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 computationFri, 11 Dec 2009 09:49:18 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/11/t1260550211zefiqg59ixvp6oy.htm/, Retrieved Sun, 28 Apr 2024 20:52:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66538, Retrieved Sun, 28 Apr 2024 20:52:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D    [Exponential Smoothing] [Exponential smoot...] [2009-12-03 16:44:51] [d46757a0a8c9b00540ab7e7e0c34bfc4]
-    D      [Exponential Smoothing] [Exponential Smoot...] [2009-12-04 19:32:46] [4f1a20f787b3465111b61213cdeef1a9]
-   PD          [Exponential Smoothing] [Exponential Smoot...] [2009-12-11 16:49:18] [d1818fb1d9a1b0f34f8553ada228d3d5] [Current]
Feedback Forum

Post a new message
Dataseries X:
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66538&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66538&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66538&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.230182393893731
beta0
gamma0.28444699539051

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.230182393893731 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.28444699539051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66538&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]0.230182393893731[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.28444699539051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66538&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66538&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
alpha0.230182393893731
beta0
gamma0.28444699539051







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132222821149.82959750331078.17040249674
141397113588.7596295972382.240370402844
153684536445.3424185781399.657581421903
163533835450.8049382778-112.804938277804
173502235304.5430264437-282.543026443716
183477735144.8728998077-367.872899807655
192688729732.5753717209-2845.57537172092
202397027435.850287071-3465.85028707102
212278024233.9575488456-1453.95754884561
221735120598.4935099989-3247.49350999893
232138217937.48479894493444.51520105514
242456126008.0581728100-1447.05817281004
251740919964.8424926678-2555.84249266784
261151412243.8474802573-729.847480257307
273151432055.8959657687-541.895965768697
282707130881.6624255383-3810.66242553825
292946229865.7841584855-403.784158485501
302610529671.5674365729-3566.56743657292
312239723992.4787650306-1595.47876503061
322384322126.00732408521716.99267591479
332170520805.3919757416899.60802425836
341808917695.1369369274393.863063072622
352076417338.28043804363425.71956195636
362531623895.22882828541420.77117171457
371770418518.8460800047-814.846080004656
381554811769.68596066573778.31403933433
392802933877.5975507525-5848.59755075249
402938330701.9994781931-1318.99947819307
413643831032.37825024495405.6217497551
423203431392.211465989641.788534010993
432267926563.4959835361-3884.49598353610
442431924811.3793141501-492.379314150086
451800422654.0412966401-4650.04129664013
461753718095.0421221875-558.042122187544
472036618151.41728828102214.58271171902
482278223925.1751122384-1143.17511223840
491916917686.55554392281482.44445607718
501380712453.61120137961353.38879862038
512974330846.6773732998-1103.67737329980
522559129769.2538182288-4178.25381822879
532909630777.7198476437-1681.71984764368
542648228636.2333948486-2154.23339484863
552240522810.3158587468-405.315858746832
562704422608.86203588934435.13796411073
