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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 22 May 2014 12:16:45 -0400

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/2014/May/22/t1400775430yx25quhplc5ulyo.htm/, Retrieved Fri, 22 May 2026 23:27:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235131, Retrieved Fri, 22 May 2026 23:27:29 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

342

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

-       [Exponential Smoothing] [] [2014-05-22 16:16:45] [3fb01879614a306972947b7a96f19080] [Current]

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Dataseries X:

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2,58
2,59
2,6
2,6
2,61
2,62
2,64
2,65
2,66
2,67
2,68
2,69
2,69
2,71
2,72
2,73
2,73
2,74
2,74
2,74
2,74
2,74
2,75
2,75
2,75
2,75
2,77
2,78
2,79
2,8
2,82
2,83
2,84
2,87
2,89
2,9
2,9
2,91
2,92
2,92
2,92
2,92
2,94
2,95
2,95
2,97
2,99
3
3
3,01
3,03
3,03
3,04
3,04
3,05
3,05
3,09
3,09
3,09
3,1
3,1
3,11
3,12
3,12
3,12
3,13
3,15
3,16
3,16
3,18
3,19
3,19
3,2
3,21
3,26
3,27
3,28
3,29
3,29
3,3
3,3
3,31
3,31
3,31

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	'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235131&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235131&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235131&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.00332713811894566
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00332713811894566 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235131&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.00332713811894566[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235131&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235131&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.00332713811894566
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	2.6	2.6	4.44089209850063e-16
4	2.6	2.61	-0.00999999999999979
5	2.61	2.60996672861881	3.32713811892482e-05
6	2.62	2.61996683931729	3.3160682709088e-05
7	2.64	2.62996694964746	0.0100330503525377
8	2.65	2.65000033099174	-3.30991739794229e-07
9	2.66	2.66000032989048	-3.29890484263018e-07
10	2.67	2.67000032879289	-3.28792893355967e-07
11	2.68	2.68000032769895	-3.27698953750399e-07
12	2.69	2.69000032660865	-3.26608654344085e-07
13	2.69	2.70000032552198	-0.010000325521982
14	2.71	2.69996705305774	0.010032946942264
15	2.72	2.72000043405795	-4.34057952691802e-07
16	2.73	2.73000043261378	-4.32613782574975e-07
17	2.73	2.74000043117442	-0.0100004311744164
18	2.74	2.73996715835865	3.28416413499788e-05
19	2.74	2.74996726762733	-0.00996726762732703
20	2.74	2.74993410515126	-0.00993410515126225
21	2.74	2.74990105301134	-0.00990105301133593
22	2.74	2.74986811084044	-0.00986811084044437
23	2.75	2.74983527827271	0.000164721727294648
24	2.75	2.75983582632464	-0.00983582632464275
25	2.75	2.75980310117195	-0.00980310117194705
26	2.75	2.75977048490035	-0.0097704849003537
27	2.77	2.7597379771476	0.0102620228523986
28	2.78	2.77977212031501	0.000227879684988608
29	2.79	2.7897728785022	0.000227121497802685
30	2.8	2.79977363416679	0.000226365833209563
31	2.82	2.80977438731718	0.0102256126828171
