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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 19 Jan 2010 10:48:25 -0700

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/2010/Jan/19/t1263923353sboft419iinsbb9.htm/, Retrieved Thu, 02 May 2024 00:36:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72290, Retrieved Thu, 02 May 2024 00:36:40 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W62

Estimated Impact

199

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [Opgave 10 oefening 2] [2010-01-19 17:48:25] [243e584c296eec1181ddc9ac4f09d2dd] [Current]

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Dataseries X:

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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	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72290&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72290&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72290&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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.805432048964002
beta	0.0400555709654088
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.805432048964002 \tabularnewline
beta & 0.0400555709654088 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72290&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]0.805432048964002[/C][/ROW]
[ROW][C]beta[/C][C]0.0400555709654088[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72290&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72290&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	0.805432048964002
beta	0.0400555709654088
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	99.98	100.056026080726	-0.0760260807263364
14	99.98	99.9894142160589	-0.00941421605888593
15	99.93	99.9273995275427	0.00260047245728856
16	99.93	99.9318135632775	-0.00181356327745164
17	99.93	99.9430369798857	-0.0130369798857259
18	99.93	99.9493926268917	-0.0193926268916869
19	99.93	99.8807096461471	0.049290353852868
20	99.93	99.9119441638902	0.0180558361097809
21	99.76	99.7796609650187	-0.0196609650187014
22	99.48	99.6093286667098	-0.129328666709796
23	99.55	99.6864859490623	-0.136485949062291
24	99.56	99.5627546164881	-0.00275461648813291
25	99.57	99.5319162312653	0.0380837687347082
26	99.56	99.5628321115556	-0.00283211155557694
27	99.65	99.5015794684123	0.148420531587661
28	99.5	99.6202070215222	-0.120207021522205
29	99.5	99.527635224943	-0.0276352249430403
30	99.49	99.514240465384	-0.0242404653841106
31	99.49	99.4483368437222	0.0416631562778349
32	99.46	99.4603251872479	-0.00032518724786712
33	99.52	99.2989491745507	0.221050825449339
34	99.49	99.3017501474772	0.188249852522759
35	99.55	99.6436567937717	-0.0936567937717427
36	99.57	99.5922707859568	-0.0222707859568203
37	99.57	99.5648513202444	0.00514867975563504
38	99.57	99.571411737407	-0.00141173740699685
39	99.57	99.550874919209	0.0191250807909569
40	99.57	99.519105554924	0.0508944450759401
41	99.57	99.5939106459389	-0.0239106459389262
42	99.57	99.5958534595258	-0.0258534595258340
43	99.57	99.5530632819972	0.0169367180028104
44	99.53	99.5477633308832	-0.0177633308831702
45	100.38	99.4254972043923	0.954502795607695
46	100.32	100.045325529682	0.274674470317706
47	100.46	100.439795689661	0.0202043103392526
