Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 21:21:24 +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/Aug/19/t1282252981a5a0bqcl4pihxje.htm/, Retrieved Fri, 03 May 2024 14:29:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79392, Retrieved Fri, 03 May 2024 14:29:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsAerts Ellen
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks 1 - sta...] [2010-08-19 21:21:24] [6e43eada780a1520be8ab5bc59456d41] [Current]
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Dataseries X:
25
24
23
21
41
40
25
15
16
16
17
19
18
19
20
21
46
47
30
16
15
18
30
31
32
36
30
31
61
57
45
33
31
36
46
49
34
40
41
48
75
77
71
54
50
56
66
66
48
63
71
70
88
92
91
80
81
81
98
106
85
93
96
92
115
109
119
107
107
106
132
143
120
123
132
136
158
151
155
138
143
139
168
182
154
158
167
170
197
190
196
174
180
171
200
215
184
186
197
186
211
205
218
199
213
207
236
248
211
220
235
223
245
236
253
246
255
248
274
288




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79392&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79392&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79392&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.048882612475808
beta0.161657597483346
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.048882612475808 \tabularnewline
beta & 0.161657597483346 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79392&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]0.048882612475808[/C][/ROW]
[ROW][C]beta[/C][C]0.161657597483346[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79392&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79392&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
alpha0.048882612475808
beta0.161657597483346
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131817.34031758050760.659682419492437
141918.32222221157750.677777788422503
152019.51430801941860.485691980581375
162120.68515600137070.314843998629325
174644.6267795926921.37322040730801
184744.24103390211092.75896609788911
193026.12332739733363.87667260266644
201616.3215848230105-0.321584823010500
211517.8509300262992-2.85093002629920
221817.98842939589870.0115706041013048
233019.122793853517610.8772061464824
243121.78658175535519.2134182446449
253221.718609088548610.2813909114514
263623.642707343457612.3572926565424
273025.8169384408024.183061559198
283127.66373173347643.33626826652364
296161.684300799127-0.684300799127037
305763.6008205672313-6.60082056723132
314540.54780473634964.45219526365036
323321.990627511937311.0093724880627
333121.57622001953419.42377998046586
343626.89669703261939.10330296738067
354645.16562864894390.83437135105607
364946.40752133387452.5924786661255
373447.4558834629241-13.4558834629241
384051.6045402604209-11.6045402604209
394142.1979419471531-1.19794194715305
404843.23540745164734.76459254835267
417585.4746137366246-10.4746137366246
427779.6416181372721-2.64161813727213
437162.35139141174818.6486085882519
445444.88404323963299.11595676036709
455041.56773190282558.43226809717455
465647.75130877461178.24869122538834
476661.1624548090984.837545190902
486664.9359055281441.06409447185604
494845.52336733272922.47663266727076
506354.18494835020868.81505164979138
517156.093094518257814.9069054817422
527066.33270293995493.66729706004509
5388104.762930085779-16.7629300857786
5492107.069985011176-15.069985011176
559197.4753145285674-6.4753145285674
568073.13120009384536.86879990615469
578167.274925009588213.7250749904118
588175.37545458035055.62454541964954
599888.66151351629639.33848648370375
6010688.914647417636317.0853525823637
618565.083079879775519.9169201202245
629386.13632171388936.86367828611071
