Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 05 Jun 2009 09:48:16 -0600
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/Jun/05/t1244216931hfmc38psqc5xkkl.htm/, Retrieved Fri, 10 May 2024 06:49:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41882, Retrieved Fri, 10 May 2024 06:49:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmaandelijkse verkoop auto's
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Nick Vermeulen Ex...] [2009-06-05 15:48:16] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
14.620
16.005
16.683
15.487
15.684
15.962
12.000
13.769
14.031
16.078
15.827
13.149
15.969
16.628
16.670
16.487
16.883
16.201
12.168
14.010
16.556
17.404
16.435
13.123
16.744
17.410
16.484
17.103
17.301
17.301
12.843
13.748
16.904
17.342
15.476
15.424
15.988
19.244
18.715
17.780
17.160
17.349
11.171
13.438
16.713
18.369
17.067
14.055
15.500
18.475
19.423
18.686
19.646
19.733
12.605
16.616
19.156
21.348
20.049
18.020
20.262
21.789
20.603
21.928
21.025
19.346
11.786
19.082
20.127
20.217
20.385
16.653
13.065
20.275
21.776
20.260
22.523
23.033
14.133
20.110
19.682
22.197
17.212
11.784
15.467
17.002
15.952
18.767
20.605
19.809
14.233
19.311
20.827
23.388
20.181
14.344




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41882&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41882&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41882&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.422497061600848
beta0.0909939654833242
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.422497061600848 \tabularnewline
beta & 0.0909939654833242 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41882&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]0.422497061600848[/C][/ROW]
[ROW][C]beta[/C][C]0.0909939654833242[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41882&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41882&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
alpha0.422497061600848
beta0.0909939654833242
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
316.68317.39-0.707000000000001
415.48718.4491141865388-2.96211418653884
515.68418.4415717146605-2.75757171466052
615.96218.4144338655929-2.45243386559287
71218.4219328184999-6.42193281849994
813.76916.505440956064-2.73644095606400
914.03116.0408569708472-2.00985697084721
1016.07815.80598427019060.272015729809430
1115.82716.545653639023-0.718653639022998
1213.14916.8391396991379-3.69013969913790
1315.96915.73531537915930.233684620840727
1416.62816.29827923578910.329720764210869
1516.6716.9144940910722-0.244494091072188
1616.48717.2787053594341-0.791705359434147
1716.88317.3812846132337-0.498284613233697
1816.20117.5886768760961-1.38767687609613
1912.16817.3669547236250-5.19895472362505
2014.0115.3351067131389-1.32510671313893
2116.55614.88900479659051.66699520340947
2217.40415.77114425001861.63285574998144
2316.43516.7016345064469-0.266634506446856
2413.12316.8193450319068-3.69634503190685
2516.74415.34590812505991.39809187494006
2617.4116.07860504085981.33139495914022
2716.48416.8343077629217-0.350307762921705
2817.10316.86602855551430.236971444485693
2917.30117.15498337964860.146016620351379
3017.30117.4111236205358-0.110123620535756
3112.84317.5548116946036-4.71181169460362
3213.74815.5731559718304-1.82515597183041
3316.90414.74093626694642.16306373305364
3417.34215.67688596800721.66511403199276
3515.47616.4664681647305-0.990468164730478
3615.42416.0959964518442-0.671996451844244
