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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 15 Jan 2010 08:53:52 -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/15/t12635711404byi4k2qu9kymqs.htm/, Retrieved Fri, 03 May 2024 11:14:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72212, Retrieved Fri, 03 May 2024 11:14:35 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W62

Estimated Impact

152

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

-       [Exponential Smoothing] [opgave 10 oefenin...] [2010-01-15 15:53:52] [b37bab310ab56201887748d7a7c0dc58] [Current]

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Dataseries X:

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1,2
1,21
1,21
1,21
1,21
1,21
1,21
1,2
1,21
1,22
1,22
1,23
1,22
1,23
1,23
1,23
1,23
1,23
1,22
1,22
1,23
1,24
1,24
1,25
1,25
1,25
1,26
1,26
1,26
1,26
1,27
1,27
1,29
1,31
1,32
1,32
1,33
1,33
1,32
1,32
1,31
1,3
1,31
1,29
1,3
1,3
1,32
1,31
1,35
1,35
1,36
1,37
1,37
1,37
1,32
1,32
1,31
1,31
1,34
1,31
1,27
1,28
1,27
1,26
1,27
1,27
1,28
1,27
1,26
1,3
1,31
1,28
1,29
1,31
1,29
1,29
1,32
1,3
1,29
1,31
1,29
1,33
1,35
1,32
1,33

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=72212&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=72212&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72212&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	0.808659086679283
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.808659086679283 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72212&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]0.808659086679283[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72212&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72212&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	0.808659086679283
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	1.21	1.2	0.01
3	1.21	1.20808659086679	0.00191340913320714
4	1.21	1.20963388654890	0.000366113451103933
5	1.21	1.20992994751789	7.00524821131143e-05
6	1.21	1.20998659609409	1.34039059078717e-05
7	1.21	1.20999743528440	2.56471559856308e-06
8	1.2	1.20999950926497	-0.00999950926497495
9	1.21	1.20191331523552	0.00808668476448071
10	1.22	1.20845268635143	0.0115473136485724
11	1.22	1.21779052646008	0.00220947353991874
12	1.23	1.21957723731491	0.0104227626850861
13	1.22	1.22800569906851	-0.00800569906851045
14	1.23	1.22153181777154	0.00846818222846046
15	1.23	1.22837969027824	0.00162030972175997
16	1.23	1.22968996845798	0.000310031542023914
17	1.23	1.22994067828159	5.93217184090555e-05
18	1.23	1.22998864932822	1.13506717802636e-05
19	1.22	1.22999782815209	-0.00999782815209471
20	1.22	1.22191299356985	-0.00191299356984542
21	1.23	1.22036603393683	0.00963396606316924
22	1.24	1.22815662813457	0.0118433718654276
23	1.24	1.23773387841047	0.00226612158952788
24	1.25	1.23956639822536	0.0104336017746360
25	1.25	1.24800362510722	0.00199637489278359
26	1.25	1.24961801180468	0.000381988195315763
27	1.26	1.24992691002983	0.0100730899701695
28	1.26	1.25807260576515	0.00192739423485389
29	1.26	1.25963121062677	0.000368789373226042
30	1.26	1.25992943550450	7.05644954959173e-05
31	1.27	1.25998649812498	0.0100135018750160
32	1.27	1.26808400740570	0.00191599259430419
