Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 11 Aug 2016 18:39:39 +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/2016/Aug/11/t14709372286x1z2bfnzwylmba.htm/, Retrieved Sun, 05 May 2024 14:31:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296349, Retrieved Sun, 05 May 2024 14:31:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Reeks A stap 32] [2016-08-11 17:39:39] [efea2b8bc7c91838390b884e612c3e3f] [Current]
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Dataseries X:
40927.00
40856.00
40778.00
40635.00
42103.00
42032.00
40927.00
40194.00
40265.00
40265.00
40336.00
40486.00
40856.00
40414.00
40856.00
40486.00
41661.00
42181.00
39973.00
39381.00
39894.00
39823.00
39381.00
39453.00
40336.00
40194.00
40336.00
40336.00
41298.00
41440.00
38790.00
38790.00
39823.00
39310.00
38427.00
38790.00
39674.00
39232.00
39161.00
38206.00
39602.00
39894.00
37023.00
36952.00
38427.00
37615.00
36218.00
36810.00
37465.00
37615.00
37173.00
36290.00
38128.00
38128.00
34893.00
34673.00
35556.00
33939.00
32314.00
32835.00
33939.00
33055.00
32464.00
31210.00
32906.00
32977.00
29743.00
29664.00
30256.00
28418.00
26430.00
27235.00
28339.00
27164.00
27093.00
25910.00
27826.00
28197.00
24585.00
23780.00
24293.00
22305.00
20246.00
20909.00
22156.00
20688.00
20909.00
20026.00
21864.00
22084.00
17668.00
17375.00
18180.00
16050.00
14134.00
14797.00
16414.00
14504.00
14355.00
12880.00
14504.00
15017.00
10451.00
10451.00
11113.00
9347.00
7359.00
8392.00
10230.00
8242.00
9055.00
7950.00
9717.00
10308.00
5592.00
5229.00
5963.00
4196.00
2800.00
3384.00




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296349&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296349&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296349&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.312797874143795
beta0.158858173722887
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.312797874143795 \tabularnewline
beta & 0.158858173722887 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296349&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]0.312797874143795[/C][/ROW]
[ROW][C]beta[/C][C]0.158858173722887[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296349&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296349&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
alpha0.312797874143795
beta0.158858173722887
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134085640936.2155920221-80.2155920221485
144041440502.5500693451-88.5500693451177
154085640923.0183224605-67.0183224605134
164048640518.3200236421-32.3200236421399
174166141693.5069329309-32.5069329309481
184218142237.4909121196-56.4909121196033
193997340502.1461266788-529.146126678788
203938139556.7861062892-175.786106289248
213989439499.1999830729394.800016927125
223982339558.0842473275264.915752672518
233938139680.3980540831-299.398054083118
243945339676.2643451359-223.264345135882
254033639866.0335000654469.966499934599
264019439588.1769403194605.823059680632
274033640249.075952123986.924047876113
284033639944.712831503391.287168497038
294129841285.812489517212.1875104827632
304144041871.2504317826-431.250431782602
313879039742.533550029-952.533550029017
323879038921.2692539992-131.269253999228
333982339272.9166984585550.083301541497
343931039309.35641898150.643581018477562
353842738968.9434752157-541.943475215725
363879038930.127616567-140.127616567042
373967439605.635285708268.3647142917544
383923239274.6588013103-42.658801310281
393916139316.3217189422-155.321718942207
403820639078.8358907664-872.835890766364
413960239593.09678705148.90321294861496
423989439724.8279108187169.17208918128
433702337414.5248799699-391.524879969897
443695237255.78285811-303.782858110004
453842737897.1513534661529.848646533937
463761537486.3566602755128.643339724476
473621836765.5721638635-547.572163863544
483681036900.3244624685-90.3244624685394
