Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 17 Aug 2014 23:20:48 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Aug/17/t1408314067iz3m681m6ar572c.htm/, Retrieved Thu, 16 May 2024 07:17:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235652, Retrieved Thu, 16 May 2024 07:17:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-08-17 22:20:48] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
40927
40856
40778
40635
42103
42032
40927
40194
40265
40265
40336
40486
40856
40414
40856
40486
41661
42181
39973
39381
39894
39823
39381
39453
40336
40194
40336
40336
41298
41440
38790
38790
39823
39310
38427
38790
39674
39232
39161
38206
39602
39894
37023
36952
38427
37615
36218
36810
37465
37615
37173
36290
38128
38128
34893
34673
35556
33939
32314
32835
33939
33055
32464
31210
32906
32977
29743
29664
30256
28418
26430
27235
28339
27164
27093
25910
27826
28197
24585
23780
24293
22305
20246
20909
22156
20688
20909
20026
21864
22084
17668
17375
18180
16050
14134
14797
16414
14504
14355
12880
14504
15017
10451
10451
11113
9347
7359
8392
10230
8242
9055
7950
9717
10308
5592
5229
5963
4196
2800
3384




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235652&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235652&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235652&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.481812528047033
beta0.10413538759401
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.481812528047033 \tabularnewline
beta & 0.10413538759401 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235652&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]0.481812528047033[/C][/ROW]
[ROW][C]beta[/C][C]0.10413538759401[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235652&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235652&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
alpha0.481812528047033
beta0.10413538759401
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134085640937.9869123932-81.9869123931785
144041440490.3784313731-76.3784313731157
154085640901.3483289789-45.3483289789365
164048640497.5352903198-11.5352903198363
174166141678.7683620392-17.7683620391617
184218142225.731756639-44.7317566389975
193997340492.8761573137-519.876157313745
203938139455.130904897-74.130904897007
213989439426.223541749467.776458251043
223982339598.6756936274224.324306372568
233938139757.751403575-376.751403575014
243945339674.9016146572-221.901614657247
254033639854.3755038057481.624496194338
264019439670.4561553028523.543844697248
274033640405.8837229097-69.8837229097117
284033640025.8678759805310.132124019539
294129841393.0908523987-95.0908523987091
304144041919.184065352-479.184065351983
313879039739.3487865154-949.348786515387
323879038712.66836223477.3316377660158
333982339032.1571134468790.842886553226
343931039244.932269135765.0677308642917
353842739018.635172512-591.63517251196
363879038904.5403004306-114.540300430635
373967439497.7347388287176.26526117132
383923239170.524659614961.4753403850991
393916139334.7444926447-173.74449264475
403820639055.3249846981-849.324984698091
413960239549.46954569752.5304543029924
423989439850.606989860443.3930101395745
433702337608.09279522-585.092795220015
443695237236.374858483-284.374858482966
453842737680.6197668485746.380233151453
463761537422.9520969075192.047903092454
473621836850.978921124-632.978921123977
483681036895.5528287622-85.552828762171
493746537586.2241327777-121.224132777679
503761536974.0896237294640.910376270607
513717337242.5653511634-69.5653511634373
523629036615.455173592-325.455173592003
533812837807.8133295162320.186670483847
543812838225.0816615091-97.0816615090589
553489335574.0690794534-681.069079453446
563467335291.9788852924-618.978885292439
573555636072.3854744938-516.385474493807