32	2.83	2.82980840934293	0.000191590657070861
33	2.84	2.83980904679151	0.000190953208492051
34	2.87	2.84980968211921	0.0201903178807936
35	2.89	2.87987685809546	0.0101231419045384
36	2.9	2.89991053918678	8.94608132240293e-05
37	2.9	2.90991083683526	-0.00991083683525762
38	2.91	2.90987786211223	0.000122137887768048
39	2.92	2.91987826848185	0.000121731518145207
40	2.92	2.92987867349943	-0.00987867349942873
41	2.92	2.92984580578826	-0.00984580578826399
42	2.92	2.92981304743251	-0.00981304743251421
43	2.94	2.92978039806834	0.0102196019316616
44	2.95	2.94981440009549	0.000185599904514611
45	2.95	2.959815017612	-0.0098150176120031
46	2.97	2.95978236169277	0.0102176383072319
47	2.99	2.97981635718667	0.0101836428133346
48	3	2.99985023957286	0.000149760427140322
49	3	3.00985073784649	-0.00985073784648538
50	3.01	3.0098179630811	0.000182036918903172
51	3.03	3.01981856874307	0.0101814312569313
52	3.03	3.03985244377111	-0.00985244377110872
53	3.04	3.03981966332987	0.000180336670126735
54	3.04	3.04982026333488	-0.00982026333488273
55	3.05	3.0497875899624	0.000212410037596644
56	3.05	3.05978829667994	-0.00978829667993608
57	3.09	3.05975572966493	0.0302442703350674
58	3.09	3.09985635652964	-0.00985635652964412
59	3.09	3.09982356307012	-0.00982356307012067
60	3.1	3.09979087871897	0.000209121281034008
61	3.1	3.10979157449435	-0.00979157449435153
62	3.11	3.10975899657361	0.000241003426392883
63	3.12	3.11975979842529	0.0002402015747065
64	3.12	3.12976059760911	-0.0097605976091093
65	3.12	3.12972812275274	-0.00972812275274038
66	3.13	3.1296957559447	0.000304244055295833
67	3.15	3.1396967682067	0.0103032317933023
68	3.16	3.15973104848195	0.000268951518054728
69	3.16	3.16973194332079	-0.00973194332079341
70	3.18	3.1696995638012	0.0103004361988006
71	3.19	3.18973383477512	0.000266165224881654
72	3.19	3.19973472034358	-0.0097347203435838
73	3.2	3.19970233158445	0.000297668415548902
74	3.21	3.20970332196838	0.00029667803161626
75	3.26	3.21970430905717	0.0402956909428283
76	3.27	3.26983837838654	0.000161621613463669
77	3.28	3.27983891612397	0.000161083876032198
78	3.29	3.28983945207227	0.000160547927728238
79	3.29	3.2998399862374	-0.00983998623740234
80	3.3	3.2998072472441	0.000192752755897807
81	3.3	3.30980788855914	-0.0098078885591435
82	3.31	3.30977525635925	0.000224743640748315
83	3.31	3.31977600411239	-0.00977600411238599
84	3.31	3.31974347799645	-0.00974347799645292

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2.6 & 2.6 & 4.44089209850063e-16 \tabularnewline
4 & 2.6 & 2.61 & -0.00999999999999979 \tabularnewline
5 & 2.61 & 2.60996672861881 & 3.32713811892482e-05 \tabularnewline
6 & 2.62 & 2.61996683931729 & 3.3160682709088e-05 \tabularnewline
7 & 2.64 & 2.62996694964746 & 0.0100330503525377 \tabularnewline
8 & 2.65 & 2.65000033099174 & -3.30991739794229e-07 \tabularnewline
9 & 2.66 & 2.66000032989048 & -3.29890484263018e-07 \tabularnewline
10 & 2.67 & 2.67000032879289 & -3.28792893355967e-07 \tabularnewline
11 & 2.68 & 2.68000032769895 & -3.27698953750399e-07 \tabularnewline
12 & 2.69 & 2.69000032660865 & -3.26608654344085e-07 \tabularnewline
13 & 2.69 & 2.70000032552198 & -0.010000325521982 \tabularnewline
