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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 24 Jan 2009 06:40:50 -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/2009/Jan/24/t123280453519koyf0qxqyt1kq.htm/, Retrieved Tue, 07 May 2024 16:06:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36938, Retrieved Tue, 07 May 2024 16:06:20 +0000

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No (this computation is public)

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Estimated Impact

205

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

-       [Exponential Smoothing] [opgave 10, oef. 2...] [2009-01-24 13:40:50] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36938&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]1 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=36938&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36938&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.956576248437865
beta	0
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.956576248437865 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36938&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]0.956576248437865[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36938&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36938&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	0.956576248437865
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	9.787	9.026	0.761000000000001
3	9.536	9.75395452506122	-0.217954525061216
4	9.49	9.5454644031481	-0.0554644031481004
5	9.736	9.49240847246285	0.243591527537156
6	9.694	9.72542234202558	-0.0314223420255839
7	9.647	9.69536447597362	-0.048364475973619
8	9.753	9.64910016698911	0.103899833010887
9	10.07	9.74848827946399	0.321511720536012
10	10.137	10.0560387549231	0.0809612450768711
11	9.984	10.1334843590076	-0.149484359007621
12	9.732	9.99049117166797	-0.258491171667972
13	9.103	9.74322465641952	-0.640224656419516
14	9.155	9.13080095642431	0.0241990435756865
15	9.308	9.15394918674373	0.154050813256273
16	9.394	9.30131053575721	0.0926894642427865
17	9.948	9.3899750757323	0.558024924267706
18	10.177	9.92376846432312	0.253231535676878
19	10.002	10.1660037367071	-0.164003736707068
20	9.728	10.0091216575180	-0.28112165751803
21	10.002	9.7402073570148	0.261792642985203
22	10.063	9.99063198131022	0.0723680186897848
23	10.018	10.0598575091354	-0.0418575091353706
24	9.96	10.0198176100777	-0.0598176100777046
25	10.236	9.96259750503905	0.273402494960946
26	10.893	10.2241278379823	0.668872162017653
27	10.756	10.8639550614097	-0.107955061409719
28	10.94	10.7606878137665	0.179312186233469
29	10.997	10.9322135921729	0.0647864078270644
30	10.827	10.9941867311219	-0.167186731121914
31	10.166	10.8342598750767	-0.668259875076723
32	10.186	10.1950183507943	-0.00901835079427471
33	10.457	10.1863916106244	0.270608389375610
34	10.368	10.4452491685291	-0.077249168529125
35	10.244	10.3713544487026	-0.127354448702590
36	10.511	10.2495302079408	0.261469792059206
37	10.812	10.4996460007086	0.312353999291382
38	10.738	10.7984364175353	-0.0604364175353318
39	10.171	10.7406243759804	-0.569624375980361
40	9.721	10.1957352273863	-0.474735227386308