583393934818.9494444679-879.949444467929
593231433149.0658886977-835.065888697682
603283533215.9115850933-380.911585093272
613393933566.9421440186372.057855981431
623305533433.3066578403-378.306657840309
633246432637.3143299314-173.314329931436
643121031617.175322308-407.175322308009
653290632890.180624595715.819375404295
663297732714.7639376402262.236062359792
672974329722.474663793920.5253362061048
682966429634.011912344629.9880876554198
693025630636.2387389819-380.238738981876
702841829122.8138068254-704.813806825383
712643027432.1662901761-1002.16629017608
722723527517.0493375049-282.049337504905
732833928174.0639324917164.936067508293
742716427409.5846452351-245.584645235129
752709326648.2026228196444.797377180425
762591025700.1454364857209.854563514313
772782627416.0444080784409.95559192156
782819727504.4032009654692.596799034556
792458524561.994129685123.0058703148825
802378024447.5329457424-667.532945742365
812429324834.016698498-541.016698497984
822230522999.7750675251-694.775067525134
832024621085.2225608261-839.222560826103
842090921555.287568145-646.287568145002
852215622183.6727118204-27.6727118204144
862068821019.244364003-331.244364002967
872090920475.6188154913433.381184508689
882002619301.0250334979724.974966502105
892186421295.3591206686568.640879331404
902208421541.151245007542.848754993047
911766818106.6202802559-438.620280255887
921737517315.753983260459.2460167396457
931818018058.2740071248121.725992875206
941605016437.232650476-387.232650476013
951413414584.9958066564-450.995806656356
961479715350.5573648223-553.557364822314
971641416357.29971214356.7002878570383
981450415093.5697755152-589.569775515209
991435514826.0915067406-471.091506740629
1001288013325.8232423551-445.823242355078
1011450414575.3099477567-71.3099477566557
1021501714367.560096248649.439903752022
1031045110349.3087058399101.691294160091
104104519977.3764033294473.623596670604
1051111310873.3329791181239.6670208819
10693478972.70653810612374.293461893878
10773597419.87529932268-60.8752993226844
10883928305.363545892586.6364541074981
109102309954.01593550891275.984064491095
11082428489.28167495577-247.281674955773
11190558493.52098367306561.479016326939
11279507601.06467842742348.935321572576
11397179564.63296609757152.367033902432
114103089986.44859156584321.551408434161
11555925658.24012029262-66.2401202926221
11652295521.56144309464-292.561443094639
11759636012.11916178786-49.1191617878603
11841964112.6162343701783.3837656298274
11928002250.0286125322549.971387467804
12033843592.82420088574-208.824200885744

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 40856 & 40937.9869123932 & -81.9869123931785 \tabularnewline
14 & 40414 & 40490.3784313731 & -76.3784313731157 \tabularnewline
15 & 40856 & 40901.3483289789 & -45.3483289789365 \tabularnewline
16 & 40486 & 40497.5352903198 & -11.5352903198363 \tabularnewline
17 & 41661 & 41678.7683620392 & -17.7683620391617 \tabularnewline
18 & 42181 & 42225.731756639 & -44.7317566389975 \tabularnewline
19 & 39973 & 40492.8761573137 & -519.876157313745 \tabularnewline
20 & 39381 & 39455.130904897 & -74.130904897007 \tabularnewline
21 & 39894 & 39426.223541749 & 467.776458251043 \tabularnewline
22 & 39823 & 39598.6756936274 & 224.324306372568 \tabularnewline
23 & 39381 & 39757.751403575 & -376.751403575014 \tabularnewline
24 & 39453 & 39674.9016146572 & -221.901614657247 \tabularnewline
25 & 40336 & 39854.3755038057 & 481.624496194338 \tabularnewline
26 & 40194 & 39670.4561553028 & 523.543844697248 \tabularnewline
27 & 40336 & 40405.8837229097 & -69.8837229097117 \tabularnewline
28 & 40336 & 40025.8678759805 & 310.132124019539 \tabularnewline
29 & 41298 & 41393.0908523987 & -95.0908523987091 \tabularnewline
30 & 41440 & 41919.184065352 & -479.184065351983 \tabularnewline
