Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 16 Nov 2014 11:55:54 +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/2014/Nov/16/t1416138990d7265abv8kfvklq.htm/, Retrieved Sun, 19 May 2024 17:13:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=255084, Retrieved Sun, 19 May 2024 17:13:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-16 11:55:54] [b4b65124834fa3a3e625dd03af063494] [Current]
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Dataseries X:
41
39
50
40
43
38
44
35
39
35
29
49
50
59
63
32
39
47
53
60
57
52
70
90
74
62
55
84
94
70
108
139
120
97
126
149
158
124
140
109
114
77
120
133
110
92
97
78
99
107
112
90
98
125
155
190
236
189
174
178
136
161
171
149
184
155
276
224
213
279
268
287
238
213
257
293
212
246
353
339
308
247
257
322
298
273
312
249
286
279
309
401
309
328
353
354
327
324
285
243
241
287
355
460
364
487
452
391
500
451
375
372
302
316
398
394
431
431




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=255084&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=255084&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=255084&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.650645263111997
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.650645263111997 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=255084&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]0.650645263111997[/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=255084&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=255084&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
alpha0.650645263111997
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23941-2
35039.69870947377610.301290526224
44046.4011953586041-6.40119535860413
54342.23628792027390.763712079726147
63842.7331935673291-4.73319356732908
74439.65356359335424.34643640664576
83542.4815518527558-7.48155185275583
93937.61371557903351.38628442096653
103538.5156949708613-3.5156949708613
112936.2282246915237-7.22822469152373
124931.525214535274617.4747854647254
135042.89510092179667.10489907820343
145947.517869851918411.4821301480816
156354.98866344320328.01133655679685
163260.201201625079-28.201201625079
173941.852223373655-2.852223373655
184739.99643774624917.00356225375094
195344.55327235156218.44672764843791
206050.04909568481539.95090431518465
215756.5236044411710.476395558829026
225256.8335689548907-4.83356895489067
237053.688630210465816.3113697895342
249064.301545698894425.6984543011056
257481.0221232592089-7.02212325920887
266276.453212023616-14.453212023616
275567.0492980836969-12.0492980836969
288459.209479361715124.7905206382849
299475.339314185095318.6606858149047
307087.4808010169843-17.4808010169843
3110876.107000639880131.8929993601199
3213996.85802959997642.141970400024
33120124.277503018958-4.27750301895762
3497121.494365941726-24.4943659417256
35126105.5572227688120.44277723119
36149118.85821893913830.1417810608624
37158138.46982600814719.5301739918534
38124151.177041203699-27.1770412036991
39140133.4944280791136.50557192088726
40109137.727247633272-28.7272476332724
41114119.036000038438-5.0360000384384
4277115.759350468397-38.7593504683966
4312090.540762684836629.4592373151634
44133109.7082758988423.2917241011602
45110124.862925854971-14.8629258549712
4692115.192433551449-23.1924335514494
4797100.102386521159-3.10238652115909
487898.0838334268244-20.0838334268244
499985.016382342530713.9836176574693
5010794.114756932532412.8852430674676
51112102.4984792984279.50152070157313
5290108.680598735266-18.680598735266
539896.52615565606921.47384434393078
5412597.485105497012227.5148945029878
55155115.38754127040839.6124587295925
56190141.16119990303648.8388000969637
57236172.93793384219963.0620661578005
58189213.968968469828-24.9689684698277
59174197.723027410142-23.7230274101415
60178182.287751999057-4.28775199905687
61136179.497946471472-43.4979464714715