14 & 2.71 & 2.69996705305774 & 0.010032946942264 \tabularnewline
15 & 2.72 & 2.72000043405795 & -4.34057952691802e-07 \tabularnewline
16 & 2.73 & 2.73000043261378 & -4.32613782574975e-07 \tabularnewline
17 & 2.73 & 2.74000043117442 & -0.0100004311744164 \tabularnewline
18 & 2.74 & 2.73996715835865 & 3.28416413499788e-05 \tabularnewline
19 & 2.74 & 2.74996726762733 & -0.00996726762732703 \tabularnewline
20 & 2.74 & 2.74993410515126 & -0.00993410515126225 \tabularnewline
21 & 2.74 & 2.74990105301134 & -0.00990105301133593 \tabularnewline
22 & 2.74 & 2.74986811084044 & -0.00986811084044437 \tabularnewline
23 & 2.75 & 2.74983527827271 & 0.000164721727294648 \tabularnewline
24 & 2.75 & 2.75983582632464 & -0.00983582632464275 \tabularnewline
25 & 2.75 & 2.75980310117195 & -0.00980310117194705 \tabularnewline
26 & 2.75 & 2.75977048490035 & -0.0097704849003537 \tabularnewline
27 & 2.77 & 2.7597379771476 & 0.0102620228523986 \tabularnewline
28 & 2.78 & 2.77977212031501 & 0.000227879684988608 \tabularnewline
29 & 2.79 & 2.7897728785022 & 0.000227121497802685 \tabularnewline
30 & 2.8 & 2.79977363416679 & 0.000226365833209563 \tabularnewline
31 & 2.82 & 2.80977438731718 & 0.0102256126828171 \tabularnewline
32 & 2.83 & 2.82980840934293 & 0.000191590657070861 \tabularnewline
33 & 2.84 & 2.83980904679151 & 0.000190953208492051 \tabularnewline
34 & 2.87 & 2.84980968211921 & 0.0201903178807936 \tabularnewline
35 & 2.89 & 2.87987685809546 & 0.0101231419045384 \tabularnewline
36 & 2.9 & 2.89991053918678 & 8.94608132240293e-05 \tabularnewline
37 & 2.9 & 2.90991083683526 & -0.00991083683525762 \tabularnewline
38 & 2.91 & 2.90987786211223 & 0.000122137887768048 \tabularnewline
39 & 2.92 & 2.91987826848185 & 0.000121731518145207 \tabularnewline
40 & 2.92 & 2.92987867349943 & -0.00987867349942873 \tabularnewline
41 & 2.92 & 2.92984580578826 & -0.00984580578826399 \tabularnewline
42 & 2.92 & 2.92981304743251 & -0.00981304743251421 \tabularnewline
43 & 2.94 & 2.92978039806834 & 0.0102196019316616 \tabularnewline
44 & 2.95 & 2.94981440009549 & 0.000185599904514611 \tabularnewline
45 & 2.95 & 2.959815017612 & -0.0098150176120031 \tabularnewline
46 & 2.97 & 2.95978236169277 & 0.0102176383072319 \tabularnewline
47 & 2.99 & 2.97981635718667 & 0.0101836428133346 \tabularnewline
48 & 3 & 2.99985023957286 & 0.000149760427140322 \tabularnewline
49 & 3 & 3.00985073784649 & -0.00985073784648538 \tabularnewline
50 & 3.01 & 3.0098179630811 & 0.000182036918903172 \tabularnewline
51 & 3.03 & 3.01981856874307 & 0.0101814312569313 \tabularnewline
52 & 3.03 & 3.03985244377111 & -0.00985244377110872 \tabularnewline
53 & 3.04 & 3.03981966332987 & 0.000180336670126735 \tabularnewline
54 & 3.04 & 3.04982026333488 & -0.00982026333488273 \tabularnewline
55 & 3.05 & 3.0497875899624 & 0.000212410037596644 \tabularnewline
56 & 3.05 & 3.05978829667994 & -0.00978829667993608 \tabularnewline
57 & 3.09 & 3.05975572966493 & 0.0302442703350674 \tabularnewline
58 & 3.09 & 3.09985635652964 & -0.00985635652964412 \tabularnewline
59 & 3.09 & 3.09982356307012 & -0.00982356307012067 \tabularnewline
60 & 3.1 & 3.09979087871897 & 0.000209121281034008 \tabularnewline
