Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 27 Nov 2016 13:45:20 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/27/t1480254470cmszi46kiqxevnm.htm/, Retrieved Tue, 21 Apr 2026 18:52:58 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 21 Apr 2026 18:52:58 +0200

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0626252314263217
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0626252314263217 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0626252314263217[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Parameter	Value
alpha	1
beta	0.0626252314263217
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	72.03	70.99	1.04000000000001
4	72.31	72.0951302406834	0.214869759316628
5	72.33	72.3885865090871	-0.0585865090871067
6	72.33	72.4049175153971	-0.0749175153970612
7	73.14	72.4002257886574	0.739774211342578
8	73.28	73.256554319846	0.0234456801540119
9	73.28	73.3980226109916	-0.118022610991574
10	73.28	73.3906314176647	-0.110631417664692
11	73.28	73.3837030995304	-0.103703099530421
12	73.28	73.3772086689227	-0.0972086689227041
13	73.28	73.3711209535348	-0.0911209535347695
14	73.28	73.3654144827319	-0.0854144827318635
15	74.33	73.3600653809836	0.969934619016371
16	75.71	74.4708077609679	1.23919223903206
17	76.65	75.928412461719	0.721587538281
18	76.65	76.9136020482982	-0.26360204829821
19	76.66	76.8970939090191	-0.237093909019094
20	76.66	76.892245848097	-0.232245848096994
21	76.66	76.8777013981121	-0.217701398112112
22	76.66	76.8640677976735	-0.204067797673503
23	76.66	76.8512880046175	-0.191288004617547
24	76.17	76.8393085490593	-0.669308549059281
25	76.05	76.3073929462788	-0.257392946278841
26	76.06	76.1712736534506	-0.111273653450624
27	76.08	76.1743051151516	-0.0943051151516272
28	79.02	76.1883992354906	2.83160076450943
29	80.21	79.3057288886749	0.904271111325073
30	79.8	80.5523590762938	-0.752359076293786
31	80.22	80.0952424150252	0.124757584974802
32	81.28	80.5230553876564	0.756944612343574
33	82.1	81.6304592191814	0.469540780818633
34	82.13	82.4798643192442	-0.349864319244219
35	82.12	82.4879539852837	-0.367953985283734
36	82.13	82.4549107818011	-0.324910781801123
37	82.13	82.4445631688979	-0.314563168897905
38	82.13	82.4248635776475	-0.294863577647476
39	82.13	82.4063976778581	-0.276397677858114
40	82.68	82.3890882093165	0.290911790683467
41	83.81	82.9573066275328	0.852693372467243
42	84.52	84.1407067473192	0.379293252680796
43	84.53	84.8744600750468	-0.344460075046769
44	84.57	84.8628881831298	-0.292888183129847
45	84.59	84.8845459928793	-0.294545992879293
46	85.28	84.8860999819095	0.393900018090463
47	86.5	85.6007680617013	0.899231938298712
48	86.79	86.8770826699432	-0.0870826699431717
49	86.83	87.1616290975848	-0.331629097584781
50	88.45	87.1808607486008	1.26913925139918
51	93.64	88.8803408879319	4.75965911206808
52	95.75	94.3684156413356	1.38158435866441
53	95.9	96.5649376815319	-0.664937681531924
54	96.01	96.6732958053419	-0.663295805341917