571797020741.2948231539-2771.29482315392
581873017567.71883724111162.28116275894
591968418613.55369896371070.44630103632
601978523317.8696718011-3532.86967180106
611847917306.65780886081172.34219113921
621069812203.4019613282-1505.40196132819
633195627777.52958049394178.47041950614
642950627291.57733177932214.42266822073
653450630305.17207372964200.8279262704
662716529329.6346858415-2164.63468584151
672673623677.13895265253058.86104734754
682369125363.6832163915-1672.68321639146
691815720424.4120690273-2267.41206902729
701732818189.8409635505-861.840963550465
711820518742.3652604285-537.365260428542
722099521954.7512370020-959.75123700203
731738217561.6668823415-179.666882341469
74936711655.7105238571-2288.71052385711
753112427670.20162988883453.79837011123
762655126652.8408876847-101.840887684688
773065129367.23926598851283.76073401151
782585926578.4534003276-719.45340032757
792510022657.5180933472442.48190665300
802577823162.78726039262615.21273960745
812041819228.27680877731189.7231912227
821868818088.3098553626599.6901446374
832042419067.57607743081356.42392256924
842477622776.42852306241999.57147693764
851981418918.4361508756895.56384912437
861273812178.6161757851559.38382421489
873156632900.2593318825-1334.25933188250
883011129706.9363832271404.063616772899
893001933207.3254338703-3188.32543387033
903193428654.50172339663279.49827660344
912582625967.3458825070-141.345882507041
922683525900.6731709862934.32682901384
932020520910.5442576052-705.544257605234
941778919128.1665817947-1339.16658179469
952052019847.8475332951672.15246670493
962251823590.1985439608-1072.19854396078
971557218844.7977293402-3272.79772934022
981150911516.4325405584-7.43254055842954
992544730202.2039985014-4755.20399850137
1002409026846.3398832316-2756.33988323155
1012778628492.0808521020-706.080852102026
1022619526167.478807974027.5211920259644
1032051622528.9946074653-2012.99460746532
1042275922231.5700946494527.429905350604
1051902817623.0212087041404.97879129598
1061697116406.9627957891564.037204210872
1072003617844.04968835892191.95031164107
1082248521263.1646706431221.83532935697
1091873016871.88108725621858.11891274379

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 22228 & 21149.8295975033 & 1078.17040249674 \tabularnewline
14 & 13971 & 13588.7596295972 & 382.240370402844 \tabularnewline
15 & 36845 & 36445.3424185781 & 399.657581421903 \tabularnewline
16 & 35338 & 35450.8049382778 & -112.804938277804 \tabularnewline
17 & 35022 & 35304.5430264437 & -282.543026443716 \tabularnewline
18 & 34777 & 35144.8728998077 & -367.872899807655 \tabularnewline
19 & 26887 & 29732.5753717209 & -2845.57537172092 \tabularnewline
20 & 23970 & 27435.850287071 & -3465.85028707102 \tabularnewline
21 & 22780 & 24233.9575488456 & -1453.95754884561 \tabularnewline
22 & 17351 & 20598.4935099989 & -3247.49350999893 \tabularnewline
23 & 21382 & 17937.4847989449 & 3444.51520105514 \tabularnewline
24 & 24561 & 26008.0581728100 & -1447.05817281004 \tabularnewline
25 & 17409 & 19964.8424926678 & -2555.84249266784 \tabularnewline
26 & 11514 & 12243.8474802573 & -729.847480257307 \tabularnewline
27 & 31514 & 32055.8959657687 & -541.895965768697 \tabularnewline
28 & 27071 & 30881.6624255383 & -3810.66242553825 \tabularnewline
29 & 29462 & 29865.7841584855 & -403.784158485501 \tabularnewline
30 & 26105 & 29671.5674365729 & -3566.56743657292 \tabularnewline
31 & 22397 & 23992.4787650306 & -1595.47876503061 \tabularnewline