61 & 3.1 & 3.10979157449435 & -0.00979157449435153 \tabularnewline
62 & 3.11 & 3.10975899657361 & 0.000241003426392883 \tabularnewline
63 & 3.12 & 3.11975979842529 & 0.0002402015747065 \tabularnewline
64 & 3.12 & 3.12976059760911 & -0.0097605976091093 \tabularnewline
65 & 3.12 & 3.12972812275274 & -0.00972812275274038 \tabularnewline
66 & 3.13 & 3.1296957559447 & 0.000304244055295833 \tabularnewline
67 & 3.15 & 3.1396967682067 & 0.0103032317933023 \tabularnewline
68 & 3.16 & 3.15973104848195 & 0.000268951518054728 \tabularnewline
69 & 3.16 & 3.16973194332079 & -0.00973194332079341 \tabularnewline
70 & 3.18 & 3.1696995638012 & 0.0103004361988006 \tabularnewline
71 & 3.19 & 3.18973383477512 & 0.000266165224881654 \tabularnewline
72 & 3.19 & 3.19973472034358 & -0.0097347203435838 \tabularnewline
73 & 3.2 & 3.19970233158445 & 0.000297668415548902 \tabularnewline
74 & 3.21 & 3.20970332196838 & 0.00029667803161626 \tabularnewline
75 & 3.26 & 3.21970430905717 & 0.0402956909428283 \tabularnewline
76 & 3.27 & 3.26983837838654 & 0.000161621613463669 \tabularnewline
77 & 3.28 & 3.27983891612397 & 0.000161083876032198 \tabularnewline
78 & 3.29 & 3.28983945207227 & 0.000160547927728238 \tabularnewline
79 & 3.29 & 3.2998399862374 & -0.00983998623740234 \tabularnewline
80 & 3.3 & 3.2998072472441 & 0.000192752755897807 \tabularnewline
81 & 3.3 & 3.30980788855914 & -0.0098078885591435 \tabularnewline
82 & 3.31 & 3.30977525635925 & 0.000224743640748315 \tabularnewline
83 & 3.31 & 3.31977600411239 & -0.00977600411238599 \tabularnewline
84 & 3.31 & 3.31974347799645 & -0.00974347799645292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235131&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]2.6[/C][C]2.6[/C][C]4.44089209850063e-16[/C][/ROW]
[ROW][C]4[/C][C]2.6[/C][C]2.61[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]5[/C][C]2.61[/C][C]2.60996672861881[/C][C]3.32713811892482e-05[/C][/ROW]
[ROW][C]6[/C][C]2.62[/C][C]2.61996683931729[/C][C]3.3160682709088e-05[/C][/ROW]
[ROW][C]7[/C][C]2.64[/C][C]2.62996694964746[/C][C]0.0100330503525377[/C][/ROW]
[ROW][C]8[/C][C]2.65[/C][C]2.65000033099174[/C][C]-3.30991739794229e-07[/C][/ROW]
[ROW][C]9[/C][C]2.66[/C][C]2.66000032989048[/C][C]-3.29890484263018e-07[/C][/ROW]
[ROW][C]10[/C][C]2.67[/C][C]2.67000032879289[/C][C]-3.28792893355967e-07[/C][/ROW]
[ROW][C]11[/C][C]2.68[/C][C]2.68000032769895[/C][C]-3.27698953750399e-07[/C][/ROW]
[ROW][C]12[/C][C]2.69[/C][C]2.69000032660865[/C][C]-3.26608654344085e-07[/C][/ROW]
[ROW][C]13[/C][C]2.69[/C][C]2.70000032552198[/C][C]-0.010000325521982[/C][/ROW]
[ROW][C]14[/C][C]2.71[/C][C]2.69996705305774[/C][C]0.010032946942264[/C][/ROW]
[ROW][C]15[/C][C]2.72[/C][C]2.72000043405795[/C][C]-4.34057952691802e-07[/C][/ROW]
[ROW][C]16[/C][C]2.73[/C][C]2.73000043261378[/C][C]-4.32613782574975e-07[/C][/ROW]
[ROW][C]17[/C][C]2.73[/C][C]2.74000043117442[/C][C]-0.0100004311744164[/C][/ROW]
[ROW][C]18[/C][C]2.74[/C][C]2.73996715835865[/C][C]3.28416413499788e-05[/C][/ROW]
[ROW][C]19[/C][C]2.74[/C][C]2.74996726762733[/C][C]-0.00996726762732703[/C][/ROW]
[ROW][C]20[/C][C]2.74[/C][C]2.74993410515126[/C][C]-0.00993410515126225[/C][/ROW]
