Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 31 Jul 2016 12:42:30 +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/Jul/31/t1469965392jssi6wupa8fh7hh.htm/, Retrieved Sat, 04 May 2024 08:30:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295973, Retrieved Sat, 04 May 2024 08:30:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-07-31 11:42:30] [1b498ae19017f51f703ef2d779b672b0] [Current]
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Dataseries X:
36439.00
36368.00
36290.00
36147.00
37615.00
37543.00
36439.00
35705.00
35777.00
35777.00
35848.00
35998.00
35998.00
35335.00
35043.00
35335.00
36368.00
36218.00
34822.00
33640.00
33419.00
32977.00
33276.00
33640.00
33497.00
33198.00
32614.00
33198.00
33718.00
33568.00
31873.00
31139.00
30405.00
29814.00
29743.00
30184.00
29593.00
29372.00
29151.00
30405.00
30548.00
29814.00
27826.00
26943.00
25547.00
24955.00
25247.00
25689.00
25689.00
25326.00
25247.00
26430.00
27385.00
26943.00
25468.00
24735.00
23189.00
22234.00
22968.00
23702.00
23702.00
22747.00
22676.00
23922.00
24735.00
24442.00
22968.00
22013.00
19947.00
19142.00
19434.00
20688.00
20759.00
18921.00
19584.00
21201.00
21935.00
21493.00
19506.00
18109.00
16492.00
15238.00
15751.00
16855.00
16563.00
14946.00
15459.00
17076.00
17960.00
17447.00
15459.00
14576.00
13251.00
11854.00
12075.00
13179.00
13322.00
11997.00
12218.00
14063.00
14504.00
13764.00
11042.00
9646.00
7801.00
5963.00
6554.00
7359.00
7217.00
5813.00
6625.00
8613.00
9496.00
9055.00
7288.00
5892.00
4417.00
2721.00
3021.00
3534.00




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=295973&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=295973&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295973&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
alpha0.400851431467812
beta0.0368982697381642
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.400851431467812 \tabularnewline
beta & 0.0368982697381642 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295973&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]0.400851431467812[/C][/ROW]
[ROW][C]beta[/C][C]0.0368982697381642[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295973&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295973&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
alpha0.400851431467812
beta0.0368982697381642
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133599836579.1669337607-581.166933760695
143533535689.5399635774-354.539963577423
153504335287.3878359669-244.387835966867
163533535540.400673298-205.400673298027
173636836555.9202125424-187.920212542405
183621836374.2506767933-156.250676793279
193482234828.9231924432-6.92319244318787
203364033989.3931115887-349.393111588659
213341933846.9990295774-427.999029577353
223297733585.5569038623-608.556903862256
233327633313.7368984259-37.7368984259301
243364033370.5477532208269.452246779198
253349733071.6925407071425.307459292933
263319832693.4246131305504.575386869452
273261432686.4836480022-72.483648002235
283319833019.1422701799178.857729820054
293371834192.2278358069-474.227835806865
303356833903.5936417379-335.593641737854
313187332362.0204146131-489.020414613133
323113931103.094836208435.9051637915545
333040531052.7945626115-647.7945626115
342981430576.5582222426-762.558222242627
352974330564.2268973073-821.226897307257
363018430458.6525568823-274.65255688228
372959329994.650834072-401.65083407201
382937229279.735695739992.2643042600612
392915128703.0237082764447.976291723644
403040529343.84680853881061.15319146122
413054830441.3028195307106.697180469288
422981430439.1843588223-625.184358822255
432782628655.9082205167-829.908220516667
442694327536.1090821427-593.109082142666
452554726775.9896551224-1228.98965512236
462495525941.3834710794-986.383471079364
472524725744.2332080407-497.233208040703
482568926040.8565226955-351.856522695507