31 & 38790 & 39739.3487865154 & -949.348786515387 \tabularnewline
32 & 38790 & 38712.668362234 & 77.3316377660158 \tabularnewline
33 & 39823 & 39032.1571134468 & 790.842886553226 \tabularnewline
34 & 39310 & 39244.9322691357 & 65.0677308642917 \tabularnewline
35 & 38427 & 39018.635172512 & -591.63517251196 \tabularnewline
36 & 38790 & 38904.5403004306 & -114.540300430635 \tabularnewline
37 & 39674 & 39497.7347388287 & 176.26526117132 \tabularnewline
38 & 39232 & 39170.5246596149 & 61.4753403850991 \tabularnewline
39 & 39161 & 39334.7444926447 & -173.74449264475 \tabularnewline
40 & 38206 & 39055.3249846981 & -849.324984698091 \tabularnewline
41 & 39602 & 39549.469545697 & 52.5304543029924 \tabularnewline
42 & 39894 & 39850.6069898604 & 43.3930101395745 \tabularnewline
43 & 37023 & 37608.09279522 & -585.092795220015 \tabularnewline
44 & 36952 & 37236.374858483 & -284.374858482966 \tabularnewline
45 & 38427 & 37680.6197668485 & 746.380233151453 \tabularnewline
46 & 37615 & 37422.9520969075 & 192.047903092454 \tabularnewline
47 & 36218 & 36850.978921124 & -632.978921123977 \tabularnewline
48 & 36810 & 36895.5528287622 & -85.552828762171 \tabularnewline
49 & 37465 & 37586.2241327777 & -121.224132777679 \tabularnewline
50 & 37615 & 36974.0896237294 & 640.910376270607 \tabularnewline
51 & 37173 & 37242.5653511634 & -69.5653511634373 \tabularnewline
52 & 36290 & 36615.455173592 & -325.455173592003 \tabularnewline
53 & 38128 & 37807.8133295162 & 320.186670483847 \tabularnewline
54 & 38128 & 38225.0816615091 & -97.0816615090589 \tabularnewline
55 & 34893 & 35574.0690794534 & -681.069079453446 \tabularnewline
56 & 34673 & 35291.9788852924 & -618.978885292439 \tabularnewline
57 & 35556 & 36072.3854744938 & -516.385474493807 \tabularnewline
58 & 33939 & 34818.9494444679 & -879.949444467929 \tabularnewline
59 & 32314 & 33149.0658886977 & -835.065888697682 \tabularnewline
60 & 32835 & 33215.9115850933 & -380.911585093272 \tabularnewline
61 & 33939 & 33566.9421440186 & 372.057855981431 \tabularnewline
62 & 33055 & 33433.3066578403 & -378.306657840309 \tabularnewline
63 & 32464 & 32637.3143299314 & -173.314329931436 \tabularnewline
64 & 31210 & 31617.175322308 & -407.175322308009 \tabularnewline
65 & 32906 & 32890.1806245957 & 15.819375404295 \tabularnewline
66 & 32977 & 32714.7639376402 & 262.236062359792 \tabularnewline
67 & 29743 & 29722.4746637939 & 20.5253362061048 \tabularnewline
68 & 29664 & 29634.0119123446 & 29.9880876554198 \tabularnewline
69 & 30256 & 30636.2387389819 & -380.238738981876 \tabularnewline
70 & 28418 & 29122.8138068254 & -704.813806825383 \tabularnewline
71 & 26430 & 27432.1662901761 & -1002.16629017608 \tabularnewline
72 & 27235 & 27517.0493375049 & -282.049337504905 \tabularnewline
73 & 28339 & 28174.0639324917 & 164.936067508293 \tabularnewline
74 & 27164 & 27409.5846452351 & -245.584645235129 \tabularnewline
75 & 27093 & 26648.2026228196 & 444.797377180425 \tabularnewline
76 & 25910 & 25700.1454364857 & 209.854563514313 \tabularnewline
77 & 27826 & 27416.0444080784 & 409.95559192156 \tabularnewline
78 & 28197 & 27504.4032009654 & 692.596799034556 \tabularnewline
79 & 24585 & 24561.9941296851 & 23.0058703148825 \tabularnewline
80 & 23780 & 24447.5329457424 & -667.532945742365 \tabularnewline
81 & 24293 & 24834.016698498 & -541.016698497984 \tabularnewline
82 & 22305 & 22999.7750675251 & -694.775067525134 \tabularnewline
83 & 20246 & 21085.2225608261 & -839.222560826103 \tabularnewline
84 & 20909 & 21555.287568145 & -646.287568145002 \tabularnewline
85 & 22156 & 22183.6727118204 & -27.6727118204144 \tabularnewline
86 & 20688 & 21019.244364003 & -331.244364002967 \tabularnewline
87 & 20909 & 20475.6188154913 & 433.381184508689 \tabularnewline
88 & 20026 & 19301.0250334979 & 724.974966502105 \tabularnewline