[ROW][C]21[/C][C]2.74[/C][C]2.74990105301134[/C][C]-0.00990105301133593[/C][/ROW]
[ROW][C]22[/C][C]2.74[/C][C]2.74986811084044[/C][C]-0.00986811084044437[/C][/ROW]
[ROW][C]23[/C][C]2.75[/C][C]2.74983527827271[/C][C]0.000164721727294648[/C][/ROW]
[ROW][C]24[/C][C]2.75[/C][C]2.75983582632464[/C][C]-0.00983582632464275[/C][/ROW]
[ROW][C]25[/C][C]2.75[/C][C]2.75980310117195[/C][C]-0.00980310117194705[/C][/ROW]
[ROW][C]26[/C][C]2.75[/C][C]2.75977048490035[/C][C]-0.0097704849003537[/C][/ROW]
[ROW][C]27[/C][C]2.77[/C][C]2.7597379771476[/C][C]0.0102620228523986[/C][/ROW]
[ROW][C]28[/C][C]2.78[/C][C]2.77977212031501[/C][C]0.000227879684988608[/C][/ROW]
[ROW][C]29[/C][C]2.79[/C][C]2.7897728785022[/C][C]0.000227121497802685[/C][/ROW]
[ROW][C]30[/C][C]2.8[/C][C]2.79977363416679[/C][C]0.000226365833209563[/C][/ROW]
[ROW][C]31[/C][C]2.82[/C][C]2.80977438731718[/C][C]0.0102256126828171[/C][/ROW]
[ROW][C]32[/C][C]2.83[/C][C]2.82980840934293[/C][C]0.000191590657070861[/C][/ROW]
[ROW][C]33[/C][C]2.84[/C][C]2.83980904679151[/C][C]0.000190953208492051[/C][/ROW]
[ROW][C]34[/C][C]2.87[/C][C]2.84980968211921[/C][C]0.0201903178807936[/C][/ROW]
[ROW][C]35[/C][C]2.89[/C][C]2.87987685809546[/C][C]0.0101231419045384[/C][/ROW]
[ROW][C]36[/C][C]2.9[/C][C]2.89991053918678[/C][C]8.94608132240293e-05[/C][/ROW]
[ROW][C]37[/C][C]2.9[/C][C]2.90991083683526[/C][C]-0.00991083683525762[/C][/ROW]
[ROW][C]38[/C][C]2.91[/C][C]2.90987786211223[/C][C]0.000122137887768048[/C][/ROW]
[ROW][C]39[/C][C]2.92[/C][C]2.91987826848185[/C][C]0.000121731518145207[/C][/ROW]
[ROW][C]40[/C][C]2.92[/C][C]2.92987867349943[/C][C]-0.00987867349942873[/C][/ROW]
[ROW][C]41[/C][C]2.92[/C][C]2.92984580578826[/C][C]-0.00984580578826399[/C][/ROW]
[ROW][C]42[/C][C]2.92[/C][C]2.92981304743251[/C][C]-0.00981304743251421[/C][/ROW]
[ROW][C]43[/C][C]2.94[/C][C]2.92978039806834[/C][C]0.0102196019316616[/C][/ROW]
[ROW][C]44[/C][C]2.95[/C][C]2.94981440009549[/C][C]0.000185599904514611[/C][/ROW]
[ROW][C]45[/C][C]2.95[/C][C]2.959815017612[/C][C]-0.0098150176120031[/C][/ROW]
[ROW][C]46[/C][C]2.97[/C][C]2.95978236169277[/C][C]0.0102176383072319[/C][/ROW]
[ROW][C]47[/C][C]2.99[/C][C]2.97981635718667[/C][C]0.0101836428133346[/C][/ROW]
[ROW][C]48[/C][C]3[/C][C]2.99985023957286[/C][C]0.000149760427140322[/C][/ROW]
[ROW][C]49[/C][C]3[/C][C]3.00985073784649[/C][C]-0.00985073784648538[/C][/ROW]
[ROW][C]50[/C][C]3.01[/C][C]3.0098179630811[/C][C]0.000182036918903172[/C][/ROW]
[ROW][C]51[/C][C]3.03[/C][C]3.01981856874307[/C][C]0.0101814312569313[/C][/ROW]
[ROW][C]52[/C][C]3.03[/C][C]3.03985244377111[/C][C]-0.00985244377110872[/C][/ROW]
[ROW][C]53[/C][C]3.04[/C][C]3.03981966332987[/C][C]0.000180336670126735[/C][/ROW]
[ROW][C]54[/C][C]3.04[/C][C]3.04982026333488[/C][C]-0.00982026333488273[/C][/ROW]
[ROW][C]55[/C][C]3.05[/C][C]3.0497875899624[/C][C]0.000212410037596644[/C][/ROW]
[ROW][C]56[/C][C]3.05[/C][C]3.05978829667994[/C][C]-0.00978829667993608[/C][/ROW]
[ROW][C]57[/C][C]3.09[/C][C]3.05975572966493[/C][C]0.0302442703350674[/C][/ROW]
[ROW][C]58[/C][C]3.09[/C][C]3.09985635652964[/C][C]-0.00985635652964412[/C][/ROW]
[ROW][C]59[/C][C]3.09[/C][C]3.09982356307012[/C][C]-0.00982356307012067[/C][/ROW]