33	1.29	1.26963339222709	0.0203666077729099
34	1.31	1.28610303466749	0.0238969653325136
35	1.32	1.30542753282768	0.0145724671723166
36	1.32	1.31721169082191	0.00278830917808714
37	1.33	1.31946648237524	0.0105335176247556
38	1.33	1.3279845071172	0.00201549288280067
39	1.32	1.32961435375101	-0.0096143537510136
40	1.32	1.32183961922771	-0.00183961922770748
41	1.31	1.32035199442319	-0.0103519944231918
42	1.3	1.31198076006762	-0.0119807600676245
43	1.31	1.30229240957362	0.00770759042638436
44	1.29	1.30852522260831	-0.0185252226083135
45	1.3	1.29354463301334	0.00645536698665583
46	1.3	1.29876482418495	0.00123517581504728
47	1.32	1.29976366033144	0.020236339668563
48	1.31	1.31612796028555	-0.00612796028554885
49	1.35	1.31117252951783	0.0388274704821701
50	1.35	1.34257071633601	0.00742928366399154
51	1.36	1.34857847407841	0.0114215259215869
52	1.37	1.35781459479865	0.0121854052013526
53	1.37	1.36766843343959	0.00233156656040978
54	1.37	1.36955387592486	0.000446124075136778
55	1.32	1.36991463821201	-0.049914638212009
56	1.32	1.32955071246356	-0.00955071246355899
57	1.31	1.32182744204564	-0.0118274420456408
58	1.31	1.31226307356326	-0.00226307356326072
59	1.34	1.31043301856251	0.0295669814374937
60	1.31	1.33434262676761	-0.0243426267676132
61	1.27	1.31465774043834	-0.0446577404383404
62	1.28	1.27854485284231	0.00145514715768846
63	1.27	1.27972157081383	-0.00972157081383207
64	1.26	1.27186013423843	-0.0118601342384308
65	1.27	1.26226932891729	0.0077306710827123
66	1.27	1.26852080633445	0.00147919366554827
67	1.28	1.26971696973306	0.0102830302669441
68	1.27	1.27803243559702	-0.0080324355970185
69	1.26	1.27153693356332	-0.0115369335633235
70	1.3	1.26220748740493	0.0377925125950733
71	1.31	1.29276874612337	0.0172312538766262
72	1.28	1.30670295614559	-0.0267029561455852
73	1.29	1.28510936801726	0.00489063198274065
74	1.31	1.28906422200971	0.0209357779902932
75	1.29	1.30599412911826	-0.0159941291182575
76	1.29	1.29306033127326	-0.00306033127325667
77	1.32	1.29058556658089	0.0294144334191113
78	1.3	1.31437181544478	-0.0143718154447758
79	1.29	1.30274991629328	-0.0127499162932803
80	1.31	1.29243958062832	0.0175604193716812
81	1.29	1.30663997331913	-0.0166399733191276
82	1.33	1.29318390769251	0.0368160923074858
83	1.35	1.32295557527299	0.0270444247270141
84	1.32	1.3448252950725	-0.0248252950724999
85	1.33	1.32475009463263	0.00524990536737158

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.21 & 1.2 & 0.01 \tabularnewline
3 & 1.21 & 1.20808659086679 & 0.00191340913320714 \tabularnewline
4 & 1.21 & 1.20963388654890 & 0.000366113451103933 \tabularnewline
5 & 1.21 & 1.20992994751789 & 7.00524821131143e-05 \tabularnewline
6 & 1.21 & 1.20998659609409 & 1.34039059078717e-05 \tabularnewline
7 & 1.21 & 1.20999743528440 & 2.56471559856308e-06 \tabularnewline
8 & 1.2 & 1.20999950926497 & -0.00999950926497495 \tabularnewline
9 & 1.21 & 1.20191331523552 & 0.00808668476448071 \tabularnewline
10 & 1.22 & 1.20845268635143 & 0.0115473136485724 \tabularnewline
11 & 1.22 & 1.21779052646008 & 0.00220947353991874 \tabularnewline
12 & 1.23 & 1.21957723731491 & 0.0104227626850861 \tabularnewline
13 & 1.22 & 1.22800569906851 & -0.00800569906851045 \tabularnewline
