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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 16 Aug 2009 11:12:06 -0600

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/Aug/16/t1250442741phg6kdiys3lwn0a.htm/, Retrieved Sun, 05 May 2024 19:30:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42668, Retrieved Sun, 05 May 2024 19:30:07 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

127

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

-     [Exponential Smoothing] [Maarten Verhaegen...] [2008-08-17 19:40:03] [b57209f6d0b19d479b8c06a8ae81c48a]
-   PD    [Exponential Smoothing] [] [2009-08-16 17:12:06] [e921d89db97faa9283224ee60d8fb091] [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	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42668&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42668&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42668&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	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.917280045034661
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.917280045034661 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42668&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]0.917280045034661[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42668&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42668&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	0.917280045034661
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	98.97	98.8947702991453	0.0752297008546776
14	98.9	98.691154624911	0.208845375089126
15	99.78	99.3430186090222	0.436981390977792
16	104.4	103.844147208062	0.555852791938108
17	106.21	105.573064171128	0.636935828872225
18	105.46	104.553023652631	0.906976347369152
19	108.33	107.905685913102	0.424314086898022
20	111.72	108.270611713552	3.44938828644841
21	111.88	111.435794378665	0.444205621335371
22	112.86	111.835632953385	1.02436704661459
23	113.09	113.010558693080	0.0794413069196622
24	116.9	110.992889574380	5.90711042561983
25	114.62	116.263714711462	-1.64371471146183
26	118.86	114.494398311841	4.36560168815905
27	124.71	118.978043314963	5.73195668503654
28	122.53	128.345980127129	-5.81598012712888
29	127.89	124.236849088403	3.65315091159671
30	136.16	126.005860216351	10.1541397836490
31	134.12	137.800835169646	-3.68083516964612
32	130.26	134.650423476733	-4.39042347673256
33	135.35	130.375714679931	4.97428532006907
34	131.43	134.978895891689	-3.54889589168852
35	129.61	131.880694582748	-2.27069458274826
36	123.96	128.189357236388	-4.22935723638771
37	121.1	123.53759894468	-2.43759894468016
38	125.38	121.537158761810	3.84284123819043
39	123.1	125.654310859651	-2.5543108596509
40	129.92	126.466174992211	3.45382500778871
41	136.68	131.643337318190	5.0366626818103
42	131.17	135.219177691751	-4.04917769175128
43	124.82	132.841304446486	-8.02130444648648
44	122.47	125.650769787035	-3.18076978703509
45	126.15	123.260300471130	2.88969952886958
46	118.74	125.24629556846	-6.50629556845993
47	116.8	119.541063305537	-2.74106330553747
48	116.64	115.256245629453	1.38375437054744
49	116.53	115.901496770538	0.628503229462126
50	117.68	117.233048657135	0.446951342865049