639696.2787162212688-0.278716221268837
649294.5586586943847-2.55865869438473
65115119.473439411829-4.47343941182881
66109125.461671730956-16.4616717309559
67119123.638077994263-4.63807799426318
68107107.963704240528-0.963704240527619
69107108.078811227408-1.07881122740775
70106107.376115080397-1.3761150803967
71132128.7930223672783.20697763272221
72143137.7220703766835.27792962331702
73120108.55767421971211.4423257802884
74123118.2938008884144.70619911158637
75132121.71289233262310.2871076673769
76136116.74948976734619.2505102326544
77158146.93619178059211.0638082194077
78151140.38277425330110.6172257466991
79155154.0086419913840.99135800861609
80138138.535149672799-0.535149672799463
81143138.5359366469874.46406335301339
82139137.5443498344051.45565016559530
83168171.190314126318-3.19031412631762
84182184.915039224158-2.91503922415833
85154154.181022699430-0.181022699430315
86158157.5277111661540.472288833846278
87167168.14309287129-1.14309287129001
88170171.452391716854-1.45239171685412
89197197.758183304578-0.758183304578125
90190187.5998796805782.40012031942177
91196191.8909998642954.10900013570509
92174170.4415274011333.5584725988667
93180175.9373581279884.06264187201239
94171170.5658752460750.434124753924976
95200205.707759817235-5.70775981723472
96215222.018637118999-7.01863711899881
97184186.989891114585-2.98989111458459
98186191.062430557554-5.06243055755434
99197201.090801555265-4.09080155526541
100186203.9151303878-17.9151303877999
101211234.450066175983-23.4500661759826
102205223.899734702572-18.8997347025715
103218228.648686161373-10.6486861613727
104199201.250187125254-2.25018712525417
105213206.7285540766136.27144592338664
106207195.64474352063311.3552564793668
107236228.7234163631887.27658363681212
108248245.6360498529082.36395014709171
109211209.7079700361711.29202996382949
110220211.5984249221488.40157507785165
111235224.12638837221910.8736116277811
112223212.53841651835210.4615834816476
113245242.5673991348682.43260086513197
114236236.659599269668-0.659599269667865
115253252.2499750556330.750024944367482
116246230.54583657243715.4541634275628
117255247.4751326007467.52486739925425
118248240.4344390571907.5655609428103
119274274.344258319853-0.344258319852543
120288288.308135318980-0.308135318979623

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 18 & 17.3403175805076 & 0.659682419492437 \tabularnewline
14 & 19 & 18.3222222115775 & 0.677777788422503 \tabularnewline
15 & 20 & 19.5143080194186 & 0.485691980581375 \tabularnewline
16 & 21 & 20.6851560013707 & 0.314843998629325 \tabularnewline
17 & 46 & 44.626779592692 & 1.37322040730801 \tabularnewline
18 & 47 & 44.2410339021109 & 2.75896609788911 \tabularnewline
19 & 30 & 26.1233273973336 & 3.87667260266644 \tabularnewline
20 & 16 & 16.3215848230105 & -0.321584823010500 \tabularnewline
21 & 15 & 17.8509300262992 & -2.85093002629920 \tabularnewline
22 & 18 & 17.9884293958987 & 0.0115706041013048 \tabularnewline
23 & 30 & 19.1227938535176 & 10.8772061464824 \tabularnewline
24 & 31 & 21.7865817553551 & 9.2134182446449 \tabularnewline
25 & 32 & 21.7186090885486 & 10.2813909114514 \tabularnewline
26 & 36 & 23.6427073434576 & 12.3572926565424 \tabularnewline
27 & 30 & 25.816938440802 & 4.183061559198 \tabularnewline
28 & 31 & 27.6637317334764 & 3.33626826652364 \tabularnewline
29 & 61 & 61.684300799127 & -0.684300799127037 \tabularnewline
30 & 57 & 63.6008205672313 & -6.60082056723132 \tabularnewline
31 & 45 & 40.5478047363496 & 4.45219526365036 \tabularnewline
32 & 33 & 21.9906275119373 & 11.0093724880627 \tabularnewline
33 & 31 & 21.5762200195341 & 9.42377998046586 \tabularnewline