14 & 1.23 & 1.22153181777154 & 0.00846818222846046 \tabularnewline
15 & 1.23 & 1.22837969027824 & 0.00162030972175997 \tabularnewline
16 & 1.23 & 1.22968996845798 & 0.000310031542023914 \tabularnewline
17 & 1.23 & 1.22994067828159 & 5.93217184090555e-05 \tabularnewline
18 & 1.23 & 1.22998864932822 & 1.13506717802636e-05 \tabularnewline
19 & 1.22 & 1.22999782815209 & -0.00999782815209471 \tabularnewline
20 & 1.22 & 1.22191299356985 & -0.00191299356984542 \tabularnewline
21 & 1.23 & 1.22036603393683 & 0.00963396606316924 \tabularnewline
22 & 1.24 & 1.22815662813457 & 0.0118433718654276 \tabularnewline
23 & 1.24 & 1.23773387841047 & 0.00226612158952788 \tabularnewline
24 & 1.25 & 1.23956639822536 & 0.0104336017746360 \tabularnewline
25 & 1.25 & 1.24800362510722 & 0.00199637489278359 \tabularnewline
26 & 1.25 & 1.24961801180468 & 0.000381988195315763 \tabularnewline
27 & 1.26 & 1.24992691002983 & 0.0100730899701695 \tabularnewline
28 & 1.26 & 1.25807260576515 & 0.00192739423485389 \tabularnewline
29 & 1.26 & 1.25963121062677 & 0.000368789373226042 \tabularnewline
30 & 1.26 & 1.25992943550450 & 7.05644954959173e-05 \tabularnewline
31 & 1.27 & 1.25998649812498 & 0.0100135018750160 \tabularnewline
32 & 1.27 & 1.26808400740570 & 0.00191599259430419 \tabularnewline
33 & 1.29 & 1.26963339222709 & 0.0203666077729099 \tabularnewline
34 & 1.31 & 1.28610303466749 & 0.0238969653325136 \tabularnewline
35 & 1.32 & 1.30542753282768 & 0.0145724671723166 \tabularnewline
36 & 1.32 & 1.31721169082191 & 0.00278830917808714 \tabularnewline
37 & 1.33 & 1.31946648237524 & 0.0105335176247556 \tabularnewline
38 & 1.33 & 1.3279845071172 & 0.00201549288280067 \tabularnewline
39 & 1.32 & 1.32961435375101 & -0.0096143537510136 \tabularnewline
40 & 1.32 & 1.32183961922771 & -0.00183961922770748 \tabularnewline
41 & 1.31 & 1.32035199442319 & -0.0103519944231918 \tabularnewline
42 & 1.3 & 1.31198076006762 & -0.0119807600676245 \tabularnewline
43 & 1.31 & 1.30229240957362 & 0.00770759042638436 \tabularnewline
44 & 1.29 & 1.30852522260831 & -0.0185252226083135 \tabularnewline
45 & 1.3 & 1.29354463301334 & 0.00645536698665583 \tabularnewline
46 & 1.3 & 1.29876482418495 & 0.00123517581504728 \tabularnewline
47 & 1.32 & 1.29976366033144 & 0.020236339668563 \tabularnewline
48 & 1.31 & 1.31612796028555 & -0.00612796028554885 \tabularnewline
49 & 1.35 & 1.31117252951783 & 0.0388274704821701 \tabularnewline
50 & 1.35 & 1.34257071633601 & 0.00742928366399154 \tabularnewline
51 & 1.36 & 1.34857847407841 & 0.0114215259215869 \tabularnewline
52 & 1.37 & 1.35781459479865 & 0.0121854052013526 \tabularnewline
53 & 1.37 & 1.36766843343959 & 0.00233156656040978 \tabularnewline
54 & 1.37 & 1.36955387592486 & 0.000446124075136778 \tabularnewline
55 & 1.32 & 1.36991463821201 & -0.049914638212009 \tabularnewline
56 & 1.32 & 1.32955071246356 & -0.00955071246355899 \tabularnewline
57 & 1.31 & 1.32182744204564 & -0.0118274420456408 \tabularnewline
58 & 1.31 & 1.31226307356326 & -0.00226307356326072 \tabularnewline
59 & 1.34 & 1.31043301856251 & 0.0295669814374937 \tabularnewline
60 & 1.31 & 1.33434262676761 & -0.0243426267676132 \tabularnewline
61 & 1.27 & 1.31465774043834 & -0.0446577404383404 \tabularnewline