51	119.46	117.706046585420	1.75395341458039
52	126.19	122.966788293848	3.22321170615166
53	124.39	128.063345901228	-3.67334590122805
54	121.9	122.898088902965	-0.998088902964625
55	122.53	122.990344373014	-0.460344373014479
56	122.93	123.135736319301	-0.205736319300740
57	124.66	123.976354785089	0.683645214910825
58	124.41	123.161543990656	1.24845600934395
59	120.93	124.881050447477	-3.95105044747712
60	120.18	119.827540443748	0.352459556251546
61	123.44	119.464331090754	3.97566890924568
62	126.1	123.851153298959	2.24884670104143
63	125.82	126.085109035051	-0.265109035050898
64	122.18	129.615342028465	-7.4353420284653
65	117.27	124.364538051453	-7.0945380514529
66	117.86	116.282386901976	1.57761309802395
67	119.09	118.781764622789	0.308235377211105
68	123.08	119.653220603712	3.42677939628817
69	125.42	123.899442849142	1.52055715085825
70	121.81	123.899035796484	-2.08903579648397
71	121.66	122.127024679402	-0.467024679402158
72	121.27	120.625328142817	0.644671857183454
73	120.92	120.829871016891	0.0901289831094374
74	122.16	121.509722331369	0.650277668631219
75	124.17	122.069388288146	2.10061171185360
76	127.26	127.176528364515	0.0834716354854521
77	134.16	128.850773413409	5.30922658659139
78	134.09	132.863708002254	1.22629199774627
79	135.57	134.935823020483	0.634176979517349
80	136.13	136.364224549863	-0.234224549863200
81	136.23	137.094598312399	-0.864598312399465
82	140.6	134.607750382943	5.99224961705735
83	136.5	140.382713800490	-3.88271380049025
84	130.59	135.83983328053	-5.24983328053005
85	129.5	130.591592454855	-1.09159245485546
86	135.25	130.233809749539	5.01619025046091
87	138.06	134.918211762735	3.14178823726508
88	146.28	140.813544552946	5.46645544705441
89	145.04	147.857767449152	-2.81776744915183
90	147.96	144.078232417578	3.88176758242173
91	156.71	148.537182472065	8.17281752793545
92	160.97	156.808794407796	4.16120559220406
93	168.17	161.518864039746	6.65113596025392
94	163.91	166.493247334306	-2.58324733430612
95	153.05	163.585221992929	-10.5352219929285
96	151.76	152.827040396794	-1.06704039679400

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 98.97 & 98.8947702991453 & 0.0752297008546776 \tabularnewline
14 & 98.9 & 98.691154624911 & 0.208845375089126 \tabularnewline
15 & 99.78 & 99.3430186090222 & 0.436981390977792 \tabularnewline
16 & 104.4 & 103.844147208062 & 0.555852791938108 \tabularnewline
17 & 106.21 & 105.573064171128 & 0.636935828872225 \tabularnewline
18 & 105.46 & 104.553023652631 & 0.906976347369152 \tabularnewline
19 & 108.33 & 107.905685913102 & 0.424314086898022 \tabularnewline
20 & 111.72 & 108.270611713552 & 3.44938828644841 \tabularnewline
21 & 111.88 & 111.435794378665 & 0.444205621335371 \tabularnewline
22 & 112.86 & 111.835632953385 & 1.02436704661459 \tabularnewline
23 & 113.09 & 113.010558693080 & 0.0794413069196622 \tabularnewline
24 & 116.9 & 110.992889574380 & 5.90711042561983 \tabularnewline
25 & 114.62 & 116.263714711462 & -1.64371471146183 \tabularnewline
26 & 118.86 & 114.494398311841 & 4.36560168815905 \tabularnewline
27 & 124.71 & 118.978043314963 & 5.73195668503654 \tabularnewline
28 & 122.53 & 128.345980127129 & -5.81598012712888 \tabularnewline