48	100.47	100.534848558395	-0.0648485583945302
49	100.47	100.517568201039	-0.0475682010389562
50	100.47	100.517841675767	-0.0478416757673159
51	100.51	100.499704602518	0.0102953974815705
52	100.5	100.502260013732	-0.00226001373219731
53	100.51	100.553802081625	-0.0438020816253584
54	100.51	100.572847276984	-0.062847276983831
55	100.51	100.540575244873	-0.0305752448729635
56	100.51	100.520588403206	-0.0105884032060573
57	101.65	100.623483529554	1.02651647044583
58	102.13	101.198623155551	0.931376844448621
59	102.2	102.128217819249	0.0717821807507306
60	102.13	102.304674947031	-0.174674947031377
61	102.13	102.254796868257	-0.124796868256709
62	102.12	102.242856712216	-0.122856712216446
63	102.13	102.223152374765	-0.0931523747653245
64	102.05	102.183475917548	-0.133475917548068
65	102	102.16141160718	-0.161411607179957
66	102.01	102.118488968804	-0.108488968803996
67	102.01	102.090370631631	-0.0803706316307569
68	102.02	102.066965518238	-0.0469655182383093
69	102.78	102.377025189081	0.402974810919275
70	103.39	102.438403407218	0.951596592782167
71	103.41	103.228532419715	0.181467580284917
72	103.5	103.460957371917	0.0390426280828251
73	103.5	103.615869397064	-0.115869397063804
74	103.49	103.634643508598	-0.144643508598023
75	103.38	103.625628357974	-0.24562835797407
76	103.24	103.472105246967	-0.232105246966967
77	103.25	103.379491254403	-0.129491254403462
78	103.25	103.388246551634	-0.138246551633856
79	103.25	103.355986363042	-0.105986363042319
80	103.25	103.331805950095	-0.0818059500950596
81	103.83	103.718129933297	0.111870066703219
82	104.33	103.651118282643	0.678881717356617
83	104.36	104.064054390805	0.295945609194931
84	104.48	104.358381412519	0.121618587480512
85	104.5	104.550002703813	-0.0500027038132913
86	104.48	104.618845407868	-0.138845407867848
87	104.35	104.597456454143	-0.247456454143233
88	104.48	104.447318458697	0.0326815413028640
89	104.48	104.599583821849	-0.119583821848664
90	104.47	104.626603128107	-0.156603128107491
91	104.47	104.596981309612	-0.126981309611551
92	104.86	104.570876764188	0.289123235811758
93	105.22	105.322398830352	-0.102398830351973
94	105.96	105.206306941881	0.753693058118785
95	106.03	105.618396343367	0.411603656632536
96	106.03	105.992253162990	0.0377468370102605

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 99.98 & 100.056026080726 & -0.0760260807263364 \tabularnewline
14 & 99.98 & 99.9894142160589 & -0.00941421605888593 \tabularnewline
15 & 99.93 & 99.9273995275427 & 0.00260047245728856 \tabularnewline
16 & 99.93 & 99.9318135632775 & -0.00181356327745164 \tabularnewline
17 & 99.93 & 99.9430369798857 & -0.0130369798857259 \tabularnewline
18 & 99.93 & 99.9493926268917 & -0.0193926268916869 \tabularnewline
19 & 99.93 & 99.8807096461471 & 0.049290353852868 \tabularnewline
20 & 99.93 & 99.9119441638902 & 0.0180558361097809 \tabularnewline
21 & 99.76 & 99.7796609650187 & -0.0196609650187014 \tabularnewline
22 & 99.48 & 99.6093286667098 & -0.129328666709796 \tabularnewline
23 & 99.55 & 99.6864859490623 & -0.136485949062291 \tabularnewline
24 & 99.56 & 99.5627546164881 & -0.00275461648813291 \tabularnewline
25 & 99.57 & 99.5319162312653 & 0.0380837687347082 \tabularnewline
26 & 99.56 & 99.5628321115556 & -0.00283211155557694 \tabularnewline