55	95.99	96.7417567520283	-0.751756752028285
56	95.96	96.6746778114562	-0.714677811456198
57	96	96.5999209481185	-0.599920948118495
58	96.02	96.6023507599051	-0.582350759905083
59	96.04	96.5858809087947	-0.545880908794715
60	96.04	96.5716949905503	-0.53169499055025
61	96.04	96.5383974687188	-0.498397468718821
62	96.04	96.507185211898	-0.467185211898013
63	96.13	96.477927629884	-0.347927629883955
64	96.17	96.5461385815428	-0.376138581542847
65	96.19	96.5625828158254	-0.372582815825368
66	96.16	96.5592497307588	-0.399249730758825
67	96.45	96.5042466239732	-0.0542466239731567
68	96.47	96.7908494165927	-0.32084941659275
69	96.47	96.7907561476256	-0.320756147625616
70	96.76	96.7706687196492	-0.0106687196491464
71	97.24	97.0600005886121	0.179999411387882
72	97.26	97.5512730934069	-0.291273093406858
73	98.3	97.553032048524	0.74696795147598
74	98.87	98.6398110893532	0.230188910646774
75	100.49	99.2242267231543	1.26577327684574
76	100.53	100.92349606755	-0.393496067549975
77	99.66	100.938853285254	-1.27885328525431
78	99.31	99.9887648023049	-0.67876480230494
79	100.36	99.5962569994766	0.763743000523434
80	100.77	100.694086581635	0.0759134183654169
81	100.39	101.108840677028	-0.718840677028069
82	100.42	100.683823113271	-0.263823113270533
83	100.44	100.697301129746	-0.257301129746367
84	100.44	100.70118758695	-0.261187586949731

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 72.03 & 70.99 & 1.04000000000001 \tabularnewline
4 & 72.31 & 72.0951302406834 & 0.214869759316628 \tabularnewline
5 & 72.33 & 72.3885865090871 & -0.0585865090871067 \tabularnewline
6 & 72.33 & 72.4049175153971 & -0.0749175153970612 \tabularnewline
7 & 73.14 & 72.4002257886574 & 0.739774211342578 \tabularnewline
8 & 73.28 & 73.256554319846 & 0.0234456801540119 \tabularnewline
9 & 73.28 & 73.3980226109916 & -0.118022610991574 \tabularnewline
10 & 73.28 & 73.3906314176647 & -0.110631417664692 \tabularnewline
11 & 73.28 & 73.3837030995304 & -0.103703099530421 \tabularnewline
12 & 73.28 & 73.3772086689227 & -0.0972086689227041 \tabularnewline
13 & 73.28 & 73.3711209535348 & -0.0911209535347695 \tabularnewline
14 & 73.28 & 73.3654144827319 & -0.0854144827318635 \tabularnewline
15 & 74.33 & 73.3600653809836 & 0.969934619016371 \tabularnewline
16 & 75.71 & 74.4708077609679 & 1.23919223903206 \tabularnewline
17 & 76.65 & 75.928412461719 & 0.721587538281 \tabularnewline
18 & 76.65 & 76.9136020482982 & -0.26360204829821 \tabularnewline
19 & 76.66 & 76.8970939090191 & -0.237093909019094 \tabularnewline
20 & 76.66 & 76.892245848097 & -0.232245848096994 \tabularnewline
21 & 76.66 & 76.8777013981121 & -0.217701398112112 \tabularnewline
22 & 76.66 & 76.8640677976735 & -0.204067797673503 \tabularnewline
23 & 76.66 & 76.8512880046175 & -0.191288004617547 \tabularnewline
24 & 76.17 & 76.8393085490593 & -0.669308549059281 \tabularnewline
25 & 76.05 & 76.3073929462788 & -0.257392946278841 \tabularnewline
26 & 76.06 & 76.1712736534506 & -0.111273653450624 \tabularnewline