29 & 127.89 & 124.236849088403 & 3.65315091159671 \tabularnewline
30 & 136.16 & 126.005860216351 & 10.1541397836490 \tabularnewline
31 & 134.12 & 137.800835169646 & -3.68083516964612 \tabularnewline
32 & 130.26 & 134.650423476733 & -4.39042347673256 \tabularnewline
33 & 135.35 & 130.375714679931 & 4.97428532006907 \tabularnewline
34 & 131.43 & 134.978895891689 & -3.54889589168852 \tabularnewline
35 & 129.61 & 131.880694582748 & -2.27069458274826 \tabularnewline
36 & 123.96 & 128.189357236388 & -4.22935723638771 \tabularnewline
37 & 121.1 & 123.53759894468 & -2.43759894468016 \tabularnewline
38 & 125.38 & 121.537158761810 & 3.84284123819043 \tabularnewline
39 & 123.1 & 125.654310859651 & -2.5543108596509 \tabularnewline
40 & 129.92 & 126.466174992211 & 3.45382500778871 \tabularnewline
41 & 136.68 & 131.643337318190 & 5.0366626818103 \tabularnewline
42 & 131.17 & 135.219177691751 & -4.04917769175128 \tabularnewline
43 & 124.82 & 132.841304446486 & -8.02130444648648 \tabularnewline
44 & 122.47 & 125.650769787035 & -3.18076978703509 \tabularnewline
45 & 126.15 & 123.260300471130 & 2.88969952886958 \tabularnewline
46 & 118.74 & 125.24629556846 & -6.50629556845993 \tabularnewline
47 & 116.8 & 119.541063305537 & -2.74106330553747 \tabularnewline
48 & 116.64 & 115.256245629453 & 1.38375437054744 \tabularnewline
49 & 116.53 & 115.901496770538 & 0.628503229462126 \tabularnewline
50 & 117.68 & 117.233048657135 & 0.446951342865049 \tabularnewline
51 & 119.46 & 117.706046585420 & 1.75395341458039 \tabularnewline
52 & 126.19 & 122.966788293848 & 3.22321170615166 \tabularnewline
53 & 124.39 & 128.063345901228 & -3.67334590122805 \tabularnewline
54 & 121.9 & 122.898088902965 & -0.998088902964625 \tabularnewline
55 & 122.53 & 122.990344373014 & -0.460344373014479 \tabularnewline
56 & 122.93 & 123.135736319301 & -0.205736319300740 \tabularnewline
57 & 124.66 & 123.976354785089 & 0.683645214910825 \tabularnewline
58 & 124.41 & 123.161543990656 & 1.24845600934395 \tabularnewline
59 & 120.93 & 124.881050447477 & -3.95105044747712 \tabularnewline
60 & 120.18 & 119.827540443748 & 0.352459556251546 \tabularnewline
61 & 123.44 & 119.464331090754 & 3.97566890924568 \tabularnewline
62 & 126.1 & 123.851153298959 & 2.24884670104143 \tabularnewline
63 & 125.82 & 126.085109035051 & -0.265109035050898 \tabularnewline
64 & 122.18 & 129.615342028465 & -7.4353420284653 \tabularnewline
65 & 117.27 & 124.364538051453 & -7.0945380514529 \tabularnewline
66 & 117.86 & 116.282386901976 & 1.57761309802395 \tabularnewline
67 & 119.09 & 118.781764622789 & 0.308235377211105 \tabularnewline
68 & 123.08 & 119.653220603712 & 3.42677939628817 \tabularnewline
69 & 125.42 & 123.899442849142 & 1.52055715085825 \tabularnewline
70 & 121.81 & 123.899035796484 & -2.08903579648397 \tabularnewline
71 & 121.66 & 122.127024679402 & -0.467024679402158 \tabularnewline
72 & 121.27 & 120.625328142817 & 0.644671857183454 \tabularnewline
73 & 120.92 & 120.829871016891 & 0.0901289831094374 \tabularnewline
74 & 122.16 & 121.509722331369 & 0.650277668631219 \tabularnewline
75 & 124.17 & 122.069388288146 & 2.10061171185360 \tabularnewline
76 & 127.26 & 127.176528364515 & 0.0834716354854521 \tabularnewline