27 & 99.65 & 99.5015794684123 & 0.148420531587661 \tabularnewline
28 & 99.5 & 99.6202070215222 & -0.120207021522205 \tabularnewline
29 & 99.5 & 99.527635224943 & -0.0276352249430403 \tabularnewline
30 & 99.49 & 99.514240465384 & -0.0242404653841106 \tabularnewline
31 & 99.49 & 99.4483368437222 & 0.0416631562778349 \tabularnewline
32 & 99.46 & 99.4603251872479 & -0.00032518724786712 \tabularnewline
33 & 99.52 & 99.2989491745507 & 0.221050825449339 \tabularnewline
34 & 99.49 & 99.3017501474772 & 0.188249852522759 \tabularnewline
35 & 99.55 & 99.6436567937717 & -0.0936567937717427 \tabularnewline
36 & 99.57 & 99.5922707859568 & -0.0222707859568203 \tabularnewline
37 & 99.57 & 99.5648513202444 & 0.00514867975563504 \tabularnewline
38 & 99.57 & 99.571411737407 & -0.00141173740699685 \tabularnewline
39 & 99.57 & 99.550874919209 & 0.0191250807909569 \tabularnewline
40 & 99.57 & 99.519105554924 & 0.0508944450759401 \tabularnewline
41 & 99.57 & 99.5939106459389 & -0.0239106459389262 \tabularnewline
42 & 99.57 & 99.5958534595258 & -0.0258534595258340 \tabularnewline
43 & 99.57 & 99.5530632819972 & 0.0169367180028104 \tabularnewline
44 & 99.53 & 99.5477633308832 & -0.0177633308831702 \tabularnewline
45 & 100.38 & 99.4254972043923 & 0.954502795607695 \tabularnewline
46 & 100.32 & 100.045325529682 & 0.274674470317706 \tabularnewline
47 & 100.46 & 100.439795689661 & 0.0202043103392526 \tabularnewline
48 & 100.47 & 100.534848558395 & -0.0648485583945302 \tabularnewline
49 & 100.47 & 100.517568201039 & -0.0475682010389562 \tabularnewline
50 & 100.47 & 100.517841675767 & -0.0478416757673159 \tabularnewline
51 & 100.51 & 100.499704602518 & 0.0102953974815705 \tabularnewline
52 & 100.5 & 100.502260013732 & -0.00226001373219731 \tabularnewline
53 & 100.51 & 100.553802081625 & -0.0438020816253584 \tabularnewline
54 & 100.51 & 100.572847276984 & -0.062847276983831 \tabularnewline
55 & 100.51 & 100.540575244873 & -0.0305752448729635 \tabularnewline
56 & 100.51 & 100.520588403206 & -0.0105884032060573 \tabularnewline
57 & 101.65 & 100.623483529554 & 1.02651647044583 \tabularnewline
58 & 102.13 & 101.198623155551 & 0.931376844448621 \tabularnewline
59 & 102.2 & 102.128217819249 & 0.0717821807507306 \tabularnewline
60 & 102.13 & 102.304674947031 & -0.174674947031377 \tabularnewline
61 & 102.13 & 102.254796868257 & -0.124796868256709 \tabularnewline
62 & 102.12 & 102.242856712216 & -0.122856712216446 \tabularnewline
63 & 102.13 & 102.223152374765 & -0.0931523747653245 \tabularnewline
64 & 102.05 & 102.183475917548 & -0.133475917548068 \tabularnewline
65 & 102 & 102.16141160718 & -0.161411607179957 \tabularnewline
66 & 102.01 & 102.118488968804 & -0.108488968803996 \tabularnewline
67 & 102.01 & 102.090370631631 & -0.0803706316307569 \tabularnewline
68 & 102.02 & 102.066965518238 & -0.0469655182383093 \tabularnewline
69 & 102.78 & 102.377025189081 & 0.402974810919275 \tabularnewline
70 & 103.39 & 102.438403407218 & 0.951596592782167 \tabularnewline
71 & 103.41 & 103.228532419715 & 0.181467580284917 \tabularnewline
72 & 103.5 & 103.460957371917 & 0.0390426280828251 \tabularnewline
73 & 103.5 & 103.615869397064 & -0.115869397063804 \tabularnewline
74 & 103.49 & 103.634643508598 & -0.144643508598023 \tabularnewline