34 & 36 & 26.8966970326193 & 9.10330296738067 \tabularnewline
35 & 46 & 45.1656286489439 & 0.83437135105607 \tabularnewline
36 & 49 & 46.4075213338745 & 2.5924786661255 \tabularnewline
37 & 34 & 47.4558834629241 & -13.4558834629241 \tabularnewline
38 & 40 & 51.6045402604209 & -11.6045402604209 \tabularnewline
39 & 41 & 42.1979419471531 & -1.19794194715305 \tabularnewline
40 & 48 & 43.2354074516473 & 4.76459254835267 \tabularnewline
41 & 75 & 85.4746137366246 & -10.4746137366246 \tabularnewline
42 & 77 & 79.6416181372721 & -2.64161813727213 \tabularnewline
43 & 71 & 62.3513914117481 & 8.6486085882519 \tabularnewline
44 & 54 & 44.8840432396329 & 9.11595676036709 \tabularnewline
45 & 50 & 41.5677319028255 & 8.43226809717455 \tabularnewline
46 & 56 & 47.7513087746117 & 8.24869122538834 \tabularnewline
47 & 66 & 61.162454809098 & 4.837545190902 \tabularnewline
48 & 66 & 64.935905528144 & 1.06409447185604 \tabularnewline
49 & 48 & 45.5233673327292 & 2.47663266727076 \tabularnewline
50 & 63 & 54.1849483502086 & 8.81505164979138 \tabularnewline
51 & 71 & 56.0930945182578 & 14.9069054817422 \tabularnewline
52 & 70 & 66.3327029399549 & 3.66729706004509 \tabularnewline
53 & 88 & 104.762930085779 & -16.7629300857786 \tabularnewline
54 & 92 & 107.069985011176 & -15.069985011176 \tabularnewline
55 & 91 & 97.4753145285674 & -6.4753145285674 \tabularnewline
56 & 80 & 73.1312000938453 & 6.86879990615469 \tabularnewline
57 & 81 & 67.2749250095882 & 13.7250749904118 \tabularnewline
58 & 81 & 75.3754545803505 & 5.62454541964954 \tabularnewline
59 & 98 & 88.6615135162963 & 9.33848648370375 \tabularnewline
60 & 106 & 88.9146474176363 & 17.0853525823637 \tabularnewline
61 & 85 & 65.0830798797755 & 19.9169201202245 \tabularnewline
62 & 93 & 86.1363217138893 & 6.86367828611071 \tabularnewline
63 & 96 & 96.2787162212688 & -0.278716221268837 \tabularnewline
64 & 92 & 94.5586586943847 & -2.55865869438473 \tabularnewline
65 & 115 & 119.473439411829 & -4.47343941182881 \tabularnewline
66 & 109 & 125.461671730956 & -16.4616717309559 \tabularnewline
67 & 119 & 123.638077994263 & -4.63807799426318 \tabularnewline
68 & 107 & 107.963704240528 & -0.963704240527619 \tabularnewline
69 & 107 & 108.078811227408 & -1.07881122740775 \tabularnewline
70 & 106 & 107.376115080397 & -1.3761150803967 \tabularnewline
71 & 132 & 128.793022367278 & 3.20697763272221 \tabularnewline
72 & 143 & 137.722070376683 & 5.27792962331702 \tabularnewline
73 & 120 & 108.557674219712 & 11.4423257802884 \tabularnewline
74 & 123 & 118.293800888414 & 4.70619911158637 \tabularnewline
75 & 132 & 121.712892332623 & 10.2871076673769 \tabularnewline
76 & 136 & 116.749489767346 & 19.2505102326544 \tabularnewline
77 & 158 & 146.936191780592 & 11.0638082194077 \tabularnewline
78 & 151 & 140.382774253301 & 10.6172257466991 \tabularnewline
79 & 155 & 154.008641991384 & 0.99135800861609 \tabularnewline
80 & 138 & 138.535149672799 & -0.535149672799463 \tabularnewline
81 & 143 & 138.535936646987 & 4.46406335301339 \tabularnewline
82 & 139 & 137.544349834405 & 1.45565016559530 \tabularnewline
83 & 168 & 171.190314126318 & -3.19031412631762 \tabularnewline
84 & 182 & 184.915039224158 & -2.91503922415833 \tabularnewline
85 & 154 & 154.181022699430 & -0.181022699430315 \tabularnewline
86 & 158 & 157.527711166154 & 0.472288833846278 \tabularnewline
87 & 167 & 168.14309287129 & -1.14309287129001 \tabularnewline
88 & 170 & 171.452391716854 & -1.45239171685412 \tabularnewline
89 & 197 & 197.758183304578 & -0.758183304578125 \tabularnewline
90 & 190 & 187.599879680578 & 2.40012031942177 \tabularnewline
91 & 196 & 191.890999864295 & 4.10900013570509 \tabularnewline