77 & 134.16 & 128.850773413409 & 5.30922658659139 \tabularnewline
78 & 134.09 & 132.863708002254 & 1.22629199774627 \tabularnewline
79 & 135.57 & 134.935823020483 & 0.634176979517349 \tabularnewline
80 & 136.13 & 136.364224549863 & -0.234224549863200 \tabularnewline
81 & 136.23 & 137.094598312399 & -0.864598312399465 \tabularnewline
82 & 140.6 & 134.607750382943 & 5.99224961705735 \tabularnewline
83 & 136.5 & 140.382713800490 & -3.88271380049025 \tabularnewline
84 & 130.59 & 135.83983328053 & -5.24983328053005 \tabularnewline
85 & 129.5 & 130.591592454855 & -1.09159245485546 \tabularnewline
86 & 135.25 & 130.233809749539 & 5.01619025046091 \tabularnewline
87 & 138.06 & 134.918211762735 & 3.14178823726508 \tabularnewline
88 & 146.28 & 140.813544552946 & 5.46645544705441 \tabularnewline
89 & 145.04 & 147.857767449152 & -2.81776744915183 \tabularnewline
90 & 147.96 & 144.078232417578 & 3.88176758242173 \tabularnewline
91 & 156.71 & 148.537182472065 & 8.17281752793545 \tabularnewline
92 & 160.97 & 156.808794407796 & 4.16120559220406 \tabularnewline
93 & 168.17 & 161.518864039746 & 6.65113596025392 \tabularnewline
94 & 163.91 & 166.493247334306 & -2.58324733430612 \tabularnewline
95 & 153.05 & 163.585221992929 & -10.5352219929285 \tabularnewline
96 & 151.76 & 152.827040396794 & -1.06704039679400 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42668&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]98.97[/C][C]98.8947702991453[/C][C]0.0752297008546776[/C][/ROW]
[ROW][C]14[/C][C]98.9[/C][C]98.691154624911[/C][C]0.208845375089126[/C][/ROW]
[ROW][C]15[/C][C]99.78[/C][C]99.3430186090222[/C][C]0.436981390977792[/C][/ROW]
[ROW][C]16[/C][C]104.4[/C][C]103.844147208062[/C][C]0.555852791938108[/C][/ROW]
[ROW][C]17[/C][C]106.21[/C][C]105.573064171128[/C][C]0.636935828872225[/C][/ROW]
[ROW][C]18[/C][C]105.46[/C][C]104.553023652631[/C][C]0.906976347369152[/C][/ROW]
[ROW][C]19[/C][C]108.33[/C][C]107.905685913102[/C][C]0.424314086898022[/C][/ROW]
[ROW][C]20[/C][C]111.72[/C][C]108.270611713552[/C][C]3.44938828644841[/C][/ROW]
[ROW][C]21[/C][C]111.88[/C][C]111.435794378665[/C][C]0.444205621335371[/C][/ROW]
[ROW][C]22[/C][C]112.86[/C][C]111.835632953385[/C][C]1.02436704661459[/C][/ROW]
[ROW][C]23[/C][C]113.09[/C][C]113.010558693080[/C][C]0.0794413069196622[/C][/ROW]
[ROW][C]24[/C][C]116.9[/C][C]110.992889574380[/C][C]5.90711042561983[/C][/ROW]
[ROW][C]25[/C][C]114.62[/C][C]116.263714711462[/C][C]-1.64371471146183[/C][/ROW]
[ROW][C]26[/C][C]118.86[/C][C]114.494398311841[/C][C]4.36560168815905[/C][/ROW]
[ROW][C]27[/C][C]124.71[/C][C]118.978043314963[/C][C]5.73195668503654[/C][/ROW]
[ROW][C]28[/C][C]122.53[/C][C]128.345980127129[/C][C]-5.81598012712888[/C][/ROW]
[ROW][C]29[/C][C]127.89[/C][C]124.236849088403[/C][C]3.65315091159671[/C][/ROW]
[ROW][C]30[/C][C]136.16[/C][C]126.005860216351[/C][C]10.1541397836490[/C][/ROW]
[ROW][C]31[/C][C]134.12[/C][C]137.800835169646[/C][C]-3.68083516964612[/C][/ROW]
[ROW][C]32[/C][C]130.26[/C][C]134.650423476733[/C][C]-4.39042347673256[/C][/ROW]
[ROW][C]33[/C][C]135.35[/C][C]130.375714679931[/C][C]4.97428532006907[/C][/ROW]
[ROW][C]34[/C][C]131.43[/C][C]134.978895891689[/C][C]-3.54889589168852[/C][/ROW]