62161151.1962136447099.80378635529061
63171157.57500079734113.4249992026587
64149166.309912935833-17.3099129358335
65184155.04730007925228.9526999207476
66155173.88523713699-18.8852371369899
67276161.597647051061114.402352948939
68224236.032996086155-12.0329960861548
69213228.203784181653-15.203784181653
70279218.31151402248360.6884859775166
71268257.79818994919310.2018100508066
72287264.43594933391922.5640506660809
73238279.117142016424-41.1171420164237
74213252.364468330734-39.3644683307344
75257226.7521634764230.2478365235801
76293246.43277502987346.5672249701267
77212276.731519372957-64.7315193729569
78246234.614262918911.3857370811
79353242.022338817756110.977661182244
80339314.22942837723124.7705716227687
81308330.346283468162-22.3462834681622
82247315.806779981445-68.8067799814445
83257271.037974516528-14.0379745165283
84322261.90423289366260.0957671063378
85298301.005259094483-3.00525909448265
86273299.049901500233-26.0499015002333
87312282.10065648457229.8993435154276
88249301.554522713044-52.5545227130438
89286267.3601714546918.63982854531
90279279.488087602916-0.488087602915698
91309279.17051571609529.8294842839051
92401298.578928366491102.421071633509
93309365.218713467688-56.2187134676883
94328328.640273851686-0.640273851686288
95353328.22368270299224.7763172970079
96354344.344276189659.65572381034985
97327350.626727148772-23.626727148772
98324335.254109046584-11.2541090465839
99285327.931676304878-42.9316763048782
100243299.998384479652-56.9983844796516
101241262.91265561293-21.9126556129299
102287248.65529003617338.3447099638274
103355273.6040939395481.3959060604598
104460326.563954654487133.436045345513
105364413.383485486943-49.3834854869428
106487381.252354578903105.747645421097
107452450.0565591573871.94344084261309
108391451.321049735771-60.3210497357715
109500412.07344445924987.9265555407515
110451469.282441323592-18.2824413235924
111375457.387057478274-82.387057478274
112372403.782308788299-31.7823087882992
113302383.10330012443-81.1033001244296
114316330.333822075719-14.3338220757188
115398321.00758863986276.9924113601378
116394371.10233638690622.8976636130939
117431386.00059275309844.9994072469024
118431415.27924392114215.7207560788577

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 39 & 41 & -2 \tabularnewline
3 & 50 & 39.698709473776 & 10.301290526224 \tabularnewline
4 & 40 & 46.4011953586041 & -6.40119535860413 \tabularnewline
5 & 43 & 42.2362879202739 & 0.763712079726147 \tabularnewline
6 & 38 & 42.7331935673291 & -4.73319356732908 \tabularnewline
7 & 44 & 39.6535635933542 & 4.34643640664576 \tabularnewline
8 & 35 & 42.4815518527558 & -7.48155185275583 \tabularnewline
9 & 39 & 37.6137155790335 & 1.38628442096653 \tabularnewline
10 & 35 & 38.5156949708613 & -3.5156949708613 \tabularnewline
11 & 29 & 36.2282246915237 & -7.22822469152373 \tabularnewline
12 & 49 & 31.5252145352746 & 17.4747854647254 \tabularnewline
13 & 50 & 42.8951009217966 & 7.10489907820343 \tabularnewline
14 & 59 & 47.5178698519184 & 11.4821301480816 \tabularnewline
15 & 63 & 54.9886634432032 & 8.01133655679685 \tabularnewline
16 & 32 & 60.201201625079 & -28.201201625079 \tabularnewline
17 & 39 & 41.852223373655 & -2.852223373655 \tabularnewline
18 & 47 & 39.9964377462491 & 7.00356225375094 \tabularnewline
19 & 53 & 44.5532723515621 & 8.44672764843791 \tabularnewline
20 & 60 & 50.0490956848153 & 9.95090431518465 \tabularnewline
21 & 57 & 56.523604441171 & 0.476395558829026 \tabularnewline
22 & 52 & 56.8335689548907 & -4.83356895489067 \tabularnewline
23 & 70 & 53.6886302104658 & 16.3113697895342 \tabularnewline
24 & 90 & 64.3015456988944 & 25.6984543011056 \tabularnewline
25 & 74 & 81.0221232592089 & -7.02212325920887 \tabularnewline
26 & 62 & 76.453212023616 & -14.453212023616 \tabularnewline
27 & 55 & 67.0492980836969 & -12.0492980836969 \tabularnewline