3715.98815.83424341126020.153756588739805
3819.24415.92727972725033.31672027274969
3918.71517.48416916530341.23083083469664
4017.7818.2070953462707-0.427095346270672
4117.1618.2131330422129-1.05313304221290
4217.34917.9141842851612-0.565184285161223
4311.17117.7996641134734-6.62866411347339
4413.43814.8685046404258-1.43050464042579
4516.71314.07855697298482.63444302701516
4618.36915.10731807775973.26168192224026
4717.06716.52648010036720.540519899632798
4814.05516.8167392805015-2.76173928050145
4915.515.6056294691062-0.105629469106244
5018.47515.51265735685522.96234264314479
5119.42316.82978077107552.59321922892450
5218.68618.09064611872920.595353881270832
5319.64618.53030741878721.11569258121283
5419.73319.23270273826280.500297261737202
5512.60519.6943291131904-7.08932911319039
5616.61616.6768136353391-0.0608136353391231
5719.15616.62648733336102.52951266663903
5821.34817.76781259527093.58018740472914
5920.04919.49068401672110.55831598327892
6018.0219.9582879230864-1.93828792308639
6120.26219.29656715018760.965432849812373
6221.78919.89877563145551.89022436854452
6320.60320.9643748887044-0.361374888704443
6421.92821.06478713280820.863212867191827
6521.02521.7157700505258-0.690770050525792
6619.34621.6836433160837-2.33764331608373
6711.78620.8658475097668-9.07984750976678
6819.08216.85041838334032.23158161665973
6920.12717.69982727326582.42717272673416
7020.21718.7251847186361.49181528136400
7120.38519.41270875743720.972291242562768
7216.65319.9181148450569-3.26511484505695
7313.06518.50770300654-5.44270300654
7420.27515.96802357645184.30697642354823
7521.77617.71313540059064.06286459940941
7620.2619.51130623808790.748693761912065
7722.52319.93803292947022.58496707052975
7823.03321.23995793773521.79304206226475
7914.13322.2762298907614-8.14322989076142
8020.1118.8013922482941.30860775170598
8119.68219.37023724673550.311762753264453
8222.19719.5299037826972.66709621730300
8317.21220.7872274550166-3.57522745501657
8411.78419.2697392319153-7.4857392319153
8515.46715.8122844016269-0.345284401626868
8617.00215.35837640624961.64362359375035
8715.95215.80796478281270.144035217187284
8818.76715.62951886493853.13748113506152
8920.60516.83641451920893.76858548079106
9019.80918.45483197943221.35416802056776
9114.23319.1052257175672-4.8722257175672
9219.31116.93767522355852.37332477644154
9320.82717.92259024173052.90440975826947
9423.38819.24354621676054.14445378323948
9520.18121.2477493606671-1.06674936066707
9614.34421.0092236478139-6.66522364781392

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 16.683 & 17.39 & -0.707000000000001 \tabularnewline
4 & 15.487 & 18.4491141865388 & -2.96211418653884 \tabularnewline
5 & 15.684 & 18.4415717146605 & -2.75757171466052 \tabularnewline
6 & 15.962 & 18.4144338655929 & -2.45243386559287 \tabularnewline
7 & 12 & 18.4219328184999 & -6.42193281849994 \tabularnewline
8 & 13.769 & 16.505440956064 & -2.73644095606400 \tabularnewline
9 & 14.031 & 16.0408569708472 & -2.00985697084721 \tabularnewline
10 & 16.078 & 15.8059842701906 & 0.272015729809430 \tabularnewline
11 & 15.827 & 16.545653639023 & -0.718653639022998 \tabularnewline
12 & 13.149 & 16.8391396991379 & -3.69013969913790 \tabularnewline
13 & 15.969 & 15.7353153791593 & 0.233684620840727 \tabularnewline
14 & 16.628 & 16.2982792357891 & 0.329720764210869 \tabularnewline
15 & 16.67 & 16.9144940910722 & -0.244494091072188 \tabularnewline
16 & 16.487 & 17.2787053594341 & -0.791705359434147 \tabularnewline