41	9.897	9.74161478457182	0.155385215428183
42	9.828	9.89025259100882	-0.0622525910088179
43	9.924	9.83070324104606	0.0932967589539349
44	10.371	9.91994870471763	0.451051295282369
45	10.846	10.3514136606119	0.494586339388121
46	10.413	10.8245232056724	-0.411523205672385
47	10.709	10.4308698814452	0.278130118554829
48	10.662	10.6969225468299	-0.034922546829927
49	10.57	10.6635164679975	-0.0935164679974605
50	10.297	10.5740608358733	-0.277060835873289
51	10.635	10.3090310209046	0.325968979095441
52	10.872	10.6208452040348	0.251154795965203
53	10.296	10.8610939165364	-0.56509391653637
54	10.383	10.3205384978409	0.0624615021590511
55	10.431	10.3802876872480	0.0507123127519513
56	10.574	10.4287978811299	0.145202118870083
57	10.653	10.5676947792639	0.0853052207361102
58	10.805	10.6492957272878	0.155704272712196
59	10.872	10.7982387363446	0.0737612636554168
60	10.625	10.8687970092121	-0.243797009212118
61	10.407	10.6355865807596	-0.228586580759618
62	10.463	10.4169260868933	0.046073913106655
63	10.556	10.4609992978438	0.0950007021562396
64	10.646	10.5518747131113	0.0941252868886622
65	10.702	10.6419127269264	0.0600872730735684
66	11.353	10.699390785182	0.653609214817992
67	11.346	11.3246178358370	0.0213821641629792
68	11.451	11.3450715062155	0.105928493784475
69	11.964	11.4464001874026	0.517599812597448
70	12.574	11.9415238743292	0.63247612567084
71	13.031	12.5465355138499	0.484464486150113
72	13.812	13.0099627345127	0.802037265487259
73	14.544	13.7771725330399	0.766827466960093
74	14.931	14.5107014745837	0.420298525416294
75	14.886	14.9127490612504	-0.026749061250392
76	16.005	14.8871615445903	1.11783845540974
77	17.064	15.9564592606257	1.10754073937431
78	15.168	17.0159064260885	-1.84790642608847
79	16.05	15.2482430295565	0.801756970443464
80	15.839	16.0151847045023	-0.176184704502253
81	15.137	15.8466506008374	-0.709650600837353
82	14.954	15.1678156913867	-0.213815691386682
83	15.648	14.9632846794629	0.684715320537139
84	15.305	15.6182670920302	-0.313267092030207

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 9.787 & 9.026 & 0.761000000000001 \tabularnewline
3 & 9.536 & 9.75395452506122 & -0.217954525061216 \tabularnewline
4 & 9.49 & 9.5454644031481 & -0.0554644031481004 \tabularnewline
5 & 9.736 & 9.49240847246285 & 0.243591527537156 \tabularnewline
6 & 9.694 & 9.72542234202558 & -0.0314223420255839 \tabularnewline
7 & 9.647 & 9.69536447597362 & -0.048364475973619 \tabularnewline
8 & 9.753 & 9.64910016698911 & 0.103899833010887 \tabularnewline
9 & 10.07 & 9.74848827946399 & 0.321511720536012 \tabularnewline
10 & 10.137 & 10.0560387549231 & 0.0809612450768711 \tabularnewline
11 & 9.984 & 10.1334843590076 & -0.149484359007621 \tabularnewline
12 & 9.732 & 9.99049117166797 & -0.258491171667972 \tabularnewline
13 & 9.103 & 9.74322465641952 & -0.640224656419516 \tabularnewline
14 & 9.155 & 9.13080095642431 & 0.0241990435756865 \tabularnewline
15 & 9.308 & 9.15394918674373 & 0.154050813256273 \tabularnewline
16 & 9.394 & 9.30131053575721 & 0.0926894642427865 \tabularnewline
17 & 9.948 & 9.3899750757323 & 0.558024924267706 \tabularnewline
18 & 10.177 & 9.92376846432312 & 0.253231535676878 \tabularnewline