27 & 76.08 & 76.1743051151516 & -0.0943051151516272 \tabularnewline
28 & 79.02 & 76.1883992354906 & 2.83160076450943 \tabularnewline
29 & 80.21 & 79.3057288886749 & 0.904271111325073 \tabularnewline
30 & 79.8 & 80.5523590762938 & -0.752359076293786 \tabularnewline
31 & 80.22 & 80.0952424150252 & 0.124757584974802 \tabularnewline
32 & 81.28 & 80.5230553876564 & 0.756944612343574 \tabularnewline
33 & 82.1 & 81.6304592191814 & 0.469540780818633 \tabularnewline
34 & 82.13 & 82.4798643192442 & -0.349864319244219 \tabularnewline
35 & 82.12 & 82.4879539852837 & -0.367953985283734 \tabularnewline
36 & 82.13 & 82.4549107818011 & -0.324910781801123 \tabularnewline
37 & 82.13 & 82.4445631688979 & -0.314563168897905 \tabularnewline
38 & 82.13 & 82.4248635776475 & -0.294863577647476 \tabularnewline
39 & 82.13 & 82.4063976778581 & -0.276397677858114 \tabularnewline
40 & 82.68 & 82.3890882093165 & 0.290911790683467 \tabularnewline
41 & 83.81 & 82.9573066275328 & 0.852693372467243 \tabularnewline
42 & 84.52 & 84.1407067473192 & 0.379293252680796 \tabularnewline
43 & 84.53 & 84.8744600750468 & -0.344460075046769 \tabularnewline
44 & 84.57 & 84.8628881831298 & -0.292888183129847 \tabularnewline
45 & 84.59 & 84.8845459928793 & -0.294545992879293 \tabularnewline
46 & 85.28 & 84.8860999819095 & 0.393900018090463 \tabularnewline
47 & 86.5 & 85.6007680617013 & 0.899231938298712 \tabularnewline
48 & 86.79 & 86.8770826699432 & -0.0870826699431717 \tabularnewline
49 & 86.83 & 87.1616290975848 & -0.331629097584781 \tabularnewline
50 & 88.45 & 87.1808607486008 & 1.26913925139918 \tabularnewline
51 & 93.64 & 88.8803408879319 & 4.75965911206808 \tabularnewline
52 & 95.75 & 94.3684156413356 & 1.38158435866441 \tabularnewline
53 & 95.9 & 96.5649376815319 & -0.664937681531924 \tabularnewline
54 & 96.01 & 96.6732958053419 & -0.663295805341917 \tabularnewline
55 & 95.99 & 96.7417567520283 & -0.751756752028285 \tabularnewline
56 & 95.96 & 96.6746778114562 & -0.714677811456198 \tabularnewline
57 & 96 & 96.5999209481185 & -0.599920948118495 \tabularnewline
58 & 96.02 & 96.6023507599051 & -0.582350759905083 \tabularnewline
59 & 96.04 & 96.5858809087947 & -0.545880908794715 \tabularnewline
60 & 96.04 & 96.5716949905503 & -0.53169499055025 \tabularnewline
61 & 96.04 & 96.5383974687188 & -0.498397468718821 \tabularnewline
62 & 96.04 & 96.507185211898 & -0.467185211898013 \tabularnewline
63 & 96.13 & 96.477927629884 & -0.347927629883955 \tabularnewline
64 & 96.17 & 96.5461385815428 & -0.376138581542847 \tabularnewline
65 & 96.19 & 96.5625828158254 & -0.372582815825368 \tabularnewline
66 & 96.16 & 96.5592497307588 & -0.399249730758825 \tabularnewline
67 & 96.45 & 96.5042466239732 & -0.0542466239731567 \tabularnewline
68 & 96.47 & 96.7908494165927 & -0.32084941659275 \tabularnewline
69 & 96.47 & 96.7907561476256 & -0.320756147625616 \tabularnewline
70 & 96.76 & 96.7706687196492 & -0.0106687196491464 \tabularnewline