62 & 1.28 & 1.27854485284231 & 0.00145514715768846 \tabularnewline
63 & 1.27 & 1.27972157081383 & -0.00972157081383207 \tabularnewline
64 & 1.26 & 1.27186013423843 & -0.0118601342384308 \tabularnewline
65 & 1.27 & 1.26226932891729 & 0.0077306710827123 \tabularnewline
66 & 1.27 & 1.26852080633445 & 0.00147919366554827 \tabularnewline
67 & 1.28 & 1.26971696973306 & 0.0102830302669441 \tabularnewline
68 & 1.27 & 1.27803243559702 & -0.0080324355970185 \tabularnewline
69 & 1.26 & 1.27153693356332 & -0.0115369335633235 \tabularnewline
70 & 1.3 & 1.26220748740493 & 0.0377925125950733 \tabularnewline
71 & 1.31 & 1.29276874612337 & 0.0172312538766262 \tabularnewline
72 & 1.28 & 1.30670295614559 & -0.0267029561455852 \tabularnewline
73 & 1.29 & 1.28510936801726 & 0.00489063198274065 \tabularnewline
74 & 1.31 & 1.28906422200971 & 0.0209357779902932 \tabularnewline
75 & 1.29 & 1.30599412911826 & -0.0159941291182575 \tabularnewline
76 & 1.29 & 1.29306033127326 & -0.00306033127325667 \tabularnewline
77 & 1.32 & 1.29058556658089 & 0.0294144334191113 \tabularnewline
78 & 1.3 & 1.31437181544478 & -0.0143718154447758 \tabularnewline
79 & 1.29 & 1.30274991629328 & -0.0127499162932803 \tabularnewline
80 & 1.31 & 1.29243958062832 & 0.0175604193716812 \tabularnewline
81 & 1.29 & 1.30663997331913 & -0.0166399733191276 \tabularnewline
82 & 1.33 & 1.29318390769251 & 0.0368160923074858 \tabularnewline
83 & 1.35 & 1.32295557527299 & 0.0270444247270141 \tabularnewline
84 & 1.32 & 1.3448252950725 & -0.0248252950724999 \tabularnewline
85 & 1.33 & 1.32475009463263 & 0.00524990536737158 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72212&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]1.21[/C][C]1.2[/C][C]0.01[/C][/ROW]
[ROW][C]3[/C][C]1.21[/C][C]1.20808659086679[/C][C]0.00191340913320714[/C][/ROW]
[ROW][C]4[/C][C]1.21[/C][C]1.20963388654890[/C][C]0.000366113451103933[/C][/ROW]
[ROW][C]5[/C][C]1.21[/C][C]1.20992994751789[/C][C]7.00524821131143e-05[/C][/ROW]
[ROW][C]6[/C][C]1.21[/C][C]1.20998659609409[/C][C]1.34039059078717e-05[/C][/ROW]
[ROW][C]7[/C][C]1.21[/C][C]1.20999743528440[/C][C]2.56471559856308e-06[/C][/ROW]
[ROW][C]8[/C][C]1.2[/C][C]1.20999950926497[/C][C]-0.00999950926497495[/C][/ROW]
[ROW][C]9[/C][C]1.21[/C][C]1.20191331523552[/C][C]0.00808668476448071[/C][/ROW]
[ROW][C]10[/C][C]1.22[/C][C]1.20845268635143[/C][C]0.0115473136485724[/C][/ROW]
[ROW][C]11[/C][C]1.22[/C][C]1.21779052646008[/C][C]0.00220947353991874[/C][/ROW]
[ROW][C]12[/C][C]1.23[/C][C]1.21957723731491[/C][C]0.0104227626850861[/C][/ROW]
[ROW][C]13[/C][C]1.22[/C][C]1.22800569906851[/C][C]-0.00800569906851045[/C][/ROW]
[ROW][C]14[/C][C]1.23[/C][C]1.22153181777154[/C][C]0.00846818222846046[/C][/ROW]
[ROW][C]15[/C][C]1.23[/C][C]1.22837969027824[/C][C]0.00162030972175997[/C][/ROW]
[ROW][C]16[/C][C]1.23[/C][C]1.22968996845798[/C][C]0.000310031542023914[/C][/ROW]
[ROW][C]17[/C][C]1.23[/C][C]1.22994067828159[/C][C]5.93217184090555e-05[/C][/ROW]
[ROW][C]18[/C][C]1.23[/C][C]1.22998864932822[/C][C]1.13506717802636e-05[/C][/ROW]
[ROW][C]19[/C][C]1.22[/C][C]1.22999782815209[/C][C]-0.00999782815209471[/C][/ROW]
[ROW][C]20[/C][C]1.22[/C][C]1.22191299356985[/C][C]-0.00191299356984542[/C][/ROW]
[ROW][C]21[/C][C]1.23[/C][C]1.22036603393683[/C][C]0.00963396606316924[/C][/ROW]
