/C][C]75[/C][C]105.524537084000[/C][C]-30.5245370839998[/C][/ROW]
[ROW][C]62[/C][C]83.7[/C][C]102.136280005717[/C][C]-18.4362800057172[/C][/ROW]
[ROW][C]63[/C][C]99.7[/C][C]100.089832714652[/C][C]-0.389832714651973[/C][/ROW]
[ROW][C]64[/C][C]104.9[/C][C]100.046560855979[/C][C]4.85343914402129[/C][/ROW]
[ROW][C]65[/C][C]98.9[/C][C]100.585297921458[/C][C]-1.68529792145787[/C][/ROW]
[ROW][C]66[/C][C]117.3[/C][C]100.398228004699[/C][C]16.9017719953006[/C][/ROW]
[ROW][C]67[/C][C]115.7[/C][C]102.274343224432[/C][C]13.4256567755676[/C][/ROW]
[ROW][C]68[/C][C]102.2[/C][C]103.764605844148[/C][C]-1.56460584414809[/C][/ROW]
[ROW][C]69[/C][C]101.9[/C][C]103.590932880277[/C][C]-1.69093288027746[/C][/ROW]
[ROW][C]70[/C][C]96.6[/C][C]103.403237476913[/C][C]-6.80323747691281[/C][/ROW]
[ROW][C]71[/C][C]110[/C][C]102.648070659052[/C][C]7.35192934094765[/C][/ROW]
[ROW][C]72[/C][C]203.7[/C][C]103.464142875314[/C][C]100.235857124686[/C][/ROW]
[ROW][C]73[/C][C]82.3[/C][C]114.590432897857[/C][C]-32.2904328978567[/C][/ROW]
[ROW][C]74[/C][C]93.3[/C][C]111.006159448405[/C][C]-17.7061594484054[/C][/ROW]
[ROW][C]75[/C][C]121.9[/C][C]109.040756339583[/C][C]12.8592436604171[/C][/ROW]
[ROW][C]76[/C][C]100.9[/C][C]110.468146482597[/C][C]-9.56814648259696[/C][/ROW]
[ROW][C]77[/C][C]107.7[/C][C]109.406071734125[/C][C]-1.70607173412526[/C][/ROW]
[ROW][C]78[/C][C]130[/C][C]109.216695901388[/C][C]20.7833040986122[/C][/ROW]
[ROW][C]79[/C][C]123.2[/C][C]111.523665439646[/C][C]11.6763345603539[/C][/ROW]
[ROW][C]80[/C][C]116.1[/C][C]112.819751375811[/C][C]3.28024862418903[/C][/ROW]
[ROW][C]81[/C][C]105.3[/C][C]113.183862569008[/C][C]-7.88386256900777[/C][/ROW]
[ROW][C]82[/C][C]107.7[/C][C]112.308745181310[/C][C]-4.60874518130953[/C][/ROW]
[ROW][C]83[/C][C]123.9[/C][C]111.797169413933[/C][C]12.1028305860674[/C][/ROW]
[ROW][C]84[/C][C]205.2[/C][C]113.14059687649[/C][C]92.05940312351[/C][/ROW]
[ROW][C]85[/C][C]90.3[/C][C]123.359291541616[/C][C]-33.0592915416159[/C][/ROW]
[ROW][C]86[/C][C]106.9[/C][C]119.689673939860[/C][C]-12.7896739398603[/C][/ROW]
[ROW][C]87[/C][C]122.4[/C][C]118.270006112093[/C][C]4.12999388790749[/C][/ROW]
[ROW][C]88[/C][C]111.3[/C][C]118.728439961080[/C][C]-7.42843996107958[/C][/ROW]
[ROW][C]89[/C][C]122.6[/C][C]117.90387498211[/C][C]4.69612501789004[/C][/ROW]
[ROW][C]90[/C][C]124.8[/C][C]118.425150007136[/C][C]6.37484999286414[/C][/ROW]
[ROW][C]91[/C][C]139.5[/C][C]119.132765344655[/C][C]20.3672346553449[/C][/ROW]
[ROW][C]92[/C][C]118.8[/C][C]121.393550718602[/C][C]-2.59355071860224[/C][/ROW]
[ROW][C]93[/C][C]111[/C][C]121.105663745705[/C][C]-10.1056637457054[/C][/ROW]
[ROW][C]94[/C][C]121.2[/C][C]119.983923991785[/C][C]1.21607600821466[/C][/ROW]
[ROW][C]95[/C][C]120.6[/C][C]120.118909761798[/C][C]0.481090238202015[/C][/ROW]
[ROW][C]96[/C][C]219.1[/C][C]120.172311305625[/C][C]98.9276886943753[/C][/ROW]
[ROW][C]97[/C][C]101.3[/C][C]131.153393198348[/C][C]-29.8533931983475[/C][/ROW]
[ROW][C]98[/C][C]105[/C][C]127.839633827101[/C][C]-22.8396338271014[/C][/ROW]
[ROW][C]99[/C][C]113.4[/C][C]125.304409434767[/C][C]-11.9044094347674[/C][/ROW]
[ROW][C]100[/C][C]133.6[/C][C]123.983006937520[/C][C]9.61699306248023[/C][/ROW]
[ROW][C]101[/C][C]123.9[/C][C]125.050503709906[/C][C]-1.15050370990565[/C][/ROW]
[ROW][C]102[/C][C]136.2[/C][C]124.922796536888[/C][C]11.2772034631122[/C][/ROW]
[ROW][C]103[/C][C]151.7[/C][C]126.174578483719[/C][C]25.5254215162813[/C][/ROW]
[ROW][C]104[/C][C]121.9[/C][C]129.007928253797[/C][C]-7.10792825379667[/C][/ROW]
[ROW][C]105[/C][C]120.2[/C][C]128.218940425691[/C][C]-8.0189404256905[/C][/ROW]
[ROW][C]106[/C][C]132.2[/C][C]127.328829247824[/C][C]4.87117075217611[/C][/ROW]
[ROW][C]107[/C][C]125.2[/C][C]127.869534541246[/C][C]-2.66953454124616[/C][/ROW]
[ROW][C]108[/C][C]233.8[/C][C]127.57321328074[/C][C]106.22678671926[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113768&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113768&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