492568925413.5198284096275.4801715904
502532625219.6806137977106.319386202264
512524724815.653281691431.346718308989
522643025770.874819488659.125180512034
532738526083.05045274771301.94954725228
542694326086.9575644457856.042435554275
552546824762.094442191705.905557808965
562473524409.8432620726325.156737927366
572318923660.4438269231-471.443826923132
582223423309.6815303352-1075.68153033517
592296823403.3123192759-435.31231927585
602370223846.2774255055-144.277425505523
612370223715.5057187785-13.5057187785205
622274723337.6880702449-590.688070244945
632267622871.9091334832-195.909133483172
642392223725.7950076703196.204992329742
652473524244.336398048490.663601952045
662444223650.6549409273791.345059072744
672296822203.7277376147764.272262385271
682201321641.4353603078371.564639692209
691994720428.7304535021-481.73045350211
701914219707.0383888274-565.038388827445
711943420391.8120859967-957.812085996688
722068820794.7519806711-106.751980671099
732075920752.97553950016.02446049994251
741892120033.0589335077-1112.05893350768
751958419582.99784394571.00215605431731
762120120741.8418373988459.158162601194
772193521537.1934345671397.806565432933
782149321080.0501408637412.949859136261
791950619453.232488367352.7675116326827
801810918347.9289684234-238.928968423352
811649216347.7134138563144.286586143684
821523815804.763713431-566.763713430959
831575116231.2068625282-480.206862528245
841685517320.2619148858-465.261914885774
851656317181.7984514443-618.798451444312
861494615511.7333931377-565.733393137671
871545915925.8479587668-466.847958766775
881707617143.0285592194-67.0285592193904
891796017654.287531154305.712468845984
901744717131.5279284103315.472071589735
911545915210.6183189077248.381681092289
921457613972.6356571597603.364342840348
931325112515.7939280094735.206071990557
941185411768.566802311585.4331976884896
951207512502.8273168976-427.827316897592
961317913617.1306472556-438.13064725565
971332213393.2505044508-71.2505044507816
981199711978.262218177118.7377818228542
991221812698.3522493297-480.352249329699
1001406314161.9134101885-98.913410188452
1011450414895.4895010294-391.489501029384
1021376414100.5617742348-336.56177423482
1031104211869.9011316109-827.901131610923
104964610389.072093848-743.072093847957
10578018427.48318139917-626.483181399168
10659636680.95111793983-717.951117939832
10765546709.61257729871-155.612577298711
10873597854.84460351437-495.844603514368
10972177754.77607335783-537.776073357829
11058136126.92706908075-313.927069080748
11166256329.94885794446295.051142055539
11286138259.64890752692353.35109247308
11394968932.68744005946563.312559940538
11490558500.99368345722554.006316542782
11572886293.69573765859994.304262341409
11658925581.83974998483310.160250015169
11744174115.58689235372301.413107646278
11827212703.2170416161117.7829583838902
11930213391.62147039297-370.621470392974
12035344271.53578539834-737.535785398335

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 35998 & 36579.1669337607 & -581.166933760695 \tabularnewline
14 & 35335 & 35689.5399635774 & -354.539963577423 \tabularnewline
15 & 35043 & 35287.3878359669 & -244.387835966867 \tabularnewline
16 & 35335 & 35540.400673298 & -205.400673298027 \tabularnewline
17 & 36368 & 36555.9202125424 & -187.920212542405 \tabularnewline
18 & 36218 & 36374.2506767933 & -156.250676793279 \tabularnewline
19 & 34822 & 34828.9231924432 & -6.92319244318787 \tabularnewline
20 & 33640 & 33989.3931115887 & -349.393111588659 \tabularnewline
21 & 33419 & 33846.9990295774 & -427.999029577353 \tabularnewline
22 & 32977 & 33585.5569038623 & -608.556903862256 \tabularnewline
23 & 33276 & 33313.7368984259 & -37.7368984259301 \tabularnewline
24 & 33640 & 33370.5477532208 & 269.452246779198 \tabularnewline
25 & 33497 & 33071.6925407071 & 425.307459292933 \tabularnewline