493746537610.7583128351-145.758312835096
503761537068.0540249301546.945975069932
513717337155.789193446217.2108065538414
523629036457.025166931-167.025166931046
533812837711.2520728646416.747927135402
543812838069.512476040958.4875239591056
553489335457.5813009921-564.581300992111
563467335288.1419483177-615.141948317694
573555636304.4557624052-748.455762405218
583393935174.8818033119-1235.88180331194
593231433493.3003343526-1179.30033435262
603283533492.4717619583-657.471761958281
613393933685.4828434683253.517156531736
623305533527.2249462162-472.224946216244
633246432717.4924603234-253.492460323443
643121031634.1672510939-424.167251093932
653290632678.3410131006227.658986899442
663297732420.2557273731556.744272626893
672974329711.561308592531.4386914075294
682966429453.2700008764210.729999123581
693025630253.13233464332.86766535674178
702841829021.295799086-603.295799086049
712643027605.2830880492-1175.28308804918
722723527677.9087969249-442.908796924927
732833928225.0494709376113.9505290624
742716427467.7628642708-303.762864270771
752709326773.1394543937319.860545606283
762591025797.9540614891112.045938510895
772782627046.2497287315779.750271268498
782819727100.6038340491096.39616595095
792458524680.2295416902-95.2295416901688
802378024458.4456869544-678.445686954401
812429324607.3585868653-314.35858686535
822230523036.3557347449-731.355734744873
832024621355.2697533615-1109.26975336147
842090921592.8416731022-683.841673102244
852215622021.2944490707134.705550929324
862068821029.0935100169-341.093510016901
872090920585.2054375982323.794562401821
882002619557.6948800828468.305119917197
892186420775.84799368491088.15200631506
902208420954.27237305141129.7276269486
911766818455.5015219131-787.501521913109
921737517582.4876007648-207.487600764838
931818017787.7546832738392.245316726166
941605016469.5883751761-419.588375176096
951413414946.1496322225-812.149632222452
961479715182.3258065362-385.325806536215
971641415776.8885618527637.111438147278
981450414872.7822673852-368.782267385204
991435514705.8564366211-350.856436621089
1001288013705.5454379092-825.545437909152
1011450414177.3815718689326.618428131127
1021501713879.5540779471137.44592205297
1031045111302.1343591694-851.134359169406
1041045110622.1054633261-171.105463326136
1051111310682.6976351068430.302364893183
10693479355.38486507017-8.38486507017114
10773598134.20070495267-775.200704952675
10883928031.73655467569360.263445324314
109102308612.87098116671617.1290188333
11082427896.05242031985345.947579680145
11190557775.248964534541279.75103546546
11279507359.01346894979590.986531050207
11397178368.484340118431348.51565988157
114103088879.135795257591428.86420474241
11555926684.18405539476-1092.18405539476
11652296375.11187712161-1146.11187712161
11759636241.76973713998-278.769737139983
11841965074.91882447864-878.918824478645
11928003750.72318685183-950.723186851829
12033843648.41090745557-264.410907455574

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 40856 & 40936.2155920221 & -80.2155920221485 \tabularnewline
14 & 40414 & 40502.5500693451 & -88.5500693451177 \tabularnewline
15 & 40856 & 40923.0183224605 & -67.0183224605134 \tabularnewline
16 & 40486 & 40518.3200236421 & -32.3200236421399 \tabularnewline
17 & 41661 & 41693.5069329309 & -32.5069329309481 \tabularnewline
18 & 42181 & 42237.4909121196 & -56.4909121196033 \tabularnewline
19 & 39973 & 40502.1461266788 & -529.146126678788 \tabularnewline
20 & 39381 & 39556.7861062892 & -175.786106289248 \tabularnewline
21 & 39894 & 39499.1999830729 & 394.800016927125 \tabularnewline
22 & 39823 & 39558.0842473275 & 264.915752672518 \tabularnewline
23 & 39381 & 39680.3980540831 & -299.398054083118 \tabularnewline
24 & 39453 & 39676.2643451359 & -223.264345135882 \tabularnewline
25 & 40336 & 39866.0335000654 & 469.966499934599 \tabularnewline