263.657.75.9
37858.354906467765819.6450935322342
477.460.535533385413816.8644666145862
574.162.407507666992211.6924923330078
685.963.705387133634322.1946128663657
78266.169013492234315.8309865077657
878.467.926270349022210.4737296509778
968.169.088865821913-0.988865821912952
1070.968.97910063165481.92089936834525
1185.269.192322567291516.0076774327085
12149.670.969192310442178.6308076895579
1357.979.6972981615502-21.7972981615502
1463.777.2777741707336-13.5777741707336
158575.77062635339869.22937364660142
1666.176.7950969457013-10.6950969457013
1780.275.60792946042654.59207053957354
1883.476.11765432429147.28234567570857
1985.776.92600267743178.77399732256829
2081.877.89992599856893.90007400143108
2169.478.3328384881117-8.93283848811167
2276.477.3412836234725-0.941283623472458
2390.377.236800109402313.0631998905977
24157.378.686829617549678.6131703824504
2565.387.4129777082342-22.1129777082342
2668.484.9584129416778-16.5584129416778
2772.783.1204109532979-10.4204109532979
2886.681.96373391429934.63626608570071
2982.682.4783645322330.121635467767078
3084.882.49186620249572.30813379750431
3193.482.748071584267610.6519284157324
3282.283.9304473153932-1.73044731539321
3375.283.7383657664137-8.53836576641373
3483.982.79059780631641.10940219368358
3585.482.91374266597692.48625733402309
36166.383.18971995556783.110280044433
3770.492.4150521486049-22.0150521486049
3873.989.9713572265164-16.0713572265164
3982.488.1874189564453-5.78741895644529
4092.387.5450091079294.75499089207101
4182.788.0728183095196-5.3728183095196
4295.887.47642958731038.32357041268968
43105.888.400355027678817.3996449723212
4484.290.3317346936452-6.13173469364516
4582.789.65110542085-6.95110542084991
4688.488.879525099115-0.479525099114937
4790.288.82629728744271.37370271255733
48176.688.978779794432787.6212202055673
4969.598.704831290391-29.2048312903911
5077.395.463063001902-18.1630630019021
5198.693.44694309776945.15305690223059
5286.494.0189380628602-7.6189380628602
5390.893.173227585763-2.37322758576293
54101.592.90979672213648.59020327786357
55112.293.863318702830618.3366812971694
5693.695.8987104280638-2.2987104280638
5793.895.64355105063-1.84355105062997
5890.895.4389148630513-4.63891486305134
5998.194.92399022792813.17600977207189
60187.695.2765307942792.32346920573
6175105.524537084000-30.5245370839998
6283.7102.136280005717-18.4362800057172
6399.7100.089832714652-0.389832714651973
64104.9100.0465608559794.85343914402129
6598.9100.585297921458-1.68529792145787
66117.3100.39822800469916.9017719953006
67115.7102.27434322443213.4256567755676
68102.2103.764605844148-1.56460584414809
69101.9103.590932880277-1.69093288027746
7096.6103.403237476913-6.80323747691281
71110102.6480706590527.35192934094765
72203.7103.464142875314100.235857124686
7382.3114.590432897857-32.2904328978567
7493.3111.006159448405-17.7061594484054
75121.9109.04075633958312.8592436604171
76100.9110.468146482597-9.56814648259696
77107.7109.406071734125-1.70607173412526
78130109.21669590138820.7833040986122
79123.2111.52366543964611.6763345603539
80116.1112.8197513758113.28024862418903
81105.3113.183862569008-7.88386256900777
82107.7112.308745181310-4.60874518130953
83123.9111.79716941393312.1028305860674
84205.2113.1405968764992.05940312351
8590.3123.359291541616-33.0592915416159
86106.9119.689673939860-12.7896739398603
87122.4118.2700061120934.12999388790749
88111.3118.728439961080-7.42843996107958
89122.6117.903874982114.69612501789004
90124.8118.4251500071366.37484999286414
91139.5119.13276534465520.3672346553449
92118.8121.393550718602-2.59355071860224
93111121.105663745705-10.1056637457054
94121.2119.9839239917851.21607600821466
95120.6120.1189097617980.481090238202015
96219.1120.17231130562598.9276886943753
97101.3131.153393198348-29.8533931983475
98105127.839633827101-22.8396338271014
99113.4125.304409434767-11.9044094347674
100133.6123.9830069375209.61699306248023
101123.9125.050503709906-1.15050370990565