92 & 174 & 170.441527401133 & 3.5584725988667 \tabularnewline
93 & 180 & 175.937358127988 & 4.06264187201239 \tabularnewline
94 & 171 & 170.565875246075 & 0.434124753924976 \tabularnewline
95 & 200 & 205.707759817235 & -5.70775981723472 \tabularnewline
96 & 215 & 222.018637118999 & -7.01863711899881 \tabularnewline
97 & 184 & 186.989891114585 & -2.98989111458459 \tabularnewline
98 & 186 & 191.062430557554 & -5.06243055755434 \tabularnewline
99 & 197 & 201.090801555265 & -4.09080155526541 \tabularnewline
100 & 186 & 203.9151303878 & -17.9151303877999 \tabularnewline
101 & 211 & 234.450066175983 & -23.4500661759826 \tabularnewline
102 & 205 & 223.899734702572 & -18.8997347025715 \tabularnewline
103 & 218 & 228.648686161373 & -10.6486861613727 \tabularnewline
104 & 199 & 201.250187125254 & -2.25018712525417 \tabularnewline
105 & 213 & 206.728554076613 & 6.27144592338664 \tabularnewline
106 & 207 & 195.644743520633 & 11.3552564793668 \tabularnewline
107 & 236 & 228.723416363188 & 7.27658363681212 \tabularnewline
108 & 248 & 245.636049852908 & 2.36395014709171 \tabularnewline
109 & 211 & 209.707970036171 & 1.29202996382949 \tabularnewline
110 & 220 & 211.598424922148 & 8.40157507785165 \tabularnewline
111 & 235 & 224.126388372219 & 10.8736116277811 \tabularnewline
112 & 223 & 212.538416518352 & 10.4615834816476 \tabularnewline
113 & 245 & 242.567399134868 & 2.43260086513197 \tabularnewline
114 & 236 & 236.659599269668 & -0.659599269667865 \tabularnewline
115 & 253 & 252.249975055633 & 0.750024944367482 \tabularnewline
116 & 246 & 230.545836572437 & 15.4541634275628 \tabularnewline
117 & 255 & 247.475132600746 & 7.52486739925425 \tabularnewline
118 & 248 & 240.434439057190 & 7.5655609428103 \tabularnewline
119 & 274 & 274.344258319853 & -0.344258319852543 \tabularnewline
120 & 288 & 288.308135318980 & -0.308135318979623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79392&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]18[/C][C]17.3403175805076[/C][C]0.659682419492437[/C][/ROW]
[ROW][C]14[/C][C]19[/C][C]18.3222222115775[/C][C]0.677777788422503[/C][/ROW]
[ROW][C]15[/C][C]20[/C][C]19.5143080194186[/C][C]0.485691980581375[/C][/ROW]
[ROW][C]16[/C][C]21[/C][C]20.6851560013707[/C][C]0.314843998629325[/C][/ROW]
[ROW][C]17[/C][C]46[/C][C]44.626779592692[/C][C]1.37322040730801[/C][/ROW]
[ROW][C]18[/C][C]47[/C][C]44.2410339021109[/C][C]2.75896609788911[/C][/ROW]
[ROW][C]19[/C][C]30[/C][C]26.1233273973336[/C][C]3.87667260266644[/C][/ROW]
[ROW][C]20[/C][C]16[/C][C]16.3215848230105[/C][C]-0.321584823010500[/C][/ROW]
[ROW][C]21[/C][C]15[/C][C]17.8509300262992[/C][C]-2.85093002629920[/C][/ROW]
[ROW][C]22[/C][C]18[/C][C]17.9884293958987[/C][C]0.0115706041013048[/C][/ROW]
[ROW][C]23[/C][C]30[/C][C]19.1227938535176[/C][C]10.8772061464824[/C][/ROW]
[ROW][C]24[/C][C]31[/C][C]21.7865817553551[/C][C]9.2134182446449[/C][/ROW]
[ROW][C]25[/C][C]32[/C][C]21.7186090885486[/C][C]10.2813909114514[/C][/ROW]
[ROW][C]26[/C][C]36[/C][C]23.6427073434576[/C][C]12.3572926565424[/C][/ROW]
[ROW][C]27[/C][C]30[/C][C]25.816938440802[/C][C]4.183061559198[/C][/ROW]
[ROW][C]28[/C][C]31[/C][C]27.6637317334764[/C][C]3.33626826652364[/C][/ROW]
[ROW][C]29[/C][C]61[/C][C]61.684300799127[/C][C]-0.684300799127037[/C][/ROW]
[ROW][C]30[/C][C]57[/C][C]63.6008205672313[/C][C]-6.60082056723132[/C][/ROW]
[ROW][C]31[/C][C]45[/C][C]40.5478047363496[/C][C]4.45219526365036[/C][/ROW]
[ROW][C]32[/C][C]33[/C][C]21.9906275119373[/C][C]11.0093724880627[/C][/ROW]
[ROW][C]33[/C][C]31[/C][C]21.5762200195341[/C][C]9.42377998046586[/C][/ROW]
[ROW][C]34[/C][C]36[/C][C]26.8966970326193[/C][C]9.10330296738067[/C][/ROW]