[ROW][C]60[/C][C]3.1[/C][C]3.09979087871897[/C][C]0.000209121281034008[/C][/ROW]
[ROW][C]61[/C][C]3.1[/C][C]3.10979157449435[/C][C]-0.00979157449435153[/C][/ROW]
[ROW][C]62[/C][C]3.11[/C][C]3.10975899657361[/C][C]0.000241003426392883[/C][/ROW]
[ROW][C]63[/C][C]3.12[/C][C]3.11975979842529[/C][C]0.0002402015747065[/C][/ROW]
[ROW][C]64[/C][C]3.12[/C][C]3.12976059760911[/C][C]-0.0097605976091093[/C][/ROW]
[ROW][C]65[/C][C]3.12[/C][C]3.12972812275274[/C][C]-0.00972812275274038[/C][/ROW]
[ROW][C]66[/C][C]3.13[/C][C]3.1296957559447[/C][C]0.000304244055295833[/C][/ROW]
[ROW][C]67[/C][C]3.15[/C][C]3.1396967682067[/C][C]0.0103032317933023[/C][/ROW]
[ROW][C]68[/C][C]3.16[/C][C]3.15973104848195[/C][C]0.000268951518054728[/C][/ROW]
[ROW][C]69[/C][C]3.16[/C][C]3.16973194332079[/C][C]-0.00973194332079341[/C][/ROW]
[ROW][C]70[/C][C]3.18[/C][C]3.1696995638012[/C][C]0.0103004361988006[/C][/ROW]
[ROW][C]71[/C][C]3.19[/C][C]3.18973383477512[/C][C]0.000266165224881654[/C][/ROW]
[ROW][C]72[/C][C]3.19[/C][C]3.19973472034358[/C][C]-0.0097347203435838[/C][/ROW]
[ROW][C]73[/C][C]3.2[/C][C]3.19970233158445[/C][C]0.000297668415548902[/C][/ROW]
[ROW][C]74[/C][C]3.21[/C][C]3.20970332196838[/C][C]0.00029667803161626[/C][/ROW]
[ROW][C]75[/C][C]3.26[/C][C]3.21970430905717[/C][C]0.0402956909428283[/C][/ROW]
[ROW][C]76[/C][C]3.27[/C][C]3.26983837838654[/C][C]0.000161621613463669[/C][/ROW]
[ROW][C]77[/C][C]3.28[/C][C]3.27983891612397[/C][C]0.000161083876032198[/C][/ROW]
[ROW][C]78[/C][C]3.29[/C][C]3.28983945207227[/C][C]0.000160547927728238[/C][/ROW]
[ROW][C]79[/C][C]3.29[/C][C]3.2998399862374[/C][C]-0.00983998623740234[/C][/ROW]
[ROW][C]80[/C][C]3.3[/C][C]3.2998072472441[/C][C]0.000192752755897807[/C][/ROW]
[ROW][C]81[/C][C]3.3[/C][C]3.30980788855914[/C][C]-0.0098078885591435[/C][/ROW]
[ROW][C]82[/C][C]3.31[/C][C]3.30977525635925[/C][C]0.000224743640748315[/C][/ROW]
[ROW][C]83[/C][C]3.31[/C][C]3.31977600411239[/C][C]-0.00977600411238599[/C][/ROW]
[ROW][C]84[/C][C]3.31[/C][C]3.31974347799645[/C][C]-0.00974347799645292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235131&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235131&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	2.6	2.6	4.44089209850063e-16
4	2.6	2.61	-0.00999999999999979
5	2.61	2.60996672861881	3.32713811892482e-05
6	2.62	2.61996683931729	3.3160682709088e-05
7	2.64	2.62996694964746	0.0100330503525377
8	2.65	2.65000033099174	-3.30991739794229e-07
9	2.66	2.66000032989048	-3.29890484263018e-07
10	2.67	2.67000032879289	-3.28792893355967e-07
11	2.68	2.68000032769895	-3.27698953750399e-07
12	2.69	2.69000032660865	-3.26608654344085e-07
13	2.69	2.70000032552198	-0.010000325521982
14	2.71	2.69996705305774	0.010032946942264
15	2.72	2.72000043405795	-4.34057952691802e-07
16	2.73	2.73000043261378	-4.32613782574975e-07
17	2.73	2.74000043117442	-0.0100004311744164
18	2.74	2.73996715835865	3.28416413499788e-05
19	2.74	2.74996726762733	-0.00996726762732703
20	2.74	2.74993410515126	-0.00993410515126225
21	2.74	2.74990105301134	-0.00990105301133593
22	2.74	2.74986811084044	-0.00986811084044437
23	2.75	2.74983527827271	0.000164721727294648
24	2.75	2.75983582632464	-0.00983582632464275