71 & 97.24 & 97.0600005886121 & 0.179999411387882 \tabularnewline
72 & 97.26 & 97.5512730934069 & -0.291273093406858 \tabularnewline
73 & 98.3 & 97.553032048524 & 0.74696795147598 \tabularnewline
74 & 98.87 & 98.6398110893532 & 0.230188910646774 \tabularnewline
75 & 100.49 & 99.2242267231543 & 1.26577327684574 \tabularnewline
76 & 100.53 & 100.92349606755 & -0.393496067549975 \tabularnewline
77 & 99.66 & 100.938853285254 & -1.27885328525431 \tabularnewline
78 & 99.31 & 99.9887648023049 & -0.67876480230494 \tabularnewline
79 & 100.36 & 99.5962569994766 & 0.763743000523434 \tabularnewline
80 & 100.77 & 100.694086581635 & 0.0759134183654169 \tabularnewline
81 & 100.39 & 101.108840677028 & -0.718840677028069 \tabularnewline
82 & 100.42 & 100.683823113271 & -0.263823113270533 \tabularnewline
83 & 100.44 & 100.697301129746 & -0.257301129746367 \tabularnewline
84 & 100.44 & 100.70118758695 & -0.261187586949731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]72.03[/C][C]70.99[/C][C]1.04000000000001[/C][/ROW]
[ROW][C]4[/C][C]72.31[/C][C]72.0951302406834[/C][C]0.214869759316628[/C][/ROW]
[ROW][C]5[/C][C]72.33[/C][C]72.3885865090871[/C][C]-0.0585865090871067[/C][/ROW]
[ROW][C]6[/C][C]72.33[/C][C]72.4049175153971[/C][C]-0.0749175153970612[/C][/ROW]
[ROW][C]7[/C][C]73.14[/C][C]72.4002257886574[/C][C]0.739774211342578[/C][/ROW]
[ROW][C]8[/C][C]73.28[/C][C]73.256554319846[/C][C]0.0234456801540119[/C][/ROW]
[ROW][C]9[/C][C]73.28[/C][C]73.3980226109916[/C][C]-0.118022610991574[/C][/ROW]
[ROW][C]10[/C][C]73.28[/C][C]73.3906314176647[/C][C]-0.110631417664692[/C][/ROW]
[ROW][C]11[/C][C]73.28[/C][C]73.3837030995304[/C][C]-0.103703099530421[/C][/ROW]
[ROW][C]12[/C][C]73.28[/C][C]73.3772086689227[/C][C]-0.0972086689227041[/C][/ROW]
[ROW][C]13[/C][C]73.28[/C][C]73.3711209535348[/C][C]-0.0911209535347695[/C][/ROW]
[ROW][C]14[/C][C]73.28[/C][C]73.3654144827319[/C][C]-0.0854144827318635[/C][/ROW]
[ROW][C]15[/C][C]74.33[/C][C]73.3600653809836[/C][C]0.969934619016371[/C][/ROW]
[ROW][C]16[/C][C]75.71[/C][C]74.4708077609679[/C][C]1.23919223903206[/C][/ROW]
[ROW][C]17[/C][C]76.65[/C][C]75.928412461719[/C][C]0.721587538281[/C][/ROW]
[ROW][C]18[/C][C]76.65[/C][C]76.9136020482982[/C][C]-0.26360204829821[/C][/ROW]
[ROW][C]19[/C][C]76.66[/C][C]76.8970939090191[/C][C]-0.237093909019094[/C][/ROW]
[ROW][C]20[/C][C]76.66[/C][C]76.892245848097[/C][C]-0.232245848096994[/C][/ROW]
[ROW][C]21[/C][C]76.66[/C][C]76.8777013981121[/C][C]-0.217701398112112[/C][/ROW]
[ROW][C]22[/C][C]76.66[/C][C]76.8640677976735[/C][C]-0.204067797673503[/C][/ROW]
[ROW][C]23[/C][C]76.66[/C][C]76.8512880046175[/C][C]-0.191288004617547[/C][/ROW]
[ROW][C]24[/C][C]76.17[/C][C]76.8393085490593[/C][C]-0.669308549059281[/C][/ROW]
[ROW][C]25[/C][C]76.05[/C][C]76.3073929462788[/C][C]-0.257392946278841[/C][/ROW]
[ROW][C]26[/C][C]76.06[/C][C]76.1712736534506[/C][C]-0.111273653450624[/C][/ROW]
[ROW][C]27[/C][C]76.08[/C][C]76.1743051151516[/C][C]-0.0943051151516272[/C][/ROW]