26 & 33198 & 32693.4246131305 & 504.575386869452 \tabularnewline
27 & 32614 & 32686.4836480022 & -72.483648002235 \tabularnewline
28 & 33198 & 33019.1422701799 & 178.857729820054 \tabularnewline
29 & 33718 & 34192.2278358069 & -474.227835806865 \tabularnewline
30 & 33568 & 33903.5936417379 & -335.593641737854 \tabularnewline
31 & 31873 & 32362.0204146131 & -489.020414613133 \tabularnewline
32 & 31139 & 31103.0948362084 & 35.9051637915545 \tabularnewline
33 & 30405 & 31052.7945626115 & -647.7945626115 \tabularnewline
34 & 29814 & 30576.5582222426 & -762.558222242627 \tabularnewline
35 & 29743 & 30564.2268973073 & -821.226897307257 \tabularnewline
36 & 30184 & 30458.6525568823 & -274.65255688228 \tabularnewline
37 & 29593 & 29994.650834072 & -401.65083407201 \tabularnewline
38 & 29372 & 29279.7356957399 & 92.2643042600612 \tabularnewline
39 & 29151 & 28703.0237082764 & 447.976291723644 \tabularnewline
40 & 30405 & 29343.8468085388 & 1061.15319146122 \tabularnewline
41 & 30548 & 30441.3028195307 & 106.697180469288 \tabularnewline
42 & 29814 & 30439.1843588223 & -625.184358822255 \tabularnewline
43 & 27826 & 28655.9082205167 & -829.908220516667 \tabularnewline
44 & 26943 & 27536.1090821427 & -593.109082142666 \tabularnewline
45 & 25547 & 26775.9896551224 & -1228.98965512236 \tabularnewline
46 & 24955 & 25941.3834710794 & -986.383471079364 \tabularnewline
47 & 25247 & 25744.2332080407 & -497.233208040703 \tabularnewline
48 & 25689 & 26040.8565226955 & -351.856522695507 \tabularnewline
49 & 25689 & 25413.5198284096 & 275.4801715904 \tabularnewline
50 & 25326 & 25219.6806137977 & 106.319386202264 \tabularnewline
51 & 25247 & 24815.653281691 & 431.346718308989 \tabularnewline
52 & 26430 & 25770.874819488 & 659.125180512034 \tabularnewline
53 & 27385 & 26083.0504527477 & 1301.94954725228 \tabularnewline
54 & 26943 & 26086.9575644457 & 856.042435554275 \tabularnewline
55 & 25468 & 24762.094442191 & 705.905557808965 \tabularnewline
56 & 24735 & 24409.8432620726 & 325.156737927366 \tabularnewline
57 & 23189 & 23660.4438269231 & -471.443826923132 \tabularnewline
58 & 22234 & 23309.6815303352 & -1075.68153033517 \tabularnewline
59 & 22968 & 23403.3123192759 & -435.31231927585 \tabularnewline
60 & 23702 & 23846.2774255055 & -144.277425505523 \tabularnewline
61 & 23702 & 23715.5057187785 & -13.5057187785205 \tabularnewline
62 & 22747 & 23337.6880702449 & -590.688070244945 \tabularnewline
63 & 22676 & 22871.9091334832 & -195.909133483172 \tabularnewline
64 & 23922 & 23725.7950076703 & 196.204992329742 \tabularnewline
65 & 24735 & 24244.336398048 & 490.663601952045 \tabularnewline
66 & 24442 & 23650.6549409273 & 791.345059072744 \tabularnewline
67 & 22968 & 22203.7277376147 & 764.272262385271 \tabularnewline
68 & 22013 & 21641.4353603078 & 371.564639692209 \tabularnewline
69 & 19947 & 20428.7304535021 & -481.73045350211 \tabularnewline
70 & 19142 & 19707.0383888274 & -565.038388827445 \tabularnewline
71 & 19434 & 20391.8120859967 & -957.812085996688 \tabularnewline
72 & 20688 & 20794.7519806711 & -106.751980671099 \tabularnewline
73 & 20759 & 20752.9755395001 & 6.02446049994251 \tabularnewline
74 & 18921 & 20033.0589335077 & -1112.05893350768 \tabularnewline
75 & 19584 & 19582.9978439457 & 1.00215605431731 \tabularnewline
76 & 21201 & 20741.8418373988 & 459.158162601194 \tabularnewline
77 & 21935 & 21537.1934345671 & 397.806565432933 \tabularnewline
78 & 21493 & 21080.0501408637 & 412.949859136261 \tabularnewline
79 & 19506 & 19453.2324883673 & 52.7675116326827 \tabularnewline
80 & 18109 & 18347.9289684234 & -238.928968423352 \tabularnewline
81 & 16492 & 16347.7134138563 & 144.286586143684 \tabularnewline
82 & 15238 & 15804.763713431 & -566.763713430959 \tabularnewline
83 & 15751 & 16231.2068625282 & -480.206862528245 \tabularnewline
84 & 16855 & 17320.2619148858 & -465.261914885774 \tabularnewline