26 & 40194 & 39588.1769403194 & 605.823059680632 \tabularnewline
27 & 40336 & 40249.0759521239 & 86.924047876113 \tabularnewline
28 & 40336 & 39944.712831503 & 391.287168497038 \tabularnewline
29 & 41298 & 41285.8124895172 & 12.1875104827632 \tabularnewline
30 & 41440 & 41871.2504317826 & -431.250431782602 \tabularnewline
31 & 38790 & 39742.533550029 & -952.533550029017 \tabularnewline
32 & 38790 & 38921.2692539992 & -131.269253999228 \tabularnewline
33 & 39823 & 39272.9166984585 & 550.083301541497 \tabularnewline
34 & 39310 & 39309.3564189815 & 0.643581018477562 \tabularnewline
35 & 38427 & 38968.9434752157 & -541.943475215725 \tabularnewline
36 & 38790 & 38930.127616567 & -140.127616567042 \tabularnewline
37 & 39674 & 39605.6352857082 & 68.3647142917544 \tabularnewline
38 & 39232 & 39274.6588013103 & -42.658801310281 \tabularnewline
39 & 39161 & 39316.3217189422 & -155.321718942207 \tabularnewline
40 & 38206 & 39078.8358907664 & -872.835890766364 \tabularnewline
41 & 39602 & 39593.0967870514 & 8.90321294861496 \tabularnewline
42 & 39894 & 39724.8279108187 & 169.17208918128 \tabularnewline
43 & 37023 & 37414.5248799699 & -391.524879969897 \tabularnewline
44 & 36952 & 37255.78285811 & -303.782858110004 \tabularnewline
45 & 38427 & 37897.1513534661 & 529.848646533937 \tabularnewline
46 & 37615 & 37486.3566602755 & 128.643339724476 \tabularnewline
47 & 36218 & 36765.5721638635 & -547.572163863544 \tabularnewline
48 & 36810 & 36900.3244624685 & -90.3244624685394 \tabularnewline
49 & 37465 & 37610.7583128351 & -145.758312835096 \tabularnewline
50 & 37615 & 37068.0540249301 & 546.945975069932 \tabularnewline
51 & 37173 & 37155.7891934462 & 17.2108065538414 \tabularnewline
52 & 36290 & 36457.025166931 & -167.025166931046 \tabularnewline
53 & 38128 & 37711.2520728646 & 416.747927135402 \tabularnewline
54 & 38128 & 38069.5124760409 & 58.4875239591056 \tabularnewline
55 & 34893 & 35457.5813009921 & -564.581300992111 \tabularnewline
56 & 34673 & 35288.1419483177 & -615.141948317694 \tabularnewline
57 & 35556 & 36304.4557624052 & -748.455762405218 \tabularnewline
58 & 33939 & 35174.8818033119 & -1235.88180331194 \tabularnewline
59 & 32314 & 33493.3003343526 & -1179.30033435262 \tabularnewline
60 & 32835 & 33492.4717619583 & -657.471761958281 \tabularnewline
61 & 33939 & 33685.4828434683 & 253.517156531736 \tabularnewline
62 & 33055 & 33527.2249462162 & -472.224946216244 \tabularnewline
63 & 32464 & 32717.4924603234 & -253.492460323443 \tabularnewline
64 & 31210 & 31634.1672510939 & -424.167251093932 \tabularnewline
65 & 32906 & 32678.3410131006 & 227.658986899442 \tabularnewline
66 & 32977 & 32420.2557273731 & 556.744272626893 \tabularnewline
67 & 29743 & 29711.5613085925 & 31.4386914075294 \tabularnewline
68 & 29664 & 29453.2700008764 & 210.729999123581 \tabularnewline
69 & 30256 & 30253.1323346433 & 2.86766535674178 \tabularnewline
70 & 28418 & 29021.295799086 & -603.295799086049 \tabularnewline
71 & 26430 & 27605.2830880492 & -1175.28308804918 \tabularnewline
72 & 27235 & 27677.9087969249 & -442.908796924927 \tabularnewline
73 & 28339 & 28225.0494709376 & 113.9505290624 \tabularnewline
74 & 27164 & 27467.7628642708 & -303.762864270771 \tabularnewline
75 & 27093 & 26773.1394543937 & 319.860545606283 \tabularnewline
76 & 25910 & 25797.9540614891 & 112.045938510895 \tabularnewline
77 & 27826 & 27046.2497287315 & 779.750271268498 \tabularnewline
78 & 28197 & 27100.603834049 & 1096.39616595095 \tabularnewline
79 & 24585 & 24680.2295416902 & -95.2295416901688 \tabularnewline
80 & 23780 & 24458.4456869544 & -678.445686954401 \tabularnewline
81 & 24293 & 24607.3585868653 & -314.35858686535 \tabularnewline
82 & 22305 & 23036.3557347449 & -731.355734744873 \tabularnewline
83 & 20246 & 21355.2697533615 & -1109.26975336147 \tabularnewline
84 & 20909 & 21592.8416731022 & -683.841673102244 \tabularnewline