[ROW][C]28[/C][C]79.02[/C][C]76.1883992354906[/C][C]2.83160076450943[/C][/ROW]
[ROW][C]29[/C][C]80.21[/C][C]79.3057288886749[/C][C]0.904271111325073[/C][/ROW]
[ROW][C]30[/C][C]79.8[/C][C]80.5523590762938[/C][C]-0.752359076293786[/C][/ROW]
[ROW][C]31[/C][C]80.22[/C][C]80.0952424150252[/C][C]0.124757584974802[/C][/ROW]
[ROW][C]32[/C][C]81.28[/C][C]80.5230553876564[/C][C]0.756944612343574[/C][/ROW]
[ROW][C]33[/C][C]82.1[/C][C]81.6304592191814[/C][C]0.469540780818633[/C][/ROW]
[ROW][C]34[/C][C]82.13[/C][C]82.4798643192442[/C][C]-0.349864319244219[/C][/ROW]
[ROW][C]35[/C][C]82.12[/C][C]82.4879539852837[/C][C]-0.367953985283734[/C][/ROW]
[ROW][C]36[/C][C]82.13[/C][C]82.4549107818011[/C][C]-0.324910781801123[/C][/ROW]
[ROW][C]37[/C][C]82.13[/C][C]82.4445631688979[/C][C]-0.314563168897905[/C][/ROW]
[ROW][C]38[/C][C]82.13[/C][C]82.4248635776475[/C][C]-0.294863577647476[/C][/ROW]
[ROW][C]39[/C][C]82.13[/C][C]82.4063976778581[/C][C]-0.276397677858114[/C][/ROW]
[ROW][C]40[/C][C]82.68[/C][C]82.3890882093165[/C][C]0.290911790683467[/C][/ROW]
[ROW][C]41[/C][C]83.81[/C][C]82.9573066275328[/C][C]0.852693372467243[/C][/ROW]
[ROW][C]42[/C][C]84.52[/C][C]84.1407067473192[/C][C]0.379293252680796[/C][/ROW]
[ROW][C]43[/C][C]84.53[/C][C]84.8744600750468[/C][C]-0.344460075046769[/C][/ROW]
[ROW][C]44[/C][C]84.57[/C][C]84.8628881831298[/C][C]-0.292888183129847[/C][/ROW]
[ROW][C]45[/C][C]84.59[/C][C]84.8845459928793[/C][C]-0.294545992879293[/C][/ROW]
[ROW][C]46[/C][C]85.28[/C][C]84.8860999819095[/C][C]0.393900018090463[/C][/ROW]
[ROW][C]47[/C][C]86.5[/C][C]85.6007680617013[/C][C]0.899231938298712[/C][/ROW]
[ROW][C]48[/C][C]86.79[/C][C]86.8770826699432[/C][C]-0.0870826699431717[/C][/ROW]
[ROW][C]49[/C][C]86.83[/C][C]87.1616290975848[/C][C]-0.331629097584781[/C][/ROW]
[ROW][C]50[/C][C]88.45[/C][C]87.1808607486008[/C][C]1.26913925139918[/C][/ROW]
[ROW][C]51[/C][C]93.64[/C][C]88.8803408879319[/C][C]4.75965911206808[/C][/ROW]
[ROW][C]52[/C][C]95.75[/C][C]94.3684156413356[/C][C]1.38158435866441[/C][/ROW]
[ROW][C]53[/C][C]95.9[/C][C]96.5649376815319[/C][C]-0.664937681531924[/C][/ROW]
[ROW][C]54[/C][C]96.01[/C][C]96.6732958053419[/C][C]-0.663295805341917[/C][/ROW]
[ROW][C]55[/C][C]95.99[/C][C]96.7417567520283[/C][C]-0.751756752028285[/C][/ROW]
[ROW][C]56[/C][C]95.96[/C][C]96.6746778114562[/C][C]-0.714677811456198[/C][/ROW]
[ROW][C]57[/C][C]96[/C][C]96.5999209481185[/C][C]-0.599920948118495[/C][/ROW]
[ROW][C]58[/C][C]96.02[/C][C]96.6023507599051[/C][C]-0.582350759905083[/C][/ROW]
[ROW][C]59[/C][C]96.04[/C][C]96.5858809087947[/C][C]-0.545880908794715[/C][/ROW]
[ROW][C]60[/C][C]96.04[/C][C]96.5716949905503[/C][C]-0.53169499055025[/C][/ROW]
[ROW][C]61[/C][C]96.04[/C][C]96.5383974687188[/C][C]-0.498397468718821[/C][/ROW]
[ROW][C]62[/C][C]96.04[/C][C]96.507185211898[/C][C]-0.467185211898013[/C][/ROW]
[ROW][C]63[/C][C]96.13[/C][C]96.477927629884[/C][C]-0.347927629883955[/C][/ROW]
[ROW][C]64[/C][C]96.17[/C][C]96.5461385815428[/C][C]-0.376138581542847[/C][/ROW]