17 & 16.883 & 17.3812846132337 & -0.498284613233697 \tabularnewline
18 & 16.201 & 17.5886768760961 & -1.38767687609613 \tabularnewline
19 & 12.168 & 17.3669547236250 & -5.19895472362505 \tabularnewline
20 & 14.01 & 15.3351067131389 & -1.32510671313893 \tabularnewline
21 & 16.556 & 14.8890047965905 & 1.66699520340947 \tabularnewline
22 & 17.404 & 15.7711442500186 & 1.63285574998144 \tabularnewline
23 & 16.435 & 16.7016345064469 & -0.266634506446856 \tabularnewline
24 & 13.123 & 16.8193450319068 & -3.69634503190685 \tabularnewline
25 & 16.744 & 15.3459081250599 & 1.39809187494006 \tabularnewline
26 & 17.41 & 16.0786050408598 & 1.33139495914022 \tabularnewline
27 & 16.484 & 16.8343077629217 & -0.350307762921705 \tabularnewline
28 & 17.103 & 16.8660285555143 & 0.236971444485693 \tabularnewline
29 & 17.301 & 17.1549833796486 & 0.146016620351379 \tabularnewline
30 & 17.301 & 17.4111236205358 & -0.110123620535756 \tabularnewline
31 & 12.843 & 17.5548116946036 & -4.71181169460362 \tabularnewline
32 & 13.748 & 15.5731559718304 & -1.82515597183041 \tabularnewline
33 & 16.904 & 14.7409362669464 & 2.16306373305364 \tabularnewline
34 & 17.342 & 15.6768859680072 & 1.66511403199276 \tabularnewline
35 & 15.476 & 16.4664681647305 & -0.990468164730478 \tabularnewline
36 & 15.424 & 16.0959964518442 & -0.671996451844244 \tabularnewline
37 & 15.988 & 15.8342434112602 & 0.153756588739805 \tabularnewline
38 & 19.244 & 15.9272797272503 & 3.31672027274969 \tabularnewline
39 & 18.715 & 17.4841691653034 & 1.23083083469664 \tabularnewline
40 & 17.78 & 18.2070953462707 & -0.427095346270672 \tabularnewline
41 & 17.16 & 18.2131330422129 & -1.05313304221290 \tabularnewline
42 & 17.349 & 17.9141842851612 & -0.565184285161223 \tabularnewline
43 & 11.171 & 17.7996641134734 & -6.62866411347339 \tabularnewline
44 & 13.438 & 14.8685046404258 & -1.43050464042579 \tabularnewline
45 & 16.713 & 14.0785569729848 & 2.63444302701516 \tabularnewline
46 & 18.369 & 15.1073180777597 & 3.26168192224026 \tabularnewline
47 & 17.067 & 16.5264801003672 & 0.540519899632798 \tabularnewline
48 & 14.055 & 16.8167392805015 & -2.76173928050145 \tabularnewline
49 & 15.5 & 15.6056294691062 & -0.105629469106244 \tabularnewline
50 & 18.475 & 15.5126573568552 & 2.96234264314479 \tabularnewline
51 & 19.423 & 16.8297807710755 & 2.59321922892450 \tabularnewline
52 & 18.686 & 18.0906461187292 & 0.595353881270832 \tabularnewline
53 & 19.646 & 18.5303074187872 & 1.11569258121283 \tabularnewline
54 & 19.733 & 19.2327027382628 & 0.500297261737202 \tabularnewline
55 & 12.605 & 19.6943291131904 & -7.08932911319039 \tabularnewline
56 & 16.616 & 16.6768136353391 & -0.0608136353391231 \tabularnewline
57 & 19.156 & 16.6264873333610 & 2.52951266663903 \tabularnewline
58 & 21.348 & 17.7678125952709 & 3.58018740472914 \tabularnewline
59 & 20.049 & 19.4906840167211 & 0.55831598327892 \tabularnewline
60 & 18.02 & 19.9582879230864 & -1.93828792308639 \tabularnewline
61 & 20.262 & 19.2965671501876 & 0.965432849812373 \tabularnewline
62 & 21.789 & 19.8987756314555 & 1.89022436854452 \tabularnewline
63 & 20.603 & 20.9643748887044 & -0.361374888704443 \tabularnewline
64 & 21.928 & 21.0647871328082 & 0.863212867191827 \tabularnewline
65 & 21.025 & 21.7157700505258 & -0.690770050525792 \tabularnewline
66 & 19.346 & 21.6836433160837 & -2.33764331608373 \tabularnewline
67 & 11.786 & 20.8658475097668 & -9.07984750976678 \tabularnewline
68 & 19.082 & 16.8504183833403 & 2.23158161665973 \tabularnewline