28 & 84 & 59.2094793617151 & 24.7905206382849 \tabularnewline
29 & 94 & 75.3393141850953 & 18.6606858149047 \tabularnewline
30 & 70 & 87.4808010169843 & -17.4808010169843 \tabularnewline
31 & 108 & 76.1070006398801 & 31.8929993601199 \tabularnewline
32 & 139 & 96.858029599976 & 42.141970400024 \tabularnewline
33 & 120 & 124.277503018958 & -4.27750301895762 \tabularnewline
34 & 97 & 121.494365941726 & -24.4943659417256 \tabularnewline
35 & 126 & 105.55722276881 & 20.44277723119 \tabularnewline
36 & 149 & 118.858218939138 & 30.1417810608624 \tabularnewline
37 & 158 & 138.469826008147 & 19.5301739918534 \tabularnewline
38 & 124 & 151.177041203699 & -27.1770412036991 \tabularnewline
39 & 140 & 133.494428079113 & 6.50557192088726 \tabularnewline
40 & 109 & 137.727247633272 & -28.7272476332724 \tabularnewline
41 & 114 & 119.036000038438 & -5.0360000384384 \tabularnewline
42 & 77 & 115.759350468397 & -38.7593504683966 \tabularnewline
43 & 120 & 90.5407626848366 & 29.4592373151634 \tabularnewline
44 & 133 & 109.70827589884 & 23.2917241011602 \tabularnewline
45 & 110 & 124.862925854971 & -14.8629258549712 \tabularnewline
46 & 92 & 115.192433551449 & -23.1924335514494 \tabularnewline
47 & 97 & 100.102386521159 & -3.10238652115909 \tabularnewline
48 & 78 & 98.0838334268244 & -20.0838334268244 \tabularnewline
49 & 99 & 85.0163823425307 & 13.9836176574693 \tabularnewline
50 & 107 & 94.1147569325324 & 12.8852430674676 \tabularnewline
51 & 112 & 102.498479298427 & 9.50152070157313 \tabularnewline
52 & 90 & 108.680598735266 & -18.680598735266 \tabularnewline
53 & 98 & 96.5261556560692 & 1.47384434393078 \tabularnewline
54 & 125 & 97.4851054970122 & 27.5148945029878 \tabularnewline
55 & 155 & 115.387541270408 & 39.6124587295925 \tabularnewline
56 & 190 & 141.161199903036 & 48.8388000969637 \tabularnewline
57 & 236 & 172.937933842199 & 63.0620661578005 \tabularnewline
58 & 189 & 213.968968469828 & -24.9689684698277 \tabularnewline
59 & 174 & 197.723027410142 & -23.7230274101415 \tabularnewline
60 & 178 & 182.287751999057 & -4.28775199905687 \tabularnewline
61 & 136 & 179.497946471472 & -43.4979464714715 \tabularnewline
62 & 161 & 151.196213644709 & 9.80378635529061 \tabularnewline
63 & 171 & 157.575000797341 & 13.4249992026587 \tabularnewline
64 & 149 & 166.309912935833 & -17.3099129358335 \tabularnewline
65 & 184 & 155.047300079252 & 28.9526999207476 \tabularnewline
66 & 155 & 173.88523713699 & -18.8852371369899 \tabularnewline
67 & 276 & 161.597647051061 & 114.402352948939 \tabularnewline
68 & 224 & 236.032996086155 & -12.0329960861548 \tabularnewline
69 & 213 & 228.203784181653 & -15.203784181653 \tabularnewline
70 & 279 & 218.311514022483 & 60.6884859775166 \tabularnewline
71 & 268 & 257.798189949193 & 10.2018100508066 \tabularnewline
72 & 287 & 264.435949333919 & 22.5640506660809 \tabularnewline
73 & 238 & 279.117142016424 & -41.1171420164237 \tabularnewline
74 & 213 & 252.364468330734 & -39.3644683307344 \tabularnewline
75 & 257 & 226.75216347642 & 30.2478365235801 \tabularnewline
76 & 293 & 246.432775029873 & 46.5672249701267 \tabularnewline
77 & 212 & 276.731519372957 & -64.7315193729569 \tabularnewline
78 & 246 & 234.6142629189 & 11.3857370811 \tabularnewline
79 & 353 & 242.022338817756 & 110.977661182244 \tabularnewline
80 & 339 & 314.229428377231 & 24.7705716227687 \tabularnewline
81 & 308 & 330.346283468162 & -22.3462834681622 \tabularnewline
82 & 247 & 315.806779981445 & -68.8067799814445 \tabularnewline
83 & 257 & 271.037974516528 & -14.0379745165283 \tabularnewline
84 & 322 & 261.904232893662 & 60.0957671063378 \tabularnewline
85 & 298 & 301.005259094483 & -3.00525909448265 \tabularnewline
86 & 273 & 299.049901500233 & -26.0499015002333 \tabularnewline
87 & 312 & 282.100656484572 & 29.8993435154276 \tabularnewline
88 & 249 & 301.554522713044 & -52.5545227130438 \tabularnewline