19 & 10.002 & 10.1660037367071 & -0.164003736707068 \tabularnewline
20 & 9.728 & 10.0091216575180 & -0.28112165751803 \tabularnewline
21 & 10.002 & 9.7402073570148 & 0.261792642985203 \tabularnewline
22 & 10.063 & 9.99063198131022 & 0.0723680186897848 \tabularnewline
23 & 10.018 & 10.0598575091354 & -0.0418575091353706 \tabularnewline
24 & 9.96 & 10.0198176100777 & -0.0598176100777046 \tabularnewline
25 & 10.236 & 9.96259750503905 & 0.273402494960946 \tabularnewline
26 & 10.893 & 10.2241278379823 & 0.668872162017653 \tabularnewline
27 & 10.756 & 10.8639550614097 & -0.107955061409719 \tabularnewline
28 & 10.94 & 10.7606878137665 & 0.179312186233469 \tabularnewline
29 & 10.997 & 10.9322135921729 & 0.0647864078270644 \tabularnewline
30 & 10.827 & 10.9941867311219 & -0.167186731121914 \tabularnewline
31 & 10.166 & 10.8342598750767 & -0.668259875076723 \tabularnewline
32 & 10.186 & 10.1950183507943 & -0.00901835079427471 \tabularnewline
33 & 10.457 & 10.1863916106244 & 0.270608389375610 \tabularnewline
34 & 10.368 & 10.4452491685291 & -0.077249168529125 \tabularnewline
35 & 10.244 & 10.3713544487026 & -0.127354448702590 \tabularnewline
36 & 10.511 & 10.2495302079408 & 0.261469792059206 \tabularnewline
37 & 10.812 & 10.4996460007086 & 0.312353999291382 \tabularnewline
38 & 10.738 & 10.7984364175353 & -0.0604364175353318 \tabularnewline
39 & 10.171 & 10.7406243759804 & -0.569624375980361 \tabularnewline
40 & 9.721 & 10.1957352273863 & -0.474735227386308 \tabularnewline
41 & 9.897 & 9.74161478457182 & 0.155385215428183 \tabularnewline
42 & 9.828 & 9.89025259100882 & -0.0622525910088179 \tabularnewline
43 & 9.924 & 9.83070324104606 & 0.0932967589539349 \tabularnewline
44 & 10.371 & 9.91994870471763 & 0.451051295282369 \tabularnewline
45 & 10.846 & 10.3514136606119 & 0.494586339388121 \tabularnewline
46 & 10.413 & 10.8245232056724 & -0.411523205672385 \tabularnewline
47 & 10.709 & 10.4308698814452 & 0.278130118554829 \tabularnewline
48 & 10.662 & 10.6969225468299 & -0.034922546829927 \tabularnewline
49 & 10.57 & 10.6635164679975 & -0.0935164679974605 \tabularnewline
50 & 10.297 & 10.5740608358733 & -0.277060835873289 \tabularnewline
51 & 10.635 & 10.3090310209046 & 0.325968979095441 \tabularnewline
52 & 10.872 & 10.6208452040348 & 0.251154795965203 \tabularnewline
53 & 10.296 & 10.8610939165364 & -0.56509391653637 \tabularnewline
54 & 10.383 & 10.3205384978409 & 0.0624615021590511 \tabularnewline
55 & 10.431 & 10.3802876872480 & 0.0507123127519513 \tabularnewline
56 & 10.574 & 10.4287978811299 & 0.145202118870083 \tabularnewline
57 & 10.653 & 10.5676947792639 & 0.0853052207361102 \tabularnewline
58 & 10.805 & 10.6492957272878 & 0.155704272712196 \tabularnewline
59 & 10.872 & 10.7982387363446 & 0.0737612636554168 \tabularnewline
60 & 10.625 & 10.8687970092121 & -0.243797009212118 \tabularnewline
61 & 10.407 & 10.6355865807596 & -0.228586580759618 \tabularnewline
62 & 10.463 & 10.4169260868933 & 0.046073913106655 \tabularnewline
63 & 10.556 & 10.4609992978438 & 0.0950007021562396 \tabularnewline
64 & 10.646 & 10.5518747131113 & 0.0941252868886622 \tabularnewline
65 & 10.702 & 10.6419127269264 & 0.0600872730735684 \tabularnewline