85 & 16563 & 17181.7984514443 & -618.798451444312 \tabularnewline
86 & 14946 & 15511.7333931377 & -565.733393137671 \tabularnewline
87 & 15459 & 15925.8479587668 & -466.847958766775 \tabularnewline
88 & 17076 & 17143.0285592194 & -67.0285592193904 \tabularnewline
89 & 17960 & 17654.287531154 & 305.712468845984 \tabularnewline
90 & 17447 & 17131.5279284103 & 315.472071589735 \tabularnewline
91 & 15459 & 15210.6183189077 & 248.381681092289 \tabularnewline
92 & 14576 & 13972.6356571597 & 603.364342840348 \tabularnewline
93 & 13251 & 12515.7939280094 & 735.206071990557 \tabularnewline
94 & 11854 & 11768.5668023115 & 85.4331976884896 \tabularnewline
95 & 12075 & 12502.8273168976 & -427.827316897592 \tabularnewline
96 & 13179 & 13617.1306472556 & -438.13064725565 \tabularnewline
97 & 13322 & 13393.2505044508 & -71.2505044507816 \tabularnewline
98 & 11997 & 11978.2622181771 & 18.7377818228542 \tabularnewline
99 & 12218 & 12698.3522493297 & -480.352249329699 \tabularnewline
100 & 14063 & 14161.9134101885 & -98.913410188452 \tabularnewline
101 & 14504 & 14895.4895010294 & -391.489501029384 \tabularnewline
102 & 13764 & 14100.5617742348 & -336.56177423482 \tabularnewline
103 & 11042 & 11869.9011316109 & -827.901131610923 \tabularnewline
104 & 9646 & 10389.072093848 & -743.072093847957 \tabularnewline
105 & 7801 & 8427.48318139917 & -626.483181399168 \tabularnewline
106 & 5963 & 6680.95111793983 & -717.951117939832 \tabularnewline
107 & 6554 & 6709.61257729871 & -155.612577298711 \tabularnewline
108 & 7359 & 7854.84460351437 & -495.844603514368 \tabularnewline
109 & 7217 & 7754.77607335783 & -537.776073357829 \tabularnewline
110 & 5813 & 6126.92706908075 & -313.927069080748 \tabularnewline
111 & 6625 & 6329.94885794446 & 295.051142055539 \tabularnewline
112 & 8613 & 8259.64890752692 & 353.35109247308 \tabularnewline
113 & 9496 & 8932.68744005946 & 563.312559940538 \tabularnewline
114 & 9055 & 8500.99368345722 & 554.006316542782 \tabularnewline
115 & 7288 & 6293.69573765859 & 994.304262341409 \tabularnewline
116 & 5892 & 5581.83974998483 & 310.160250015169 \tabularnewline
117 & 4417 & 4115.58689235372 & 301.413107646278 \tabularnewline
118 & 2721 & 2703.21704161611 & 17.7829583838902 \tabularnewline
119 & 3021 & 3391.62147039297 & -370.621470392974 \tabularnewline
120 & 3534 & 4271.53578539834 & -737.535785398335 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295973&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]35998[/C][C]36579.1669337607[/C][C]-581.166933760695[/C][/ROW]
[ROW][C]14[/C][C]35335[/C][C]35689.5399635774[/C][C]-354.539963577423[/C][/ROW]
[ROW][C]15[/C][C]35043[/C][C]35287.3878359669[/C][C]-244.387835966867[/C][/ROW]
[ROW][C]16[/C][C]35335[/C][C]35540.400673298[/C][C]-205.400673298027[/C][/ROW]
[ROW][C]17[/C][C]36368[/C][C]36555.9202125424[/C][C]-187.920212542405[/C][/ROW]
[ROW][C]18[/C][C]36218[/C][C]36374.2506767933[/C][C]-156.250676793279[/C][/ROW]
[ROW][C]19[/C][C]34822[/C][C]34828.9231924432[/C][C]-6.92319244318787[/C][/ROW]
[ROW][C]20[/C][C]33640[/C][C]33989.3931115887[/C][C]-349.393111588659[/C][/ROW]
[ROW][C]21[/C][C]33419[/C][C]33846.9990295774[/C][C]-427.999029577353[/C][/ROW]
[ROW][C]22[/C][C]32977[/C][C]33585.5569038623[/C][C]-608.556903862256[/C][/ROW]
[ROW][C]23[/C][C]33276[/C][C]33313.7368984259[/C][C]-37.7368984259301[/C][/ROW]
[ROW][C]24[/C][C]33640[/C][C]33370.5477532208[/C][C]269.452246779198[/C][/ROW]
[ROW][C]25[/C][C]33497[/C][C]33071.6925407071[/C][C]425.307459292933[/C][/ROW]
[ROW][C]26[/C][C]33198[/C][C]32693.4246131305[/C][C]504.575386869452[/C][/ROW]
[ROW][C]27[/C][C]32614[/C][C]32686.4836480022[/C][C]-72.483648002235[/C][/ROW]
[ROW][C]28[/C][C]33198[/C][C]33019.1422701799[/C][C]178.857729820054[/C][/ROW]
[ROW][C]29[/C][C]33718[/C][C]34192.2278358069[/C][C]-474.227835806865[/C][/ROW]
[ROW][C]30[/C][C]33568[/C][C]33903.5936417379[/C][C]-335.593641737854[/C][/ROW]