[ROW][C]35[/C][C]129.61[/C][C]131.880694582748[/C][C]-2.27069458274826[/C][/ROW]
[ROW][C]36[/C][C]123.96[/C][C]128.189357236388[/C][C]-4.22935723638771[/C][/ROW]
[ROW][C]37[/C][C]121.1[/C][C]123.53759894468[/C][C]-2.43759894468016[/C][/ROW]
[ROW][C]38[/C][C]125.38[/C][C]121.537158761810[/C][C]3.84284123819043[/C][/ROW]
[ROW][C]39[/C][C]123.1[/C][C]125.654310859651[/C][C]-2.5543108596509[/C][/ROW]
[ROW][C]40[/C][C]129.92[/C][C]126.466174992211[/C][C]3.45382500778871[/C][/ROW]
[ROW][C]41[/C][C]136.68[/C][C]131.643337318190[/C][C]5.0366626818103[/C][/ROW]
[ROW][C]42[/C][C]131.17[/C][C]135.219177691751[/C][C]-4.04917769175128[/C][/ROW]
[ROW][C]43[/C][C]124.82[/C][C]132.841304446486[/C][C]-8.02130444648648[/C][/ROW]
[ROW][C]44[/C][C]122.47[/C][C]125.650769787035[/C][C]-3.18076978703509[/C][/ROW]
[ROW][C]45[/C][C]126.15[/C][C]123.260300471130[/C][C]2.88969952886958[/C][/ROW]
[ROW][C]46[/C][C]118.74[/C][C]125.24629556846[/C][C]-6.50629556845993[/C][/ROW]
[ROW][C]47[/C][C]116.8[/C][C]119.541063305537[/C][C]-2.74106330553747[/C][/ROW]
[ROW][C]48[/C][C]116.64[/C][C]115.256245629453[/C][C]1.38375437054744[/C][/ROW]
[ROW][C]49[/C][C]116.53[/C][C]115.901496770538[/C][C]0.628503229462126[/C][/ROW]
[ROW][C]50[/C][C]117.68[/C][C]117.233048657135[/C][C]0.446951342865049[/C][/ROW]
[ROW][C]51[/C][C]119.46[/C][C]117.706046585420[/C][C]1.75395341458039[/C][/ROW]
[ROW][C]52[/C][C]126.19[/C][C]122.966788293848[/C][C]3.22321170615166[/C][/ROW]
[ROW][C]53[/C][C]124.39[/C][C]128.063345901228[/C][C]-3.67334590122805[/C][/ROW]
[ROW][C]54[/C][C]121.9[/C][C]122.898088902965[/C][C]-0.998088902964625[/C][/ROW]
[ROW][C]55[/C][C]122.53[/C][C]122.990344373014[/C][C]-0.460344373014479[/C][/ROW]
[ROW][C]56[/C][C]122.93[/C][C]123.135736319301[/C][C]-0.205736319300740[/C][/ROW]
[ROW][C]57[/C][C]124.66[/C][C]123.976354785089[/C][C]0.683645214910825[/C][/ROW]
[ROW][C]58[/C][C]124.41[/C][C]123.161543990656[/C][C]1.24845600934395[/C][/ROW]
[ROW][C]59[/C][C]120.93[/C][C]124.881050447477[/C][C]-3.95105044747712[/C][/ROW]
[ROW][C]60[/C][C]120.18[/C][C]119.827540443748[/C][C]0.352459556251546[/C][/ROW]
[ROW][C]61[/C][C]123.44[/C][C]119.464331090754[/C][C]3.97566890924568[/C][/ROW]
[ROW][C]62[/C][C]126.1[/C][C]123.851153298959[/C][C]2.24884670104143[/C][/ROW]
[ROW][C]63[/C][C]125.82[/C][C]126.085109035051[/C][C]-0.265109035050898[/C][/ROW]
[ROW][C]64[/C][C]122.18[/C][C]129.615342028465[/C][C]-7.4353420284653[/C][/ROW]
[ROW][C]65[/C][C]117.27[/C][C]124.364538051453[/C][C]-7.0945380514529[/C][/ROW]
[ROW][C]66[/C][C]117.86[/C][C]116.282386901976[/C][C]1.57761309802395[/C][/ROW]
[ROW][C]67[/C][C]119.09[/C][C]118.781764622789[/C][C]0.308235377211105[/C][/ROW]
[ROW][C]68[/C][C]123.08[/C][C]119.653220603712[/C][C]3.42677939628817[/C][/ROW]
[ROW][C]69[/C][C]125.42[/C][C]123.899442849142[/C][C]1.52055715085825[/C][/ROW]
[ROW][C]70[/C][C]121.81[/C][C]123.899035796484[/C][C]-2.08903579648397[/C][/ROW]
[ROW][C]71[/C][C]121.66[/C][C]122.127024679402[/C][C]-0.467024679402158[/C][/ROW]
[ROW][C]72[/C][C]121.27[/C][C]120.625328142817[/C][C]0.644671857183454[/C][/ROW]
[ROW][C]73[/C][C]120.92[/C][C]120.829871016891[/C][C]0.0901289831094374[/C][/ROW]
[ROW][C]74[/C][C]122.16[/C][C]121.509722331369[/C][C]0.650277668631219[/C][/ROW]