69 & 20.127 & 17.6998272732658 & 2.42717272673416 \tabularnewline
70 & 20.217 & 18.725184718636 & 1.49181528136400 \tabularnewline
71 & 20.385 & 19.4127087574372 & 0.972291242562768 \tabularnewline
72 & 16.653 & 19.9181148450569 & -3.26511484505695 \tabularnewline
73 & 13.065 & 18.50770300654 & -5.44270300654 \tabularnewline
74 & 20.275 & 15.9680235764518 & 4.30697642354823 \tabularnewline
75 & 21.776 & 17.7131354005906 & 4.06286459940941 \tabularnewline
76 & 20.26 & 19.5113062380879 & 0.748693761912065 \tabularnewline
77 & 22.523 & 19.9380329294702 & 2.58496707052975 \tabularnewline
78 & 23.033 & 21.2399579377352 & 1.79304206226475 \tabularnewline
79 & 14.133 & 22.2762298907614 & -8.14322989076142 \tabularnewline
80 & 20.11 & 18.801392248294 & 1.30860775170598 \tabularnewline
81 & 19.682 & 19.3702372467355 & 0.311762753264453 \tabularnewline
82 & 22.197 & 19.529903782697 & 2.66709621730300 \tabularnewline
83 & 17.212 & 20.7872274550166 & -3.57522745501657 \tabularnewline
84 & 11.784 & 19.2697392319153 & -7.4857392319153 \tabularnewline
85 & 15.467 & 15.8122844016269 & -0.345284401626868 \tabularnewline
86 & 17.002 & 15.3583764062496 & 1.64362359375035 \tabularnewline
87 & 15.952 & 15.8079647828127 & 0.144035217187284 \tabularnewline
88 & 18.767 & 15.6295188649385 & 3.13748113506152 \tabularnewline
89 & 20.605 & 16.8364145192089 & 3.76858548079106 \tabularnewline
90 & 19.809 & 18.4548319794322 & 1.35416802056776 \tabularnewline
91 & 14.233 & 19.1052257175672 & -4.8722257175672 \tabularnewline
92 & 19.311 & 16.9376752235585 & 2.37332477644154 \tabularnewline
93 & 20.827 & 17.9225902417305 & 2.90440975826947 \tabularnewline
94 & 23.388 & 19.2435462167605 & 4.14445378323948 \tabularnewline
95 & 20.181 & 21.2477493606671 & -1.06674936066707 \tabularnewline
96 & 14.344 & 21.0092236478139 & -6.66522364781392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41882&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]3[/C][C]16.683[/C][C]17.39[/C][C]-0.707000000000001[/C][/ROW]
[ROW][C]4[/C][C]15.487[/C][C]18.4491141865388[/C][C]-2.96211418653884[/C][/ROW]
[ROW][C]5[/C][C]15.684[/C][C]18.4415717146605[/C][C]-2.75757171466052[/C][/ROW]
[ROW][C]6[/C][C]15.962[/C][C]18.4144338655929[/C][C]-2.45243386559287[/C][/ROW]
[ROW][C]7[/C][C]12[/C][C]18.4219328184999[/C][C]-6.42193281849994[/C][/ROW]
[ROW][C]8[/C][C]13.769[/C][C]16.505440956064[/C][C]-2.73644095606400[/C][/ROW]
[ROW][C]9[/C][C]14.031[/C][C]16.0408569708472[/C][C]-2.00985697084721[/C][/ROW]
[ROW][C]10[/C][C]16.078[/C][C]15.8059842701906[/C][C]0.272015729809430[/C][/ROW]
[ROW][C]11[/C][C]15.827[/C][C]16.545653639023[/C][C]-0.718653639022998[/C][/ROW]
[ROW][C]12[/C][C]13.149[/C][C]16.8391396991379[/C][C]-3.69013969913790[/C][/ROW]
[ROW][C]13[/C][C]15.969[/C][C]15.7353153791593[/C][C]0.233684620840727[/C][/ROW]
[ROW][C]14[/C][C]16.628[/C][C]16.2982792357891[/C][C]0.329720764210869[/C][/ROW]
[ROW][C]15[/C][C]16.67[/C][C]16.9144940910722[/C][C]-0.244494091072188[/C][/ROW]
[ROW][C]16[/C][C]16.487[/C][C]17.2787053594341[/C][C]-0.791705359434147[/C][/ROW]
[ROW][C]17[/C][C]16.883[/C][C]17.3812846132337[/C][C]-0.498284613233697[/C][/ROW]
[ROW][C]18[/C][C]16.201[/C][C]17.5886768760961[/C][C]-1.38767687609613[/C][/ROW]
[ROW][C]19[/C][C]12.168[/C][C]17.3669547236250[/C][C]-5.19895472362505[/C][/ROW]
[ROW][C]20[/C][C]14.01[/C][C]15.3351067131389[/C][C]-1.32510671313893[/C][/ROW]
[ROW][C]21[/C][C]16.556[/C][C]14.8890047965905[/C][C]1.66699520340947[/C][/ROW]