32 & 23843 & 22126.0073240852 & 1716.99267591479 \tabularnewline
33 & 21705 & 20805.3919757416 & 899.60802425836 \tabularnewline
34 & 18089 & 17695.1369369274 & 393.863063072622 \tabularnewline
35 & 20764 & 17338.2804380436 & 3425.71956195636 \tabularnewline
36 & 25316 & 23895.2288282854 & 1420.77117171457 \tabularnewline
37 & 17704 & 18518.8460800047 & -814.846080004656 \tabularnewline
38 & 15548 & 11769.6859606657 & 3778.31403933433 \tabularnewline
39 & 28029 & 33877.5975507525 & -5848.59755075249 \tabularnewline
40 & 29383 & 30701.9994781931 & -1318.99947819307 \tabularnewline
41 & 36438 & 31032.3782502449 & 5405.6217497551 \tabularnewline
42 & 32034 & 31392.211465989 & 641.788534010993 \tabularnewline
43 & 22679 & 26563.4959835361 & -3884.49598353610 \tabularnewline
44 & 24319 & 24811.3793141501 & -492.379314150086 \tabularnewline
45 & 18004 & 22654.0412966401 & -4650.04129664013 \tabularnewline
46 & 17537 & 18095.0421221875 & -558.042122187544 \tabularnewline
47 & 20366 & 18151.4172882810 & 2214.58271171902 \tabularnewline
48 & 22782 & 23925.1751122384 & -1143.17511223840 \tabularnewline
49 & 19169 & 17686.5555439228 & 1482.44445607718 \tabularnewline
50 & 13807 & 12453.6112013796 & 1353.38879862038 \tabularnewline
51 & 29743 & 30846.6773732998 & -1103.67737329980 \tabularnewline
52 & 25591 & 29769.2538182288 & -4178.25381822879 \tabularnewline
53 & 29096 & 30777.7198476437 & -1681.71984764368 \tabularnewline
54 & 26482 & 28636.2333948486 & -2154.23339484863 \tabularnewline
55 & 22405 & 22810.3158587468 & -405.315858746832 \tabularnewline
56 & 27044 & 22608.8620358893 & 4435.13796411073 \tabularnewline
57 & 17970 & 20741.2948231539 & -2771.29482315392 \tabularnewline
58 & 18730 & 17567.7188372411 & 1162.28116275894 \tabularnewline
59 & 19684 & 18613.5536989637 & 1070.44630103632 \tabularnewline
60 & 19785 & 23317.8696718011 & -3532.86967180106 \tabularnewline
61 & 18479 & 17306.6578088608 & 1172.34219113921 \tabularnewline
62 & 10698 & 12203.4019613282 & -1505.40196132819 \tabularnewline
63 & 31956 & 27777.5295804939 & 4178.47041950614 \tabularnewline
64 & 29506 & 27291.5773317793 & 2214.42266822073 \tabularnewline
65 & 34506 & 30305.1720737296 & 4200.8279262704 \tabularnewline
66 & 27165 & 29329.6346858415 & -2164.63468584151 \tabularnewline
67 & 26736 & 23677.1389526525 & 3058.86104734754 \tabularnewline
68 & 23691 & 25363.6832163915 & -1672.68321639146 \tabularnewline
69 & 18157 & 20424.4120690273 & -2267.41206902729 \tabularnewline
70 & 17328 & 18189.8409635505 & -861.840963550465 \tabularnewline
71 & 18205 & 18742.3652604285 & -537.365260428542 \tabularnewline
72 & 20995 & 21954.7512370020 & -959.75123700203 \tabularnewline
73 & 17382 & 17561.6668823415 & -179.666882341469 \tabularnewline
74 & 9367 & 11655.7105238571 & -2288.71052385711 \tabularnewline
75 & 31124 & 27670.2016298888 & 3453.79837011123 \tabularnewline
76 & 26551 & 26652.8408876847 & -101.840887684688 \tabularnewline
77 & 30651 & 29367.2392659885 & 1283.76073401151 \tabularnewline
78 & 25859 & 26578.4534003276 & -719.45340032757 \tabularnewline
79 & 25100 & 22657.518093347 & 2442.48190665300 \tabularnewline
80 & 25778 & 23162.7872603926 & 2615.21273960745 \tabularnewline
81 & 20418 & 19228.2768087773 & 1189.7231912227 \tabularnewline
82 & 18688 & 18088.3098553626 & 599.6901446374 \tabularnewline
83 & 20424 & 19067.5760774308 & 1356.42392256924 \tabularnewline
84 & 24776 & 22776.4285230624 & 1999.57147693764 \tabularnewline