[ROW][C]65[/C][C]96.19[/C][C]96.5625828158254[/C][C]-0.372582815825368[/C][/ROW]
[ROW][C]66[/C][C]96.16[/C][C]96.5592497307588[/C][C]-0.399249730758825[/C][/ROW]
[ROW][C]67[/C][C]96.45[/C][C]96.5042466239732[/C][C]-0.0542466239731567[/C][/ROW]
[ROW][C]68[/C][C]96.47[/C][C]96.7908494165927[/C][C]-0.32084941659275[/C][/ROW]
[ROW][C]69[/C][C]96.47[/C][C]96.7907561476256[/C][C]-0.320756147625616[/C][/ROW]
[ROW][C]70[/C][C]96.76[/C][C]96.7706687196492[/C][C]-0.0106687196491464[/C][/ROW]
[ROW][C]71[/C][C]97.24[/C][C]97.0600005886121[/C][C]0.179999411387882[/C][/ROW]
[ROW][C]72[/C][C]97.26[/C][C]97.5512730934069[/C][C]-0.291273093406858[/C][/ROW]
[ROW][C]73[/C][C]98.3[/C][C]97.553032048524[/C][C]0.74696795147598[/C][/ROW]
[ROW][C]74[/C][C]98.87[/C][C]98.6398110893532[/C][C]0.230188910646774[/C][/ROW]
[ROW][C]75[/C][C]100.49[/C][C]99.2242267231543[/C][C]1.26577327684574[/C][/ROW]
[ROW][C]76[/C][C]100.53[/C][C]100.92349606755[/C][C]-0.393496067549975[/C][/ROW]
[ROW][C]77[/C][C]99.66[/C][C]100.938853285254[/C][C]-1.27885328525431[/C][/ROW]
[ROW][C]78[/C][C]99.31[/C][C]99.9887648023049[/C][C]-0.67876480230494[/C][/ROW]
[ROW][C]79[/C][C]100.36[/C][C]99.5962569994766[/C][C]0.763743000523434[/C][/ROW]
[ROW][C]80[/C][C]100.77[/C][C]100.694086581635[/C][C]0.0759134183654169[/C][/ROW]
[ROW][C]81[/C][C]100.39[/C][C]101.108840677028[/C][C]-0.718840677028069[/C][/ROW]
[ROW][C]82[/C][C]100.42[/C][C]100.683823113271[/C][C]-0.263823113270533[/C][/ROW]
[ROW][C]83[/C][C]100.44[/C][C]100.697301129746[/C][C]-0.257301129746367[/C][/ROW]
[ROW][C]84[/C][C]100.44[/C][C]100.70118758695[/C][C]-0.261187586949731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
t	Observed	Fitted	Residuals
3	72.03	70.99	1.04000000000001
4	72.31	72.0951302406834	0.214869759316628
5	72.33	72.3885865090871	-0.0585865090871067
6	72.33	72.4049175153971	-0.0749175153970612
7	73.14	72.4002257886574	0.739774211342578
8	73.28	73.256554319846	0.0234456801540119
9	73.28	73.3980226109916	-0.118022610991574
10	73.28	73.3906314176647	-0.110631417664692
11	73.28	73.3837030995304	-0.103703099530421
12	73.28	73.3772086689227	-0.0972086689227041
13	73.28	73.3711209535348	-0.0911209535347695
14	73.28	73.3654144827319	-0.0854144827318635
15	74.33	73.3600653809836	0.969934619016371
16	75.71	74.4708077609679	1.23919223903206
17	76.65	75.928412461719	0.721587538281
18	76.65	76.9136020482982	-0.26360204829821
19	76.66	76.8970939090191	-0.237093909019094
20	76.66	76.892245848097	-0.232245848096994
21	76.66	76.8777013981121	-0.217701398112112
22	76.66	76.8640677976735	-0.204067797673503
23	76.66	76.8512880046175	-0.191288004617547
24	76.17	76.8393085490593	-0.669308549059281
25	76.05	76.3073929462788	-0.257392946278841
26	76.06	76.1712736534506	-0.111273653450624
27	76.08	76.1743051151516	-0.0943051151516272
28	79.02	76.1883992354906	2.83160076450943
29	80.21	79.3057288886749	0.904271111325073
30	79.8	80.5523590762938	-0.752359076293786
31	80.22	80.0952424150252	0.124757584974802