89 & 21864 & 21295.3591206686 & 568.640879331404 \tabularnewline
90 & 22084 & 21541.151245007 & 542.848754993047 \tabularnewline
91 & 17668 & 18106.6202802559 & -438.620280255887 \tabularnewline
92 & 17375 & 17315.7539832604 & 59.2460167396457 \tabularnewline
93 & 18180 & 18058.2740071248 & 121.725992875206 \tabularnewline
94 & 16050 & 16437.232650476 & -387.232650476013 \tabularnewline
95 & 14134 & 14584.9958066564 & -450.995806656356 \tabularnewline
96 & 14797 & 15350.5573648223 & -553.557364822314 \tabularnewline
97 & 16414 & 16357.299712143 & 56.7002878570383 \tabularnewline
98 & 14504 & 15093.5697755152 & -589.569775515209 \tabularnewline
99 & 14355 & 14826.0915067406 & -471.091506740629 \tabularnewline
100 & 12880 & 13325.8232423551 & -445.823242355078 \tabularnewline
101 & 14504 & 14575.3099477567 & -71.3099477566557 \tabularnewline
102 & 15017 & 14367.560096248 & 649.439903752022 \tabularnewline
103 & 10451 & 10349.3087058399 & 101.691294160091 \tabularnewline
104 & 10451 & 9977.3764033294 & 473.623596670604 \tabularnewline
105 & 11113 & 10873.3329791181 & 239.6670208819 \tabularnewline
106 & 9347 & 8972.70653810612 & 374.293461893878 \tabularnewline
107 & 7359 & 7419.87529932268 & -60.8752993226844 \tabularnewline
108 & 8392 & 8305.3635458925 & 86.6364541074981 \tabularnewline
109 & 10230 & 9954.01593550891 & 275.984064491095 \tabularnewline
110 & 8242 & 8489.28167495577 & -247.281674955773 \tabularnewline
111 & 9055 & 8493.52098367306 & 561.479016326939 \tabularnewline
112 & 7950 & 7601.06467842742 & 348.935321572576 \tabularnewline
113 & 9717 & 9564.63296609757 & 152.367033902432 \tabularnewline
114 & 10308 & 9986.44859156584 & 321.551408434161 \tabularnewline
115 & 5592 & 5658.24012029262 & -66.2401202926221 \tabularnewline
116 & 5229 & 5521.56144309464 & -292.561443094639 \tabularnewline
117 & 5963 & 6012.11916178786 & -49.1191617878603 \tabularnewline
118 & 4196 & 4112.61623437017 & 83.3837656298274 \tabularnewline
119 & 2800 & 2250.0286125322 & 549.971387467804 \tabularnewline
120 & 3384 & 3592.82420088574 & -208.824200885744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235652&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]40856[/C][C]40937.9869123932[/C][C]-81.9869123931785[/C][/ROW]
[ROW][C]14[/C][C]40414[/C][C]40490.3784313731[/C][C]-76.3784313731157[/C][/ROW]
[ROW][C]15[/C][C]40856[/C][C]40901.3483289789[/C][C]-45.3483289789365[/C][/ROW]
[ROW][C]16[/C][C]40486[/C][C]40497.5352903198[/C][C]-11.5352903198363[/C][/ROW]
[ROW][C]17[/C][C]41661[/C][C]41678.7683620392[/C][C]-17.7683620391617[/C][/ROW]
[ROW][C]18[/C][C]42181[/C][C]42225.731756639[/C][C]-44.7317566389975[/C][/ROW]
[ROW][C]19[/C][C]39973[/C][C]40492.8761573137[/C][C]-519.876157313745[/C][/ROW]
[ROW][C]20[/C][C]39381[/C][C]39455.130904897[/C][C]-74.130904897007[/C][/ROW]
[ROW][C]21[/C][C]39894[/C][C]39426.223541749[/C][C]467.776458251043[/C][/ROW]
[ROW][C]22[/C][C]39823[/C][C]39598.6756936274[/C][C]224.324306372568[/C][/ROW]
[ROW][C]23[/C][C]39381[/C][C]39757.751403575[/C][C]-376.751403575014[/C][/ROW]
[ROW][C]24[/C][C]39453[/C][C]39674.9016146572[/C][C]-221.901614657247[/C][/ROW]
[ROW][C]25[/C][C]40336[/C][C]39854.3755038057[/C][C]481.624496194338[/C][/ROW]
[ROW][C]26[/C][C]40194[/C][C]39670.4561553028[/C][C]523.543844697248[/C][/ROW]
[ROW][C]27[/C][C]40336[/C][C]40405.8837229097[/C][C]-69.8837229097117[/C][/ROW]
[ROW][C]28[/C][C]40336[/C][C]40025.8678759805[/C][C]310.132124019539[/C][/ROW]
[ROW][C]29[/C][C]41298[/C][C]41393.0908523987[/C][C]-95.0908523987091[/C][/ROW]
[ROW][C]30[/C][C]41440[/C][C]41919.184065352[/C][C]-479.184065351983[/C][/ROW]
[ROW][C]31[/C][C]38790[/C][C]39739.3487865154[/C][C]-949.348786515387[/C][/ROW]
[ROW][C]32[/C][C]38790[/C][C]38712.668362234[/C][C]77.3316377660158[/C][/ROW]
[ROW][C]33[/C][C]39823[/C][C]39032.1571134468[/C][C]790.842886553226[/C][/ROW]