[ROW][C]22[/C][C]17.404[/C][C]15.7711442500186[/C][C]1.63285574998144[/C][/ROW]
[ROW][C]23[/C][C]16.435[/C][C]16.7016345064469[/C][C]-0.266634506446856[/C][/ROW]
[ROW][C]24[/C][C]13.123[/C][C]16.8193450319068[/C][C]-3.69634503190685[/C][/ROW]
[ROW][C]25[/C][C]16.744[/C][C]15.3459081250599[/C][C]1.39809187494006[/C][/ROW]
[ROW][C]26[/C][C]17.41[/C][C]16.0786050408598[/C][C]1.33139495914022[/C][/ROW]
[ROW][C]27[/C][C]16.484[/C][C]16.8343077629217[/C][C]-0.350307762921705[/C][/ROW]
[ROW][C]28[/C][C]17.103[/C][C]16.8660285555143[/C][C]0.236971444485693[/C][/ROW]
[ROW][C]29[/C][C]17.301[/C][C]17.1549833796486[/C][C]0.146016620351379[/C][/ROW]
[ROW][C]30[/C][C]17.301[/C][C]17.4111236205358[/C][C]-0.110123620535756[/C][/ROW]
[ROW][C]31[/C][C]12.843[/C][C]17.5548116946036[/C][C]-4.71181169460362[/C][/ROW]
[ROW][C]32[/C][C]13.748[/C][C]15.5731559718304[/C][C]-1.82515597183041[/C][/ROW]
[ROW][C]33[/C][C]16.904[/C][C]14.7409362669464[/C][C]2.16306373305364[/C][/ROW]
[ROW][C]34[/C][C]17.342[/C][C]15.6768859680072[/C][C]1.66511403199276[/C][/ROW]
[ROW][C]35[/C][C]15.476[/C][C]16.4664681647305[/C][C]-0.990468164730478[/C][/ROW]
[ROW][C]36[/C][C]15.424[/C][C]16.0959964518442[/C][C]-0.671996451844244[/C][/ROW]
[ROW][C]37[/C][C]15.988[/C][C]15.8342434112602[/C][C]0.153756588739805[/C][/ROW]
[ROW][C]38[/C][C]19.244[/C][C]15.9272797272503[/C][C]3.31672027274969[/C][/ROW]
[ROW][C]39[/C][C]18.715[/C][C]17.4841691653034[/C][C]1.23083083469664[/C][/ROW]
[ROW][C]40[/C][C]17.78[/C][C]18.2070953462707[/C][C]-0.427095346270672[/C][/ROW]
[ROW][C]41[/C][C]17.16[/C][C]18.2131330422129[/C][C]-1.05313304221290[/C][/ROW]
[ROW][C]42[/C][C]17.349[/C][C]17.9141842851612[/C][C]-0.565184285161223[/C][/ROW]
[ROW][C]43[/C][C]11.171[/C][C]17.7996641134734[/C][C]-6.62866411347339[/C][/ROW]
[ROW][C]44[/C][C]13.438[/C][C]14.8685046404258[/C][C]-1.43050464042579[/C][/ROW]
[ROW][C]45[/C][C]16.713[/C][C]14.0785569729848[/C][C]2.63444302701516[/C][/ROW]
[ROW][C]46[/C][C]18.369[/C][C]15.1073180777597[/C][C]3.26168192224026[/C][/ROW]
[ROW][C]47[/C][C]17.067[/C][C]16.5264801003672[/C][C]0.540519899632798[/C][/ROW]
[ROW][C]48[/C][C]14.055[/C][C]16.8167392805015[/C][C]-2.76173928050145[/C][/ROW]
[ROW][C]49[/C][C]15.5[/C][C]15.6056294691062[/C][C]-0.105629469106244[/C][/ROW]
[ROW][C]50[/C][C]18.475[/C][C]15.5126573568552[/C][C]2.96234264314479[/C][/ROW]
[ROW][C]51[/C][C]19.423[/C][C]16.8297807710755[/C][C]2.59321922892450[/C][/ROW]
[ROW][C]52[/C][C]18.686[/C][C]18.0906461187292[/C][C]0.595353881270832[/C][/ROW]
[ROW][C]53[/C][C]19.646[/C][C]18.5303074187872[/C][C]1.11569258121283[/C][/ROW]
[ROW][C]54[/C][C]19.733[/C][C]19.2327027382628[/C][C]0.500297261737202[/C][/ROW]
[ROW][C]55[/C][C]12.605[/C][C]19.6943291131904[/C][C]-7.08932911319039[/C][/ROW]
[ROW][C]56[/C][C]16.616[/C][C]16.6768136353391[/C][C]-0.0608136353391231[/C][/ROW]
[ROW][C]57[/C][C]19.156[/C][C]16.6264873333610[/C][C]2.52951266663903[/C][/ROW]
[ROW][C]58[/C][C]21.348[/C][C]17.7678125952709[/C][C]3.58018740472914[/C][/ROW]
[ROW][C]59[/C][C]20.049[/C][C]19.4906840167211[/C][C]0.55831598327892[/C][/ROW]
[ROW][C]60[/C][C]18.02[/C][C]19.9582879230864[/C][C]-1.93828792308639[/C][/ROW]
[ROW][C]61[/C][C]20.262[/C][C]19.2965671501876[/C][C]0.965432849812373[/C][/ROW]
[ROW][C]62[/C][C]21.789[/C][C]19.8987756314555[/C][C]1.89022436854452[/C][/ROW]
[ROW][C]63[/C][C]20.603[/C][C]20.9643748887044[/C][C]-0.361374888704443[/C][/ROW]