85 & 19814 & 18918.4361508756 & 895.56384912437 \tabularnewline
86 & 12738 & 12178.6161757851 & 559.38382421489 \tabularnewline
87 & 31566 & 32900.2593318825 & -1334.25933188250 \tabularnewline
88 & 30111 & 29706.9363832271 & 404.063616772899 \tabularnewline
89 & 30019 & 33207.3254338703 & -3188.32543387033 \tabularnewline
90 & 31934 & 28654.5017233966 & 3279.49827660344 \tabularnewline
91 & 25826 & 25967.3458825070 & -141.345882507041 \tabularnewline
92 & 26835 & 25900.6731709862 & 934.32682901384 \tabularnewline
93 & 20205 & 20910.5442576052 & -705.544257605234 \tabularnewline
94 & 17789 & 19128.1665817947 & -1339.16658179469 \tabularnewline
95 & 20520 & 19847.8475332951 & 672.15246670493 \tabularnewline
96 & 22518 & 23590.1985439608 & -1072.19854396078 \tabularnewline
97 & 15572 & 18844.7977293402 & -3272.79772934022 \tabularnewline
98 & 11509 & 11516.4325405584 & -7.43254055842954 \tabularnewline
99 & 25447 & 30202.2039985014 & -4755.20399850137 \tabularnewline
100 & 24090 & 26846.3398832316 & -2756.33988323155 \tabularnewline
101 & 27786 & 28492.0808521020 & -706.080852102026 \tabularnewline
102 & 26195 & 26167.4788079740 & 27.5211920259644 \tabularnewline
103 & 20516 & 22528.9946074653 & -2012.99460746532 \tabularnewline
104 & 22759 & 22231.5700946494 & 527.429905350604 \tabularnewline
105 & 19028 & 17623.021208704 & 1404.97879129598 \tabularnewline
106 & 16971 & 16406.9627957891 & 564.037204210872 \tabularnewline
107 & 20036 & 17844.0496883589 & 2191.95031164107 \tabularnewline
108 & 22485 & 21263.164670643 & 1221.83532935697 \tabularnewline
109 & 18730 & 16871.8810872562 & 1858.11891274379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66538&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]22228[/C][C]21149.8295975033[/C][C]1078.17040249674[/C][/ROW]
[ROW][C]14[/C][C]13971[/C][C]13588.7596295972[/C][C]382.240370402844[/C][/ROW]
[ROW][C]15[/C][C]36845[/C][C]36445.3424185781[/C][C]399.657581421903[/C][/ROW]
[ROW][C]16[/C][C]35338[/C][C]35450.8049382778[/C][C]-112.804938277804[/C][/ROW]
[ROW][C]17[/C][C]35022[/C][C]35304.5430264437[/C][C]-282.543026443716[/C][/ROW]
[ROW][C]18[/C][C]34777[/C][C]35144.8728998077[/C][C]-367.872899807655[/C][/ROW]
[ROW][C]19[/C][C]26887[/C][C]29732.5753717209[/C][C]-2845.57537172092[/C][/ROW]
[ROW][C]20[/C][C]23970[/C][C]27435.850287071[/C][C]-3465.85028707102[/C][/ROW]
[ROW][C]21[/C][C]22780[/C][C]24233.9575488456[/C][C]-1453.95754884561[/C][/ROW]
[ROW][C]22[/C][C]17351[/C][C]20598.4935099989[/C][C]-3247.49350999893[/C][/ROW]
[ROW][C]23[/C][C]21382[/C][C]17937.4847989449[/C][C]3444.51520105514[/C][/ROW]
[ROW][C]24[/C][C]24561[/C][C]26008.0581728100[/C][C]-1447.05817281004[/C][/ROW]
[ROW][C]25[/C][C]17409[/C][C]19964.8424926678[/C][C]-2555.84249266784[/C][/ROW]
[ROW][C]26[/C][C]11514[/C][C]12243.8474802573[/C][C]-729.847480257307[/C][/ROW]
[ROW][C]27[/C][C]31514[/C][C]32055.8959657687[/C][C]-541.895965768697[/C][/ROW]
[ROW][C]28[/C][C]27071[/C][C]30881.6624255383[/C][C]-3810.66242553825[/C][/ROW]
[ROW][C]29[/C][C]29462[/C][C]29865.7841584855[/C][C]-403.784158485501[/C][/ROW]
[ROW][C]30[/C][C]26105[/C][C]29671.5674365729[/C][C]-3566.56743657292[/C][/ROW]
[ROW][C]31[/C][C]22397[/C][C]23992.4787650306[/C][C]-1595.47876503061[/C][/ROW]
[ROW][C]32[/C][C]23843[/C][C]22126.0073240852[/C][C]1716.99267591479[/C][/ROW]
[ROW][C]33[/C][C]21705[/C][C]20805.3919757416[/C][C]899.60802425836[/C][/ROW]