32	81.28	80.5230553876564	0.756944612343574
33	82.1	81.6304592191814	0.469540780818633
34	82.13	82.4798643192442	-0.349864319244219
35	82.12	82.4879539852837	-0.367953985283734
36	82.13	82.4549107818011	-0.324910781801123
37	82.13	82.4445631688979	-0.314563168897905
38	82.13	82.4248635776475	-0.294863577647476
39	82.13	82.4063976778581	-0.276397677858114
40	82.68	82.3890882093165	0.290911790683467
41	83.81	82.9573066275328	0.852693372467243
42	84.52	84.1407067473192	0.379293252680796
43	84.53	84.8744600750468	-0.344460075046769
44	84.57	84.8628881831298	-0.292888183129847
45	84.59	84.8845459928793	-0.294545992879293
46	85.28	84.8860999819095	0.393900018090463
47	86.5	85.6007680617013	0.899231938298712
48	86.79	86.8770826699432	-0.0870826699431717
49	86.83	87.1616290975848	-0.331629097584781
50	88.45	87.1808607486008	1.26913925139918
51	93.64	88.8803408879319	4.75965911206808
52	95.75	94.3684156413356	1.38158435866441
53	95.9	96.5649376815319	-0.664937681531924
54	96.01	96.6732958053419	-0.663295805341917
55	95.99	96.7417567520283	-0.751756752028285
56	95.96	96.6746778114562	-0.714677811456198
57	96	96.5999209481185	-0.599920948118495
58	96.02	96.6023507599051	-0.582350759905083
59	96.04	96.5858809087947	-0.545880908794715
60	96.04	96.5716949905503	-0.53169499055025
61	96.04	96.5383974687188	-0.498397468718821
62	96.04	96.507185211898	-0.467185211898013
63	96.13	96.477927629884	-0.347927629883955
64	96.17	96.5461385815428	-0.376138581542847
65	96.19	96.5625828158254	-0.372582815825368
66	96.16	96.5592497307588	-0.399249730758825
67	96.45	96.5042466239732	-0.0542466239731567
68	96.47	96.7908494165927	-0.32084941659275
69	96.47	96.7907561476256	-0.320756147625616
70	96.76	96.7706687196492	-0.0106687196491464
71	97.24	97.0600005886121	0.179999411387882
72	97.26	97.5512730934069	-0.291273093406858
73	98.3	97.553032048524	0.74696795147598
74	98.87	98.6398110893532	0.230188910646774
75	100.49	99.2242267231543	1.26577327684574
76	100.53	100.92349606755	-0.393496067549975
77	99.66	100.938853285254	-1.27885328525431
78	99.31	99.9887648023049	-0.67876480230494
79	100.36	99.5962569994766	0.763743000523434
80	100.77	100.694086581635	0.0759134183654169
81	100.39	101.108840677028	-0.718840677028069
82	100.42	100.683823113271	-0.263823113270533
83	100.44	100.697301129746	-0.257301129746367
84	100.44	100.70118758695	-0.261187586949731

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	100.684830653871	99.0682860054198	102.301375302323
86	100.929661307743	98.5708504600808	103.288472155404
87	101.174491961614	98.1957651035928	104.153218819635
88	101.419322615485	97.8752868523682	104.963358378602
89	101.664153269357	97.584127086526	105.744179452187
90	101.908983923228	97.3097900990285	106.508177747427
91	102.153814577099	97.0451359141734	107.262493240025
92	102.398645230971	96.7857001173169	108.011590344624
93	102.643475884842	96.52851497025	108.758436799434
94	102.888306538713	96.2715189687369	109.50509410869