75 & 103.38 & 103.625628357974 & -0.24562835797407 \tabularnewline
76 & 103.24 & 103.472105246967 & -0.232105246966967 \tabularnewline
77 & 103.25 & 103.379491254403 & -0.129491254403462 \tabularnewline
78 & 103.25 & 103.388246551634 & -0.138246551633856 \tabularnewline
79 & 103.25 & 103.355986363042 & -0.105986363042319 \tabularnewline
80 & 103.25 & 103.331805950095 & -0.0818059500950596 \tabularnewline
81 & 103.83 & 103.718129933297 & 0.111870066703219 \tabularnewline
82 & 104.33 & 103.651118282643 & 0.678881717356617 \tabularnewline
83 & 104.36 & 104.064054390805 & 0.295945609194931 \tabularnewline
84 & 104.48 & 104.358381412519 & 0.121618587480512 \tabularnewline
85 & 104.5 & 104.550002703813 & -0.0500027038132913 \tabularnewline
86 & 104.48 & 104.618845407868 & -0.138845407867848 \tabularnewline
87 & 104.35 & 104.597456454143 & -0.247456454143233 \tabularnewline
88 & 104.48 & 104.447318458697 & 0.0326815413028640 \tabularnewline
89 & 104.48 & 104.599583821849 & -0.119583821848664 \tabularnewline
90 & 104.47 & 104.626603128107 & -0.156603128107491 \tabularnewline
91 & 104.47 & 104.596981309612 & -0.126981309611551 \tabularnewline
92 & 104.86 & 104.570876764188 & 0.289123235811758 \tabularnewline
93 & 105.22 & 105.322398830352 & -0.102398830351973 \tabularnewline
94 & 105.96 & 105.206306941881 & 0.753693058118785 \tabularnewline
95 & 106.03 & 105.618396343367 & 0.411603656632536 \tabularnewline
96 & 106.03 & 105.992253162990 & 0.0377468370102605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72290&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]99.98[/C][C]100.056026080726[/C][C]-0.0760260807263364[/C][/ROW]
[ROW][C]14[/C][C]99.98[/C][C]99.9894142160589[/C][C]-0.00941421605888593[/C][/ROW]
[ROW][C]15[/C][C]99.93[/C][C]99.9273995275427[/C][C]0.00260047245728856[/C][/ROW]
[ROW][C]16[/C][C]99.93[/C][C]99.9318135632775[/C][C]-0.00181356327745164[/C][/ROW]
[ROW][C]17[/C][C]99.93[/C][C]99.9430369798857[/C][C]-0.0130369798857259[/C][/ROW]
[ROW][C]18[/C][C]99.93[/C][C]99.9493926268917[/C][C]-0.0193926268916869[/C][/ROW]
[ROW][C]19[/C][C]99.93[/C][C]99.8807096461471[/C][C]0.049290353852868[/C][/ROW]
[ROW][C]20[/C][C]99.93[/C][C]99.9119441638902[/C][C]0.0180558361097809[/C][/ROW]
[ROW][C]21[/C][C]99.76[/C][C]99.7796609650187[/C][C]-0.0196609650187014[/C][/ROW]
[ROW][C]22[/C][C]99.48[/C][C]99.6093286667098[/C][C]-0.129328666709796[/C][/ROW]
[ROW][C]23[/C][C]99.55[/C][C]99.6864859490623[/C][C]-0.136485949062291[/C][/ROW]
[ROW][C]24[/C][C]99.56[/C][C]99.5627546164881[/C][C]-0.00275461648813291[/C][/ROW]
[ROW][C]25[/C][C]99.57[/C][C]99.5319162312653[/C][C]0.0380837687347082[/C][/ROW]
[ROW][C]26[/C][C]99.56[/C][C]99.5628321115556[/C][C]-0.00283211155557694[/C][/ROW]
[ROW][C]27[/C][C]99.65[/C][C]99.5015794684123[/C][C]0.148420531587661[/C][/ROW]
[ROW][C]28[/C][C]99.5[/C][C]99.6202070215222[/C][C]-0.120207021522205[/C][/ROW]
[ROW][C]29[/C][C]99.5[/C][C]99.527635224943[/C][C]-0.0276352249430403[/C][/ROW]
[ROW][C]30[/C][C]99.49[/C][C]99.514240465384[/C][C]-0.0242404653841106[/C][/ROW]
[ROW][C]31[/C][C]99.49[/C][C]99.4483368437222[/C][C]0.0416631562778349[/C][/ROW]
[ROW][C]32[/C][C]99.46[/C][C]99.4603251872479[/C][C]-0.00032518724786712[/C][/ROW]
[ROW][C]33[/C][C]99.52[/C][C]99.2989491745507[/C][C]0.221050825449339[/C][/ROW]