89 & 286 & 267.36017145469 & 18.63982854531 \tabularnewline
90 & 279 & 279.488087602916 & -0.488087602915698 \tabularnewline
91 & 309 & 279.170515716095 & 29.8294842839051 \tabularnewline
92 & 401 & 298.578928366491 & 102.421071633509 \tabularnewline
93 & 309 & 365.218713467688 & -56.2187134676883 \tabularnewline
94 & 328 & 328.640273851686 & -0.640273851686288 \tabularnewline
95 & 353 & 328.223682702992 & 24.7763172970079 \tabularnewline
96 & 354 & 344.34427618965 & 9.65572381034985 \tabularnewline
97 & 327 & 350.626727148772 & -23.626727148772 \tabularnewline
98 & 324 & 335.254109046584 & -11.2541090465839 \tabularnewline
99 & 285 & 327.931676304878 & -42.9316763048782 \tabularnewline
100 & 243 & 299.998384479652 & -56.9983844796516 \tabularnewline
101 & 241 & 262.91265561293 & -21.9126556129299 \tabularnewline
102 & 287 & 248.655290036173 & 38.3447099638274 \tabularnewline
103 & 355 & 273.60409393954 & 81.3959060604598 \tabularnewline
104 & 460 & 326.563954654487 & 133.436045345513 \tabularnewline
105 & 364 & 413.383485486943 & -49.3834854869428 \tabularnewline
106 & 487 & 381.252354578903 & 105.747645421097 \tabularnewline
107 & 452 & 450.056559157387 & 1.94344084261309 \tabularnewline
108 & 391 & 451.321049735771 & -60.3210497357715 \tabularnewline
109 & 500 & 412.073444459249 & 87.9265555407515 \tabularnewline
110 & 451 & 469.282441323592 & -18.2824413235924 \tabularnewline
111 & 375 & 457.387057478274 & -82.387057478274 \tabularnewline
112 & 372 & 403.782308788299 & -31.7823087882992 \tabularnewline
113 & 302 & 383.10330012443 & -81.1033001244296 \tabularnewline
114 & 316 & 330.333822075719 & -14.3338220757188 \tabularnewline
115 & 398 & 321.007588639862 & 76.9924113601378 \tabularnewline
116 & 394 & 371.102336386906 & 22.8976636130939 \tabularnewline
117 & 431 & 386.000592753098 & 44.9994072469024 \tabularnewline
118 & 431 & 415.279243921142 & 15.7207560788577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=255084&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]39[/C][C]41[/C][C]-2[/C][/ROW]
[ROW][C]3[/C][C]50[/C][C]39.698709473776[/C][C]10.301290526224[/C][/ROW]
[ROW][C]4[/C][C]40[/C][C]46.4011953586041[/C][C]-6.40119535860413[/C][/ROW]
[ROW][C]5[/C][C]43[/C][C]42.2362879202739[/C][C]0.763712079726147[/C][/ROW]
[ROW][C]6[/C][C]38[/C][C]42.7331935673291[/C][C]-4.73319356732908[/C][/ROW]
[ROW][C]7[/C][C]44[/C][C]39.6535635933542[/C][C]4.34643640664576[/C][/ROW]
[ROW][C]8[/C][C]35[/C][C]42.4815518527558[/C][C]-7.48155185275583[/C][/ROW]
[ROW][C]9[/C][C]39[/C][C]37.6137155790335[/C][C]1.38628442096653[/C][/ROW]
[ROW][C]10[/C][C]35[/C][C]38.5156949708613[/C][C]-3.5156949708613[/C][/ROW]
[ROW][C]11[/C][C]29[/C][C]36.2282246915237[/C][C]-7.22822469152373[/C][/ROW]
[ROW][C]12[/C][C]49[/C][C]31.5252145352746[/C][C]17.4747854647254[/C][/ROW]
[ROW][C]13[/C][C]50[/C][C]42.8951009217966[/C][C]7.10489907820343[/C][/ROW]
[ROW][C]14[/C][C]59[/C][C]47.5178698519184[/C][C]11.4821301480816[/C][/ROW]
[ROW][C]15[/C][C]63[/C][C]54.9886634432032[/C][C]8.01133655679685[/C][/ROW]
[ROW][C]16[/C][C]32[/C][C]60.201201625079[/C][C]-28.201201625079[/C][/ROW]
[ROW][C]17[/C][C]39[/C][C]41.852223373655[/C][C]-2.852223373655[/C][/ROW]
[ROW][C]18[/C][C]47[/C][C]39.9964377462491[/C][C]7.00356225375094[/C][/ROW]
[ROW][C]19[/C][C]53[/C][C]44.5532723515621[/C][C]8.44672764843791[/C][/ROW]
[ROW][C]20[/C][C]60[/C][C]50.0490956848153[/C][C]9.95090431518465[/C][/ROW]
[ROW][C]21[/C][C]57[/C][C]56.523604441171[/C][C]0.476395558829026[/C][/ROW]
[ROW][C]22[/C][C]52[/C][C]56.8335689548907[/C][C]-4.83356895489067[/C][/ROW]
[ROW][C]23[/C][C]70[/C][C]53.6886302104658[/C][C]16.3113697895342[/C][/ROW]
[ROW][C]24[/C][C]90[/C][C]64.3015456988944[/C][C]25.6984543011056[/C][/ROW]
[ROW][C]25[/C][C]74[/C][C]81.0221232592089[/C][C]-7.02212325920887[/C][/ROW]
[ROW][C]26[/C][C]62[/C][C]76.453212023616[/C][C]-14.453212023616[/C][/ROW]