[ROW][C]34[/C][C]18089[/C][C]17695.1369369274[/C][C]393.863063072622[/C][/ROW]
[ROW][C]35[/C][C]20764[/C][C]17338.2804380436[/C][C]3425.71956195636[/C][/ROW]
[ROW][C]36[/C][C]25316[/C][C]23895.2288282854[/C][C]1420.77117171457[/C][/ROW]
[ROW][C]37[/C][C]17704[/C][C]18518.8460800047[/C][C]-814.846080004656[/C][/ROW]
[ROW][C]38[/C][C]15548[/C][C]11769.6859606657[/C][C]3778.31403933433[/C][/ROW]
[ROW][C]39[/C][C]28029[/C][C]33877.5975507525[/C][C]-5848.59755075249[/C][/ROW]
[ROW][C]40[/C][C]29383[/C][C]30701.9994781931[/C][C]-1318.99947819307[/C][/ROW]
[ROW][C]41[/C][C]36438[/C][C]31032.3782502449[/C][C]5405.6217497551[/C][/ROW]
[ROW][C]42[/C][C]32034[/C][C]31392.211465989[/C][C]641.788534010993[/C][/ROW]
[ROW][C]43[/C][C]22679[/C][C]26563.4959835361[/C][C]-3884.49598353610[/C][/ROW]
[ROW][C]44[/C][C]24319[/C][C]24811.3793141501[/C][C]-492.379314150086[/C][/ROW]
[ROW][C]45[/C][C]18004[/C][C]22654.0412966401[/C][C]-4650.04129664013[/C][/ROW]
[ROW][C]46[/C][C]17537[/C][C]18095.0421221875[/C][C]-558.042122187544[/C][/ROW]
[ROW][C]47[/C][C]20366[/C][C]18151.4172882810[/C][C]2214.58271171902[/C][/ROW]
[ROW][C]48[/C][C]22782[/C][C]23925.1751122384[/C][C]-1143.17511223840[/C][/ROW]
[ROW][C]49[/C][C]19169[/C][C]17686.5555439228[/C][C]1482.44445607718[/C][/ROW]
[ROW][C]50[/C][C]13807[/C][C]12453.6112013796[/C][C]1353.38879862038[/C][/ROW]
[ROW][C]51[/C][C]29743[/C][C]30846.6773732998[/C][C]-1103.67737329980[/C][/ROW]
[ROW][C]52[/C][C]25591[/C][C]29769.2538182288[/C][C]-4178.25381822879[/C][/ROW]
[ROW][C]53[/C][C]29096[/C][C]30777.7198476437[/C][C]-1681.71984764368[/C][/ROW]
[ROW][C]54[/C][C]26482[/C][C]28636.2333948486[/C][C]-2154.23339484863[/C][/ROW]
[ROW][C]55[/C][C]22405[/C][C]22810.3158587468[/C][C]-405.315858746832[/C][/ROW]
[ROW][C]56[/C][C]27044[/C][C]22608.8620358893[/C][C]4435.13796411073[/C][/ROW]
[ROW][C]57[/C][C]17970[/C][C]20741.2948231539[/C][C]-2771.29482315392[/C][/ROW]
[ROW][C]58[/C][C]18730[/C][C]17567.7188372411[/C][C]1162.28116275894[/C][/ROW]
[ROW][C]59[/C][C]19684[/C][C]18613.5536989637[/C][C]1070.44630103632[/C][/ROW]
[ROW][C]60[/C][C]19785[/C][C]23317.8696718011[/C][C]-3532.86967180106[/C][/ROW]
[ROW][C]61[/C][C]18479[/C][C]17306.6578088608[/C][C]1172.34219113921[/C][/ROW]
[ROW][C]62[/C][C]10698[/C][C]12203.4019613282[/C][C]-1505.40196132819[/C][/ROW]
[ROW][C]63[/C][C]31956[/C][C]27777.5295804939[/C][C]4178.47041950614[/C][/ROW]
[ROW][C]64[/C][C]29506[/C][C]27291.5773317793[/C][C]2214.42266822073[/C][/ROW]
[ROW][C]65[/C][C]34506[/C][C]30305.1720737296[/C][C]4200.8279262704[/C][/ROW]
[ROW][C]66[/C][C]27165[/C][C]29329.6346858415[/C][C]-2164.63468584151[/C][/ROW]
[ROW][C]67[/C][C]26736[/C][C]23677.1389526525[/C][C]3058.86104734754[/C][/ROW]
[ROW][C]68[/C][C]23691[/C][C]25363.6832163915[/C][C]-1672.68321639146[/C][/ROW]
[ROW][C]69[/C][C]18157[/C][C]20424.4120690273[/C][C]-2267.41206902729[/C][/ROW]
[ROW][C]70[/C][C]17328[/C][C]18189.8409635505[/C][C]-861.840963550465[/C][/ROW]
[ROW][C]71[/C][C]18205[/C][C]18742.3652604285[/C][C]-537.365260428542[/C][/ROW]
[ROW][C]72[/C][C]20995[/C][C]21954.7512370020[/C][C]-959.75123700203[/C][/ROW]
[ROW][C]73[/C][C]17382[/C][C]17561.6668823415[/C][C]-179.666882341469[/C][/ROW]
[ROW][C]74[/C][C]9367[/C][C]11655.7105238571[/C][C]-2288.71052385711[/C][/ROW]
[ROW][C]75[/C][C]31124[/C][C]27670.2016298888[/C][C]3453.79837011123[/C][/ROW]
[ROW][C]76[/C][C]26551[/C][C]26652.8408876847[/C][C]-101.840887684688[/C][/ROW]
[ROW][C]77[/C][C]30651[/C][C]29367.2392659885[/C][C]1283.76073401151[/C][/ROW]