25	2.75	2.75980310117195	-0.00980310117194705
26	2.75	2.75977048490035	-0.0097704849003537
27	2.77	2.7597379771476	0.0102620228523986
28	2.78	2.77977212031501	0.000227879684988608
29	2.79	2.7897728785022	0.000227121497802685
30	2.8	2.79977363416679	0.000226365833209563
31	2.82	2.80977438731718	0.0102256126828171
32	2.83	2.82980840934293	0.000191590657070861
33	2.84	2.83980904679151	0.000190953208492051
34	2.87	2.84980968211921	0.0201903178807936
35	2.89	2.87987685809546	0.0101231419045384
36	2.9	2.89991053918678	8.94608132240293e-05
37	2.9	2.90991083683526	-0.00991083683525762
38	2.91	2.90987786211223	0.000122137887768048
39	2.92	2.91987826848185	0.000121731518145207
40	2.92	2.92987867349943	-0.00987867349942873
41	2.92	2.92984580578826	-0.00984580578826399
42	2.92	2.92981304743251	-0.00981304743251421
43	2.94	2.92978039806834	0.0102196019316616
44	2.95	2.94981440009549	0.000185599904514611
45	2.95	2.959815017612	-0.0098150176120031
46	2.97	2.95978236169277	0.0102176383072319
47	2.99	2.97981635718667	0.0101836428133346
48	3	2.99985023957286	0.000149760427140322
49	3	3.00985073784649	-0.00985073784648538
50	3.01	3.0098179630811	0.000182036918903172
51	3.03	3.01981856874307	0.0101814312569313
52	3.03	3.03985244377111	-0.00985244377110872
53	3.04	3.03981966332987	0.000180336670126735
54	3.04	3.04982026333488	-0.00982026333488273
55	3.05	3.0497875899624	0.000212410037596644
56	3.05	3.05978829667994	-0.00978829667993608
57	3.09	3.05975572966493	0.0302442703350674
58	3.09	3.09985635652964	-0.00985635652964412
59	3.09	3.09982356307012	-0.00982356307012067
60	3.1	3.09979087871897	0.000209121281034008
61	3.1	3.10979157449435	-0.00979157449435153
62	3.11	3.10975899657361	0.000241003426392883
63	3.12	3.11975979842529	0.0002402015747065
64	3.12	3.12976059760911	-0.0097605976091093
65	3.12	3.12972812275274	-0.00972812275274038
66	3.13	3.1296957559447	0.000304244055295833
67	3.15	3.1396967682067	0.0103032317933023
68	3.16	3.15973104848195	0.000268951518054728
69	3.16	3.16973194332079	-0.00973194332079341
70	3.18	3.1696995638012	0.0103004361988006
71	3.19	3.18973383477512	0.000266165224881654
72	3.19	3.19973472034358	-0.0097347203435838
73	3.2	3.19970233158445	0.000297668415548902
74	3.21	3.20970332196838	0.00029667803161626
75	3.26	3.21970430905717	0.0402956909428283
76	3.27	3.26983837838654	0.000161621613463669
77	3.28	3.27983891612397	0.000161083876032198
78	3.29	3.28983945207227	0.000160547927728238
79	3.29	3.2998399862374	-0.00983998623740234
80	3.3	3.2998072472441	0.000192752755897807
81	3.3	3.30980788855914	-0.0098078885591435
82	3.31	3.30977525635925	0.000224743640748315
83	3.31	3.31977600411239	-0.00977600411238599
84	3.31	3.31974347799645	-0.00974347799645292

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	3.3197110600994	3.30161694415236	3.33780517604644
86	3.3294221201988	3.30379057170218	3.35505366869542
87	3.3391331802982	3.30768886463129	3.37057749596511
88	3.3488442403976	3.31247515450514	3.38521332629006
89	3.358555300497	3.31782595248499	3.39928464850901
90	3.3682663605964	3.32357564143994	3.41295707975286
91	3.3779774206958	3.32962600474094	3.42632883665066
92	3.3876884807952	3.33591315678552	3.43946380480488