[ROW][C]27[/C][C]55[/C][C]67.0492980836969[/C][C]-12.0492980836969[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]59.2094793617151[/C][C]24.7905206382849[/C][/ROW]
[ROW][C]29[/C][C]94[/C][C]75.3393141850953[/C][C]18.6606858149047[/C][/ROW]
[ROW][C]30[/C][C]70[/C][C]87.4808010169843[/C][C]-17.4808010169843[/C][/ROW]
[ROW][C]31[/C][C]108[/C][C]76.1070006398801[/C][C]31.8929993601199[/C][/ROW]
[ROW][C]32[/C][C]139[/C][C]96.858029599976[/C][C]42.141970400024[/C][/ROW]
[ROW][C]33[/C][C]120[/C][C]124.277503018958[/C][C]-4.27750301895762[/C][/ROW]
[ROW][C]34[/C][C]97[/C][C]121.494365941726[/C][C]-24.4943659417256[/C][/ROW]
[ROW][C]35[/C][C]126[/C][C]105.55722276881[/C][C]20.44277723119[/C][/ROW]
[ROW][C]36[/C][C]149[/C][C]118.858218939138[/C][C]30.1417810608624[/C][/ROW]
[ROW][C]37[/C][C]158[/C][C]138.469826008147[/C][C]19.5301739918534[/C][/ROW]
[ROW][C]38[/C][C]124[/C][C]151.177041203699[/C][C]-27.1770412036991[/C][/ROW]
[ROW][C]39[/C][C]140[/C][C]133.494428079113[/C][C]6.50557192088726[/C][/ROW]
[ROW][C]40[/C][C]109[/C][C]137.727247633272[/C][C]-28.7272476332724[/C][/ROW]
[ROW][C]41[/C][C]114[/C][C]119.036000038438[/C][C]-5.0360000384384[/C][/ROW]
[ROW][C]42[/C][C]77[/C][C]115.759350468397[/C][C]-38.7593504683966[/C][/ROW]
[ROW][C]43[/C][C]120[/C][C]90.5407626848366[/C][C]29.4592373151634[/C][/ROW]
[ROW][C]44[/C][C]133[/C][C]109.70827589884[/C][C]23.2917241011602[/C][/ROW]
[ROW][C]45[/C][C]110[/C][C]124.862925854971[/C][C]-14.8629258549712[/C][/ROW]
[ROW][C]46[/C][C]92[/C][C]115.192433551449[/C][C]-23.1924335514494[/C][/ROW]
[ROW][C]47[/C][C]97[/C][C]100.102386521159[/C][C]-3.10238652115909[/C][/ROW]
[ROW][C]48[/C][C]78[/C][C]98.0838334268244[/C][C]-20.0838334268244[/C][/ROW]
[ROW][C]49[/C][C]99[/C][C]85.0163823425307[/C][C]13.9836176574693[/C][/ROW]
[ROW][C]50[/C][C]107[/C][C]94.1147569325324[/C][C]12.8852430674676[/C][/ROW]
[ROW][C]51[/C][C]112[/C][C]102.498479298427[/C][C]9.50152070157313[/C][/ROW]
[ROW][C]52[/C][C]90[/C][C]108.680598735266[/C][C]-18.680598735266[/C][/ROW]
[ROW][C]53[/C][C]98[/C][C]96.5261556560692[/C][C]1.47384434393078[/C][/ROW]
[ROW][C]54[/C][C]125[/C][C]97.4851054970122[/C][C]27.5148945029878[/C][/ROW]
[ROW][C]55[/C][C]155[/C][C]115.387541270408[/C][C]39.6124587295925[/C][/ROW]
[ROW][C]56[/C][C]190[/C][C]141.161199903036[/C][C]48.8388000969637[/C][/ROW]
[ROW][C]57[/C][C]236[/C][C]172.937933842199[/C][C]63.0620661578005[/C][/ROW]
[ROW][C]58[/C][C]189[/C][C]213.968968469828[/C][C]-24.9689684698277[/C][/ROW]
[ROW][C]59[/C][C]174[/C][C]197.723027410142[/C][C]-23.7230274101415[/C][/ROW]
[ROW][C]60[/C][C]178[/C][C]182.287751999057[/C][C]-4.28775199905687[/C][/ROW]
[ROW][C]61[/C][C]136[/C][C]179.497946471472[/C][C]-43.4979464714715[/C][/ROW]
[ROW][C]62[/C][C]161[/C][C]151.196213644709[/C][C]9.80378635529061[/C][/ROW]
[ROW][C]63[/C][C]171[/C][C]157.575000797341[/C][C]13.4249992026587[/C][/ROW]
[ROW][C]64[/C][C]149[/C][C]166.309912935833[/C][C]-17.3099129358335[/C][/ROW]
[ROW][C]65[/C][C]184[/C][C]155.047300079252[/C][C]28.9526999207476[/C][/ROW]
[ROW][C]66[/C][C]155[/C][C]173.88523713699[/C][C]-18.8852371369899[/C][/ROW]
[ROW][C]67[/C][C]276[/C][C]161.597647051061[/C][C]114.402352948939[/C][/ROW]
[ROW][C]68[/C][C]224[/C][C]236.032996086155[/C][C]-12.0329960861548[/C][/ROW]
[ROW][C]69[/C][C]213[/C][C]228.203784181653[/C][C]-15.203784181653[/C][/ROW]
[ROW][C]70[/C][C]279[/C][C]218.311514022483[/C][C]60.6884859775166[/C][/ROW]
[ROW][C]71[/C][C]268[/C][C]257.798189949193[/C][C]10.2018100508066[/C][/ROW]
[ROW][C]72[/C][C]287[/C][C]264.435949333919[/C][C]22.5640506660809[/C][/ROW]
[ROW][C]73[/C][C]238[/C][C]279.117142016424[/C][C]-41.1171420164237[/C][/ROW]
[ROW][C]74[/C][C]213[/C][C]252.364468330734[/C][C]-39.3644683307344[/C][/ROW]
[ROW][C]75[/C][C]257[/C][C]226.75216347642[/C][C]30.2478365235801[/C][/ROW]
[ROW][C]76[/C][C]293[/C][C]246.432775029873[/C][C]46.5672249701267[/C][/ROW]