66 & 11.353 & 10.699390785182 & 0.653609214817992 \tabularnewline
67 & 11.346 & 11.3246178358370 & 0.0213821641629792 \tabularnewline
68 & 11.451 & 11.3450715062155 & 0.105928493784475 \tabularnewline
69 & 11.964 & 11.4464001874026 & 0.517599812597448 \tabularnewline
70 & 12.574 & 11.9415238743292 & 0.63247612567084 \tabularnewline
71 & 13.031 & 12.5465355138499 & 0.484464486150113 \tabularnewline
72 & 13.812 & 13.0099627345127 & 0.802037265487259 \tabularnewline
73 & 14.544 & 13.7771725330399 & 0.766827466960093 \tabularnewline
74 & 14.931 & 14.5107014745837 & 0.420298525416294 \tabularnewline
75 & 14.886 & 14.9127490612504 & -0.026749061250392 \tabularnewline
76 & 16.005 & 14.8871615445903 & 1.11783845540974 \tabularnewline
77 & 17.064 & 15.9564592606257 & 1.10754073937431 \tabularnewline
78 & 15.168 & 17.0159064260885 & -1.84790642608847 \tabularnewline
79 & 16.05 & 15.2482430295565 & 0.801756970443464 \tabularnewline
80 & 15.839 & 16.0151847045023 & -0.176184704502253 \tabularnewline
81 & 15.137 & 15.8466506008374 & -0.709650600837353 \tabularnewline
82 & 14.954 & 15.1678156913867 & -0.213815691386682 \tabularnewline
83 & 15.648 & 14.9632846794629 & 0.684715320537139 \tabularnewline
84 & 15.305 & 15.6182670920302 & -0.313267092030207 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36938&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]2[/C][C]9.787[/C][C]9.026[/C][C]0.761000000000001[/C][/ROW]
[ROW][C]3[/C][C]9.536[/C][C]9.75395452506122[/C][C]-0.217954525061216[/C][/ROW]
[ROW][C]4[/C][C]9.49[/C][C]9.5454644031481[/C][C]-0.0554644031481004[/C][/ROW]
[ROW][C]5[/C][C]9.736[/C][C]9.49240847246285[/C][C]0.243591527537156[/C][/ROW]
[ROW][C]6[/C][C]9.694[/C][C]9.72542234202558[/C][C]-0.0314223420255839[/C][/ROW]
[ROW][C]7[/C][C]9.647[/C][C]9.69536447597362[/C][C]-0.048364475973619[/C][/ROW]
[ROW][C]8[/C][C]9.753[/C][C]9.64910016698911[/C][C]0.103899833010887[/C][/ROW]
[ROW][C]9[/C][C]10.07[/C][C]9.74848827946399[/C][C]0.321511720536012[/C][/ROW]
[ROW][C]10[/C][C]10.137[/C][C]10.0560387549231[/C][C]0.0809612450768711[/C][/ROW]
[ROW][C]11[/C][C]9.984[/C][C]10.1334843590076[/C][C]-0.149484359007621[/C][/ROW]
[ROW][C]12[/C][C]9.732[/C][C]9.99049117166797[/C][C]-0.258491171667972[/C][/ROW]
[ROW][C]13[/C][C]9.103[/C][C]9.74322465641952[/C][C]-0.640224656419516[/C][/ROW]
[ROW][C]14[/C][C]9.155[/C][C]9.13080095642431[/C][C]0.0241990435756865[/C][/ROW]
[ROW][C]15[/C][C]9.308[/C][C]9.15394918674373[/C][C]0.154050813256273[/C][/ROW]
[ROW][C]16[/C][C]9.394[/C][C]9.30131053575721[/C][C]0.0926894642427865[/C][/ROW]
[ROW][C]17[/C][C]9.948[/C][C]9.3899750757323[/C][C]0.558024924267706[/C][/ROW]
[ROW][C]18[/C][C]10.177[/C][C]9.92376846432312[/C][C]0.253231535676878[/C][/ROW]
[ROW][C]19[/C][C]10.002[/C][C]10.1660037367071[/C][C]-0.164003736707068[/C][/ROW]
[ROW][C]20[/C][C]9.728[/C][C]10.0091216575180[/C][C]-0.28112165751803[/C][/ROW]
[ROW][C]21[/C][C]10.002[/C][C]9.7402073570148[/C][C]0.261792642985203[/C][/ROW]
[ROW][C]22[/C][C]10.063[/C][C]9.99063198131022[/C][C]0.0723680186897848[/C][/ROW]
[ROW][C]23[/C][C]10.018[/C][C]10.0598575091354[/C][C]-0.0418575091353706[/C][/ROW]
[ROW][C]24[/C][C]9.96[/C][C]10.0198176100777[/C][C]-0.0598176100777046[/C][/ROW]