85 & 22156 & 22021.2944490707 & 134.705550929324 \tabularnewline
86 & 20688 & 21029.0935100169 & -341.093510016901 \tabularnewline
87 & 20909 & 20585.2054375982 & 323.794562401821 \tabularnewline
88 & 20026 & 19557.6948800828 & 468.305119917197 \tabularnewline
89 & 21864 & 20775.8479936849 & 1088.15200631506 \tabularnewline
90 & 22084 & 20954.2723730514 & 1129.7276269486 \tabularnewline
91 & 17668 & 18455.5015219131 & -787.501521913109 \tabularnewline
92 & 17375 & 17582.4876007648 & -207.487600764838 \tabularnewline
93 & 18180 & 17787.7546832738 & 392.245316726166 \tabularnewline
94 & 16050 & 16469.5883751761 & -419.588375176096 \tabularnewline
95 & 14134 & 14946.1496322225 & -812.149632222452 \tabularnewline
96 & 14797 & 15182.3258065362 & -385.325806536215 \tabularnewline
97 & 16414 & 15776.8885618527 & 637.111438147278 \tabularnewline
98 & 14504 & 14872.7822673852 & -368.782267385204 \tabularnewline
99 & 14355 & 14705.8564366211 & -350.856436621089 \tabularnewline
100 & 12880 & 13705.5454379092 & -825.545437909152 \tabularnewline
101 & 14504 & 14177.3815718689 & 326.618428131127 \tabularnewline
102 & 15017 & 13879.554077947 & 1137.44592205297 \tabularnewline
103 & 10451 & 11302.1343591694 & -851.134359169406 \tabularnewline
104 & 10451 & 10622.1054633261 & -171.105463326136 \tabularnewline
105 & 11113 & 10682.6976351068 & 430.302364893183 \tabularnewline
106 & 9347 & 9355.38486507017 & -8.38486507017114 \tabularnewline
107 & 7359 & 8134.20070495267 & -775.200704952675 \tabularnewline
108 & 8392 & 8031.73655467569 & 360.263445324314 \tabularnewline
109 & 10230 & 8612.8709811667 & 1617.1290188333 \tabularnewline
110 & 8242 & 7896.05242031985 & 345.947579680145 \tabularnewline
111 & 9055 & 7775.24896453454 & 1279.75103546546 \tabularnewline
112 & 7950 & 7359.01346894979 & 590.986531050207 \tabularnewline
113 & 9717 & 8368.48434011843 & 1348.51565988157 \tabularnewline
114 & 10308 & 8879.13579525759 & 1428.86420474241 \tabularnewline
115 & 5592 & 6684.18405539476 & -1092.18405539476 \tabularnewline
116 & 5229 & 6375.11187712161 & -1146.11187712161 \tabularnewline
117 & 5963 & 6241.76973713998 & -278.769737139983 \tabularnewline
118 & 4196 & 5074.91882447864 & -878.918824478645 \tabularnewline
119 & 2800 & 3750.72318685183 & -950.723186851829 \tabularnewline
120 & 3384 & 3648.41090745557 & -264.410907455574 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296349&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]40936.2155920221[/C][C]-80.2155920221485[/C][/ROW]
[ROW][C]14[/C][C]40414[/C][C]40502.5500693451[/C][C]-88.5500693451177[/C][/ROW]
[ROW][C]15[/C][C]40856[/C][C]40923.0183224605[/C][C]-67.0183224605134[/C][/ROW]
[ROW][C]16[/C][C]40486[/C][C]40518.3200236421[/C][C]-32.3200236421399[/C][/ROW]
[ROW][C]17[/C][C]41661[/C][C]41693.5069329309[/C][C]-32.5069329309481[/C][/ROW]
[ROW][C]18[/C][C]42181[/C][C]42237.4909121196[/C][C]-56.4909121196033[/C][/ROW]
[ROW][C]19[/C][C]39973[/C][C]40502.1461266788[/C][C]-529.146126678788[/C][/ROW]
[ROW][C]20[/C][C]39381[/C][C]39556.7861062892[/C][C]-175.786106289248[/C][/ROW]
[ROW][C]21[/C][C]39894[/C][C]39499.1999830729[/C][C]394.800016927125[/C][/ROW]
[ROW][C]22[/C][C]39823[/C][C]39558.0842473275[/C][C]264.915752672518[/C][/ROW]
[ROW][C]23[/C][C]39381[/C][C]39680.3980540831[/C][C]-299.398054083118[/C][/ROW]
[ROW][C]24[/C][C]39453[/C][C]39676.2643451359[/C][C]-223.264345135882[/C][/ROW]
[ROW][C]25[/C][C]40336[/C][C]39866.0335000654[/C][C]469.966499934599[/C][/ROW]
[ROW][C]26[/C][C]40194[/C][C]39588.1769403194[/C][C]605.823059680632[/C][/ROW]
[ROW][C]27[/C][C]40336[/C][C]40249.0759521239[/C][C]86.924047876113[/C][/ROW]
[ROW][C]28[/C][C]40336[/C][C]39944.712831503[/C][C]391.287168497038[/C][/ROW]
[ROW][C]29[/C][C]41298[/C][C]41285.8124895172[/C][C]12.1875104827632[/C][/ROW]
[ROW][C]30[/C][C]41440[/C][C]41871.2504317826[/C][C]-431.250431782602[/C][/ROW]