[ROW][C]77[/C][C]212[/C][C]276.731519372957[/C][C]-64.7315193729569[/C][/ROW]
[ROW][C]78[/C][C]246[/C][C]234.6142629189[/C][C]11.3857370811[/C][/ROW]
[ROW][C]79[/C][C]353[/C][C]242.022338817756[/C][C]110.977661182244[/C][/ROW]
[ROW][C]80[/C][C]339[/C][C]314.229428377231[/C][C]24.7705716227687[/C][/ROW]
[ROW][C]81[/C][C]308[/C][C]330.346283468162[/C][C]-22.3462834681622[/C][/ROW]
[ROW][C]82[/C][C]247[/C][C]315.806779981445[/C][C]-68.8067799814445[/C][/ROW]
[ROW][C]83[/C][C]257[/C][C]271.037974516528[/C][C]-14.0379745165283[/C][/ROW]
[ROW][C]84[/C][C]322[/C][C]261.904232893662[/C][C]60.0957671063378[/C][/ROW]
[ROW][C]85[/C][C]298[/C][C]301.005259094483[/C][C]-3.00525909448265[/C][/ROW]
[ROW][C]86[/C][C]273[/C][C]299.049901500233[/C][C]-26.0499015002333[/C][/ROW]
[ROW][C]87[/C][C]312[/C][C]282.100656484572[/C][C]29.8993435154276[/C][/ROW]
[ROW][C]88[/C][C]249[/C][C]301.554522713044[/C][C]-52.5545227130438[/C][/ROW]
[ROW][C]89[/C][C]286[/C][C]267.36017145469[/C][C]18.63982854531[/C][/ROW]
[ROW][C]90[/C][C]279[/C][C]279.488087602916[/C][C]-0.488087602915698[/C][/ROW]
[ROW][C]91[/C][C]309[/C][C]279.170515716095[/C][C]29.8294842839051[/C][/ROW]
[ROW][C]92[/C][C]401[/C][C]298.578928366491[/C][C]102.421071633509[/C][/ROW]
[ROW][C]93[/C][C]309[/C][C]365.218713467688[/C][C]-56.2187134676883[/C][/ROW]
[ROW][C]94[/C][C]328[/C][C]328.640273851686[/C][C]-0.640273851686288[/C][/ROW]
[ROW][C]95[/C][C]353[/C][C]328.223682702992[/C][C]24.7763172970079[/C][/ROW]
[ROW][C]96[/C][C]354[/C][C]344.34427618965[/C][C]9.65572381034985[/C][/ROW]
[ROW][C]97[/C][C]327[/C][C]350.626727148772[/C][C]-23.626727148772[/C][/ROW]
[ROW][C]98[/C][C]324[/C][C]335.254109046584[/C][C]-11.2541090465839[/C][/ROW]
[ROW][C]99[/C][C]285[/C][C]327.931676304878[/C][C]-42.9316763048782[/C][/ROW]
[ROW][C]100[/C][C]243[/C][C]299.998384479652[/C][C]-56.9983844796516[/C][/ROW]
[ROW][C]101[/C][C]241[/C][C]262.91265561293[/C][C]-21.9126556129299[/C][/ROW]
[ROW][C]102[/C][C]287[/C][C]248.655290036173[/C][C]38.3447099638274[/C][/ROW]
[ROW][C]103[/C][C]355[/C][C]273.60409393954[/C][C]81.3959060604598[/C][/ROW]
[ROW][C]104[/C][C]460[/C][C]326.563954654487[/C][C]133.436045345513[/C][/ROW]
[ROW][C]105[/C][C]364[/C][C]413.383485486943[/C][C]-49.3834854869428[/C][/ROW]
[ROW][C]106[/C][C]487[/C][C]381.252354578903[/C][C]105.747645421097[/C][/ROW]
[ROW][C]107[/C][C]452[/C][C]450.056559157387[/C][C]1.94344084261309[/C][/ROW]
[ROW][C]108[/C][C]391[/C][C]451.321049735771[/C][C]-60.3210497357715[/C][/ROW]
[ROW][C]109[/C][C]500[/C][C]412.073444459249[/C][C]87.9265555407515[/C][/ROW]
[ROW][C]110[/C][C]451[/C][C]469.282441323592[/C][C]-18.2824413235924[/C][/ROW]
[ROW][C]111[/C][C]375[/C][C]457.387057478274[/C][C]-82.387057478274[/C][/ROW]
[ROW][C]112[/C][C]372[/C][C]403.782308788299[/C][C]-31.7823087882992[/C][/ROW]
[ROW][C]113[/C][C]302[/C][C]383.10330012443[/C][C]-81.1033001244296[/C][/ROW]
[ROW][C]114[/C][C]316[/C][C]330.333822075719[/C][C]-14.3338220757188[/C][/ROW]
[ROW][C]115[/C][C]398[/C][C]321.007588639862[/C][C]76.9924113601378[/C][/ROW]
[ROW][C]116[/C][C]394[/C][C]371.102336386906[/C][C]22.8976636130939[/C][/ROW]
[ROW][C]117[/C][C]431[/C][C]386.000592753098[/C][C]44.9994072469024[/C][/ROW]
[ROW][C]118[/C][C]431[/C][C]415.279243921142[/C][C]15.7207560788577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=255084&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=255084&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
23941-2
35039.69870947377610.301290526224
44046.4011953586041-6.40119535860413
54342.23628792027390.763712079726147
63842.7331935673291-4.73319356732908
74439.65356359335424.34643640664576
83542.4815518527558-7.48155185275583
93937.61371557903351.38628442096653
103538.5156949708613-3.5156949708613
112936.2282246915237-7.22822469152373
124931.525214535274617.4747854647254