[ROW][C]35[/C][C]46[/C][C]45.1656286489439[/C][C]0.83437135105607[/C][/ROW]
[ROW][C]36[/C][C]49[/C][C]46.4075213338745[/C][C]2.5924786661255[/C][/ROW]
[ROW][C]37[/C][C]34[/C][C]47.4558834629241[/C][C]-13.4558834629241[/C][/ROW]
[ROW][C]38[/C][C]40[/C][C]51.6045402604209[/C][C]-11.6045402604209[/C][/ROW]
[ROW][C]39[/C][C]41[/C][C]42.1979419471531[/C][C]-1.19794194715305[/C][/ROW]
[ROW][C]40[/C][C]48[/C][C]43.2354074516473[/C][C]4.76459254835267[/C][/ROW]
[ROW][C]41[/C][C]75[/C][C]85.4746137366246[/C][C]-10.4746137366246[/C][/ROW]
[ROW][C]42[/C][C]77[/C][C]79.6416181372721[/C][C]-2.64161813727213[/C][/ROW]
[ROW][C]43[/C][C]71[/C][C]62.3513914117481[/C][C]8.6486085882519[/C][/ROW]
[ROW][C]44[/C][C]54[/C][C]44.8840432396329[/C][C]9.11595676036709[/C][/ROW]
[ROW][C]45[/C][C]50[/C][C]41.5677319028255[/C][C]8.43226809717455[/C][/ROW]
[ROW][C]46[/C][C]56[/C][C]47.7513087746117[/C][C]8.24869122538834[/C][/ROW]
[ROW][C]47[/C][C]66[/C][C]61.162454809098[/C][C]4.837545190902[/C][/ROW]
[ROW][C]48[/C][C]66[/C][C]64.935905528144[/C][C]1.06409447185604[/C][/ROW]
[ROW][C]49[/C][C]48[/C][C]45.5233673327292[/C][C]2.47663266727076[/C][/ROW]
[ROW][C]50[/C][C]63[/C][C]54.1849483502086[/C][C]8.81505164979138[/C][/ROW]
[ROW][C]51[/C][C]71[/C][C]56.0930945182578[/C][C]14.9069054817422[/C][/ROW]
[ROW][C]52[/C][C]70[/C][C]66.3327029399549[/C][C]3.66729706004509[/C][/ROW]
[ROW][C]53[/C][C]88[/C][C]104.762930085779[/C][C]-16.7629300857786[/C][/ROW]
[ROW][C]54[/C][C]92[/C][C]107.069985011176[/C][C]-15.069985011176[/C][/ROW]
[ROW][C]55[/C][C]91[/C][C]97.4753145285674[/C][C]-6.4753145285674[/C][/ROW]
[ROW][C]56[/C][C]80[/C][C]73.1312000938453[/C][C]6.86879990615469[/C][/ROW]
[ROW][C]57[/C][C]81[/C][C]67.2749250095882[/C][C]13.7250749904118[/C][/ROW]
[ROW][C]58[/C][C]81[/C][C]75.3754545803505[/C][C]5.62454541964954[/C][/ROW]
[ROW][C]59[/C][C]98[/C][C]88.6615135162963[/C][C]9.33848648370375[/C][/ROW]
[ROW][C]60[/C][C]106[/C][C]88.9146474176363[/C][C]17.0853525823637[/C][/ROW]
[ROW][C]61[/C][C]85[/C][C]65.0830798797755[/C][C]19.9169201202245[/C][/ROW]
[ROW][C]62[/C][C]93[/C][C]86.1363217138893[/C][C]6.86367828611071[/C][/ROW]
[ROW][C]63[/C][C]96[/C][C]96.2787162212688[/C][C]-0.278716221268837[/C][/ROW]
[ROW][C]64[/C][C]92[/C][C]94.5586586943847[/C][C]-2.55865869438473[/C][/ROW]
[ROW][C]65[/C][C]115[/C][C]119.473439411829[/C][C]-4.47343941182881[/C][/ROW]
[ROW][C]66[/C][C]109[/C][C]125.461671730956[/C][C]-16.4616717309559[/C][/ROW]
[ROW][C]67[/C][C]119[/C][C]123.638077994263[/C][C]-4.63807799426318[/C][/ROW]
[ROW][C]68[/C][C]107[/C][C]107.963704240528[/C][C]-0.963704240527619[/C][/ROW]
[ROW][C]69[/C][C]107[/C][C]108.078811227408[/C][C]-1.07881122740775[/C][/ROW]
[ROW][C]70[/C][C]106[/C][C]107.376115080397[/C][C]-1.3761150803967[/C][/ROW]
[ROW][C]71[/C][C]132[/C][C]128.793022367278[/C][C]3.20697763272221[/C][/ROW]
[ROW][C]72[/C][C]143[/C][C]137.722070376683[/C][C]5.27792962331702[/C][/ROW]
[ROW][C]73[/C][C]120[/C][C]108.557674219712[/C][C]11.4423257802884[/C][/ROW]
[ROW][C]74[/C][C]123[/C][C]118.293800888414[/C][C]4.70619911158637[/C][/ROW]
[ROW][C]75[/C][C]132[/C][C]121.712892332623[/C][C]10.2871076673769[/C][/ROW]
[ROW][C]76[/C][C]136[/C][C]116.749489767346[/C][C]19.2505102326544[/C][/ROW]
[ROW][C]77[/C][C]158[/C][C]146.936191780592[/C][C]11.0638082194077[/C][/ROW]
[ROW][C]78[/C][C]151[/C][C]140.382774253301[/C][C]10.6172257466991[/C][/ROW]
[ROW][C]79[/C][C]155[/C][C]154.008641991384[/C][C]0.99135800861609[/C][/ROW]
[ROW][C]80[/C][C]138[/C][C]138.535149672799[/C][C]-0.535149672799463[/C][/ROW]
[ROW][C]81[/C][C]143[/C][C]138.535936646987[/C][C]4.46406335301339[/C][/ROW]
[ROW][C]82[/C][C]139[/C][C]137.544349834405[/C][C]1.45565016559530[/C][/ROW]