[ROW][C]31[/C][C]38790[/C][C]39742.533550029[/C][C]-952.533550029017[/C][/ROW]
[ROW][C]32[/C][C]38790[/C][C]38921.2692539992[/C][C]-131.269253999228[/C][/ROW]
[ROW][C]33[/C][C]39823[/C][C]39272.9166984585[/C][C]550.083301541497[/C][/ROW]
[ROW][C]34[/C][C]39310[/C][C]39309.3564189815[/C][C]0.643581018477562[/C][/ROW]
[ROW][C]35[/C][C]38427[/C][C]38968.9434752157[/C][C]-541.943475215725[/C][/ROW]
[ROW][C]36[/C][C]38790[/C][C]38930.127616567[/C][C]-140.127616567042[/C][/ROW]
[ROW][C]37[/C][C]39674[/C][C]39605.6352857082[/C][C]68.3647142917544[/C][/ROW]
[ROW][C]38[/C][C]39232[/C][C]39274.6588013103[/C][C]-42.658801310281[/C][/ROW]
[ROW][C]39[/C][C]39161[/C][C]39316.3217189422[/C][C]-155.321718942207[/C][/ROW]
[ROW][C]40[/C][C]38206[/C][C]39078.8358907664[/C][C]-872.835890766364[/C][/ROW]
[ROW][C]41[/C][C]39602[/C][C]39593.0967870514[/C][C]8.90321294861496[/C][/ROW]
[ROW][C]42[/C][C]39894[/C][C]39724.8279108187[/C][C]169.17208918128[/C][/ROW]
[ROW][C]43[/C][C]37023[/C][C]37414.5248799699[/C][C]-391.524879969897[/C][/ROW]
[ROW][C]44[/C][C]36952[/C][C]37255.78285811[/C][C]-303.782858110004[/C][/ROW]
[ROW][C]45[/C][C]38427[/C][C]37897.1513534661[/C][C]529.848646533937[/C][/ROW]
[ROW][C]46[/C][C]37615[/C][C]37486.3566602755[/C][C]128.643339724476[/C][/ROW]
[ROW][C]47[/C][C]36218[/C][C]36765.5721638635[/C][C]-547.572163863544[/C][/ROW]
[ROW][C]48[/C][C]36810[/C][C]36900.3244624685[/C][C]-90.3244624685394[/C][/ROW]
[ROW][C]49[/C][C]37465[/C][C]37610.7583128351[/C][C]-145.758312835096[/C][/ROW]
[ROW][C]50[/C][C]37615[/C][C]37068.0540249301[/C][C]546.945975069932[/C][/ROW]
[ROW][C]51[/C][C]37173[/C][C]37155.7891934462[/C][C]17.2108065538414[/C][/ROW]
[ROW][C]52[/C][C]36290[/C][C]36457.025166931[/C][C]-167.025166931046[/C][/ROW]
[ROW][C]53[/C][C]38128[/C][C]37711.2520728646[/C][C]416.747927135402[/C][/ROW]
[ROW][C]54[/C][C]38128[/C][C]38069.5124760409[/C][C]58.4875239591056[/C][/ROW]
[ROW][C]55[/C][C]34893[/C][C]35457.5813009921[/C][C]-564.581300992111[/C][/ROW]
[ROW][C]56[/C][C]34673[/C][C]35288.1419483177[/C][C]-615.141948317694[/C][/ROW]
[ROW][C]57[/C][C]35556[/C][C]36304.4557624052[/C][C]-748.455762405218[/C][/ROW]
[ROW][C]58[/C][C]33939[/C][C]35174.8818033119[/C][C]-1235.88180331194[/C][/ROW]
[ROW][C]59[/C][C]32314[/C][C]33493.3003343526[/C][C]-1179.30033435262[/C][/ROW]
[ROW][C]60[/C][C]32835[/C][C]33492.4717619583[/C][C]-657.471761958281[/C][/ROW]
[ROW][C]61[/C][C]33939[/C][C]33685.4828434683[/C][C]253.517156531736[/C][/ROW]
[ROW][C]62[/C][C]33055[/C][C]33527.2249462162[/C][C]-472.224946216244[/C][/ROW]
[ROW][C]63[/C][C]32464[/C][C]32717.4924603234[/C][C]-253.492460323443[/C][/ROW]
[ROW][C]64[/C][C]31210[/C][C]31634.1672510939[/C][C]-424.167251093932[/C][/ROW]
[ROW][C]65[/C][C]32906[/C][C]32678.3410131006[/C][C]227.658986899442[/C][/ROW]
[ROW][C]66[/C][C]32977[/C][C]32420.2557273731[/C][C]556.744272626893[/C][/ROW]
[ROW][C]67[/C][C]29743[/C][C]29711.5613085925[/C][C]31.4386914075294[/C][/ROW]
[ROW][C]68[/C][C]29664[/C][C]29453.2700008764[/C][C]210.729999123581[/C][/ROW]
[ROW][C]69[/C][C]30256[/C][C]30253.1323346433[/C][C]2.86766535674178[/C][/ROW]
[ROW][C]70[/C][C]28418[/C][C]29021.295799086[/C][C]-603.295799086049[/C][/ROW]
[ROW][C]71[/C][C]26430[/C][C]27605.2830880492[/C][C]-1175.28308804918[/C][/ROW]
[ROW][C]72[/C][C]27235[/C][C]27677.9087969249[/C][C]-442.908796924927[/C][/ROW]
[ROW][C]73[/C][C]28339[/C][C]28225.0494709376[/C][C]113.9505290624[/C][/ROW]
[ROW][C]74[/C][C]27164[/C][C]27467.7628642708[/C][C]-303.762864270771[/C][/ROW]
[ROW][C]75[/C][C]27093[/C][C]26773.1394543937[/C][C]319.860545606283[/C][/ROW]
[ROW][C]76[/C][C]25910[/C][C]25797.9540614891[/C][C]112.045938510895[/C][/ROW]
[ROW][C]77[/C][C]27826[/C][C]27046.2497287315[/C][C]779.750271268498[/C][/ROW]
[ROW][C]78[/C][C]28197[/C][C]27100.603834049[/C][C]1096.39616595095[/C][/ROW]