135042.89510092179667.10489907820343
145947.517869851918411.4821301480816
156354.98866344320328.01133655679685
163260.201201625079-28.201201625079
173941.852223373655-2.852223373655
184739.99643774624917.00356225375094
195344.55327235156218.44672764843791
206050.04909568481539.95090431518465
215756.5236044411710.476395558829026
225256.8335689548907-4.83356895489067
237053.688630210465816.3113697895342
249064.301545698894425.6984543011056
257481.0221232592089-7.02212325920887
266276.453212023616-14.453212023616
275567.0492980836969-12.0492980836969
288459.209479361715124.7905206382849
299475.339314185095318.6606858149047
307087.4808010169843-17.4808010169843
3110876.107000639880131.8929993601199
3213996.85802959997642.141970400024
33120124.277503018958-4.27750301895762
3497121.494365941726-24.4943659417256
35126105.5572227688120.44277723119
36149118.85821893913830.1417810608624
37158138.46982600814719.5301739918534
38124151.177041203699-27.1770412036991
39140133.4944280791136.50557192088726
40109137.727247633272-28.7272476332724
41114119.036000038438-5.0360000384384
4277115.759350468397-38.7593504683966
4312090.540762684836629.4592373151634
44133109.7082758988423.2917241011602
45110124.862925854971-14.8629258549712
4692115.192433551449-23.1924335514494
4797100.102386521159-3.10238652115909
487898.0838334268244-20.0838334268244
499985.016382342530713.9836176574693
5010794.114756932532412.8852430674676
51112102.4984792984279.50152070157313
5290108.680598735266-18.680598735266
539896.52615565606921.47384434393078
5412597.485105497012227.5148945029878
55155115.38754127040839.6124587295925
56190141.16119990303648.8388000969637
57236172.93793384219963.0620661578005
58189213.968968469828-24.9689684698277
59174197.723027410142-23.7230274101415
60178182.287751999057-4.28775199905687
61136179.497946471472-43.4979464714715
62161151.1962136447099.80378635529061
63171157.57500079734113.4249992026587
64149166.309912935833-17.3099129358335
65184155.04730007925228.9526999207476
66155173.88523713699-18.8852371369899
67276161.597647051061114.402352948939
68224236.032996086155-12.0329960861548
69213228.203784181653-15.203784181653
70279218.31151402248360.6884859775166
71268257.79818994919310.2018100508066
72287264.43594933391922.5640506660809
73238279.117142016424-41.1171420164237
74213252.364468330734-39.3644683307344
75257226.7521634764230.2478365235801
76293246.43277502987346.5672249701267
77212276.731519372957-64.7315193729569
78246234.614262918911.3857370811
79353242.022338817756110.977661182244
80339314.22942837723124.7705716227687
81308330.346283468162-22.3462834681622
82247315.806779981445-68.8067799814445
83257271.037974516528-14.0379745165283
84322261.90423289366260.0957671063378
85298301.005259094483-3.00525909448265
86273299.049901500233-26.0499015002333
87312282.10065648457229.8993435154276
88249301.554522713044-52.5545227130438
89286267.3601714546918.63982854531
90279279.488087602916-0.488087602915698
91309279.17051571609529.8294842839051
92401298.578928366491102.421071633509
93309365.218713467688-56.2187134676883
94328328.640273851686-0.640273851686288
95353328.22368270299224.7763172970079
96354344.344276189659.65572381034985
97327350.626727148772-23.626727148772
98324335.254109046584-11.2541090465839
99285327.931676304878-42.9316763048782
100243299.998384479652-56.9983844796516
101241262.91265561293-21.9126556129299
102287248.65529003617338.3447099638274
103355273.6040939395481.3959060604598
104460326.563954654487133.436045345513
105364413.383485486943-49.3834854869428
106487381.252354578903105.747645421097
107452450.0565591573871.94344084261309
108391451.321049735771-60.3210497357715
109500412.07344445924987.9265555407515
110451469.282441323592-18.2824413235924
111375457.387057478274-82.387057478274
112372403.782308788299-31.7823087882992
113302383.10330012443-81.1033001244296