[ROW][C]78[/C][C]25859[/C][C]26578.4534003276[/C][C]-719.45340032757[/C][/ROW]
[ROW][C]79[/C][C]25100[/C][C]22657.518093347[/C][C]2442.48190665300[/C][/ROW]
[ROW][C]80[/C][C]25778[/C][C]23162.7872603926[/C][C]2615.21273960745[/C][/ROW]
[ROW][C]81[/C][C]20418[/C][C]19228.2768087773[/C][C]1189.7231912227[/C][/ROW]
[ROW][C]82[/C][C]18688[/C][C]18088.3098553626[/C][C]599.6901446374[/C][/ROW]
[ROW][C]83[/C][C]20424[/C][C]19067.5760774308[/C][C]1356.42392256924[/C][/ROW]
[ROW][C]84[/C][C]24776[/C][C]22776.4285230624[/C][C]1999.57147693764[/C][/ROW]
[ROW][C]85[/C][C]19814[/C][C]18918.4361508756[/C][C]895.56384912437[/C][/ROW]
[ROW][C]86[/C][C]12738[/C][C]12178.6161757851[/C][C]559.38382421489[/C][/ROW]
[ROW][C]87[/C][C]31566[/C][C]32900.2593318825[/C][C]-1334.25933188250[/C][/ROW]
[ROW][C]88[/C][C]30111[/C][C]29706.9363832271[/C][C]404.063616772899[/C][/ROW]
[ROW][C]89[/C][C]30019[/C][C]33207.3254338703[/C][C]-3188.32543387033[/C][/ROW]
[ROW][C]90[/C][C]31934[/C][C]28654.5017233966[/C][C]3279.49827660344[/C][/ROW]
[ROW][C]91[/C][C]25826[/C][C]25967.3458825070[/C][C]-141.345882507041[/C][/ROW]
[ROW][C]92[/C][C]26835[/C][C]25900.6731709862[/C][C]934.32682901384[/C][/ROW]
[ROW][C]93[/C][C]20205[/C][C]20910.5442576052[/C][C]-705.544257605234[/C][/ROW]
[ROW][C]94[/C][C]17789[/C][C]19128.1665817947[/C][C]-1339.16658179469[/C][/ROW]
[ROW][C]95[/C][C]20520[/C][C]19847.8475332951[/C][C]672.15246670493[/C][/ROW]
[ROW][C]96[/C][C]22518[/C][C]23590.1985439608[/C][C]-1072.19854396078[/C][/ROW]
[ROW][C]97[/C][C]15572[/C][C]18844.7977293402[/C][C]-3272.79772934022[/C][/ROW]
[ROW][C]98[/C][C]11509[/C][C]11516.4325405584[/C][C]-7.43254055842954[/C][/ROW]
[ROW][C]99[/C][C]25447[/C][C]30202.2039985014[/C][C]-4755.20399850137[/C][/ROW]
[ROW][C]100[/C][C]24090[/C][C]26846.3398832316[/C][C]-2756.33988323155[/C][/ROW]
[ROW][C]101[/C][C]27786[/C][C]28492.0808521020[/C][C]-706.080852102026[/C][/ROW]
[ROW][C]102[/C][C]26195[/C][C]26167.4788079740[/C][C]27.5211920259644[/C][/ROW]
[ROW][C]103[/C][C]20516[/C][C]22528.9946074653[/C][C]-2012.99460746532[/C][/ROW]
[ROW][C]104[/C][C]22759[/C][C]22231.5700946494[/C][C]527.429905350604[/C][/ROW]
[ROW][C]105[/C][C]19028[/C][C]17623.021208704[/C][C]1404.97879129598[/C][/ROW]
[ROW][C]106[/C][C]16971[/C][C]16406.9627957891[/C][C]564.037204210872[/C][/ROW]
[ROW][C]107[/C][C]20036[/C][C]17844.0496883589[/C][C]2191.95031164107[/C][/ROW]
[ROW][C]108[/C][C]22485[/C][C]21263.164670643[/C][C]1221.83532935697[/C][/ROW]
[ROW][C]109[/C][C]18730[/C][C]16871.8810872562[/C][C]1858.11891274379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66538&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66538&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
132222821149.82959750331078.17040249674
141397113588.7596295972382.240370402844
153684536445.3424185781399.657581421903
163533835450.8049382778-112.804938277804
173502235304.5430264437-282.543026443716
183477735144.8728998077-367.872899807655
192688729732.5753717209-2845.57537172092
202397027435.850287071-3465.85028707102
212278024233.9575488456-1453.95754884561
221735120598.4935099989-3247.49350999893
232138217937.48479894493444.51520105514
242456126008.0581728100-1447.05817281004
251740919964.8424926678-2555.84249266784
261151412243.8474802573-729.847480257307
273151432055.8959657687-541.895965768697
282707130881.6624255383-3810.66242553825
292946229865.7841584855-403.784158485501
302610529671.5674365729-3566.56743657292