[ROW][C]31[/C][C]31873[/C][C]32362.0204146131[/C][C]-489.020414613133[/C][/ROW]
[ROW][C]32[/C][C]31139[/C][C]31103.0948362084[/C][C]35.9051637915545[/C][/ROW]
[ROW][C]33[/C][C]30405[/C][C]31052.7945626115[/C][C]-647.7945626115[/C][/ROW]
[ROW][C]34[/C][C]29814[/C][C]30576.5582222426[/C][C]-762.558222242627[/C][/ROW]
[ROW][C]35[/C][C]29743[/C][C]30564.2268973073[/C][C]-821.226897307257[/C][/ROW]
[ROW][C]36[/C][C]30184[/C][C]30458.6525568823[/C][C]-274.65255688228[/C][/ROW]
[ROW][C]37[/C][C]29593[/C][C]29994.650834072[/C][C]-401.65083407201[/C][/ROW]
[ROW][C]38[/C][C]29372[/C][C]29279.7356957399[/C][C]92.2643042600612[/C][/ROW]
[ROW][C]39[/C][C]29151[/C][C]28703.0237082764[/C][C]447.976291723644[/C][/ROW]
[ROW][C]40[/C][C]30405[/C][C]29343.8468085388[/C][C]1061.15319146122[/C][/ROW]
[ROW][C]41[/C][C]30548[/C][C]30441.3028195307[/C][C]106.697180469288[/C][/ROW]
[ROW][C]42[/C][C]29814[/C][C]30439.1843588223[/C][C]-625.184358822255[/C][/ROW]
[ROW][C]43[/C][C]27826[/C][C]28655.9082205167[/C][C]-829.908220516667[/C][/ROW]
[ROW][C]44[/C][C]26943[/C][C]27536.1090821427[/C][C]-593.109082142666[/C][/ROW]
[ROW][C]45[/C][C]25547[/C][C]26775.9896551224[/C][C]-1228.98965512236[/C][/ROW]
[ROW][C]46[/C][C]24955[/C][C]25941.3834710794[/C][C]-986.383471079364[/C][/ROW]
[ROW][C]47[/C][C]25247[/C][C]25744.2332080407[/C][C]-497.233208040703[/C][/ROW]
[ROW][C]48[/C][C]25689[/C][C]26040.8565226955[/C][C]-351.856522695507[/C][/ROW]
[ROW][C]49[/C][C]25689[/C][C]25413.5198284096[/C][C]275.4801715904[/C][/ROW]
[ROW][C]50[/C][C]25326[/C][C]25219.6806137977[/C][C]106.319386202264[/C][/ROW]
[ROW][C]51[/C][C]25247[/C][C]24815.653281691[/C][C]431.346718308989[/C][/ROW]
[ROW][C]52[/C][C]26430[/C][C]25770.874819488[/C][C]659.125180512034[/C][/ROW]
[ROW][C]53[/C][C]27385[/C][C]26083.0504527477[/C][C]1301.94954725228[/C][/ROW]
[ROW][C]54[/C][C]26943[/C][C]26086.9575644457[/C][C]856.042435554275[/C][/ROW]
[ROW][C]55[/C][C]25468[/C][C]24762.094442191[/C][C]705.905557808965[/C][/ROW]
[ROW][C]56[/C][C]24735[/C][C]24409.8432620726[/C][C]325.156737927366[/C][/ROW]
[ROW][C]57[/C][C]23189[/C][C]23660.4438269231[/C][C]-471.443826923132[/C][/ROW]
[ROW][C]58[/C][C]22234[/C][C]23309.6815303352[/C][C]-1075.68153033517[/C][/ROW]
[ROW][C]59[/C][C]22968[/C][C]23403.3123192759[/C][C]-435.31231927585[/C][/ROW]
[ROW][C]60[/C][C]23702[/C][C]23846.2774255055[/C][C]-144.277425505523[/C][/ROW]
[ROW][C]61[/C][C]23702[/C][C]23715.5057187785[/C][C]-13.5057187785205[/C][/ROW]
[ROW][C]62[/C][C]22747[/C][C]23337.6880702449[/C][C]-590.688070244945[/C][/ROW]
[ROW][C]63[/C][C]22676[/C][C]22871.9091334832[/C][C]-195.909133483172[/C][/ROW]
[ROW][C]64[/C][C]23922[/C][C]23725.7950076703[/C][C]196.204992329742[/C][/ROW]
[ROW][C]65[/C][C]24735[/C][C]24244.336398048[/C][C]490.663601952045[/C][/ROW]
[ROW][C]66[/C][C]24442[/C][C]23650.6549409273[/C][C]791.345059072744[/C][/ROW]
[ROW][C]67[/C][C]22968[/C][C]22203.7277376147[/C][C]764.272262385271[/C][/ROW]
[ROW][C]68[/C][C]22013[/C][C]21641.4353603078[/C][C]371.564639692209[/C][/ROW]
[ROW][C]69[/C][C]19947[/C][C]20428.7304535021[/C][C]-481.73045350211[/C][/ROW]
[ROW][C]70[/C][C]19142[/C][C]19707.0383888274[/C][C]-565.038388827445[/C][/ROW]
[ROW][C]71[/C][C]19434[/C][C]20391.8120859967[/C][C]-957.812085996688[/C][/ROW]
[ROW][C]72[/C][C]20688[/C][C]20794.7519806711[/C][C]-106.751980671099[/C][/ROW]
[ROW][C]73[/C][C]20759[/C][C]20752.9755395001[/C][C]6.02446049994251[/C][/ROW]
[ROW][C]74[/C][C]18921[/C][C]20033.0589335077[/C][C]-1112.05893350768[/C][/ROW]
[ROW][C]75[/C][C]19584[/C][C]19582.9978439457[/C][C]1.00215605431731[/C][/ROW]
[ROW][C]76[/C][C]21201[/C][C]20741.8418373988[/C][C]459.158162601194[/C][/ROW]
[ROW][C]77[/C][C]21935[/C][C]21537.1934345671[/C][C]397.806565432933[/C][/ROW]
[ROW][C]78[/C][C]21493[/C][C]21080.0501408637[/C][C]412.949859136261[/C][/ROW]