114316330.333822075719-14.3338220757188
115398321.00758863986276.9924113601378
116394371.10233638690622.8976636130939
117431386.00059275309844.9994072469024
118431415.27924392114215.7207560788577







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
119425.50787939639348.768396760238502.247362032542
120425.50787939639333.954773730537517.060985062243
121425.50787939639321.224639521225529.791119271556
122425.50787939639309.887738068593541.128020724188
123425.50787939639299.567258298754551.448500494027
124425.50787939639290.030711562629560.985047230151
125425.50787939639281.122679441355569.893079351426
126425.50787939639272.733179501892578.282579290889
127425.50787939639264.780993376494586.234765416286
128425.50787939639257.204121709727593.811637083054
129425.50787939639249.953962284724601.061796508056
130425.50787939639242.991576631272608.024182161508

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
119 & 425.50787939639 & 348.768396760238 & 502.247362032542 \tabularnewline
120 & 425.50787939639 & 333.954773730537 & 517.060985062243 \tabularnewline
121 & 425.50787939639 & 321.224639521225 & 529.791119271556 \tabularnewline
122 & 425.50787939639 & 309.887738068593 & 541.128020724188 \tabularnewline
123 & 425.50787939639 & 299.567258298754 & 551.448500494027 \tabularnewline
124 & 425.50787939639 & 290.030711562629 & 560.985047230151 \tabularnewline
125 & 425.50787939639 & 281.122679441355 & 569.893079351426 \tabularnewline
126 & 425.50787939639 & 272.733179501892 & 578.282579290889 \tabularnewline
127 & 425.50787939639 & 264.780993376494 & 586.234765416286 \tabularnewline
128 & 425.50787939639 & 257.204121709727 & 593.811637083054 \tabularnewline
129 & 425.50787939639 & 249.953962284724 & 601.061796508056 \tabularnewline
130 & 425.50787939639 & 242.991576631272 & 608.024182161508 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=255084&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]119[/C][C]425.50787939639[/C][C]348.768396760238[/C][C]502.247362032542[/C][/ROW]
[ROW][C]120[/C][C]425.50787939639[/C][C]333.954773730537[/C][C]517.060985062243[/C][/ROW]
[ROW][C]121[/C][C]425.50787939639[/C][C]321.224639521225[/C][C]529.791119271556[/C][/ROW]
[ROW][C]122[/C][C]425.50787939639[/C][C]309.887738068593[/C][C]541.128020724188[/C][/ROW]
[ROW][C]123[/C][C]425.50787939639[/C][C]299.567258298754[/C][C]551.448500494027[/C][/ROW]
[ROW][C]124[/C][C]425.50787939639[/C][C]290.030711562629[/C][C]560.985047230151[/C][/ROW]
[ROW][C]125[/C][C]425.50787939639[/C][C]281.122679441355[/C][C]569.893079351426[/C][/ROW]
[ROW][C]126[/C][C]425.50787939639[/C][C]272.733179501892[/C][C]578.282579290889[/C][/ROW]
[ROW][C]127[/C][C]425.50787939639[/C][C]264.780993376494[/C][C]586.234765416286[/C][/ROW]
[ROW][C]128[/C][C]425.50787939639[/C][C]257.204121709727[/C][C]593.811637083054[/C][/ROW]
[ROW][C]129[/C][C]425.50787939639[/C][C]249.953962284724[/C][C]601.061796508056[/C][/ROW]
[ROW][C]130[/C][C]425.50787939639[/C][C]242.991576631272[/C][C]608.024182161508[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=255084&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=255084&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
119425.50787939639348.768396760238502.247362032542
120425.50787939639333.954773730537517.060985062243
121425.50787939639321.224639521225529.791119271556
122425.50787939639309.887738068593541.128020724188
123425.50787939639299.567258298754551.448500494027
124425.50787939639290.030711562629560.985047230151
125425.50787939639281.122679441355569.893079351426
126425.50787939639272.733179501892578.282579290889
127425.50787939639264.780993376494586.234765416286
128425.50787939639257.204121709727593.811637083054
129425.50787939639249.953962284724601.061796508056
130425.50787939639242.991576631272608.024182161508



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')