312239723992.4787650306-1595.47876503061
322384322126.00732408521716.99267591479
332170520805.3919757416899.60802425836
341808917695.1369369274393.863063072622
352076417338.28043804363425.71956195636
362531623895.22882828541420.77117171457
371770418518.8460800047-814.846080004656
381554811769.68596066573778.31403933433
392802933877.5975507525-5848.59755075249
402938330701.9994781931-1318.99947819307
413643831032.37825024495405.6217497551
423203431392.211465989641.788534010993
432267926563.4959835361-3884.49598353610
442431924811.3793141501-492.379314150086
451800422654.0412966401-4650.04129664013
461753718095.0421221875-558.042122187544
472036618151.41728828102214.58271171902
482278223925.1751122384-1143.17511223840
491916917686.55554392281482.44445607718
501380712453.61120137961353.38879862038
512974330846.6773732998-1103.67737329980
522559129769.2538182288-4178.25381822879
532909630777.7198476437-1681.71984764368
542648228636.2333948486-2154.23339484863
552240522810.3158587468-405.315858746832
562704422608.86203588934435.13796411073
571797020741.2948231539-2771.29482315392
581873017567.71883724111162.28116275894
591968418613.55369896371070.44630103632
601978523317.8696718011-3532.86967180106
611847917306.65780886081172.34219113921
621069812203.4019613282-1505.40196132819
633195627777.52958049394178.47041950614
642950627291.57733177932214.42266822073
653450630305.17207372964200.8279262704
662716529329.6346858415-2164.63468584151
672673623677.13895265253058.86104734754
682369125363.6832163915-1672.68321639146
691815720424.4120690273-2267.41206902729
701732818189.8409635505-861.840963550465
711820518742.3652604285-537.365260428542
722099521954.7512370020-959.75123700203
731738217561.6668823415-179.666882341469
74936711655.7105238571-2288.71052385711
753112427670.20162988883453.79837011123
762655126652.8408876847-101.840887684688
773065129367.23926598851283.76073401151
782585926578.4534003276-719.45340032757
792510022657.5180933472442.48190665300
802577823162.78726039262615.21273960745
812041819228.27680877731189.7231912227
821868818088.3098553626599.6901446374
832042419067.57607743081356.42392256924
842477622776.42852306241999.57147693764
851981418918.4361508756895.56384912437
861273812178.6161757851559.38382421489
873156632900.2593318825-1334.25933188250
883011129706.9363832271404.063616772899
893001933207.3254338703-3188.32543387033
903193428654.50172339663279.49827660344
912582625967.3458825070-141.345882507041
922683525900.6731709862934.32682901384
932020520910.5442576052-705.544257605234
941778919128.1665817947-1339.16658179469
952052019847.8475332951672.15246670493
962251823590.1985439608-1072.19854396078
971557218844.7977293402-3272.79772934022
981150911516.4325405584-7.43254055842954
992544730202.2039985014-4755.20399850137
1002409026846.3398832316-2756.33988323155
1012778628492.0808521020-706.080852102026
1022619526167.478807974027.5211920259644
1032051622528.9946074653-2012.99460746532
1042275922231.5700946494527.429905350604
1051902817623.0212087041404.97879129598
1061697116406.9627957891564.037204210872
1072003617844.04968835892191.95031164107
1082248521263.1646706431221.83532935697
1091873016871.88108725621858.11891274379







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
11011464.89785034179473.6149233101713456.1807773733
11128999.738893427225737.272570188232262.2052166662
11227101.446613943523826.811308482230376.0819194048