[ROW][C]79[/C][C]19506[/C][C]19453.2324883673[/C][C]52.7675116326827[/C][/ROW]
[ROW][C]80[/C][C]18109[/C][C]18347.9289684234[/C][C]-238.928968423352[/C][/ROW]
[ROW][C]81[/C][C]16492[/C][C]16347.7134138563[/C][C]144.286586143684[/C][/ROW]
[ROW][C]82[/C][C]15238[/C][C]15804.763713431[/C][C]-566.763713430959[/C][/ROW]
[ROW][C]83[/C][C]15751[/C][C]16231.2068625282[/C][C]-480.206862528245[/C][/ROW]
[ROW][C]84[/C][C]16855[/C][C]17320.2619148858[/C][C]-465.261914885774[/C][/ROW]
[ROW][C]85[/C][C]16563[/C][C]17181.7984514443[/C][C]-618.798451444312[/C][/ROW]
[ROW][C]86[/C][C]14946[/C][C]15511.7333931377[/C][C]-565.733393137671[/C][/ROW]
[ROW][C]87[/C][C]15459[/C][C]15925.8479587668[/C][C]-466.847958766775[/C][/ROW]
[ROW][C]88[/C][C]17076[/C][C]17143.0285592194[/C][C]-67.0285592193904[/C][/ROW]
[ROW][C]89[/C][C]17960[/C][C]17654.287531154[/C][C]305.712468845984[/C][/ROW]
[ROW][C]90[/C][C]17447[/C][C]17131.5279284103[/C][C]315.472071589735[/C][/ROW]
[ROW][C]91[/C][C]15459[/C][C]15210.6183189077[/C][C]248.381681092289[/C][/ROW]
[ROW][C]92[/C][C]14576[/C][C]13972.6356571597[/C][C]603.364342840348[/C][/ROW]
[ROW][C]93[/C][C]13251[/C][C]12515.7939280094[/C][C]735.206071990557[/C][/ROW]
[ROW][C]94[/C][C]11854[/C][C]11768.5668023115[/C][C]85.4331976884896[/C][/ROW]
[ROW][C]95[/C][C]12075[/C][C]12502.8273168976[/C][C]-427.827316897592[/C][/ROW]
[ROW][C]96[/C][C]13179[/C][C]13617.1306472556[/C][C]-438.13064725565[/C][/ROW]
[ROW][C]97[/C][C]13322[/C][C]13393.2505044508[/C][C]-71.2505044507816[/C][/ROW]
[ROW][C]98[/C][C]11997[/C][C]11978.2622181771[/C][C]18.7377818228542[/C][/ROW]
[ROW][C]99[/C][C]12218[/C][C]12698.3522493297[/C][C]-480.352249329699[/C][/ROW]
[ROW][C]100[/C][C]14063[/C][C]14161.9134101885[/C][C]-98.913410188452[/C][/ROW]
[ROW][C]101[/C][C]14504[/C][C]14895.4895010294[/C][C]-391.489501029384[/C][/ROW]
[ROW][C]102[/C][C]13764[/C][C]14100.5617742348[/C][C]-336.56177423482[/C][/ROW]
[ROW][C]103[/C][C]11042[/C][C]11869.9011316109[/C][C]-827.901131610923[/C][/ROW]
[ROW][C]104[/C][C]9646[/C][C]10389.072093848[/C][C]-743.072093847957[/C][/ROW]
[ROW][C]105[/C][C]7801[/C][C]8427.48318139917[/C][C]-626.483181399168[/C][/ROW]
[ROW][C]106[/C][C]5963[/C][C]6680.95111793983[/C][C]-717.951117939832[/C][/ROW]
[ROW][C]107[/C][C]6554[/C][C]6709.61257729871[/C][C]-155.612577298711[/C][/ROW]
[ROW][C]108[/C][C]7359[/C][C]7854.84460351437[/C][C]-495.844603514368[/C][/ROW]
[ROW][C]109[/C][C]7217[/C][C]7754.77607335783[/C][C]-537.776073357829[/C][/ROW]
[ROW][C]110[/C][C]5813[/C][C]6126.92706908075[/C][C]-313.927069080748[/C][/ROW]
[ROW][C]111[/C][C]6625[/C][C]6329.94885794446[/C][C]295.051142055539[/C][/ROW]
[ROW][C]112[/C][C]8613[/C][C]8259.64890752692[/C][C]353.35109247308[/C][/ROW]
[ROW][C]113[/C][C]9496[/C][C]8932.68744005946[/C][C]563.312559940538[/C][/ROW]
[ROW][C]114[/C][C]9055[/C][C]8500.99368345722[/C][C]554.006316542782[/C][/ROW]
[ROW][C]115[/C][C]7288[/C][C]6293.69573765859[/C][C]994.304262341409[/C][/ROW]
[ROW][C]116[/C][C]5892[/C][C]5581.83974998483[/C][C]310.160250015169[/C][/ROW]
[ROW][C]117[/C][C]4417[/C][C]4115.58689235372[/C][C]301.413107646278[/C][/ROW]
[ROW][C]118[/C][C]2721[/C][C]2703.21704161611[/C][C]17.7829583838902[/C][/ROW]
[ROW][C]119[/C][C]3021[/C][C]3391.62147039297[/C][C]-370.621470392974[/C][/ROW]
[ROW][C]120[/C][C]3534[/C][C]4271.53578539834[/C][C]-737.535785398335[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295973&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295973&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
133599836579.1669337607-581.166933760695
143533535689.5399635774-354.539963577423
153504335287.3878359669-244.387835966867
163533535540.400673298-205.400673298027
173636836555.9202125424-187.920212542405
183621836374.2506767933-156.250676793279
193482234828.9231924432-6.92319244318787
203364033989.3931115887-349.393111588659
213341933846.9990295774-427.999029577353