[ROW][C]83[/C][C]168[/C][C]171.190314126318[/C][C]-3.19031412631762[/C][/ROW]
[ROW][C]84[/C][C]182[/C][C]184.915039224158[/C][C]-2.91503922415833[/C][/ROW]
[ROW][C]85[/C][C]154[/C][C]154.181022699430[/C][C]-0.181022699430315[/C][/ROW]
[ROW][C]86[/C][C]158[/C][C]157.527711166154[/C][C]0.472288833846278[/C][/ROW]
[ROW][C]87[/C][C]167[/C][C]168.14309287129[/C][C]-1.14309287129001[/C][/ROW]
[ROW][C]88[/C][C]170[/C][C]171.452391716854[/C][C]-1.45239171685412[/C][/ROW]
[ROW][C]89[/C][C]197[/C][C]197.758183304578[/C][C]-0.758183304578125[/C][/ROW]
[ROW][C]90[/C][C]190[/C][C]187.599879680578[/C][C]2.40012031942177[/C][/ROW]
[ROW][C]91[/C][C]196[/C][C]191.890999864295[/C][C]4.10900013570509[/C][/ROW]
[ROW][C]92[/C][C]174[/C][C]170.441527401133[/C][C]3.5584725988667[/C][/ROW]
[ROW][C]93[/C][C]180[/C][C]175.937358127988[/C][C]4.06264187201239[/C][/ROW]
[ROW][C]94[/C][C]171[/C][C]170.565875246075[/C][C]0.434124753924976[/C][/ROW]
[ROW][C]95[/C][C]200[/C][C]205.707759817235[/C][C]-5.70775981723472[/C][/ROW]
[ROW][C]96[/C][C]215[/C][C]222.018637118999[/C][C]-7.01863711899881[/C][/ROW]
[ROW][C]97[/C][C]184[/C][C]186.989891114585[/C][C]-2.98989111458459[/C][/ROW]
[ROW][C]98[/C][C]186[/C][C]191.062430557554[/C][C]-5.06243055755434[/C][/ROW]
[ROW][C]99[/C][C]197[/C][C]201.090801555265[/C][C]-4.09080155526541[/C][/ROW]
[ROW][C]100[/C][C]186[/C][C]203.9151303878[/C][C]-17.9151303877999[/C][/ROW]
[ROW][C]101[/C][C]211[/C][C]234.450066175983[/C][C]-23.4500661759826[/C][/ROW]
[ROW][C]102[/C][C]205[/C][C]223.899734702572[/C][C]-18.8997347025715[/C][/ROW]
[ROW][C]103[/C][C]218[/C][C]228.648686161373[/C][C]-10.6486861613727[/C][/ROW]
[ROW][C]104[/C][C]199[/C][C]201.250187125254[/C][C]-2.25018712525417[/C][/ROW]
[ROW][C]105[/C][C]213[/C][C]206.728554076613[/C][C]6.27144592338664[/C][/ROW]
[ROW][C]106[/C][C]207[/C][C]195.644743520633[/C][C]11.3552564793668[/C][/ROW]
[ROW][C]107[/C][C]236[/C][C]228.723416363188[/C][C]7.27658363681212[/C][/ROW]
[ROW][C]108[/C][C]248[/C][C]245.636049852908[/C][C]2.36395014709171[/C][/ROW]
[ROW][C]109[/C][C]211[/C][C]209.707970036171[/C][C]1.29202996382949[/C][/ROW]
[ROW][C]110[/C][C]220[/C][C]211.598424922148[/C][C]8.40157507785165[/C][/ROW]
[ROW][C]111[/C][C]235[/C][C]224.126388372219[/C][C]10.8736116277811[/C][/ROW]
[ROW][C]112[/C][C]223[/C][C]212.538416518352[/C][C]10.4615834816476[/C][/ROW]
[ROW][C]113[/C][C]245[/C][C]242.567399134868[/C][C]2.43260086513197[/C][/ROW]
[ROW][C]114[/C][C]236[/C][C]236.659599269668[/C][C]-0.659599269667865[/C][/ROW]
[ROW][C]115[/C][C]253[/C][C]252.249975055633[/C][C]0.750024944367482[/C][/ROW]
[ROW][C]116[/C][C]246[/C][C]230.545836572437[/C][C]15.4541634275628[/C][/ROW]
[ROW][C]117[/C][C]255[/C][C]247.475132600746[/C][C]7.52486739925425[/C][/ROW]
[ROW][C]118[/C][C]248[/C][C]240.434439057190[/C][C]7.5655609428103[/C][/ROW]
[ROW][C]119[/C][C]274[/C][C]274.344258319853[/C][C]-0.344258319852543[/C][/ROW]
[ROW][C]120[/C][C]288[/C][C]288.308135318980[/C][C]-0.308135318979623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79392&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79392&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
131817.34031758050760.659682419492437
141918.32222221157750.677777788422503
152019.51430801941860.485691980581375
162120.68515600137070.314843998629325
174644.6267795926921.37322040730801
184744.24103390211092.75896609788911
193026.12332739733363.87667260266644
201616.3215848230105-0.321584823010500
211517.8509300262992-2.85093002629920
221817.98842939589870.0115706041013048
233019.122793853517610.8772061464824
243121.78658175535519.2134182446449
253221.718609088548610.2813909114514