[ROW][C]34[/C][C]99.49[/C][C]99.3017501474772[/C][C]0.188249852522759[/C][/ROW]
[ROW][C]35[/C][C]99.55[/C][C]99.6436567937717[/C][C]-0.0936567937717427[/C][/ROW]
[ROW][C]36[/C][C]99.57[/C][C]99.5922707859568[/C][C]-0.0222707859568203[/C][/ROW]
[ROW][C]37[/C][C]99.57[/C][C]99.5648513202444[/C][C]0.00514867975563504[/C][/ROW]
[ROW][C]38[/C][C]99.57[/C][C]99.571411737407[/C][C]-0.00141173740699685[/C][/ROW]
[ROW][C]39[/C][C]99.57[/C][C]99.550874919209[/C][C]0.0191250807909569[/C][/ROW]
[ROW][C]40[/C][C]99.57[/C][C]99.519105554924[/C][C]0.0508944450759401[/C][/ROW]
[ROW][C]41[/C][C]99.57[/C][C]99.5939106459389[/C][C]-0.0239106459389262[/C][/ROW]
[ROW][C]42[/C][C]99.57[/C][C]99.5958534595258[/C][C]-0.0258534595258340[/C][/ROW]
[ROW][C]43[/C][C]99.57[/C][C]99.5530632819972[/C][C]0.0169367180028104[/C][/ROW]
[ROW][C]44[/C][C]99.53[/C][C]99.5477633308832[/C][C]-0.0177633308831702[/C][/ROW]
[ROW][C]45[/C][C]100.38[/C][C]99.4254972043923[/C][C]0.954502795607695[/C][/ROW]
[ROW][C]46[/C][C]100.32[/C][C]100.045325529682[/C][C]0.274674470317706[/C][/ROW]
[ROW][C]47[/C][C]100.46[/C][C]100.439795689661[/C][C]0.0202043103392526[/C][/ROW]
[ROW][C]48[/C][C]100.47[/C][C]100.534848558395[/C][C]-0.0648485583945302[/C][/ROW]
[ROW][C]49[/C][C]100.47[/C][C]100.517568201039[/C][C]-0.0475682010389562[/C][/ROW]
[ROW][C]50[/C][C]100.47[/C][C]100.517841675767[/C][C]-0.0478416757673159[/C][/ROW]
[ROW][C]51[/C][C]100.51[/C][C]100.499704602518[/C][C]0.0102953974815705[/C][/ROW]
[ROW][C]52[/C][C]100.5[/C][C]100.502260013732[/C][C]-0.00226001373219731[/C][/ROW]
[ROW][C]53[/C][C]100.51[/C][C]100.553802081625[/C][C]-0.0438020816253584[/C][/ROW]
[ROW][C]54[/C][C]100.51[/C][C]100.572847276984[/C][C]-0.062847276983831[/C][/ROW]
[ROW][C]55[/C][C]100.51[/C][C]100.540575244873[/C][C]-0.0305752448729635[/C][/ROW]
[ROW][C]56[/C][C]100.51[/C][C]100.520588403206[/C][C]-0.0105884032060573[/C][/ROW]
[ROW][C]57[/C][C]101.65[/C][C]100.623483529554[/C][C]1.02651647044583[/C][/ROW]
[ROW][C]58[/C][C]102.13[/C][C]101.198623155551[/C][C]0.931376844448621[/C][/ROW]
[ROW][C]59[/C][C]102.2[/C][C]102.128217819249[/C][C]0.0717821807507306[/C][/ROW]
[ROW][C]60[/C][C]102.13[/C][C]102.304674947031[/C][C]-0.174674947031377[/C][/ROW]
[ROW][C]61[/C][C]102.13[/C][C]102.254796868257[/C][C]-0.124796868256709[/C][/ROW]
[ROW][C]62[/C][C]102.12[/C][C]102.242856712216[/C][C]-0.122856712216446[/C][/ROW]
[ROW][C]63[/C][C]102.13[/C][C]102.223152374765[/C][C]-0.0931523747653245[/C][/ROW]
[ROW][C]64[/C][C]102.05[/C][C]102.183475917548[/C][C]-0.133475917548068[/C][/ROW]
[ROW][C]65[/C][C]102[/C][C]102.16141160718[/C][C]-0.161411607179957[/C][/ROW]
[ROW][C]66[/C][C]102.01[/C][C]102.118488968804[/C][C]-0.108488968803996[/C][/ROW]
[ROW][C]67[/C][C]102.01[/C][C]102.090370631631[/C][C]-0.0803706316307569[/C][/ROW]
[ROW][C]68[/C][C]102.02[/C][C]102.066965518238[/C][C]-0.0469655182383093[/C][/ROW]
[ROW][C]69[/C][C]102.78[/C][C]102.377025189081[/C][C]0.402974810919275[/C][/ROW]
[ROW][C]70[/C][C]103.39[/C][C]102.438403407218[/C][C]0.951596592782167[/C][/ROW]
[ROW][C]71[/C][C]103.41[/C][C]103.228532419715[/C][C]0.181467580284917[/C][/ROW]
[ROW][C]72[/C][C]103.5[/C][C]103.460957371917[/C][C]0.0390426280828251[/C][/ROW]