[ROW][C]34[/C][C]39310[/C][C]39244.9322691357[/C][C]65.0677308642917[/C][/ROW]
[ROW][C]35[/C][C]38427[/C][C]39018.635172512[/C][C]-591.63517251196[/C][/ROW]
[ROW][C]36[/C][C]38790[/C][C]38904.5403004306[/C][C]-114.540300430635[/C][/ROW]
[ROW][C]37[/C][C]39674[/C][C]39497.7347388287[/C][C]176.26526117132[/C][/ROW]
[ROW][C]38[/C][C]39232[/C][C]39170.5246596149[/C][C]61.4753403850991[/C][/ROW]
[ROW][C]39[/C][C]39161[/C][C]39334.7444926447[/C][C]-173.74449264475[/C][/ROW]
[ROW][C]40[/C][C]38206[/C][C]39055.3249846981[/C][C]-849.324984698091[/C][/ROW]
[ROW][C]41[/C][C]39602[/C][C]39549.469545697[/C][C]52.5304543029924[/C][/ROW]
[ROW][C]42[/C][C]39894[/C][C]39850.6069898604[/C][C]43.3930101395745[/C][/ROW]
[ROW][C]43[/C][C]37023[/C][C]37608.09279522[/C][C]-585.092795220015[/C][/ROW]
[ROW][C]44[/C][C]36952[/C][C]37236.374858483[/C][C]-284.374858482966[/C][/ROW]
[ROW][C]45[/C][C]38427[/C][C]37680.6197668485[/C][C]746.380233151453[/C][/ROW]
[ROW][C]46[/C][C]37615[/C][C]37422.9520969075[/C][C]192.047903092454[/C][/ROW]
[ROW][C]47[/C][C]36218[/C][C]36850.978921124[/C][C]-632.978921123977[/C][/ROW]
[ROW][C]48[/C][C]36810[/C][C]36895.5528287622[/C][C]-85.552828762171[/C][/ROW]
[ROW][C]49[/C][C]37465[/C][C]37586.2241327777[/C][C]-121.224132777679[/C][/ROW]
[ROW][C]50[/C][C]37615[/C][C]36974.0896237294[/C][C]640.910376270607[/C][/ROW]
[ROW][C]51[/C][C]37173[/C][C]37242.5653511634[/C][C]-69.5653511634373[/C][/ROW]
[ROW][C]52[/C][C]36290[/C][C]36615.455173592[/C][C]-325.455173592003[/C][/ROW]
[ROW][C]53[/C][C]38128[/C][C]37807.8133295162[/C][C]320.186670483847[/C][/ROW]
[ROW][C]54[/C][C]38128[/C][C]38225.0816615091[/C][C]-97.0816615090589[/C][/ROW]
[ROW][C]55[/C][C]34893[/C][C]35574.0690794534[/C][C]-681.069079453446[/C][/ROW]
[ROW][C]56[/C][C]34673[/C][C]35291.9788852924[/C][C]-618.978885292439[/C][/ROW]
[ROW][C]57[/C][C]35556[/C][C]36072.3854744938[/C][C]-516.385474493807[/C][/ROW]
[ROW][C]58[/C][C]33939[/C][C]34818.9494444679[/C][C]-879.949444467929[/C][/ROW]
[ROW][C]59[/C][C]32314[/C][C]33149.0658886977[/C][C]-835.065888697682[/C][/ROW]
[ROW][C]60[/C][C]32835[/C][C]33215.9115850933[/C][C]-380.911585093272[/C][/ROW]
[ROW][C]61[/C][C]33939[/C][C]33566.9421440186[/C][C]372.057855981431[/C][/ROW]
[ROW][C]62[/C][C]33055[/C][C]33433.3066578403[/C][C]-378.306657840309[/C][/ROW]
[ROW][C]63[/C][C]32464[/C][C]32637.3143299314[/C][C]-173.314329931436[/C][/ROW]
[ROW][C]64[/C][C]31210[/C][C]31617.175322308[/C][C]-407.175322308009[/C][/ROW]
[ROW][C]65[/C][C]32906[/C][C]32890.1806245957[/C][C]15.819375404295[/C][/ROW]
[ROW][C]66[/C][C]32977[/C][C]32714.7639376402[/C][C]262.236062359792[/C][/ROW]
[ROW][C]67[/C][C]29743[/C][C]29722.4746637939[/C][C]20.5253362061048[/C][/ROW]
[ROW][C]68[/C][C]29664[/C][C]29634.0119123446[/C][C]29.9880876554198[/C][/ROW]
[ROW][C]69[/C][C]30256[/C][C]30636.2387389819[/C][C]-380.238738981876[/C][/ROW]
[ROW][C]70[/C][C]28418[/C][C]29122.8138068254[/C][C]-704.813806825383[/C][/ROW]
[ROW][C]71[/C][C]26430[/C][C]27432.1662901761[/C][C]-1002.16629017608[/C][/ROW]
[ROW][C]72[/C][C]27235[/C][C]27517.0493375049[/C][C]-282.049337504905[/C][/ROW]
[ROW][C]73[/C][C]28339[/C][C]28174.0639324917[/C][C]164.936067508293[/C][/ROW]
[ROW][C]74[/C][C]27164[/C][C]27409.5846452351[/C][C]-245.584645235129[/C][/ROW]
[ROW][C]75[/C][C]27093[/C][C]26648.2026228196[/C][C]444.797377180425[/C][/ROW]
[ROW][C]76[/C][C]25910[/C][C]25700.1454364857[/C][C]209.854563514313[/C][/ROW]
[ROW][C]77[/C][C]27826[/C][C]27416.0444080784[/C][C]409.95559192156[/C][/ROW]
[ROW][C]78[/C][C]28197[/C][C]27504.4032009654[/C][C]692.596799034556[/C][/ROW]
[ROW][C]79[/C][C]24585[/C][C]24561.9941296851[/C][C]23.0058703148825[/C][/ROW]
[ROW][C]80[/C][C]23780[/C][C]24447.5329457424[/C][C]-667.532945742365[/C][/ROW]