263623.642707343457612.3572926565424
273025.8169384408024.183061559198
283127.66373173347643.33626826652364
296161.684300799127-0.684300799127037
305763.6008205672313-6.60082056723132
314540.54780473634964.45219526365036
323321.990627511937311.0093724880627
333121.57622001953419.42377998046586
343626.89669703261939.10330296738067
354645.16562864894390.83437135105607
364946.40752133387452.5924786661255
373447.4558834629241-13.4558834629241
384051.6045402604209-11.6045402604209
394142.1979419471531-1.19794194715305
404843.23540745164734.76459254835267
417585.4746137366246-10.4746137366246
427779.6416181372721-2.64161813727213
437162.35139141174818.6486085882519
445444.88404323963299.11595676036709
455041.56773190282558.43226809717455
465647.75130877461178.24869122538834
476661.1624548090984.837545190902
486664.9359055281441.06409447185604
494845.52336733272922.47663266727076
506354.18494835020868.81505164979138
517156.093094518257814.9069054817422
527066.33270293995493.66729706004509
5388104.762930085779-16.7629300857786
5492107.069985011176-15.069985011176
559197.4753145285674-6.4753145285674
568073.13120009384536.86879990615469
578167.274925009588213.7250749904118
588175.37545458035055.62454541964954
599888.66151351629639.33848648370375
6010688.914647417636317.0853525823637
618565.083079879775519.9169201202245
629386.13632171388936.86367828611071
639696.2787162212688-0.278716221268837
649294.5586586943847-2.55865869438473
65115119.473439411829-4.47343941182881
66109125.461671730956-16.4616717309559
67119123.638077994263-4.63807799426318
68107107.963704240528-0.963704240527619
69107108.078811227408-1.07881122740775
70106107.376115080397-1.3761150803967
71132128.7930223672783.20697763272221
72143137.7220703766835.27792962331702
73120108.55767421971211.4423257802884
74123118.2938008884144.70619911158637
75132121.71289233262310.2871076673769
76136116.74948976734619.2505102326544
77158146.93619178059211.0638082194077
78151140.38277425330110.6172257466991
79155154.0086419913840.99135800861609
80138138.535149672799-0.535149672799463
81143138.5359366469874.46406335301339
82139137.5443498344051.45565016559530
83168171.190314126318-3.19031412631762
84182184.915039224158-2.91503922415833
85154154.181022699430-0.181022699430315
86158157.5277111661540.472288833846278
87167168.14309287129-1.14309287129001
88170171.452391716854-1.45239171685412
89197197.758183304578-0.758183304578125
90190187.5998796805782.40012031942177
91196191.8909998642954.10900013570509
92174170.4415274011333.5584725988667
93180175.9373581279884.06264187201239
94171170.5658752460750.434124753924976
95200205.707759817235-5.70775981723472
96215222.018637118999-7.01863711899881
97184186.989891114585-2.98989111458459
98186191.062430557554-5.06243055755434
99197201.090801555265-4.09080155526541
100186203.9151303878-17.9151303877999
101211234.450066175983-23.4500661759826
102205223.899734702572-18.8997347025715
103218228.648686161373-10.6486861613727
104199201.250187125254-2.25018712525417
105213206.7285540766136.27144592338664
106207195.64474352063311.3552564793668
107236228.7234163631887.27658363681212
108248245.6360498529082.36395014709171
109211209.7079700361711.29202996382949
110220211.5984249221488.40157507785165
111235224.12638837221910.8736116277811
112223212.53841651835210.4615834816476
113245242.5673991348682.43260086513197
114236236.659599269668-0.659599269667865
115253252.2499750556330.750024944367482
116246230.54583657243715.4541634275628
117255247.4751326007467.52486739925425
118248240.4344390571907.5655609428103
119274274.344258319853-0.344258319852543
120288288.308135318980-0.308135318979623