93	3.3973995408946	3.34239279692992	3.45240628485928
94	3.407110600994	3.34903272405987	3.46518847792812
95	3.4168216610934	3.35580866946442	3.47783465272238
96	3.4265327211928	3.36270181014577	3.49036363223982

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3.3197110600994 & 3.30161694415236 & 3.33780517604644 \tabularnewline
86 & 3.3294221201988 & 3.30379057170218 & 3.35505366869542 \tabularnewline
87 & 3.3391331802982 & 3.30768886463129 & 3.37057749596511 \tabularnewline
88 & 3.3488442403976 & 3.31247515450514 & 3.38521332629006 \tabularnewline
89 & 3.358555300497 & 3.31782595248499 & 3.39928464850901 \tabularnewline
90 & 3.3682663605964 & 3.32357564143994 & 3.41295707975286 \tabularnewline
91 & 3.3779774206958 & 3.32962600474094 & 3.42632883665066 \tabularnewline
92 & 3.3876884807952 & 3.33591315678552 & 3.43946380480488 \tabularnewline
93 & 3.3973995408946 & 3.34239279692992 & 3.45240628485928 \tabularnewline
94 & 3.407110600994 & 3.34903272405987 & 3.46518847792812 \tabularnewline
95 & 3.4168216610934 & 3.35580866946442 & 3.47783465272238 \tabularnewline
96 & 3.4265327211928 & 3.36270181014577 & 3.49036363223982 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235131&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]3.3197110600994[/C][C]3.30161694415236[/C][C]3.33780517604644[/C][/ROW]
[ROW][C]86[/C][C]3.3294221201988[/C][C]3.30379057170218[/C][C]3.35505366869542[/C][/ROW]
[ROW][C]87[/C][C]3.3391331802982[/C][C]3.30768886463129[/C][C]3.37057749596511[/C][/ROW]
[ROW][C]88[/C][C]3.3488442403976[/C][C]3.31247515450514[/C][C]3.38521332629006[/C][/ROW]
[ROW][C]89[/C][C]3.358555300497[/C][C]3.31782595248499[/C][C]3.39928464850901[/C][/ROW]
[ROW][C]90[/C][C]3.3682663605964[/C][C]3.32357564143994[/C][C]3.41295707975286[/C][/ROW]
[ROW][C]91[/C][C]3.3779774206958[/C][C]3.32962600474094[/C][C]3.42632883665066[/C][/ROW]
[ROW][C]92[/C][C]3.3876884807952[/C][C]3.33591315678552[/C][C]3.43946380480488[/C][/ROW]
[ROW][C]93[/C][C]3.3973995408946[/C][C]3.34239279692992[/C][C]3.45240628485928[/C][/ROW]
[ROW][C]94[/C][C]3.407110600994[/C][C]3.34903272405987[/C][C]3.46518847792812[/C][/ROW]
[ROW][C]95[/C][C]3.4168216610934[/C][C]3.35580866946442[/C][C]3.47783465272238[/C][/ROW]
[ROW][C]96[/C][C]3.4265327211928[/C][C]3.36270181014577[/C][C]3.49036363223982[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235131&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235131&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	3.3197110600994	3.30161694415236	3.33780517604644
86	3.3294221201988	3.30379057170218	3.35505366869542
87	3.3391331802982	3.30768886463129	3.37057749596511
88	3.3488442403976	3.31247515450514	3.38521332629006
89	3.358555300497	3.31782595248499	3.39928464850901
90	3.3682663605964	3.32357564143994	3.41295707975286
91	3.3779774206958	3.32962600474094	3.42632883665066
92	3.3876884807952	3.33591315678552	3.43946380480488
93	3.3973995408946	3.34239279692992	3.45240628485928
94	3.407110600994	3.34903272405987	3.46518847792812
95	3.4168216610934	3.35580866946442	3.47783465272238
96	3.4265327211928	3.36270181014577	3.49036363223982

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code