[ROW][C]22[/C][C]1.24[/C][C]1.22815662813457[/C][C]0.0118433718654276[/C][/ROW]
[ROW][C]23[/C][C]1.24[/C][C]1.23773387841047[/C][C]0.00226612158952788[/C][/ROW]
[ROW][C]24[/C][C]1.25[/C][C]1.23956639822536[/C][C]0.0104336017746360[/C][/ROW]
[ROW][C]25[/C][C]1.25[/C][C]1.24800362510722[/C][C]0.00199637489278359[/C][/ROW]
[ROW][C]26[/C][C]1.25[/C][C]1.24961801180468[/C][C]0.000381988195315763[/C][/ROW]
[ROW][C]27[/C][C]1.26[/C][C]1.24992691002983[/C][C]0.0100730899701695[/C][/ROW]
[ROW][C]28[/C][C]1.26[/C][C]1.25807260576515[/C][C]0.00192739423485389[/C][/ROW]
[ROW][C]29[/C][C]1.26[/C][C]1.25963121062677[/C][C]0.000368789373226042[/C][/ROW]
[ROW][C]30[/C][C]1.26[/C][C]1.25992943550450[/C][C]7.05644954959173e-05[/C][/ROW]
[ROW][C]31[/C][C]1.27[/C][C]1.25998649812498[/C][C]0.0100135018750160[/C][/ROW]
[ROW][C]32[/C][C]1.27[/C][C]1.26808400740570[/C][C]0.00191599259430419[/C][/ROW]
[ROW][C]33[/C][C]1.29[/C][C]1.26963339222709[/C][C]0.0203666077729099[/C][/ROW]
[ROW][C]34[/C][C]1.31[/C][C]1.28610303466749[/C][C]0.0238969653325136[/C][/ROW]
[ROW][C]35[/C][C]1.32[/C][C]1.30542753282768[/C][C]0.0145724671723166[/C][/ROW]
[ROW][C]36[/C][C]1.32[/C][C]1.31721169082191[/C][C]0.00278830917808714[/C][/ROW]
[ROW][C]37[/C][C]1.33[/C][C]1.31946648237524[/C][C]0.0105335176247556[/C][/ROW]
[ROW][C]38[/C][C]1.33[/C][C]1.3279845071172[/C][C]0.00201549288280067[/C][/ROW]
[ROW][C]39[/C][C]1.32[/C][C]1.32961435375101[/C][C]-0.0096143537510136[/C][/ROW]
[ROW][C]40[/C][C]1.32[/C][C]1.32183961922771[/C][C]-0.00183961922770748[/C][/ROW]
[ROW][C]41[/C][C]1.31[/C][C]1.32035199442319[/C][C]-0.0103519944231918[/C][/ROW]
[ROW][C]42[/C][C]1.3[/C][C]1.31198076006762[/C][C]-0.0119807600676245[/C][/ROW]
[ROW][C]43[/C][C]1.31[/C][C]1.30229240957362[/C][C]0.00770759042638436[/C][/ROW]
[ROW][C]44[/C][C]1.29[/C][C]1.30852522260831[/C][C]-0.0185252226083135[/C][/ROW]
[ROW][C]45[/C][C]1.3[/C][C]1.29354463301334[/C][C]0.00645536698665583[/C][/ROW]
[ROW][C]46[/C][C]1.3[/C][C]1.29876482418495[/C][C]0.00123517581504728[/C][/ROW]
[ROW][C]47[/C][C]1.32[/C][C]1.29976366033144[/C][C]0.020236339668563[/C][/ROW]
[ROW][C]48[/C][C]1.31[/C][C]1.31612796028555[/C][C]-0.00612796028554885[/C][/ROW]
[ROW][C]49[/C][C]1.35[/C][C]1.31117252951783[/C][C]0.0388274704821701[/C][/ROW]
[ROW][C]50[/C][C]1.35[/C][C]1.34257071633601[/C][C]0.00742928366399154[/C][/ROW]
[ROW][C]51[/C][C]1.36[/C][C]1.34857847407841[/C][C]0.0114215259215869[/C][/ROW]
[ROW][C]52[/C][C]1.37[/C][C]1.35781459479865[/C][C]0.0121854052013526[/C][/ROW]
[ROW][C]53[/C][C]1.37[/C][C]1.36766843343959[/C][C]0.00233156656040978[/C][/ROW]
[ROW][C]54[/C][C]1.37[/C][C]1.36955387592486[/C][C]0.000446124075136778[/C][/ROW]
[ROW][C]55[/C][C]1.32[/C][C]1.36991463821201[/C][C]-0.049914638212009[/C][/ROW]
[ROW][C]56[/C][C]1.32[/C][C]1.32955071246356[/C][C]-0.00955071246355899[/C][/ROW]
[ROW][C]57[/C][C]1.31[/C][C]1.32182744204564[/C][C]-0.0118274420456408[/C][/ROW]
[ROW][C]58[/C][C]1.31[/C][C]1.31226307356326[/C][C]-0.00226307356326072[/C][/ROW]
[ROW][C]59[/C][C]1.34[/C][C]1.31043301856251[/C][C]0.0295669814374937[/C][/ROW]
[ROW][C]60[/C][C]1.31[/C][C]1.33434262676761[/C][C]-0.0243426267676132[/C][/ROW]