[ROW][C]64[/C][C]21.928[/C][C]21.0647871328082[/C][C]0.863212867191827[/C][/ROW]
[ROW][C]65[/C][C]21.025[/C][C]21.7157700505258[/C][C]-0.690770050525792[/C][/ROW]
[ROW][C]66[/C][C]19.346[/C][C]21.6836433160837[/C][C]-2.33764331608373[/C][/ROW]
[ROW][C]67[/C][C]11.786[/C][C]20.8658475097668[/C][C]-9.07984750976678[/C][/ROW]
[ROW][C]68[/C][C]19.082[/C][C]16.8504183833403[/C][C]2.23158161665973[/C][/ROW]
[ROW][C]69[/C][C]20.127[/C][C]17.6998272732658[/C][C]2.42717272673416[/C][/ROW]
[ROW][C]70[/C][C]20.217[/C][C]18.725184718636[/C][C]1.49181528136400[/C][/ROW]
[ROW][C]71[/C][C]20.385[/C][C]19.4127087574372[/C][C]0.972291242562768[/C][/ROW]
[ROW][C]72[/C][C]16.653[/C][C]19.9181148450569[/C][C]-3.26511484505695[/C][/ROW]
[ROW][C]73[/C][C]13.065[/C][C]18.50770300654[/C][C]-5.44270300654[/C][/ROW]
[ROW][C]74[/C][C]20.275[/C][C]15.9680235764518[/C][C]4.30697642354823[/C][/ROW]
[ROW][C]75[/C][C]21.776[/C][C]17.7131354005906[/C][C]4.06286459940941[/C][/ROW]
[ROW][C]76[/C][C]20.26[/C][C]19.5113062380879[/C][C]0.748693761912065[/C][/ROW]
[ROW][C]77[/C][C]22.523[/C][C]19.9380329294702[/C][C]2.58496707052975[/C][/ROW]
[ROW][C]78[/C][C]23.033[/C][C]21.2399579377352[/C][C]1.79304206226475[/C][/ROW]
[ROW][C]79[/C][C]14.133[/C][C]22.2762298907614[/C][C]-8.14322989076142[/C][/ROW]
[ROW][C]80[/C][C]20.11[/C][C]18.801392248294[/C][C]1.30860775170598[/C][/ROW]
[ROW][C]81[/C][C]19.682[/C][C]19.3702372467355[/C][C]0.311762753264453[/C][/ROW]
[ROW][C]82[/C][C]22.197[/C][C]19.529903782697[/C][C]2.66709621730300[/C][/ROW]
[ROW][C]83[/C][C]17.212[/C][C]20.7872274550166[/C][C]-3.57522745501657[/C][/ROW]
[ROW][C]84[/C][C]11.784[/C][C]19.2697392319153[/C][C]-7.4857392319153[/C][/ROW]
[ROW][C]85[/C][C]15.467[/C][C]15.8122844016269[/C][C]-0.345284401626868[/C][/ROW]
[ROW][C]86[/C][C]17.002[/C][C]15.3583764062496[/C][C]1.64362359375035[/C][/ROW]
[ROW][C]87[/C][C]15.952[/C][C]15.8079647828127[/C][C]0.144035217187284[/C][/ROW]
[ROW][C]88[/C][C]18.767[/C][C]15.6295188649385[/C][C]3.13748113506152[/C][/ROW]
[ROW][C]89[/C][C]20.605[/C][C]16.8364145192089[/C][C]3.76858548079106[/C][/ROW]
[ROW][C]90[/C][C]19.809[/C][C]18.4548319794322[/C][C]1.35416802056776[/C][/ROW]
[ROW][C]91[/C][C]14.233[/C][C]19.1052257175672[/C][C]-4.8722257175672[/C][/ROW]
[ROW][C]92[/C][C]19.311[/C][C]16.9376752235585[/C][C]2.37332477644154[/C][/ROW]
[ROW][C]93[/C][C]20.827[/C][C]17.9225902417305[/C][C]2.90440975826947[/C][/ROW]
[ROW][C]94[/C][C]23.388[/C][C]19.2435462167605[/C][C]4.14445378323948[/C][/ROW]
[ROW][C]95[/C][C]20.181[/C][C]21.2477493606671[/C][C]-1.06674936066707[/C][/ROW]
[ROW][C]96[/C][C]14.344[/C][C]21.0092236478139[/C][C]-6.66522364781392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41882&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41882&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
316.68317.39-0.707000000000001
415.48718.4491141865388-2.96211418653884
515.68418.4415717146605-2.75757171466052
615.96218.4144338655929-2.45243386559287
71218.4219328184999-6.42193281849994
813.76916.505440956064-2.73644095606400
914.03116.0408569708472-2.00985697084721
1016.07815.80598427019060.272015729809430
1115.82716.545653639023-0.718653639022998
1213.14916.8391396991379-3.69013969913790
1315.96915.73531537915930.233684620840727
1416.62816.29827923578910.329720764210869
1516.6716.9144940910722-0.244494091072188
1616.48717.2787053594341-0.791705359434147
1716.88317.3812846132337-0.498284613233697
1816.20117.5886768760961-1.38767687609613