223297733585.5569038623-608.556903862256
233327633313.7368984259-37.7368984259301
243364033370.5477532208269.452246779198
253349733071.6925407071425.307459292933
263319832693.4246131305504.575386869452
273261432686.4836480022-72.483648002235
283319833019.1422701799178.857729820054
293371834192.2278358069-474.227835806865
303356833903.5936417379-335.593641737854
313187332362.0204146131-489.020414613133
323113931103.094836208435.9051637915545
333040531052.7945626115-647.7945626115
342981430576.5582222426-762.558222242627
352974330564.2268973073-821.226897307257
363018430458.6525568823-274.65255688228
372959329994.650834072-401.65083407201
382937229279.735695739992.2643042600612
392915128703.0237082764447.976291723644
403040529343.84680853881061.15319146122
413054830441.3028195307106.697180469288
422981430439.1843588223-625.184358822255
432782628655.9082205167-829.908220516667
442694327536.1090821427-593.109082142666
452554726775.9896551224-1228.98965512236
462495525941.3834710794-986.383471079364
472524725744.2332080407-497.233208040703
482568926040.8565226955-351.856522695507
492568925413.5198284096275.4801715904
502532625219.6806137977106.319386202264
512524724815.653281691431.346718308989
522643025770.874819488659.125180512034
532738526083.05045274771301.94954725228
542694326086.9575644457856.042435554275
552546824762.094442191705.905557808965
562473524409.8432620726325.156737927366
572318923660.4438269231-471.443826923132
582223423309.6815303352-1075.68153033517
592296823403.3123192759-435.31231927585
602370223846.2774255055-144.277425505523
612370223715.5057187785-13.5057187785205
622274723337.6880702449-590.688070244945
632267622871.9091334832-195.909133483172
642392223725.7950076703196.204992329742
652473524244.336398048490.663601952045
662444223650.6549409273791.345059072744
672296822203.7277376147764.272262385271
682201321641.4353603078371.564639692209
691994720428.7304535021-481.73045350211
701914219707.0383888274-565.038388827445
711943420391.8120859967-957.812085996688
722068820794.7519806711-106.751980671099
732075920752.97553950016.02446049994251
741892120033.0589335077-1112.05893350768
751958419582.99784394571.00215605431731
762120120741.8418373988459.158162601194
772193521537.1934345671397.806565432933
782149321080.0501408637412.949859136261
791950619453.232488367352.7675116326827
801810918347.9289684234-238.928968423352
811649216347.7134138563144.286586143684
821523815804.763713431-566.763713430959
831575116231.2068625282-480.206862528245
841685517320.2619148858-465.261914885774
851656317181.7984514443-618.798451444312
861494615511.7333931377-565.733393137671
871545915925.8479587668-466.847958766775
881707617143.0285592194-67.0285592193904
891796017654.287531154305.712468845984
901744717131.5279284103315.472071589735
911545915210.6183189077248.381681092289
921457613972.6356571597603.364342840348
931325112515.7939280094735.206071990557
941185411768.566802311585.4331976884896
951207512502.8273168976-427.827316897592
961317913617.1306472556-438.13064725565
971332213393.2505044508-71.2505044507816
981199711978.262218177118.7377818228542
991221812698.3522493297-480.352249329699
1001406314161.9134101885-98.913410188452
1011450414895.4895010294-391.489501029384
1021376414100.5617742348-336.56177423482
1031104211869.9011316109-827.901131610923
104964610389.072093848-743.072093847957
10578018427.48318139917-626.483181399168
10659636680.95111793983-717.951117939832
10765546709.61257729871-155.612577298711
10873597854.84460351437-495.844603514368
10972177754.77607335783-537.776073357829
11058136126.92706908075-313.927069080748
11166256329.94885794446295.051142055539
11286138259.64890752692353.35109247308
11394968932.68744005946563.312559940538
11490558500.99368345722554.006316542782
11572886293.69573765859994.304262341409
11658925581.83974998483310.160250015169