[ROW][C]61[/C][C]1.27[/C][C]1.31465774043834[/C][C]-0.0446577404383404[/C][/ROW]
[ROW][C]62[/C][C]1.28[/C][C]1.27854485284231[/C][C]0.00145514715768846[/C][/ROW]
[ROW][C]63[/C][C]1.27[/C][C]1.27972157081383[/C][C]-0.00972157081383207[/C][/ROW]
[ROW][C]64[/C][C]1.26[/C][C]1.27186013423843[/C][C]-0.0118601342384308[/C][/ROW]
[ROW][C]65[/C][C]1.27[/C][C]1.26226932891729[/C][C]0.0077306710827123[/C][/ROW]
[ROW][C]66[/C][C]1.27[/C][C]1.26852080633445[/C][C]0.00147919366554827[/C][/ROW]
[ROW][C]67[/C][C]1.28[/C][C]1.26971696973306[/C][C]0.0102830302669441[/C][/ROW]
[ROW][C]68[/C][C]1.27[/C][C]1.27803243559702[/C][C]-0.0080324355970185[/C][/ROW]
[ROW][C]69[/C][C]1.26[/C][C]1.27153693356332[/C][C]-0.0115369335633235[/C][/ROW]
[ROW][C]70[/C][C]1.3[/C][C]1.26220748740493[/C][C]0.0377925125950733[/C][/ROW]
[ROW][C]71[/C][C]1.31[/C][C]1.29276874612337[/C][C]0.0172312538766262[/C][/ROW]
[ROW][C]72[/C][C]1.28[/C][C]1.30670295614559[/C][C]-0.0267029561455852[/C][/ROW]
[ROW][C]73[/C][C]1.29[/C][C]1.28510936801726[/C][C]0.00489063198274065[/C][/ROW]
[ROW][C]74[/C][C]1.31[/C][C]1.28906422200971[/C][C]0.0209357779902932[/C][/ROW]
[ROW][C]75[/C][C]1.29[/C][C]1.30599412911826[/C][C]-0.0159941291182575[/C][/ROW]
[ROW][C]76[/C][C]1.29[/C][C]1.29306033127326[/C][C]-0.00306033127325667[/C][/ROW]
[ROW][C]77[/C][C]1.32[/C][C]1.29058556658089[/C][C]0.0294144334191113[/C][/ROW]
[ROW][C]78[/C][C]1.3[/C][C]1.31437181544478[/C][C]-0.0143718154447758[/C][/ROW]
[ROW][C]79[/C][C]1.29[/C][C]1.30274991629328[/C][C]-0.0127499162932803[/C][/ROW]
[ROW][C]80[/C][C]1.31[/C][C]1.29243958062832[/C][C]0.0175604193716812[/C][/ROW]
[ROW][C]81[/C][C]1.29[/C][C]1.30663997331913[/C][C]-0.0166399733191276[/C][/ROW]
[ROW][C]82[/C][C]1.33[/C][C]1.29318390769251[/C][C]0.0368160923074858[/C][/ROW]
[ROW][C]83[/C][C]1.35[/C][C]1.32295557527299[/C][C]0.0270444247270141[/C][/ROW]
[ROW][C]84[/C][C]1.32[/C][C]1.3448252950725[/C][C]-0.0248252950724999[/C][/ROW]
[ROW][C]85[/C][C]1.33[/C][C]1.32475009463263[/C][C]0.00524990536737158[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72212&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72212&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	1.21	1.2	0.01
3	1.21	1.20808659086679	0.00191340913320714
4	1.21	1.20963388654890	0.000366113451103933
5	1.21	1.20992994751789	7.00524821131143e-05
6	1.21	1.20998659609409	1.34039059078717e-05
7	1.21	1.20999743528440	2.56471559856308e-06
8	1.2	1.20999950926497	-0.00999950926497495
9	1.21	1.20191331523552	0.00808668476448071
10	1.22	1.20845268635143	0.0115473136485724
11	1.22	1.21779052646008	0.00220947353991874
12	1.23	1.21957723731491	0.0104227626850861
13	1.22	1.22800569906851	-0.00800569906851045
14	1.23	1.22153181777154	0.00846818222846046
15	1.23	1.22837969027824	0.00162030972175997
16	1.23	1.22968996845798	0.000310031542023914
17	1.23	1.22994067828159	5.93217184090555e-05
18	1.23	1.22998864932822	1.13506717802636e-05
19	1.22	1.22999782815209	-0.00999782815209471
20	1.22	1.22191299356985	-0.00191299356984542
21	1.23	1.22036603393683	0.00963396606316924
22	1.24	1.22815662813457	0.0118433718654276
23	1.24	1.23773387841047	0.00226612158952788
24	1.25	1.23956639822536	0.0104336017746360
25	1.25	1.24800362510722	0.00199637489278359