[ROW][C]75[/C][C]124.17[/C][C]122.069388288146[/C][C]2.10061171185360[/C][/ROW]
[ROW][C]76[/C][C]127.26[/C][C]127.176528364515[/C][C]0.0834716354854521[/C][/ROW]
[ROW][C]77[/C][C]134.16[/C][C]128.850773413409[/C][C]5.30922658659139[/C][/ROW]
[ROW][C]78[/C][C]134.09[/C][C]132.863708002254[/C][C]1.22629199774627[/C][/ROW]
[ROW][C]79[/C][C]135.57[/C][C]134.935823020483[/C][C]0.634176979517349[/C][/ROW]
[ROW][C]80[/C][C]136.13[/C][C]136.364224549863[/C][C]-0.234224549863200[/C][/ROW]
[ROW][C]81[/C][C]136.23[/C][C]137.094598312399[/C][C]-0.864598312399465[/C][/ROW]
[ROW][C]82[/C][C]140.6[/C][C]134.607750382943[/C][C]5.99224961705735[/C][/ROW]
[ROW][C]83[/C][C]136.5[/C][C]140.382713800490[/C][C]-3.88271380049025[/C][/ROW]
[ROW][C]84[/C][C]130.59[/C][C]135.83983328053[/C][C]-5.24983328053005[/C][/ROW]
[ROW][C]85[/C][C]129.5[/C][C]130.591592454855[/C][C]-1.09159245485546[/C][/ROW]
[ROW][C]86[/C][C]135.25[/C][C]130.233809749539[/C][C]5.01619025046091[/C][/ROW]
[ROW][C]87[/C][C]138.06[/C][C]134.918211762735[/C][C]3.14178823726508[/C][/ROW]
[ROW][C]88[/C][C]146.28[/C][C]140.813544552946[/C][C]5.46645544705441[/C][/ROW]
[ROW][C]89[/C][C]145.04[/C][C]147.857767449152[/C][C]-2.81776744915183[/C][/ROW]
[ROW][C]90[/C][C]147.96[/C][C]144.078232417578[/C][C]3.88176758242173[/C][/ROW]
[ROW][C]91[/C][C]156.71[/C][C]148.537182472065[/C][C]8.17281752793545[/C][/ROW]
[ROW][C]92[/C][C]160.97[/C][C]156.808794407796[/C][C]4.16120559220406[/C][/ROW]
[ROW][C]93[/C][C]168.17[/C][C]161.518864039746[/C][C]6.65113596025392[/C][/ROW]
[ROW][C]94[/C][C]163.91[/C][C]166.493247334306[/C][C]-2.58324733430612[/C][/ROW]
[ROW][C]95[/C][C]153.05[/C][C]163.585221992929[/C][C]-10.5352219929285[/C][/ROW]
[ROW][C]96[/C][C]151.76[/C][C]152.827040396794[/C][C]-1.06704039679400[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42668&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42668&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	98.97	98.8947702991453	0.0752297008546776
14	98.9	98.691154624911	0.208845375089126
15	99.78	99.3430186090222	0.436981390977792
16	104.4	103.844147208062	0.555852791938108
17	106.21	105.573064171128	0.636935828872225
18	105.46	104.553023652631	0.906976347369152
19	108.33	107.905685913102	0.424314086898022
20	111.72	108.270611713552	3.44938828644841
21	111.88	111.435794378665	0.444205621335371
22	112.86	111.835632953385	1.02436704661459
23	113.09	113.010558693080	0.0794413069196622
24	116.9	110.992889574380	5.90711042561983
25	114.62	116.263714711462	-1.64371471146183
26	118.86	114.494398311841	4.36560168815905
27	124.71	118.978043314963	5.73195668503654
28	122.53	128.345980127129	-5.81598012712888
29	127.89	124.236849088403	3.65315091159671
30	136.16	126.005860216351	10.1541397836490
31	134.12	137.800835169646	-3.68083516964612
32	130.26	134.650423476733	-4.39042347673256
33	135.35	130.375714679931	4.97428532006907
34	131.43	134.978895891689	-3.54889589168852
35	129.61	131.880694582748	-2.27069458274826
36	123.96	128.189357236388	-4.22935723638771
37	121.1	123.53759894468	-2.43759894468016
38	125.38	121.537158761810	3.84284123819043
39	123.1	125.654310859651	-2.5543108596509