11744174115.58689235372301.413107646278
11827212703.2170416161117.7829583838902
11930213391.62147039297-370.621470392974
12035344271.53578539834-737.535785398335







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1214070.60547409483059.440593921525081.77035426809
1222821.541341935461726.510746323473916.57193754744
1233549.010630820692370.653870645414727.36739099596
1245424.746281046754163.318630636276686.17393145722
1256106.092257915584761.635285831597450.54922999957
1265458.836855035164031.228187543556886.44552252678
1273300.893235652041789.882664574914811.90380672917
1281773.48324278187178.7195547812983368.24693078243
129165.992059722326-1512.956625325291844.94074476994
130-1553.26369015644-3316.89423560285210.366855289964
131-1121.08999160526-2969.95197064577727.77198743525
132-323.356404690938-2258.042372155431611.32956277355

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 4070.6054740948 & 3059.44059392152 & 5081.77035426809 \tabularnewline
122 & 2821.54134193546 & 1726.51074632347 & 3916.57193754744 \tabularnewline
123 & 3549.01063082069 & 2370.65387064541 & 4727.36739099596 \tabularnewline
124 & 5424.74628104675 & 4163.31863063627 & 6686.17393145722 \tabularnewline
125 & 6106.09225791558 & 4761.63528583159 & 7450.54922999957 \tabularnewline
126 & 5458.83685503516 & 4031.22818754355 & 6886.44552252678 \tabularnewline
127 & 3300.89323565204 & 1789.88266457491 & 4811.90380672917 \tabularnewline
128 & 1773.48324278187 & 178.719554781298 & 3368.24693078243 \tabularnewline
129 & 165.992059722326 & -1512.95662532529 & 1844.94074476994 \tabularnewline
130 & -1553.26369015644 & -3316.89423560285 & 210.366855289964 \tabularnewline
131 & -1121.08999160526 & -2969.95197064577 & 727.77198743525 \tabularnewline
132 & -323.356404690938 & -2258.04237215543 & 1611.32956277355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295973&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]4070.6054740948[/C][C]3059.44059392152[/C][C]5081.77035426809[/C][/ROW]
[ROW][C]122[/C][C]2821.54134193546[/C][C]1726.51074632347[/C][C]3916.57193754744[/C][/ROW]
[ROW][C]123[/C][C]3549.01063082069[/C][C]2370.65387064541[/C][C]4727.36739099596[/C][/ROW]
[ROW][C]124[/C][C]5424.74628104675[/C][C]4163.31863063627[/C][C]6686.17393145722[/C][/ROW]
[ROW][C]125[/C][C]6106.09225791558[/C][C]4761.63528583159[/C][C]7450.54922999957[/C][/ROW]
[ROW][C]126[/C][C]5458.83685503516[/C][C]4031.22818754355[/C][C]6886.44552252678[/C][/ROW]
[ROW][C]127[/C][C]3300.89323565204[/C][C]1789.88266457491[/C][C]4811.90380672917[/C][/ROW]
[ROW][C]128[/C][C]1773.48324278187[/C][C]178.719554781298[/C][C]3368.24693078243[/C][/ROW]
[ROW][C]129[/C][C]165.992059722326[/C][C]-1512.95662532529[/C][C]1844.94074476994[/C][/ROW]
[ROW][C]130[/C][C]-1553.26369015644[/C][C]-3316.89423560285[/C][C]210.366855289964[/C][/ROW]
[ROW][C]131[/C][C]-1121.08999160526[/C][C]-2969.95197064577[/C][C]727.77198743525[/C][/ROW]
[ROW][C]132[/C][C]-323.356404690938[/C][C]-2258.04237215543[/C][C]1611.32956277355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295973&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295973&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
1214070.60547409483059.440593921525081.77035426809
1222821.541341935461726.510746323473916.57193754744
1233549.010630820692370.653870645414727.36739099596
1245424.746281046754163.318630636276686.17393145722
1256106.092257915584761.635285831597450.54922999957
1265458.836855035164031.228187543556886.44552252678
1273300.893235652041789.882664574914811.90380672917
1281773.48324278187178.7195547812983368.24693078243
129165.992059722326-1512.956625325291844.94074476994
130-1553.26369015644-3316.89423560285210.366855289964
131-1121.08999160526-2969.95197064577727.77198743525
132-323.356404690938-2258.042372155431611.32956277355



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')