[ROW][C]79[/C][C]24585[/C][C]24680.2295416902[/C][C]-95.2295416901688[/C][/ROW]
[ROW][C]80[/C][C]23780[/C][C]24458.4456869544[/C][C]-678.445686954401[/C][/ROW]
[ROW][C]81[/C][C]24293[/C][C]24607.3585868653[/C][C]-314.35858686535[/C][/ROW]
[ROW][C]82[/C][C]22305[/C][C]23036.3557347449[/C][C]-731.355734744873[/C][/ROW]
[ROW][C]83[/C][C]20246[/C][C]21355.2697533615[/C][C]-1109.26975336147[/C][/ROW]
[ROW][C]84[/C][C]20909[/C][C]21592.8416731022[/C][C]-683.841673102244[/C][/ROW]
[ROW][C]85[/C][C]22156[/C][C]22021.2944490707[/C][C]134.705550929324[/C][/ROW]
[ROW][C]86[/C][C]20688[/C][C]21029.0935100169[/C][C]-341.093510016901[/C][/ROW]
[ROW][C]87[/C][C]20909[/C][C]20585.2054375982[/C][C]323.794562401821[/C][/ROW]
[ROW][C]88[/C][C]20026[/C][C]19557.6948800828[/C][C]468.305119917197[/C][/ROW]
[ROW][C]89[/C][C]21864[/C][C]20775.8479936849[/C][C]1088.15200631506[/C][/ROW]
[ROW][C]90[/C][C]22084[/C][C]20954.2723730514[/C][C]1129.7276269486[/C][/ROW]
[ROW][C]91[/C][C]17668[/C][C]18455.5015219131[/C][C]-787.501521913109[/C][/ROW]
[ROW][C]92[/C][C]17375[/C][C]17582.4876007648[/C][C]-207.487600764838[/C][/ROW]
[ROW][C]93[/C][C]18180[/C][C]17787.7546832738[/C][C]392.245316726166[/C][/ROW]
[ROW][C]94[/C][C]16050[/C][C]16469.5883751761[/C][C]-419.588375176096[/C][/ROW]
[ROW][C]95[/C][C]14134[/C][C]14946.1496322225[/C][C]-812.149632222452[/C][/ROW]
[ROW][C]96[/C][C]14797[/C][C]15182.3258065362[/C][C]-385.325806536215[/C][/ROW]
[ROW][C]97[/C][C]16414[/C][C]15776.8885618527[/C][C]637.111438147278[/C][/ROW]
[ROW][C]98[/C][C]14504[/C][C]14872.7822673852[/C][C]-368.782267385204[/C][/ROW]
[ROW][C]99[/C][C]14355[/C][C]14705.8564366211[/C][C]-350.856436621089[/C][/ROW]
[ROW][C]100[/C][C]12880[/C][C]13705.5454379092[/C][C]-825.545437909152[/C][/ROW]
[ROW][C]101[/C][C]14504[/C][C]14177.3815718689[/C][C]326.618428131127[/C][/ROW]
[ROW][C]102[/C][C]15017[/C][C]13879.554077947[/C][C]1137.44592205297[/C][/ROW]
[ROW][C]103[/C][C]10451[/C][C]11302.1343591694[/C][C]-851.134359169406[/C][/ROW]
[ROW][C]104[/C][C]10451[/C][C]10622.1054633261[/C][C]-171.105463326136[/C][/ROW]
[ROW][C]105[/C][C]11113[/C][C]10682.6976351068[/C][C]430.302364893183[/C][/ROW]
[ROW][C]106[/C][C]9347[/C][C]9355.38486507017[/C][C]-8.38486507017114[/C][/ROW]
[ROW][C]107[/C][C]7359[/C][C]8134.20070495267[/C][C]-775.200704952675[/C][/ROW]
[ROW][C]108[/C][C]8392[/C][C]8031.73655467569[/C][C]360.263445324314[/C][/ROW]
[ROW][C]109[/C][C]10230[/C][C]8612.8709811667[/C][C]1617.1290188333[/C][/ROW]
[ROW][C]110[/C][C]8242[/C][C]7896.05242031985[/C][C]345.947579680145[/C][/ROW]
[ROW][C]111[/C][C]9055[/C][C]7775.24896453454[/C][C]1279.75103546546[/C][/ROW]
[ROW][C]112[/C][C]7950[/C][C]7359.01346894979[/C][C]590.986531050207[/C][/ROW]
[ROW][C]113[/C][C]9717[/C][C]8368.48434011843[/C][C]1348.51565988157[/C][/ROW]
[ROW][C]114[/C][C]10308[/C][C]8879.13579525759[/C][C]1428.86420474241[/C][/ROW]
[ROW][C]115[/C][C]5592[/C][C]6684.18405539476[/C][C]-1092.18405539476[/C][/ROW]
[ROW][C]116[/C][C]5229[/C][C]6375.11187712161[/C][C]-1146.11187712161[/C][/ROW]
[ROW][C]117[/C][C]5963[/C][C]6241.76973713998[/C][C]-278.769737139983[/C][/ROW]
[ROW][C]118[/C][C]4196[/C][C]5074.91882447864[/C][C]-878.918824478645[/C][/ROW]
[ROW][C]119[/C][C]2800[/C][C]3750.72318685183[/C][C]-950.723186851829[/C][/ROW]
[ROW][C]120[/C][C]3384[/C][C]3648.41090745557[/C][C]-264.410907455574[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296349&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296349&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
134085640936.2155920221-80.2155920221485
144041440502.5500693451-88.5500693451177
154085640923.0183224605-67.0183224605134
164048640518.3200236421-32.3200236421399
174166141693.5069329309-32.5069329309481
184218142237.4909121196-56.4909121196033
193997340502.1461266788-529.146126678788
203938139556.7861062892-175.786106289248
213989439499.1999830729394.800016927125