[ROW][C]73[/C][C]103.5[/C][C]103.615869397064[/C][C]-0.115869397063804[/C][/ROW]
[ROW][C]74[/C][C]103.49[/C][C]103.634643508598[/C][C]-0.144643508598023[/C][/ROW]
[ROW][C]75[/C][C]103.38[/C][C]103.625628357974[/C][C]-0.24562835797407[/C][/ROW]
[ROW][C]76[/C][C]103.24[/C][C]103.472105246967[/C][C]-0.232105246966967[/C][/ROW]
[ROW][C]77[/C][C]103.25[/C][C]103.379491254403[/C][C]-0.129491254403462[/C][/ROW]
[ROW][C]78[/C][C]103.25[/C][C]103.388246551634[/C][C]-0.138246551633856[/C][/ROW]
[ROW][C]79[/C][C]103.25[/C][C]103.355986363042[/C][C]-0.105986363042319[/C][/ROW]
[ROW][C]80[/C][C]103.25[/C][C]103.331805950095[/C][C]-0.0818059500950596[/C][/ROW]
[ROW][C]81[/C][C]103.83[/C][C]103.718129933297[/C][C]0.111870066703219[/C][/ROW]
[ROW][C]82[/C][C]104.33[/C][C]103.651118282643[/C][C]0.678881717356617[/C][/ROW]
[ROW][C]83[/C][C]104.36[/C][C]104.064054390805[/C][C]0.295945609194931[/C][/ROW]
[ROW][C]84[/C][C]104.48[/C][C]104.358381412519[/C][C]0.121618587480512[/C][/ROW]
[ROW][C]85[/C][C]104.5[/C][C]104.550002703813[/C][C]-0.0500027038132913[/C][/ROW]
[ROW][C]86[/C][C]104.48[/C][C]104.618845407868[/C][C]-0.138845407867848[/C][/ROW]
[ROW][C]87[/C][C]104.35[/C][C]104.597456454143[/C][C]-0.247456454143233[/C][/ROW]
[ROW][C]88[/C][C]104.48[/C][C]104.447318458697[/C][C]0.0326815413028640[/C][/ROW]
[ROW][C]89[/C][C]104.48[/C][C]104.599583821849[/C][C]-0.119583821848664[/C][/ROW]
[ROW][C]90[/C][C]104.47[/C][C]104.626603128107[/C][C]-0.156603128107491[/C][/ROW]
[ROW][C]91[/C][C]104.47[/C][C]104.596981309612[/C][C]-0.126981309611551[/C][/ROW]
[ROW][C]92[/C][C]104.86[/C][C]104.570876764188[/C][C]0.289123235811758[/C][/ROW]
[ROW][C]93[/C][C]105.22[/C][C]105.322398830352[/C][C]-0.102398830351973[/C][/ROW]
[ROW][C]94[/C][C]105.96[/C][C]105.206306941881[/C][C]0.753693058118785[/C][/ROW]
[ROW][C]95[/C][C]106.03[/C][C]105.618396343367[/C][C]0.411603656632536[/C][/ROW]
[ROW][C]96[/C][C]106.03[/C][C]105.992253162990[/C][C]0.0377468370102605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72290&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72290&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
13	99.98	100.056026080726	-0.0760260807263364
14	99.98	99.9894142160589	-0.00941421605888593
15	99.93	99.9273995275427	0.00260047245728856
16	99.93	99.9318135632775	-0.00181356327745164
17	99.93	99.9430369798857	-0.0130369798857259
18	99.93	99.9493926268917	-0.0193926268916869
19	99.93	99.8807096461471	0.049290353852868
20	99.93	99.9119441638902	0.0180558361097809
21	99.76	99.7796609650187	-0.0196609650187014
22	99.48	99.6093286667098	-0.129328666709796
23	99.55	99.6864859490623	-0.136485949062291
24	99.56	99.5627546164881	-0.00275461648813291
25	99.57	99.5319162312653	0.0380837687347082
26	99.56	99.5628321115556	-0.00283211155557694
27	99.65	99.5015794684123	0.148420531587661
28	99.5	99.6202070215222	-0.120207021522205
29	99.5	99.527635224943	-0.0276352249430403
30	99.49	99.514240465384	-0.0242404653841106
31	99.49	99.4483368437222	0.0416631562778349
32	99.46	99.4603251872479	-0.00032518724786712
33	99.52	99.2989491745507	0.221050825449339
34	99.49	99.3017501474772	0.188249852522759
35	99.55	99.6436567937717	-0.0936567937717427
36	99.57	99.5922707859568	-0.0222707859568203
37	99.57	99.5648513202444	0.00514867975563504