26	1.25	1.24961801180468	0.000381988195315763
27	1.26	1.24992691002983	0.0100730899701695
28	1.26	1.25807260576515	0.00192739423485389
29	1.26	1.25963121062677	0.000368789373226042
30	1.26	1.25992943550450	7.05644954959173e-05
31	1.27	1.25998649812498	0.0100135018750160
32	1.27	1.26808400740570	0.00191599259430419
33	1.29	1.26963339222709	0.0203666077729099
34	1.31	1.28610303466749	0.0238969653325136
35	1.32	1.30542753282768	0.0145724671723166
36	1.32	1.31721169082191	0.00278830917808714
37	1.33	1.31946648237524	0.0105335176247556
38	1.33	1.3279845071172	0.00201549288280067
39	1.32	1.32961435375101	-0.0096143537510136
40	1.32	1.32183961922771	-0.00183961922770748
41	1.31	1.32035199442319	-0.0103519944231918
42	1.3	1.31198076006762	-0.0119807600676245
43	1.31	1.30229240957362	0.00770759042638436
44	1.29	1.30852522260831	-0.0185252226083135
45	1.3	1.29354463301334	0.00645536698665583
46	1.3	1.29876482418495	0.00123517581504728
47	1.32	1.29976366033144	0.020236339668563
48	1.31	1.31612796028555	-0.00612796028554885
49	1.35	1.31117252951783	0.0388274704821701
50	1.35	1.34257071633601	0.00742928366399154
51	1.36	1.34857847407841	0.0114215259215869
52	1.37	1.35781459479865	0.0121854052013526
53	1.37	1.36766843343959	0.00233156656040978
54	1.37	1.36955387592486	0.000446124075136778
55	1.32	1.36991463821201	-0.049914638212009
56	1.32	1.32955071246356	-0.00955071246355899
57	1.31	1.32182744204564	-0.0118274420456408
58	1.31	1.31226307356326	-0.00226307356326072
59	1.34	1.31043301856251	0.0295669814374937
60	1.31	1.33434262676761	-0.0243426267676132
61	1.27	1.31465774043834	-0.0446577404383404
62	1.28	1.27854485284231	0.00145514715768846
63	1.27	1.27972157081383	-0.00972157081383207
64	1.26	1.27186013423843	-0.0118601342384308
65	1.27	1.26226932891729	0.0077306710827123
66	1.27	1.26852080633445	0.00147919366554827
67	1.28	1.26971696973306	0.0102830302669441
68	1.27	1.27803243559702	-0.0080324355970185
69	1.26	1.27153693356332	-0.0115369335633235
70	1.3	1.26220748740493	0.0377925125950733
71	1.31	1.29276874612337	0.0172312538766262
72	1.28	1.30670295614559	-0.0267029561455852
73	1.29	1.28510936801726	0.00489063198274065
74	1.31	1.28906422200971	0.0209357779902932
75	1.29	1.30599412911826	-0.0159941291182575
76	1.29	1.29306033127326	-0.00306033127325667
77	1.32	1.29058556658089	0.0294144334191113
78	1.3	1.31437181544478	-0.0143718154447758
79	1.29	1.30274991629328	-0.0127499162932803
80	1.31	1.29243958062832	0.0175604193716812
81	1.29	1.30663997331913	-0.0166399733191276
82	1.33	1.29318390769251	0.0368160923074858
83	1.35	1.32295557527299	0.0270444247270141
84	1.32	1.3448252950725	-0.0248252950724999
85	1.33	1.32475009463263	0.00524990536737158

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
86	1.32899547831216	1.29862367095981	1.35936728566451
87	1.32899547831216	1.28993575741808	1.36805519920624
88	1.32899547831216	1.28285572418627	1.37513523243805
89	1.32899547831216	1.27672606062579	1.38126489599853
90	1.32899547831216	1.27124336025796	1.38674759636636
91	1.32899547831216	1.26623783133411	1.39175312529021
92	1.32899547831216	1.26160306502479	1.39638789159953
93	1.32899547831216	1.25726715417748	1.40072380244684
94	1.32899547831216	1.25317880733773	1.40481214928659