223982339558.0842473275264.915752672518
233938139680.3980540831-299.398054083118
243945339676.2643451359-223.264345135882
254033639866.0335000654469.966499934599
264019439588.1769403194605.823059680632
274033640249.075952123986.924047876113
284033639944.712831503391.287168497038
294129841285.812489517212.1875104827632
304144041871.2504317826-431.250431782602
313879039742.533550029-952.533550029017
323879038921.2692539992-131.269253999228
333982339272.9166984585550.083301541497
343931039309.35641898150.643581018477562
353842738968.9434752157-541.943475215725
363879038930.127616567-140.127616567042
373967439605.635285708268.3647142917544
383923239274.6588013103-42.658801310281
393916139316.3217189422-155.321718942207
403820639078.8358907664-872.835890766364
413960239593.09678705148.90321294861496
423989439724.8279108187169.17208918128
433702337414.5248799699-391.524879969897
443695237255.78285811-303.782858110004
453842737897.1513534661529.848646533937
463761537486.3566602755128.643339724476
473621836765.5721638635-547.572163863544
483681036900.3244624685-90.3244624685394
493746537610.7583128351-145.758312835096
503761537068.0540249301546.945975069932
513717337155.789193446217.2108065538414
523629036457.025166931-167.025166931046
533812837711.2520728646416.747927135402
543812838069.512476040958.4875239591056
553489335457.5813009921-564.581300992111
563467335288.1419483177-615.141948317694
573555636304.4557624052-748.455762405218
583393935174.8818033119-1235.88180331194
593231433493.3003343526-1179.30033435262
603283533492.4717619583-657.471761958281
613393933685.4828434683253.517156531736
623305533527.2249462162-472.224946216244
633246432717.4924603234-253.492460323443
643121031634.1672510939-424.167251093932
653290632678.3410131006227.658986899442
663297732420.2557273731556.744272626893
672974329711.561308592531.4386914075294
682966429453.2700008764210.729999123581
693025630253.13233464332.86766535674178
702841829021.295799086-603.295799086049
712643027605.2830880492-1175.28308804918
722723527677.9087969249-442.908796924927
732833928225.0494709376113.9505290624
742716427467.7628642708-303.762864270771
752709326773.1394543937319.860545606283
762591025797.9540614891112.045938510895
772782627046.2497287315779.750271268498
782819727100.6038340491096.39616595095
792458524680.2295416902-95.2295416901688
802378024458.4456869544-678.445686954401
812429324607.3585868653-314.35858686535
822230523036.3557347449-731.355734744873
832024621355.2697533615-1109.26975336147
842090921592.8416731022-683.841673102244
852215622021.2944490707134.705550929324
862068821029.0935100169-341.093510016901
872090920585.2054375982323.794562401821
882002619557.6948800828468.305119917197
892186420775.84799368491088.15200631506
902208420954.27237305141129.7276269486
911766818455.5015219131-787.501521913109
921737517582.4876007648-207.487600764838
931818017787.7546832738392.245316726166
941605016469.5883751761-419.588375176096
951413414946.1496322225-812.149632222452
961479715182.3258065362-385.325806536215
971641415776.8885618527637.111438147278
981450414872.7822673852-368.782267385204
991435514705.8564366211-350.856436621089
1001288013705.5454379092-825.545437909152
1011450414177.3815718689326.618428131127
1021501713879.5540779471137.44592205297
1031045111302.1343591694-851.134359169406
1041045110622.1054633261-171.105463326136
1051111310682.6976351068430.302364893183
10693479355.38486507017-8.38486507017114
10773598134.20070495267-775.200704952675
10883928031.73655467569360.263445324314
109102308612.87098116671617.1290188333
11082427896.05242031985345.947579680145
11190557775.248964534541279.75103546546
11279507359.01346894979590.986531050207
11397178368.484340118431348.51565988157
114103088879.135795257591428.86420474241
11555926684.18405539476-1092.18405539476
11652296375.11187712161-1146.11187712161