[ROW][C]25[/C][C]10.236[/C][C]9.96259750503905[/C][C]0.273402494960946[/C][/ROW]
[ROW][C]26[/C][C]10.893[/C][C]10.2241278379823[/C][C]0.668872162017653[/C][/ROW]
[ROW][C]27[/C][C]10.756[/C][C]10.8639550614097[/C][C]-0.107955061409719[/C][/ROW]
[ROW][C]28[/C][C]10.94[/C][C]10.7606878137665[/C][C]0.179312186233469[/C][/ROW]
[ROW][C]29[/C][C]10.997[/C][C]10.9322135921729[/C][C]0.0647864078270644[/C][/ROW]
[ROW][C]30[/C][C]10.827[/C][C]10.9941867311219[/C][C]-0.167186731121914[/C][/ROW]
[ROW][C]31[/C][C]10.166[/C][C]10.8342598750767[/C][C]-0.668259875076723[/C][/ROW]
[ROW][C]32[/C][C]10.186[/C][C]10.1950183507943[/C][C]-0.00901835079427471[/C][/ROW]
[ROW][C]33[/C][C]10.457[/C][C]10.1863916106244[/C][C]0.270608389375610[/C][/ROW]
[ROW][C]34[/C][C]10.368[/C][C]10.4452491685291[/C][C]-0.077249168529125[/C][/ROW]
[ROW][C]35[/C][C]10.244[/C][C]10.3713544487026[/C][C]-0.127354448702590[/C][/ROW]
[ROW][C]36[/C][C]10.511[/C][C]10.2495302079408[/C][C]0.261469792059206[/C][/ROW]
[ROW][C]37[/C][C]10.812[/C][C]10.4996460007086[/C][C]0.312353999291382[/C][/ROW]
[ROW][C]38[/C][C]10.738[/C][C]10.7984364175353[/C][C]-0.0604364175353318[/C][/ROW]
[ROW][C]39[/C][C]10.171[/C][C]10.7406243759804[/C][C]-0.569624375980361[/C][/ROW]
[ROW][C]40[/C][C]9.721[/C][C]10.1957352273863[/C][C]-0.474735227386308[/C][/ROW]
[ROW][C]41[/C][C]9.897[/C][C]9.74161478457182[/C][C]0.155385215428183[/C][/ROW]
[ROW][C]42[/C][C]9.828[/C][C]9.89025259100882[/C][C]-0.0622525910088179[/C][/ROW]
[ROW][C]43[/C][C]9.924[/C][C]9.83070324104606[/C][C]0.0932967589539349[/C][/ROW]
[ROW][C]44[/C][C]10.371[/C][C]9.91994870471763[/C][C]0.451051295282369[/C][/ROW]
[ROW][C]45[/C][C]10.846[/C][C]10.3514136606119[/C][C]0.494586339388121[/C][/ROW]
[ROW][C]46[/C][C]10.413[/C][C]10.8245232056724[/C][C]-0.411523205672385[/C][/ROW]
[ROW][C]47[/C][C]10.709[/C][C]10.4308698814452[/C][C]0.278130118554829[/C][/ROW]
[ROW][C]48[/C][C]10.662[/C][C]10.6969225468299[/C][C]-0.034922546829927[/C][/ROW]
[ROW][C]49[/C][C]10.57[/C][C]10.6635164679975[/C][C]-0.0935164679974605[/C][/ROW]
[ROW][C]50[/C][C]10.297[/C][C]10.5740608358733[/C][C]-0.277060835873289[/C][/ROW]
[ROW][C]51[/C][C]10.635[/C][C]10.3090310209046[/C][C]0.325968979095441[/C][/ROW]
[ROW][C]52[/C][C]10.872[/C][C]10.6208452040348[/C][C]0.251154795965203[/C][/ROW]
[ROW][C]53[/C][C]10.296[/C][C]10.8610939165364[/C][C]-0.56509391653637[/C][/ROW]
[ROW][C]54[/C][C]10.383[/C][C]10.3205384978409[/C][C]0.0624615021590511[/C][/ROW]
[ROW][C]55[/C][C]10.431[/C][C]10.3802876872480[/C][C]0.0507123127519513[/C][/ROW]
[ROW][C]56[/C][C]10.574[/C][C]10.4287978811299[/C][C]0.145202118870083[/C][/ROW]
[ROW][C]57[/C][C]10.653[/C][C]10.5676947792639[/C][C]0.0853052207361102[/C][/ROW]
[ROW][C]58[/C][C]10.805[/C][C]10.6492957272878[/C][C]0.155704272712196[/C][/ROW]
[ROW][C]59[/C][C]10.872[/C][C]10.7982387363446[/C][C]0.0737612636554168[/C][/ROW]
[ROW][C]60[/C][C]10.625[/C][C]10.8687970092121[/C][C]-0.243797009212118[/C][/ROW]
[ROW][C]61[/C][C]10.407[/C][C]10.6355865807596[/C][C]-0.228586580759618[/C][/ROW]
[ROW][C]62[/C][C]10.463[/C][C]10.4169260868933[/C][C]0.046073913106655[/C][/ROW]