1912.16817.3669547236250-5.19895472362505
2014.0115.3351067131389-1.32510671313893
2116.55614.88900479659051.66699520340947
2217.40415.77114425001861.63285574998144
2316.43516.7016345064469-0.266634506446856
2413.12316.8193450319068-3.69634503190685
2516.74415.34590812505991.39809187494006
2617.4116.07860504085981.33139495914022
2716.48416.8343077629217-0.350307762921705
2817.10316.86602855551430.236971444485693
2917.30117.15498337964860.146016620351379
3017.30117.4111236205358-0.110123620535756
3112.84317.5548116946036-4.71181169460362
3213.74815.5731559718304-1.82515597183041
3316.90414.74093626694642.16306373305364
3417.34215.67688596800721.66511403199276
3515.47616.4664681647305-0.990468164730478
3615.42416.0959964518442-0.671996451844244
3715.98815.83424341126020.153756588739805
3819.24415.92727972725033.31672027274969
3918.71517.48416916530341.23083083469664
4017.7818.2070953462707-0.427095346270672
4117.1618.2131330422129-1.05313304221290
4217.34917.9141842851612-0.565184285161223
4311.17117.7996641134734-6.62866411347339
4413.43814.8685046404258-1.43050464042579
4516.71314.07855697298482.63444302701516
4618.36915.10731807775973.26168192224026
4717.06716.52648010036720.540519899632798
4814.05516.8167392805015-2.76173928050145
4915.515.6056294691062-0.105629469106244
5018.47515.51265735685522.96234264314479
5119.42316.82978077107552.59321922892450
5218.68618.09064611872920.595353881270832
5319.64618.53030741878721.11569258121283
5419.73319.23270273826280.500297261737202
5512.60519.6943291131904-7.08932911319039
5616.61616.6768136353391-0.0608136353391231
5719.15616.62648733336102.52951266663903
5821.34817.76781259527093.58018740472914
5920.04919.49068401672110.55831598327892
6018.0219.9582879230864-1.93828792308639
6120.26219.29656715018760.965432849812373
6221.78919.89877563145551.89022436854452
6320.60320.9643748887044-0.361374888704443
6421.92821.06478713280820.863212867191827
6521.02521.7157700505258-0.690770050525792
6619.34621.6836433160837-2.33764331608373
6711.78620.8658475097668-9.07984750976678
6819.08216.85041838334032.23158161665973
6920.12717.69982727326582.42717272673416
7020.21718.7251847186361.49181528136400
7120.38519.41270875743720.972291242562768
7216.65319.9181148450569-3.26511484505695
7313.06518.50770300654-5.44270300654
7420.27515.96802357645184.30697642354823
7521.77617.71313540059064.06286459940941
7620.2619.51130623808790.748693761912065
7722.52319.93803292947022.58496707052975
7823.03321.23995793773521.79304206226475
7914.13322.2762298907614-8.14322989076142
8020.1118.8013922482941.30860775170598
8119.68219.37023724673550.311762753264453
8222.19719.5299037826972.66709621730300
8317.21220.7872274550166-3.57522745501657
8411.78419.2697392319153-7.4857392319153
8515.46715.8122844016269-0.345284401626868
8617.00215.35837640624961.64362359375035
8715.95215.80796478281270.144035217187284
8818.76715.62951886493853.13748113506152
8920.60516.83641451920893.76858548079106
9019.80918.45483197943221.35416802056776
9114.23319.1052257175672-4.8722257175672
9219.31116.93767522355852.37332477644154
9320.82717.92259024173052.90440975826947
9423.38819.24354621676054.14445378323948
9520.18121.2477493606671-1.06674936066707
9614.34421.0092236478139-6.66522364781392







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9718.149116588661612.372043191243423.9261899860799
9818.105046935623211.743790531206524.4663033400399
9918.060977282584811.076081997009325.0458725681603