40	129.92	126.466174992211	3.45382500778871
41	136.68	131.643337318190	5.0366626818103
42	131.17	135.219177691751	-4.04917769175128
43	124.82	132.841304446486	-8.02130444648648
44	122.47	125.650769787035	-3.18076978703509
45	126.15	123.260300471130	2.88969952886958
46	118.74	125.24629556846	-6.50629556845993
47	116.8	119.541063305537	-2.74106330553747
48	116.64	115.256245629453	1.38375437054744
49	116.53	115.901496770538	0.628503229462126
50	117.68	117.233048657135	0.446951342865049
51	119.46	117.706046585420	1.75395341458039
52	126.19	122.966788293848	3.22321170615166
53	124.39	128.063345901228	-3.67334590122805
54	121.9	122.898088902965	-0.998088902964625
55	122.53	122.990344373014	-0.460344373014479
56	122.93	123.135736319301	-0.205736319300740
57	124.66	123.976354785089	0.683645214910825
58	124.41	123.161543990656	1.24845600934395
59	120.93	124.881050447477	-3.95105044747712
60	120.18	119.827540443748	0.352459556251546
61	123.44	119.464331090754	3.97566890924568
62	126.1	123.851153298959	2.24884670104143
63	125.82	126.085109035051	-0.265109035050898
64	122.18	129.615342028465	-7.4353420284653
65	117.27	124.364538051453	-7.0945380514529
66	117.86	116.282386901976	1.57761309802395
67	119.09	118.781764622789	0.308235377211105
68	123.08	119.653220603712	3.42677939628817
69	125.42	123.899442849142	1.52055715085825
70	121.81	123.899035796484	-2.08903579648397
71	121.66	122.127024679402	-0.467024679402158
72	121.27	120.625328142817	0.644671857183454
73	120.92	120.829871016891	0.0901289831094374
74	122.16	121.509722331369	0.650277668631219
75	124.17	122.069388288146	2.10061171185360
76	127.26	127.176528364515	0.0834716354854521
77	134.16	128.850773413409	5.30922658659139
78	134.09	132.863708002254	1.22629199774627
79	135.57	134.935823020483	0.634176979517349
80	136.13	136.364224549863	-0.234224549863200
81	136.23	137.094598312399	-0.864598312399465
82	140.6	134.607750382943	5.99224961705735
83	136.5	140.382713800490	-3.88271380049025
84	130.59	135.83983328053	-5.24983328053005
85	129.5	130.591592454855	-1.09159245485546
86	135.25	130.233809749539	5.01619025046091
87	138.06	134.918211762735	3.14178823726508
88	146.28	140.813544552946	5.46645544705441
89	145.04	147.857767449152	-2.81776744915183
90	147.96	144.078232417578	3.88176758242173
91	156.71	148.537182472065	8.17281752793545
92	160.97	156.808794407796	4.16120559220406
93	168.17	161.518864039746	6.65113596025392
94	163.91	166.493247334306	-2.58324733430612
95	153.05	163.585221992929	-10.5352219929285
96	151.76	152.827040396794	-1.06704039679400

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	151.759561509718	144.301130001953	159.217993017484
98	152.908310290873	142.787346026331	163.029274555415
99	152.836410635105	140.620043141770	165.052778128441
100	156.042140136451	142.040520522266	170.043759750636
101	157.386821989106	141.803142420133	172.970501558079
102	156.746154046288	139.726847773807	173.765460318770
103	157.999391616204	139.656477368882	176.342305863526
104	158.442400763188	138.865163466452	178.019638059924
105	159.541446470035	138.803222407671	180.279670532399
106	157.651007701183	135.813433331558	179.488582070808
107	156.454756605306	133.570583658988	179.338929551625