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121245.327944621114229.590902578786261.064986663443
122255.407562552814239.643662019886271.171463085742
123272.213213886201256.409389540769288.017038231633
124257.636372890699241.802622022783273.470123758614
125282.753077942025266.843640701815298.662515182235
126272.231355707789256.278035701007288.184675714572
127291.624554208902275.563358892922307.685749524883
128282.458554241940266.339208433247298.577900050634
129292.042617319936275.802518156576308.282716483297
130283.228052341901266.91990000235299.536204681452
131312.479099132395295.918410124013329.039788140776
132327.991553968614316.097337726568339.885770210660

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 245.327944621114 & 229.590902578786 & 261.064986663443 \tabularnewline
122 & 255.407562552814 & 239.643662019886 & 271.171463085742 \tabularnewline
123 & 272.213213886201 & 256.409389540769 & 288.017038231633 \tabularnewline
124 & 257.636372890699 & 241.802622022783 & 273.470123758614 \tabularnewline
125 & 282.753077942025 & 266.843640701815 & 298.662515182235 \tabularnewline
126 & 272.231355707789 & 256.278035701007 & 288.184675714572 \tabularnewline
127 & 291.624554208902 & 275.563358892922 & 307.685749524883 \tabularnewline
128 & 282.458554241940 & 266.339208433247 & 298.577900050634 \tabularnewline
129 & 292.042617319936 & 275.802518156576 & 308.282716483297 \tabularnewline
130 & 283.228052341901 & 266.91990000235 & 299.536204681452 \tabularnewline
131 & 312.479099132395 & 295.918410124013 & 329.039788140776 \tabularnewline
132 & 327.991553968614 & 316.097337726568 & 339.885770210660 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79392&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]245.327944621114[/C][C]229.590902578786[/C][C]261.064986663443[/C][/ROW]
[ROW][C]122[/C][C]255.407562552814[/C][C]239.643662019886[/C][C]271.171463085742[/C][/ROW]
[ROW][C]123[/C][C]272.213213886201[/C][C]256.409389540769[/C][C]288.017038231633[/C][/ROW]
[ROW][C]124[/C][C]257.636372890699[/C][C]241.802622022783[/C][C]273.470123758614[/C][/ROW]
[ROW][C]125[/C][C]282.753077942025[/C][C]266.843640701815[/C][C]298.662515182235[/C][/ROW]
[ROW][C]126[/C][C]272.231355707789[/C][C]256.278035701007[/C][C]288.184675714572[/C][/ROW]
[ROW][C]127[/C][C]291.624554208902[/C][C]275.563358892922[/C][C]307.685749524883[/C][/ROW]
[ROW][C]128[/C][C]282.458554241940[/C][C]266.339208433247[/C][C]298.577900050634[/C][/ROW]
[ROW][C]129[/C][C]292.042617319936[/C][C]275.802518156576[/C][C]308.282716483297[/C][/ROW]
[ROW][C]130[/C][C]283.228052341901[/C][C]266.91990000235[/C][C]299.536204681452[/C][/ROW]
[ROW][C]131[/C][C]312.479099132395[/C][C]295.918410124013[/C][C]329.039788140776[/C][/ROW]
[ROW][C]132[/C][C]327.991553968614[/C][C]316.097337726568[/C][C]339.885770210660[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79392&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79392&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
121245.327944621114229.590902578786261.064986663443
122255.407562552814239.643662019886271.171463085742
123272.213213886201256.409389540769288.017038231633
124257.636372890699241.802622022783273.470123758614
125282.753077942025266.843640701815298.662515182235
126272.231355707789256.278035701007288.184675714572
127291.624554208902275.563358892922307.685749524883
128282.458554241940266.339208433247298.577900050634
129292.042617319936275.802518156576308.282716483297
130283.228052341901266.91990000235299.536204681452
131312.479099132395295.918410124013329.039788140776
132327.991553968614316.097337726568339.885770210660



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