[ROW][C]63[/C][C]10.556[/C][C]10.4609992978438[/C][C]0.0950007021562396[/C][/ROW]
[ROW][C]64[/C][C]10.646[/C][C]10.5518747131113[/C][C]0.0941252868886622[/C][/ROW]
[ROW][C]65[/C][C]10.702[/C][C]10.6419127269264[/C][C]0.0600872730735684[/C][/ROW]
[ROW][C]66[/C][C]11.353[/C][C]10.699390785182[/C][C]0.653609214817992[/C][/ROW]
[ROW][C]67[/C][C]11.346[/C][C]11.3246178358370[/C][C]0.0213821641629792[/C][/ROW]
[ROW][C]68[/C][C]11.451[/C][C]11.3450715062155[/C][C]0.105928493784475[/C][/ROW]
[ROW][C]69[/C][C]11.964[/C][C]11.4464001874026[/C][C]0.517599812597448[/C][/ROW]
[ROW][C]70[/C][C]12.574[/C][C]11.9415238743292[/C][C]0.63247612567084[/C][/ROW]
[ROW][C]71[/C][C]13.031[/C][C]12.5465355138499[/C][C]0.484464486150113[/C][/ROW]
[ROW][C]72[/C][C]13.812[/C][C]13.0099627345127[/C][C]0.802037265487259[/C][/ROW]
[ROW][C]73[/C][C]14.544[/C][C]13.7771725330399[/C][C]0.766827466960093[/C][/ROW]
[ROW][C]74[/C][C]14.931[/C][C]14.5107014745837[/C][C]0.420298525416294[/C][/ROW]
[ROW][C]75[/C][C]14.886[/C][C]14.9127490612504[/C][C]-0.026749061250392[/C][/ROW]
[ROW][C]76[/C][C]16.005[/C][C]14.8871615445903[/C][C]1.11783845540974[/C][/ROW]
[ROW][C]77[/C][C]17.064[/C][C]15.9564592606257[/C][C]1.10754073937431[/C][/ROW]
[ROW][C]78[/C][C]15.168[/C][C]17.0159064260885[/C][C]-1.84790642608847[/C][/ROW]
[ROW][C]79[/C][C]16.05[/C][C]15.2482430295565[/C][C]0.801756970443464[/C][/ROW]
[ROW][C]80[/C][C]15.839[/C][C]16.0151847045023[/C][C]-0.176184704502253[/C][/ROW]
[ROW][C]81[/C][C]15.137[/C][C]15.8466506008374[/C][C]-0.709650600837353[/C][/ROW]
[ROW][C]82[/C][C]14.954[/C][C]15.1678156913867[/C][C]-0.213815691386682[/C][/ROW]
[ROW][C]83[/C][C]15.648[/C][C]14.9632846794629[/C][C]0.684715320537139[/C][/ROW]
[ROW][C]84[/C][C]15.305[/C][C]15.6182670920302[/C][C]-0.313267092030207[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36938&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36938&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
2	9.787	9.026	0.761000000000001
3	9.536	9.75395452506122	-0.217954525061216
4	9.49	9.5454644031481	-0.0554644031481004
5	9.736	9.49240847246285	0.243591527537156
6	9.694	9.72542234202558	-0.0314223420255839
7	9.647	9.69536447597362	-0.048364475973619
8	9.753	9.64910016698911	0.103899833010887
9	10.07	9.74848827946399	0.321511720536012
10	10.137	10.0560387549231	0.0809612450768711
11	9.984	10.1334843590076	-0.149484359007621
12	9.732	9.99049117166797	-0.258491171667972
13	9.103	9.74322465641952	-0.640224656419516
14	9.155	9.13080095642431	0.0241990435756865
15	9.308	9.15394918674373	0.154050813256273
16	9.394	9.30131053575721	0.0926894642427865
17	9.948	9.3899750757323	0.558024924267706
18	10.177	9.92376846432312	0.253231535676878
19	10.002	10.1660037367071	-0.164003736707068
20	9.728	10.0091216575180	-0.28112165751803
21	10.002	9.7402073570148	0.261792642985203
22	10.063	9.99063198131022	0.0723680186897848
23	10.018	10.0598575091354	-0.0418575091353706
24	9.96	10.0198176100777	-0.0598176100777046
25	10.236	9.96259750503905	0.273402494960946
26	10.893	10.2241278379823	0.668872162017653
27	10.756	10.8639550614097	-0.107955061409719
28	10.94	10.7606878137665	0.179312186233469
29	10.997	10.9322135921729	0.0647864078270644