10018.016907629546410.372120569826225.6616946892666
10117.9728379765089.634597215837526.3110787371785
10217.92876832346968.8657728826719326.9917637642672
10317.88469867043128.0675551884582427.7018421524041
10417.84062901739287.2415642866619328.4396937481236
10517.79655936435436.3891870881552529.2039316405534
10617.75248971131595.5116209424537529.9933584801781
10717.70842005827754.6099084673183130.8069316492367
10817.66435040523913.684965221337131.6437355891411

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 18.1491165886616 & 12.3720431912434 & 23.9261899860799 \tabularnewline
98 & 18.1050469356232 & 11.7437905312065 & 24.4663033400399 \tabularnewline
99 & 18.0609772825848 & 11.0760819970093 & 25.0458725681603 \tabularnewline
100 & 18.0169076295464 & 10.3721205698262 & 25.6616946892666 \tabularnewline
101 & 17.972837976508 & 9.6345972158375 & 26.3110787371785 \tabularnewline
102 & 17.9287683234696 & 8.86577288267193 & 26.9917637642672 \tabularnewline
103 & 17.8846986704312 & 8.06755518845824 & 27.7018421524041 \tabularnewline
104 & 17.8406290173928 & 7.24156428666193 & 28.4396937481236 \tabularnewline
105 & 17.7965593643543 & 6.38918708815525 & 29.2039316405534 \tabularnewline
106 & 17.7524897113159 & 5.51162094245375 & 29.9933584801781 \tabularnewline
107 & 17.7084200582775 & 4.60990846731831 & 30.8069316492367 \tabularnewline
108 & 17.6643504052391 & 3.6849652213371 & 31.6437355891411 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41882&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]97[/C][C]18.1491165886616[/C][C]12.3720431912434[/C][C]23.9261899860799[/C][/ROW]
[ROW][C]98[/C][C]18.1050469356232[/C][C]11.7437905312065[/C][C]24.4663033400399[/C][/ROW]
[ROW][C]99[/C][C]18.0609772825848[/C][C]11.0760819970093[/C][C]25.0458725681603[/C][/ROW]
[ROW][C]100[/C][C]18.0169076295464[/C][C]10.3721205698262[/C][C]25.6616946892666[/C][/ROW]
[ROW][C]101[/C][C]17.972837976508[/C][C]9.6345972158375[/C][C]26.3110787371785[/C][/ROW]
[ROW][C]102[/C][C]17.9287683234696[/C][C]8.86577288267193[/C][C]26.9917637642672[/C][/ROW]
[ROW][C]103[/C][C]17.8846986704312[/C][C]8.06755518845824[/C][C]27.7018421524041[/C][/ROW]
[ROW][C]104[/C][C]17.8406290173928[/C][C]7.24156428666193[/C][C]28.4396937481236[/C][/ROW]
[ROW][C]105[/C][C]17.7965593643543[/C][C]6.38918708815525[/C][C]29.2039316405534[/C][/ROW]
[ROW][C]106[/C][C]17.7524897113159[/C][C]5.51162094245375[/C][C]29.9933584801781[/C][/ROW]
[ROW][C]107[/C][C]17.7084200582775[/C][C]4.60990846731831[/C][C]30.8069316492367[/C][/ROW]
[ROW][C]108[/C][C]17.6643504052391[/C][C]3.6849652213371[/C][C]31.6437355891411[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41882&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41882&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
9718.149116588661612.372043191243423.9261899860799
9818.105046935623211.743790531206524.4663033400399
9918.060977282584811.076081997009325.0458725681603
10018.016907629546410.372120569826225.6616946892666
10117.9728379765089.634597215837526.3110787371785
10217.92876832346968.8657728826719326.9917637642672
10317.88469867043128.0675551884582427.7018421524041
10417.84062901739287.2415642866619328.4396937481236
10517.79655936435436.3891870881552529.2039316405534
10617.75248971131595.5116209424537529.9933584801781
10717.70842005827754.6099084673183130.8069316492367
10817.66435040523913.684965221337131.6437355891411



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')