95	1.32899547831216	1.24929991562440	1.40869104099992
96	1.32899547831216	1.24560124693736	1.41238970968696
97	1.32899547831216	1.24205979552846	1.41593116109586

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 1.32899547831216 & 1.29862367095981 & 1.35936728566451 \tabularnewline
87 & 1.32899547831216 & 1.28993575741808 & 1.36805519920624 \tabularnewline
88 & 1.32899547831216 & 1.28285572418627 & 1.37513523243805 \tabularnewline
89 & 1.32899547831216 & 1.27672606062579 & 1.38126489599853 \tabularnewline
90 & 1.32899547831216 & 1.27124336025796 & 1.38674759636636 \tabularnewline
91 & 1.32899547831216 & 1.26623783133411 & 1.39175312529021 \tabularnewline
92 & 1.32899547831216 & 1.26160306502479 & 1.39638789159953 \tabularnewline
93 & 1.32899547831216 & 1.25726715417748 & 1.40072380244684 \tabularnewline
94 & 1.32899547831216 & 1.25317880733773 & 1.40481214928659 \tabularnewline
95 & 1.32899547831216 & 1.24929991562440 & 1.40869104099992 \tabularnewline
96 & 1.32899547831216 & 1.24560124693736 & 1.41238970968696 \tabularnewline
97 & 1.32899547831216 & 1.24205979552846 & 1.41593116109586 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72212&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]86[/C][C]1.32899547831216[/C][C]1.29862367095981[/C][C]1.35936728566451[/C][/ROW]
[ROW][C]87[/C][C]1.32899547831216[/C][C]1.28993575741808[/C][C]1.36805519920624[/C][/ROW]
[ROW][C]88[/C][C]1.32899547831216[/C][C]1.28285572418627[/C][C]1.37513523243805[/C][/ROW]
[ROW][C]89[/C][C]1.32899547831216[/C][C]1.27672606062579[/C][C]1.38126489599853[/C][/ROW]
[ROW][C]90[/C][C]1.32899547831216[/C][C]1.27124336025796[/C][C]1.38674759636636[/C][/ROW]
[ROW][C]91[/C][C]1.32899547831216[/C][C]1.26623783133411[/C][C]1.39175312529021[/C][/ROW]
[ROW][C]92[/C][C]1.32899547831216[/C][C]1.26160306502479[/C][C]1.39638789159953[/C][/ROW]
[ROW][C]93[/C][C]1.32899547831216[/C][C]1.25726715417748[/C][C]1.40072380244684[/C][/ROW]
[ROW][C]94[/C][C]1.32899547831216[/C][C]1.25317880733773[/C][C]1.40481214928659[/C][/ROW]
[ROW][C]95[/C][C]1.32899547831216[/C][C]1.24929991562440[/C][C]1.40869104099992[/C][/ROW]
[ROW][C]96[/C][C]1.32899547831216[/C][C]1.24560124693736[/C][C]1.41238970968696[/C][/ROW]
[ROW][C]97[/C][C]1.32899547831216[/C][C]1.24205979552846[/C][C]1.41593116109586[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72212&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72212&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
86	1.32899547831216	1.29862367095981	1.35936728566451
87	1.32899547831216	1.28993575741808	1.36805519920624
88	1.32899547831216	1.28285572418627	1.37513523243805
89	1.32899547831216	1.27672606062579	1.38126489599853
90	1.32899547831216	1.27124336025796	1.38674759636636
91	1.32899547831216	1.26623783133411	1.39175312529021
92	1.32899547831216	1.26160306502479	1.39638789159953
93	1.32899547831216	1.25726715417748	1.40072380244684
94	1.32899547831216	1.25317880733773	1.40481214928659
95	1.32899547831216	1.24929991562440	1.40869104099992
96	1.32899547831216	1.24560124693736	1.41238970968696
97	1.32899547831216	1.24205979552846	1.41593116109586

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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