30	10.827	10.9941867311219	-0.167186731121914
31	10.166	10.8342598750767	-0.668259875076723
32	10.186	10.1950183507943	-0.00901835079427471
33	10.457	10.1863916106244	0.270608389375610
34	10.368	10.4452491685291	-0.077249168529125
35	10.244	10.3713544487026	-0.127354448702590
36	10.511	10.2495302079408	0.261469792059206
37	10.812	10.4996460007086	0.312353999291382
38	10.738	10.7984364175353	-0.0604364175353318
39	10.171	10.7406243759804	-0.569624375980361
40	9.721	10.1957352273863	-0.474735227386308
41	9.897	9.74161478457182	0.155385215428183
42	9.828	9.89025259100882	-0.0622525910088179
43	9.924	9.83070324104606	0.0932967589539349
44	10.371	9.91994870471763	0.451051295282369
45	10.846	10.3514136606119	0.494586339388121
46	10.413	10.8245232056724	-0.411523205672385
47	10.709	10.4308698814452	0.278130118554829
48	10.662	10.6969225468299	-0.034922546829927
49	10.57	10.6635164679975	-0.0935164679974605
50	10.297	10.5740608358733	-0.277060835873289
51	10.635	10.3090310209046	0.325968979095441
52	10.872	10.6208452040348	0.251154795965203
53	10.296	10.8610939165364	-0.56509391653637
54	10.383	10.3205384978409	0.0624615021590511
55	10.431	10.3802876872480	0.0507123127519513
56	10.574	10.4287978811299	0.145202118870083
57	10.653	10.5676947792639	0.0853052207361102
58	10.805	10.6492957272878	0.155704272712196
59	10.872	10.7982387363446	0.0737612636554168
60	10.625	10.8687970092121	-0.243797009212118
61	10.407	10.6355865807596	-0.228586580759618
62	10.463	10.4169260868933	0.046073913106655
63	10.556	10.4609992978438	0.0950007021562396
64	10.646	10.5518747131113	0.0941252868886622
65	10.702	10.6419127269264	0.0600872730735684
66	11.353	10.699390785182	0.653609214817992
67	11.346	11.3246178358370	0.0213821641629792
68	11.451	11.3450715062155	0.105928493784475
69	11.964	11.4464001874026	0.517599812597448
70	12.574	11.9415238743292	0.63247612567084
71	13.031	12.5465355138499	0.484464486150113
72	13.812	13.0099627345127	0.802037265487259
73	14.544	13.7771725330399	0.766827466960093
74	14.931	14.5107014745837	0.420298525416294
75	14.886	14.9127490612504	-0.026749061250392
76	16.005	14.8871615445903	1.11783845540974
77	17.064	15.9564592606257	1.10754073937431
78	15.168	17.0159064260885	-1.84790642608847
79	16.05	15.2482430295565	0.801756970443464
80	15.839	16.0151847045023	-0.176184704502253
81	15.137	15.8466506008374	-0.709650600837353
82	14.954	15.1678156913867	-0.213815691386682
83	15.648	14.9632846794629	0.684715320537139
84	15.305	15.6182670920302	-0.313267092030207

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	15.3186032323769	14.4752623683668	16.1619440963870
86	15.3186032323769	14.1515468014725	16.4856596632813
87	15.3186032323769	13.8998651970365	16.7373412677173
88	15.3186032323769	13.6865448654894	16.9506615992645
89	15.3186032323769	13.4980507302683	17.1391557344855
90	15.3186032323769	13.3273201503065	17.3098863144474
91	15.3186032323769	13.1701141788916	17.4670922858622
92	15.3186032323769	13.0236517921603	17.6135546725935
93	15.3186032323769	12.8859916700928	17.7512147946610
94	15.3186032323769	12.7557150348613	17.8814914298925
95	15.3186032323769	12.6317476700195	18.0054587947343
96	15.3186032323769	12.5132530380203	18.1239534267336