[ROW][C]81[/C][C]24293[/C][C]24834.016698498[/C][C]-541.016698497984[/C][/ROW]
[ROW][C]82[/C][C]22305[/C][C]22999.7750675251[/C][C]-694.775067525134[/C][/ROW]
[ROW][C]83[/C][C]20246[/C][C]21085.2225608261[/C][C]-839.222560826103[/C][/ROW]
[ROW][C]84[/C][C]20909[/C][C]21555.287568145[/C][C]-646.287568145002[/C][/ROW]
[ROW][C]85[/C][C]22156[/C][C]22183.6727118204[/C][C]-27.6727118204144[/C][/ROW]
[ROW][C]86[/C][C]20688[/C][C]21019.244364003[/C][C]-331.244364002967[/C][/ROW]
[ROW][C]87[/C][C]20909[/C][C]20475.6188154913[/C][C]433.381184508689[/C][/ROW]
[ROW][C]88[/C][C]20026[/C][C]19301.0250334979[/C][C]724.974966502105[/C][/ROW]
[ROW][C]89[/C][C]21864[/C][C]21295.3591206686[/C][C]568.640879331404[/C][/ROW]
[ROW][C]90[/C][C]22084[/C][C]21541.151245007[/C][C]542.848754993047[/C][/ROW]
[ROW][C]91[/C][C]17668[/C][C]18106.6202802559[/C][C]-438.620280255887[/C][/ROW]
[ROW][C]92[/C][C]17375[/C][C]17315.7539832604[/C][C]59.2460167396457[/C][/ROW]
[ROW][C]93[/C][C]18180[/C][C]18058.2740071248[/C][C]121.725992875206[/C][/ROW]
[ROW][C]94[/C][C]16050[/C][C]16437.232650476[/C][C]-387.232650476013[/C][/ROW]
[ROW][C]95[/C][C]14134[/C][C]14584.9958066564[/C][C]-450.995806656356[/C][/ROW]
[ROW][C]96[/C][C]14797[/C][C]15350.5573648223[/C][C]-553.557364822314[/C][/ROW]
[ROW][C]97[/C][C]16414[/C][C]16357.299712143[/C][C]56.7002878570383[/C][/ROW]
[ROW][C]98[/C][C]14504[/C][C]15093.5697755152[/C][C]-589.569775515209[/C][/ROW]
[ROW][C]99[/C][C]14355[/C][C]14826.0915067406[/C][C]-471.091506740629[/C][/ROW]
[ROW][C]100[/C][C]12880[/C][C]13325.8232423551[/C][C]-445.823242355078[/C][/ROW]
[ROW][C]101[/C][C]14504[/C][C]14575.3099477567[/C][C]-71.3099477566557[/C][/ROW]
[ROW][C]102[/C][C]15017[/C][C]14367.560096248[/C][C]649.439903752022[/C][/ROW]
[ROW][C]103[/C][C]10451[/C][C]10349.3087058399[/C][C]101.691294160091[/C][/ROW]
[ROW][C]104[/C][C]10451[/C][C]9977.3764033294[/C][C]473.623596670604[/C][/ROW]
[ROW][C]105[/C][C]11113[/C][C]10873.3329791181[/C][C]239.6670208819[/C][/ROW]
[ROW][C]106[/C][C]9347[/C][C]8972.70653810612[/C][C]374.293461893878[/C][/ROW]
[ROW][C]107[/C][C]7359[/C][C]7419.87529932268[/C][C]-60.8752993226844[/C][/ROW]
[ROW][C]108[/C][C]8392[/C][C]8305.3635458925[/C][C]86.6364541074981[/C][/ROW]
[ROW][C]109[/C][C]10230[/C][C]9954.01593550891[/C][C]275.984064491095[/C][/ROW]
[ROW][C]110[/C][C]8242[/C][C]8489.28167495577[/C][C]-247.281674955773[/C][/ROW]
[ROW][C]111[/C][C]9055[/C][C]8493.52098367306[/C][C]561.479016326939[/C][/ROW]
[ROW][C]112[/C][C]7950[/C][C]7601.06467842742[/C][C]348.935321572576[/C][/ROW]
[ROW][C]113[/C][C]9717[/C][C]9564.63296609757[/C][C]152.367033902432[/C][/ROW]
[ROW][C]114[/C][C]10308[/C][C]9986.44859156584[/C][C]321.551408434161[/C][/ROW]
[ROW][C]115[/C][C]5592[/C][C]5658.24012029262[/C][C]-66.2401202926221[/C][/ROW]
[ROW][C]116[/C][C]5229[/C][C]5521.56144309464[/C][C]-292.561443094639[/C][/ROW]
[ROW][C]117[/C][C]5963[/C][C]6012.11916178786[/C][C]-49.1191617878603[/C][/ROW]
[ROW][C]118[/C][C]4196[/C][C]4112.61623437017[/C][C]83.3837656298274[/C][/ROW]
[ROW][C]119[/C][C]2800[/C][C]2250.0286125322[/C][C]549.971387467804[/C][/ROW]
[ROW][C]120[/C][C]3384[/C][C]3592.82420088574[/C][C]-208.824200885744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235652&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235652&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
134085640937.9869123932-81.9869123931785
144041440490.3784313731-76.3784313731157
154085640901.3483289789-45.3483289789365
164048640497.5352903198-11.5352903198363
174166141678.7683620392-17.7683620391617
184218142225.731756639-44.7317566389975
193997340492.8761573137-519.876157313745
203938139455.130904897-74.130904897007
213989439426.223541749467.776458251043
223982339598.6756936274224.324306372568
233938139757.751403575-376.751403575014
243945339674.9016146572-221.901614657247