95	103.133137192585	96.0132325037999	110.253041881369
96	103.377967846456	95.7525668910041	111.003368801908

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 100.684830653871 & 99.0682860054198 & 102.301375302323 \tabularnewline
86 & 100.929661307743 & 98.5708504600808 & 103.288472155404 \tabularnewline
87 & 101.174491961614 & 98.1957651035928 & 104.153218819635 \tabularnewline
88 & 101.419322615485 & 97.8752868523682 & 104.963358378602 \tabularnewline
89 & 101.664153269357 & 97.584127086526 & 105.744179452187 \tabularnewline
90 & 101.908983923228 & 97.3097900990285 & 106.508177747427 \tabularnewline
91 & 102.153814577099 & 97.0451359141734 & 107.262493240025 \tabularnewline
92 & 102.398645230971 & 96.7857001173169 & 108.011590344624 \tabularnewline
93 & 102.643475884842 & 96.52851497025 & 108.758436799434 \tabularnewline
94 & 102.888306538713 & 96.2715189687369 & 109.50509410869 \tabularnewline
95 & 103.133137192585 & 96.0132325037999 & 110.253041881369 \tabularnewline
96 & 103.377967846456 & 95.7525668910041 & 111.003368801908 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]85[/C][C]100.684830653871[/C][C]99.0682860054198[/C][C]102.301375302323[/C][/ROW]
[ROW][C]86[/C][C]100.929661307743[/C][C]98.5708504600808[/C][C]103.288472155404[/C][/ROW]
[ROW][C]87[/C][C]101.174491961614[/C][C]98.1957651035928[/C][C]104.153218819635[/C][/ROW]
[ROW][C]88[/C][C]101.419322615485[/C][C]97.8752868523682[/C][C]104.963358378602[/C][/ROW]
[ROW][C]89[/C][C]101.664153269357[/C][C]97.584127086526[/C][C]105.744179452187[/C][/ROW]
[ROW][C]90[/C][C]101.908983923228[/C][C]97.3097900990285[/C][C]106.508177747427[/C][/ROW]
[ROW][C]91[/C][C]102.153814577099[/C][C]97.0451359141734[/C][C]107.262493240025[/C][/ROW]
[ROW][C]92[/C][C]102.398645230971[/C][C]96.7857001173169[/C][C]108.011590344624[/C][/ROW]
[ROW][C]93[/C][C]102.643475884842[/C][C]96.52851497025[/C][C]108.758436799434[/C][/ROW]
[ROW][C]94[/C][C]102.888306538713[/C][C]96.2715189687369[/C][C]109.50509410869[/C][/ROW]
[ROW][C]95[/C][C]103.133137192585[/C][C]96.0132325037999[/C][C]110.253041881369[/C][/ROW]
[ROW][C]96[/C][C]103.377967846456[/C][C]95.7525668910041[/C][C]111.003368801908[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
t	Forecast	95% Lower Bound	95% Upper Bound
85	100.684830653871	99.0682860054198	102.301375302323
86	100.929661307743	98.5708504600808	103.288472155404
87	101.174491961614	98.1957651035928	104.153218819635
88	101.419322615485	97.8752868523682	104.963358378602
89	101.664153269357	97.584127086526	105.744179452187
90	101.908983923228	97.3097900990285	106.508177747427
91	102.153814577099	97.0451359141734	107.262493240025
92	102.398645230971	96.7857001173169	108.011590344624
93	102.643475884842	96.52851497025	108.758436799434
94	102.888306538713	96.2715189687369	109.50509410869
95	103.133137192585	96.0132325037999	110.253041881369
96	103.377967846456	95.7525668910041	111.003368801908

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code