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 15.3186032323769 & 14.4752623683668 & 16.1619440963870 \tabularnewline
86 & 15.3186032323769 & 14.1515468014725 & 16.4856596632813 \tabularnewline
87 & 15.3186032323769 & 13.8998651970365 & 16.7373412677173 \tabularnewline
88 & 15.3186032323769 & 13.6865448654894 & 16.9506615992645 \tabularnewline
89 & 15.3186032323769 & 13.4980507302683 & 17.1391557344855 \tabularnewline
90 & 15.3186032323769 & 13.3273201503065 & 17.3098863144474 \tabularnewline
91 & 15.3186032323769 & 13.1701141788916 & 17.4670922858622 \tabularnewline
92 & 15.3186032323769 & 13.0236517921603 & 17.6135546725935 \tabularnewline
93 & 15.3186032323769 & 12.8859916700928 & 17.7512147946610 \tabularnewline
94 & 15.3186032323769 & 12.7557150348613 & 17.8814914298925 \tabularnewline
95 & 15.3186032323769 & 12.6317476700195 & 18.0054587947343 \tabularnewline
96 & 15.3186032323769 & 12.5132530380203 & 18.1239534267336 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36938&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]15.3186032323769[/C][C]14.4752623683668[/C][C]16.1619440963870[/C][/ROW]
[ROW][C]86[/C][C]15.3186032323769[/C][C]14.1515468014725[/C][C]16.4856596632813[/C][/ROW]
[ROW][C]87[/C][C]15.3186032323769[/C][C]13.8998651970365[/C][C]16.7373412677173[/C][/ROW]
[ROW][C]88[/C][C]15.3186032323769[/C][C]13.6865448654894[/C][C]16.9506615992645[/C][/ROW]
[ROW][C]89[/C][C]15.3186032323769[/C][C]13.4980507302683[/C][C]17.1391557344855[/C][/ROW]
[ROW][C]90[/C][C]15.3186032323769[/C][C]13.3273201503065[/C][C]17.3098863144474[/C][/ROW]
[ROW][C]91[/C][C]15.3186032323769[/C][C]13.1701141788916[/C][C]17.4670922858622[/C][/ROW]
[ROW][C]92[/C][C]15.3186032323769[/C][C]13.0236517921603[/C][C]17.6135546725935[/C][/ROW]
[ROW][C]93[/C][C]15.3186032323769[/C][C]12.8859916700928[/C][C]17.7512147946610[/C][/ROW]
[ROW][C]94[/C][C]15.3186032323769[/C][C]12.7557150348613[/C][C]17.8814914298925[/C][/ROW]
[ROW][C]95[/C][C]15.3186032323769[/C][C]12.6317476700195[/C][C]18.0054587947343[/C][/ROW]
[ROW][C]96[/C][C]15.3186032323769[/C][C]12.5132530380203[/C][C]18.1239534267336[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36938&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36938&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	15.3186032323769	14.4752623683668	16.1619440963870
86	15.3186032323769	14.1515468014725	16.4856596632813
87	15.3186032323769	13.8998651970365	16.7373412677173
88	15.3186032323769	13.6865448654894	16.9506615992645
89	15.3186032323769	13.4980507302683	17.1391557344855
90	15.3186032323769	13.3273201503065	17.3098863144474
91	15.3186032323769	13.1701141788916	17.4670922858622
92	15.3186032323769	13.0236517921603	17.6135546725935
93	15.3186032323769	12.8859916700928	17.7512147946610
94	15.3186032323769	12.7557150348613	17.8814914298925
95	15.3186032323769	12.6317476700195	18.0054587947343
96	15.3186032323769	12.5132530380203	18.1239534267336

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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=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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code