102136.2124.92279653688811.2772034631122
103151.7126.17457848371925.5254215162813
104121.9129.007928253797-7.10792825379667
105120.2128.218940425691-8.0189404256905
106132.2127.3288292478244.87117075217611
107125.2127.869534541246-2.66953454124616
108233.8127.57321328074106.22678671926







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109139.36450305572683.4956249755803195.233381135872
110139.36450305572683.1524916752866195.576514436166
111139.36450305572682.8114402833605195.917565828092
112139.36450305572682.4724333584864196.256572752966
113139.36450305572682.1354345683215196.593571543131
114139.36450305572681.8004086440487196.928597467404
115139.36450305572681.4673213372955197.261684774157
116139.36450305572681.1361393792717197.592866732181
117139.36450305572680.8068304419866197.922175669466
118139.36450305572680.4793631014188198.249643010033
119139.36450305572680.1537068025189198.575299308933
120139.36450305572679.8298318259353198.899174285517

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 139.364503055726 & 83.4956249755803 & 195.233381135872 \tabularnewline
110 & 139.364503055726 & 83.1524916752866 & 195.576514436166 \tabularnewline
111 & 139.364503055726 & 82.8114402833605 & 195.917565828092 \tabularnewline
112 & 139.364503055726 & 82.4724333584864 & 196.256572752966 \tabularnewline
113 & 139.364503055726 & 82.1354345683215 & 196.593571543131 \tabularnewline
114 & 139.364503055726 & 81.8004086440487 & 196.928597467404 \tabularnewline
115 & 139.364503055726 & 81.4673213372955 & 197.261684774157 \tabularnewline
116 & 139.364503055726 & 81.1361393792717 & 197.592866732181 \tabularnewline
117 & 139.364503055726 & 80.8068304419866 & 197.922175669466 \tabularnewline
118 & 139.364503055726 & 80.4793631014188 & 198.249643010033 \tabularnewline
119 & 139.364503055726 & 80.1537068025189 & 198.575299308933 \tabularnewline
120 & 139.364503055726 & 79.8298318259353 & 198.899174285517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113768&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]109[/C][C]139.364503055726[/C][C]83.4956249755803[/C][C]195.233381135872[/C][/ROW]
[ROW][C]110[/C][C]139.364503055726[/C][C]83.1524916752866[/C][C]195.576514436166[/C][/ROW]
[ROW][C]111[/C][C]139.364503055726[/C][C]82.8114402833605[/C][C]195.917565828092[/C][/ROW]
[ROW][C]112[/C][C]139.364503055726[/C][C]82.4724333584864[/C][C]196.256572752966[/C][/ROW]
[ROW][C]113[/C][C]139.364503055726[/C][C]82.1354345683215[/C][C]196.593571543131[/C][/ROW]
[ROW][C]114[/C][C]139.364503055726[/C][C]81.8004086440487[/C][C]196.928597467404[/C][/ROW]
[ROW][C]115[/C][C]139.364503055726[/C][C]81.4673213372955[/C][C]197.261684774157[/C][/ROW]
[ROW][C]116[/C][C]139.364503055726[/C][C]81.1361393792717[/C][C]197.592866732181[/C][/ROW]
[ROW][C]117[/C][C]139.364503055726[/C][C]80.8068304419866[/C][C]197.922175669466[/C][/ROW]
[ROW][C]118[/C][C]139.364503055726[/C][C]80.4793631014188[/C][C]198.249643010033[/C][/ROW]
[ROW][C]119[/C][C]139.364503055726[/C][C]80.1537068025189[/C][C]198.575299308933[/C][/ROW]
[ROW][C]120[/C][C]139.364503055726[/C][C]79.8298318259353[/C][C]198.899174285517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113768&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113768&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
109139.36450305572683.4956249755803195.233381135872
110139.36450305572683.1524916752866195.576514436166
111139.36450305572682.8114402833605195.917565828092
112139.36450305572682.4724333584864196.256572752966
113139.36450305572682.1354345683215196.593571543131
114139.36450305572681.8004086440487196.928597467404
115139.36450305572681.4673213372955197.261684774157
116139.36450305572681.1361393792717197.592866732181
117139.36450305572680.8068304419866197.922175669466
118139.36450305572680.4793631014188198.249643010033
119139.36450305572680.1537068025189198.575299308933
120139.36450305572679.8298318259353198.899174285517



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')