11329990.829159127226311.336833006833670.3214852476
11427862.497782309524236.429321818531488.5662428005
11523499.797545590120144.86491451726854.7301766633
11624286.416346299320696.852620603927875.9800719946
11719377.310425688516164.635743589222589.9851077878
11817547.88765766614378.332494224620717.4428211074
11919287.55367525515739.326858273222835.7804922368
12022052.616549101817974.477657739226130.7554404645
12117459.456828260314524.210110767520394.7035457531

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
110 & 11464.8978503417 & 9473.61492331017 & 13456.1807773733 \tabularnewline
111 & 28999.7388934272 & 25737.2725701882 & 32262.2052166662 \tabularnewline
112 & 27101.4466139435 & 23826.8113084822 & 30376.0819194048 \tabularnewline
113 & 29990.8291591272 & 26311.3368330068 & 33670.3214852476 \tabularnewline
114 & 27862.4977823095 & 24236.4293218185 & 31488.5662428005 \tabularnewline
115 & 23499.7975455901 & 20144.864914517 & 26854.7301766633 \tabularnewline
116 & 24286.4163462993 & 20696.8526206039 & 27875.9800719946 \tabularnewline
117 & 19377.3104256885 & 16164.6357435892 & 22589.9851077878 \tabularnewline
118 & 17547.887657666 & 14378.3324942246 & 20717.4428211074 \tabularnewline
119 & 19287.553675255 & 15739.3268582732 & 22835.7804922368 \tabularnewline
120 & 22052.6165491018 & 17974.4776577392 & 26130.7554404645 \tabularnewline
121 & 17459.4568282603 & 14524.2101107675 & 20394.7035457531 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66538&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]110[/C][C]11464.8978503417[/C][C]9473.61492331017[/C][C]13456.1807773733[/C][/ROW]
[ROW][C]111[/C][C]28999.7388934272[/C][C]25737.2725701882[/C][C]32262.2052166662[/C][/ROW]
[ROW][C]112[/C][C]27101.4466139435[/C][C]23826.8113084822[/C][C]30376.0819194048[/C][/ROW]
[ROW][C]113[/C][C]29990.8291591272[/C][C]26311.3368330068[/C][C]33670.3214852476[/C][/ROW]
[ROW][C]114[/C][C]27862.4977823095[/C][C]24236.4293218185[/C][C]31488.5662428005[/C][/ROW]
[ROW][C]115[/C][C]23499.7975455901[/C][C]20144.864914517[/C][C]26854.7301766633[/C][/ROW]
[ROW][C]116[/C][C]24286.4163462993[/C][C]20696.8526206039[/C][C]27875.9800719946[/C][/ROW]
[ROW][C]117[/C][C]19377.3104256885[/C][C]16164.6357435892[/C][C]22589.9851077878[/C][/ROW]
[ROW][C]118[/C][C]17547.887657666[/C][C]14378.3324942246[/C][C]20717.4428211074[/C][/ROW]
[ROW][C]119[/C][C]19287.553675255[/C][C]15739.3268582732[/C][C]22835.7804922368[/C][/ROW]
[ROW][C]120[/C][C]22052.6165491018[/C][C]17974.4776577392[/C][C]26130.7554404645[/C][/ROW]
[ROW][C]121[/C][C]17459.4568282603[/C][C]14524.2101107675[/C][C]20394.7035457531[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66538&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66538&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
11011464.89785034179473.6149233101713456.1807773733
11128999.738893427225737.272570188232262.2052166662
11227101.446613943523826.811308482230376.0819194048
11329990.829159127226311.336833006833670.3214852476
11427862.497782309524236.429321818531488.5662428005
11523499.797545590120144.86491451726854.7301766633
11624286.416346299320696.852620603927875.9800719946
11719377.310425688516164.635743589222589.9851077878
11817547.88765766614378.332494224620717.4428211074
11919287.55367525515739.326858273222835.7804922368
12022052.616549101817974.477657739226130.7554404645
12117459.456828260314524.210110767520394.7035457531



Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')