38	99.57	99.571411737407	-0.00141173740699685
39	99.57	99.550874919209	0.0191250807909569
40	99.57	99.519105554924	0.0508944450759401
41	99.57	99.5939106459389	-0.0239106459389262
42	99.57	99.5958534595258	-0.0258534595258340
43	99.57	99.5530632819972	0.0169367180028104
44	99.53	99.5477633308832	-0.0177633308831702
45	100.38	99.4254972043923	0.954502795607695
46	100.32	100.045325529682	0.274674470317706
47	100.46	100.439795689661	0.0202043103392526
48	100.47	100.534848558395	-0.0648485583945302
49	100.47	100.517568201039	-0.0475682010389562
50	100.47	100.517841675767	-0.0478416757673159
51	100.51	100.499704602518	0.0102953974815705
52	100.5	100.502260013732	-0.00226001373219731
53	100.51	100.553802081625	-0.0438020816253584
54	100.51	100.572847276984	-0.062847276983831
55	100.51	100.540575244873	-0.0305752448729635
56	100.51	100.520588403206	-0.0105884032060573
57	101.65	100.623483529554	1.02651647044583
58	102.13	101.198623155551	0.931376844448621
59	102.2	102.128217819249	0.0717821807507306
60	102.13	102.304674947031	-0.174674947031377
61	102.13	102.254796868257	-0.124796868256709
62	102.12	102.242856712216	-0.122856712216446
63	102.13	102.223152374765	-0.0931523747653245
64	102.05	102.183475917548	-0.133475917548068
65	102	102.16141160718	-0.161411607179957
66	102.01	102.118488968804	-0.108488968803996
67	102.01	102.090370631631	-0.0803706316307569
68	102.02	102.066965518238	-0.0469655182383093
69	102.78	102.377025189081	0.402974810919275
70	103.39	102.438403407218	0.951596592782167
71	103.41	103.228532419715	0.181467580284917
72	103.5	103.460957371917	0.0390426280828251
73	103.5	103.615869397064	-0.115869397063804
74	103.49	103.634643508598	-0.144643508598023
75	103.38	103.625628357974	-0.24562835797407
76	103.24	103.472105246967	-0.232105246966967
77	103.25	103.379491254403	-0.129491254403462
78	103.25	103.388246551634	-0.138246551633856
79	103.25	103.355986363042	-0.105986363042319
80	103.25	103.331805950095	-0.0818059500950596
81	103.83	103.718129933297	0.111870066703219
82	104.33	103.651118282643	0.678881717356617
83	104.36	104.064054390805	0.295945609194931
84	104.48	104.358381412519	0.121618587480512
85	104.5	104.550002703813	-0.0500027038132913
86	104.48	104.618845407868	-0.138845407867848
87	104.35	104.597456454143	-0.247456454143233
88	104.48	104.447318458697	0.0326815413028640
89	104.48	104.599583821849	-0.119583821848664
90	104.47	104.626603128107	-0.156603128107491
91	104.47	104.596981309612	-0.126981309611551
92	104.86	104.570876764188	0.289123235811758
93	105.22	105.322398830352	-0.102398830351973
94	105.96	105.206306941881	0.753693058118785
95	106.03	105.618396343367	0.411603656632536
96	106.03	105.992253162990	0.0377468370102605

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	106.101069445953	105.578672561934	106.623466329971
98	106.213113045307	105.531659391492	106.894566699122
99	106.306737881186	105.487755376750	107.125720385622
100	106.443550588108	105.498523081704	107.388578094511
101	106.571773618395	105.508028046882	107.635519189908
102	106.724152181374	105.546299324511	107.902005038237
103	106.867608062265	105.579034116346	108.156182008185
104	107.071334462219	105.673671470408	108.468997454029
105	107.556964544593	106.048285030223	109.065644058963