254033639854.3755038057481.624496194338
264019439670.4561553028523.543844697248
274033640405.8837229097-69.8837229097117
284033640025.8678759805310.132124019539
294129841393.0908523987-95.0908523987091
304144041919.184065352-479.184065351983
313879039739.3487865154-949.348786515387
323879038712.66836223477.3316377660158
333982339032.1571134468790.842886553226
343931039244.932269135765.0677308642917
353842739018.635172512-591.63517251196
363879038904.5403004306-114.540300430635
373967439497.7347388287176.26526117132
383923239170.524659614961.4753403850991
393916139334.7444926447-173.74449264475
403820639055.3249846981-849.324984698091
413960239549.46954569752.5304543029924
423989439850.606989860443.3930101395745
433702337608.09279522-585.092795220015
443695237236.374858483-284.374858482966
453842737680.6197668485746.380233151453
463761537422.9520969075192.047903092454
473621836850.978921124-632.978921123977
483681036895.5528287622-85.552828762171
493746537586.2241327777-121.224132777679
503761536974.0896237294640.910376270607
513717337242.5653511634-69.5653511634373
523629036615.455173592-325.455173592003
533812837807.8133295162320.186670483847
543812838225.0816615091-97.0816615090589
553489335574.0690794534-681.069079453446
563467335291.9788852924-618.978885292439
573555636072.3854744938-516.385474493807
583393934818.9494444679-879.949444467929
593231433149.0658886977-835.065888697682
603283533215.9115850933-380.911585093272
613393933566.9421440186372.057855981431
623305533433.3066578403-378.306657840309
633246432637.3143299314-173.314329931436
643121031617.175322308-407.175322308009
653290632890.180624595715.819375404295
663297732714.7639376402262.236062359792
672974329722.474663793920.5253362061048
682966429634.011912344629.9880876554198
693025630636.2387389819-380.238738981876
702841829122.8138068254-704.813806825383
712643027432.1662901761-1002.16629017608
722723527517.0493375049-282.049337504905
732833928174.0639324917164.936067508293
742716427409.5846452351-245.584645235129
752709326648.2026228196444.797377180425
762591025700.1454364857209.854563514313
772782627416.0444080784409.95559192156
782819727504.4032009654692.596799034556
792458524561.994129685123.0058703148825
802378024447.5329457424-667.532945742365
812429324834.016698498-541.016698497984
822230522999.7750675251-694.775067525134
832024621085.2225608261-839.222560826103
842090921555.287568145-646.287568145002
852215622183.6727118204-27.6727118204144
862068821019.244364003-331.244364002967
872090920475.6188154913433.381184508689
882002619301.0250334979724.974966502105
892186421295.3591206686568.640879331404
902208421541.151245007542.848754993047
911766818106.6202802559-438.620280255887
921737517315.753983260459.2460167396457
931818018058.2740071248121.725992875206
941605016437.232650476-387.232650476013
951413414584.9958066564-450.995806656356
961479715350.5573648223-553.557364822314
971641416357.29971214356.7002878570383
981450415093.5697755152-589.569775515209
991435514826.0915067406-471.091506740629
1001288013325.8232423551-445.823242355078
1011450414575.3099477567-71.3099477566557
1021501714367.560096248649.439903752022
1031045110349.3087058399101.691294160091
104104519977.3764033294473.623596670604
1051111310873.3329791181239.6670208819
10693478972.70653810612374.293461893878
10773597419.87529932268-60.8752993226844
10883928305.363545892586.6364541074981
109102309954.01593550891275.984064491095
11082428489.28167495577-247.281674955773
11190558493.52098367306561.479016326939
11279507601.06467842742348.935321572576
11397179564.63296609757152.367033902432
114103089986.44859156584321.551408434161
11555925658.24012029262-66.2401202926221
11652295521.56144309464-292.561443094639
11759636012.11916178786-49.1191617878603
11841964112.6162343701783.3837656298274