11759636241.76973713998-278.769737139983
11841965074.91882447864-878.918824478645
11928003750.72318685183-950.723186851829
12033843648.41090745557-264.410907455574







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1213756.223592834152571.217906987814941.22927868049
1222626.954477245351387.44885418353866.46010030719
1232310.9584357102952.6816743352083669.2351970852
1241537.25771322662117.0331155210242957.48231093221
1251204.3991837661-481.5726244208952890.3709919531
126550.740026014481-1347.972160144042449.452212173
127-102.559393301141-1657.485665314511452.36687871222
128-554.944815582588-2267.573436514771157.6838053496
129-1240.40311752654-3360.40030435754879.59406930446
130-1439.54977809202-3413.30228415322534.202727969176
131-1503.5992514909-3346.98310706169339.784604079892
132-2621.91969092214-4865.07522234535-378.764159498926

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 3756.22359283415 & 2571.21790698781 & 4941.22927868049 \tabularnewline
122 & 2626.95447724535 & 1387.4488541835 & 3866.46010030719 \tabularnewline
123 & 2310.9584357102 & 952.681674335208 & 3669.2351970852 \tabularnewline
124 & 1537.25771322662 & 117.033115521024 & 2957.48231093221 \tabularnewline
125 & 1204.3991837661 & -481.572624420895 & 2890.3709919531 \tabularnewline
126 & 550.740026014481 & -1347.97216014404 & 2449.452212173 \tabularnewline
127 & -102.559393301141 & -1657.48566531451 & 1452.36687871222 \tabularnewline
128 & -554.944815582588 & -2267.57343651477 & 1157.6838053496 \tabularnewline
129 & -1240.40311752654 & -3360.40030435754 & 879.59406930446 \tabularnewline
130 & -1439.54977809202 & -3413.30228415322 & 534.202727969176 \tabularnewline
131 & -1503.5992514909 & -3346.98310706169 & 339.784604079892 \tabularnewline
132 & -2621.91969092214 & -4865.07522234535 & -378.764159498926 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296349&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]3756.22359283415[/C][C]2571.21790698781[/C][C]4941.22927868049[/C][/ROW]
[ROW][C]122[/C][C]2626.95447724535[/C][C]1387.4488541835[/C][C]3866.46010030719[/C][/ROW]
[ROW][C]123[/C][C]2310.9584357102[/C][C]952.681674335208[/C][C]3669.2351970852[/C][/ROW]
[ROW][C]124[/C][C]1537.25771322662[/C][C]117.033115521024[/C][C]2957.48231093221[/C][/ROW]
[ROW][C]125[/C][C]1204.3991837661[/C][C]-481.572624420895[/C][C]2890.3709919531[/C][/ROW]
[ROW][C]126[/C][C]550.740026014481[/C][C]-1347.97216014404[/C][C]2449.452212173[/C][/ROW]
[ROW][C]127[/C][C]-102.559393301141[/C][C]-1657.48566531451[/C][C]1452.36687871222[/C][/ROW]
[ROW][C]128[/C][C]-554.944815582588[/C][C]-2267.57343651477[/C][C]1157.6838053496[/C][/ROW]
[ROW][C]129[/C][C]-1240.40311752654[/C][C]-3360.40030435754[/C][C]879.59406930446[/C][/ROW]
[ROW][C]130[/C][C]-1439.54977809202[/C][C]-3413.30228415322[/C][C]534.202727969176[/C][/ROW]
[ROW][C]131[/C][C]-1503.5992514909[/C][C]-3346.98310706169[/C][C]339.784604079892[/C][/ROW]
[ROW][C]132[/C][C]-2621.91969092214[/C][C]-4865.07522234535[/C][C]-378.764159498926[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296349&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296349&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
1213756.223592834152571.217906987814941.22927868049
1222626.954477245351387.44885418353866.46010030719
1232310.9584357102952.6816743352083669.2351970852
1241537.25771322662117.0331155210242957.48231093221
1251204.3991837661-481.5726244208952890.3709919531
126550.740026014481-1347.972160144042449.452212173
127-102.559393301141-1657.485665314511452.36687871222
128-554.944815582588-2267.573436514771157.6838053496
129-1240.40311752654-3360.40030435754879.59406930446
130-1439.54977809202-3413.30228415322534.202727969176
131-1503.5992514909-3346.98310706169339.784604079892
132-2621.91969092214-4865.07522234535-378.764159498926



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')