106	107.729150492297	106.114410522878	109.343890461715
107	107.475790585857	105.761837740730	109.189743430984
108	107.444598443947	102.684829795156	112.204367092738

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 106.101069445953 & 105.578672561934 & 106.623466329971 \tabularnewline
98 & 106.213113045307 & 105.531659391492 & 106.894566699122 \tabularnewline
99 & 106.306737881186 & 105.487755376750 & 107.125720385622 \tabularnewline
100 & 106.443550588108 & 105.498523081704 & 107.388578094511 \tabularnewline
101 & 106.571773618395 & 105.508028046882 & 107.635519189908 \tabularnewline
102 & 106.724152181374 & 105.546299324511 & 107.902005038237 \tabularnewline
103 & 106.867608062265 & 105.579034116346 & 108.156182008185 \tabularnewline
104 & 107.071334462219 & 105.673671470408 & 108.468997454029 \tabularnewline
105 & 107.556964544593 & 106.048285030223 & 109.065644058963 \tabularnewline
106 & 107.729150492297 & 106.114410522878 & 109.343890461715 \tabularnewline
107 & 107.475790585857 & 105.761837740730 & 109.189743430984 \tabularnewline
108 & 107.444598443947 & 102.684829795156 & 112.204367092738 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72290&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]106.101069445953[/C][C]105.578672561934[/C][C]106.623466329971[/C][/ROW]
[ROW][C]98[/C][C]106.213113045307[/C][C]105.531659391492[/C][C]106.894566699122[/C][/ROW]
[ROW][C]99[/C][C]106.306737881186[/C][C]105.487755376750[/C][C]107.125720385622[/C][/ROW]
[ROW][C]100[/C][C]106.443550588108[/C][C]105.498523081704[/C][C]107.388578094511[/C][/ROW]
[ROW][C]101[/C][C]106.571773618395[/C][C]105.508028046882[/C][C]107.635519189908[/C][/ROW]
[ROW][C]102[/C][C]106.724152181374[/C][C]105.546299324511[/C][C]107.902005038237[/C][/ROW]
[ROW][C]103[/C][C]106.867608062265[/C][C]105.579034116346[/C][C]108.156182008185[/C][/ROW]
[ROW][C]104[/C][C]107.071334462219[/C][C]105.673671470408[/C][C]108.468997454029[/C][/ROW]
[ROW][C]105[/C][C]107.556964544593[/C][C]106.048285030223[/C][C]109.065644058963[/C][/ROW]
[ROW][C]106[/C][C]107.729150492297[/C][C]106.114410522878[/C][C]109.343890461715[/C][/ROW]
[ROW][C]107[/C][C]107.475790585857[/C][C]105.761837740730[/C][C]109.189743430984[/C][/ROW]
[ROW][C]108[/C][C]107.444598443947[/C][C]102.684829795156[/C][C]112.204367092738[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72290&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72290&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
97	106.101069445953	105.578672561934	106.623466329971
98	106.213113045307	105.531659391492	106.894566699122
99	106.306737881186	105.487755376750	107.125720385622
100	106.443550588108	105.498523081704	107.388578094511
101	106.571773618395	105.508028046882	107.635519189908
102	106.724152181374	105.546299324511	107.902005038237
103	106.867608062265	105.579034116346	108.156182008185
104	107.071334462219	105.673671470408	108.468997454029
105	107.556964544593	106.048285030223	109.065644058963
106	107.729150492297	106.114410522878	109.343890461715
107	107.475790585857	105.761837740730	109.189743430984
108	107.444598443947	102.684829795156	112.204367092738

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 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code