108	156.143531468531	132.258576192771	180.028486744292

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 151.759561509718 & 144.301130001953 & 159.217993017484 \tabularnewline
98 & 152.908310290873 & 142.787346026331 & 163.029274555415 \tabularnewline
99 & 152.836410635105 & 140.620043141770 & 165.052778128441 \tabularnewline
100 & 156.042140136451 & 142.040520522266 & 170.043759750636 \tabularnewline
101 & 157.386821989106 & 141.803142420133 & 172.970501558079 \tabularnewline
102 & 156.746154046288 & 139.726847773807 & 173.765460318770 \tabularnewline
103 & 157.999391616204 & 139.656477368882 & 176.342305863526 \tabularnewline
104 & 158.442400763188 & 138.865163466452 & 178.019638059924 \tabularnewline
105 & 159.541446470035 & 138.803222407671 & 180.279670532399 \tabularnewline
106 & 157.651007701183 & 135.813433331558 & 179.488582070808 \tabularnewline
107 & 156.454756605306 & 133.570583658988 & 179.338929551625 \tabularnewline
108 & 156.143531468531 & 132.258576192771 & 180.028486744292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42668&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]151.759561509718[/C][C]144.301130001953[/C][C]159.217993017484[/C][/ROW]
[ROW][C]98[/C][C]152.908310290873[/C][C]142.787346026331[/C][C]163.029274555415[/C][/ROW]
[ROW][C]99[/C][C]152.836410635105[/C][C]140.620043141770[/C][C]165.052778128441[/C][/ROW]
[ROW][C]100[/C][C]156.042140136451[/C][C]142.040520522266[/C][C]170.043759750636[/C][/ROW]
[ROW][C]101[/C][C]157.386821989106[/C][C]141.803142420133[/C][C]172.970501558079[/C][/ROW]
[ROW][C]102[/C][C]156.746154046288[/C][C]139.726847773807[/C][C]173.765460318770[/C][/ROW]
[ROW][C]103[/C][C]157.999391616204[/C][C]139.656477368882[/C][C]176.342305863526[/C][/ROW]
[ROW][C]104[/C][C]158.442400763188[/C][C]138.865163466452[/C][C]178.019638059924[/C][/ROW]
[ROW][C]105[/C][C]159.541446470035[/C][C]138.803222407671[/C][C]180.279670532399[/C][/ROW]
[ROW][C]106[/C][C]157.651007701183[/C][C]135.813433331558[/C][C]179.488582070808[/C][/ROW]
[ROW][C]107[/C][C]156.454756605306[/C][C]133.570583658988[/C][C]179.338929551625[/C][/ROW]
[ROW][C]108[/C][C]156.143531468531[/C][C]132.258576192771[/C][C]180.028486744292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42668&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42668&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	151.759561509718	144.301130001953	159.217993017484
98	152.908310290873	142.787346026331	163.029274555415
99	152.836410635105	140.620043141770	165.052778128441
100	156.042140136451	142.040520522266	170.043759750636
101	157.386821989106	141.803142420133	172.970501558079
102	156.746154046288	139.726847773807	173.765460318770
103	157.999391616204	139.656477368882	176.342305863526
104	158.442400763188	138.865163466452	178.019638059924
105	159.541446470035	138.803222407671	180.279670532399
106	157.651007701183	135.813433331558	179.488582070808
107	156.454756605306	133.570583658988	179.338929551625
108	156.143531468531	132.258576192771	180.028486744292

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):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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