11928002250.0286125322549.971387467804
12033843592.82420088574-208.824200885744







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1215268.968153288924438.872609770696099.06369680715
1223457.995059463332517.745803101654398.24431582501
1234070.757977456053013.593043076735127.92291183536
1242839.755611327271659.452687569724020.05853508481
1254557.954920682763248.722389227385867.18745213815
1265010.994255755473567.39061744726454.59789406373
127327.742972690728-1255.383427336171910.86937271763
128109.859652515437-1617.69709054141837.41639557227
129886.361691478779-990.3242300003822763.04761295794
130-899.513348215304-2929.846256370321130.81955993971
131-2543.3798244489-4731.71859802639-355.041050871401
132-1869.24319828504-4219.80567037097481.319273800884

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 5268.96815328892 & 4438.87260977069 & 6099.06369680715 \tabularnewline
122 & 3457.99505946333 & 2517.74580310165 & 4398.24431582501 \tabularnewline
123 & 4070.75797745605 & 3013.59304307673 & 5127.92291183536 \tabularnewline
124 & 2839.75561132727 & 1659.45268756972 & 4020.05853508481 \tabularnewline
125 & 4557.95492068276 & 3248.72238922738 & 5867.18745213815 \tabularnewline
126 & 5010.99425575547 & 3567.3906174472 & 6454.59789406373 \tabularnewline
127 & 327.742972690728 & -1255.38342733617 & 1910.86937271763 \tabularnewline
128 & 109.859652515437 & -1617.6970905414 & 1837.41639557227 \tabularnewline
129 & 886.361691478779 & -990.324230000382 & 2763.04761295794 \tabularnewline
130 & -899.513348215304 & -2929.84625637032 & 1130.81955993971 \tabularnewline
131 & -2543.3798244489 & -4731.71859802639 & -355.041050871401 \tabularnewline
132 & -1869.24319828504 & -4219.80567037097 & 481.319273800884 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235652&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]5268.96815328892[/C][C]4438.87260977069[/C][C]6099.06369680715[/C][/ROW]
[ROW][C]122[/C][C]3457.99505946333[/C][C]2517.74580310165[/C][C]4398.24431582501[/C][/ROW]
[ROW][C]123[/C][C]4070.75797745605[/C][C]3013.59304307673[/C][C]5127.92291183536[/C][/ROW]
[ROW][C]124[/C][C]2839.75561132727[/C][C]1659.45268756972[/C][C]4020.05853508481[/C][/ROW]
[ROW][C]125[/C][C]4557.95492068276[/C][C]3248.72238922738[/C][C]5867.18745213815[/C][/ROW]
[ROW][C]126[/C][C]5010.99425575547[/C][C]3567.3906174472[/C][C]6454.59789406373[/C][/ROW]
[ROW][C]127[/C][C]327.742972690728[/C][C]-1255.38342733617[/C][C]1910.86937271763[/C][/ROW]
[ROW][C]128[/C][C]109.859652515437[/C][C]-1617.6970905414[/C][C]1837.41639557227[/C][/ROW]
[ROW][C]129[/C][C]886.361691478779[/C][C]-990.324230000382[/C][C]2763.04761295794[/C][/ROW]
[ROW][C]130[/C][C]-899.513348215304[/C][C]-2929.84625637032[/C][C]1130.81955993971[/C][/ROW]
[ROW][C]131[/C][C]-2543.3798244489[/C][C]-4731.71859802639[/C][C]-355.041050871401[/C][/ROW]
[ROW][C]132[/C][C]-1869.24319828504[/C][C]-4219.80567037097[/C][C]481.319273800884[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235652&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235652&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
1215268.968153288924438.872609770696099.06369680715
1223457.995059463332517.745803101654398.24431582501
1234070.757977456053013.593043076735127.92291183536
1242839.755611327271659.452687569724020.05853508481
1254557.954920682763248.722389227385867.18745213815
1265010.994255755473567.39061744726454.59789406373
127327.742972690728-1255.383427336171910.86937271763
128109.859652515437-1617.69709054141837.41639557227
129886.361691478779-990.3242300003822763.04761295794
130-899.513348215304-2929.846256370321130.81955993971
131-2543.3798244489-4731.71859802639-355.041050871401
132-1869.24319828504-4219.80567037097481.319273800884



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