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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 19 Dec 2013 13:36:42 -0500

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/2013/Dec/19/t1387478228027txhqu1cw1ite.htm/, Retrieved Sat, 20 Apr 2024 12:24:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232450, Retrieved Sat, 20 Apr 2024 12:24:42 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

192

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

-     [Exponential Smoothing] [] [2013-12-19 17:43:42] [06895adc7515545c06287091307202a6]
- R PD    [Exponential Smoothing] [] [2013-12-19 18:36:42] [db3a40fff6badd20e3b8cc4ac84d2bfb] [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	'Sir Maurice George Kendall' @ kendall.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 & 6 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232450&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232450&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232450&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.531830804972702
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.531830804972702 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232450&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]0.531830804972702[/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=232450&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232450&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	0.531830804972702
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	109.73	106.68	3.05
3	108.06	108.302083955167	-0.242083955166748
4	111.33	108.173336250419	3.15666374958056
5	105.66	109.852147273387	-4.19214727338702
6	103.65	107.622634214417	-3.97263421441748
7	100.34	105.509864962302	-5.16986496230174
8	100.56	102.760371517801	-2.20037151780065
9	102.67	101.59014616225	1.07985383775028
10	101.5	102.164445698033	-0.664445698033319
11	102.35	101.811073007588	0.538926992412385
12	104.98	102.097690983784	2.8823090162162
13	106.31	103.630591708058	2.67940829194185
14	103.73	105.055583576812	-1.32558357681211
15	106.62	104.350597396098	2.26940260390246
16	108.54	105.557535609738	2.98246439026187
17	105.12	107.143702047214	-2.02370204721352
18	105.29	106.067434958419	-0.77743495841905
19	104.62	105.653971098669	-1.03397109866913
20	104.34	105.104073416945	-0.764073416945422
21	108.23	104.697715636553	3.53228436344691
22	107.6	106.576293272958	1.02370672704244
23	106.87	107.120732045657	-0.250732045656505
24	107.96	106.987385019983	0.97261498001744
25	108.34	107.504651627734	0.835348372266267
26	109.04	107.948915624989	1.09108437501126
27	106.95	108.529187906444	-1.57918790644412
28	105.59	107.689327130957	-2.09932713095678
29	108.08	106.572840292999	1.50715970700099
30	108.48	107.374394253196	1.10560574680424
31	106.84	107.962389447501	-1.12238944750111
32	105.6	107.365468164144	-1.76546816414374
33	106.9	106.426537809253	0.473462190746517
34	106.84	106.678339587282	0.161660412717652
35	106.81	106.76431557471	0.0456844252898065
36	106.98	106.788611959387	0.191388040613219
37	107.53	106.890398015088	0.639601984911735
38	107.37	107.230558053586	0.139441946413996
39	106.98	107.304717576194	-0.324717576194317
40	108.94	107.132022766258	1.80797723374188
41	106.38	108.093560753851	-1.71356075385138
42	109.02	107.182236358761	1.83776364123904
43	106.53	108.159615675431	-1.62961567543068
44	105.02	107.29293585897	-2.27293585897026
45	109.7	106.084118551443	3.61588144855722
46	108.39	108.007155692915	0.382844307085165
47	110.18	108.210764088931	1.96923591106885
48	109.54	109.258064408696	0.281935591303949
49	109.1	109.40800644117	-0.308006441169695
50	110.85	109.244199127626	1.60580087237436
51	112.23	110.098213498206	2.13178650179364
52	110.58	111.231963229485	-0.651963229485219
53	110.77	110.885229100335	-0.115229100335497
54	108.08	110.823946715148	-2.74394671514779
55	108.05	109.364631324829	-1.31463132482854
56	108.87	108.665469889103	0.204530110897366
57	109.61	108.774245302622	0.835754697377652
58	111.27	109.218725396088	2.05127460391158
59	107.61	110.309656419907	-2.69965641990677
60	110.98	108.873895972958	2.10610402704198
61	106.63	109.993986973016	-3.36398697301601
62	106.83	108.204915073239	-1.37491507323922
63	108.77	107.473692883069	1.29630711693069
64	106.12	108.163108940558	-2.0431089405584
65	106.8	107.076520668054	-0.276520668054303
66	106.34	106.929458458571	-0.589458458571386
67	105.16	106.615966292051	-1.4559662920514
68	107.97	105.841638566937	2.12836143306342
69	106.76	106.973566741156	-0.213566741155546
70	108.78	106.859985369291	1.92001463070861
71	105.58	107.881108295901	-2.30110829590052
72	109.22	106.657308018562	2.56269198143762
73	105.67	108.020226557947	-2.35022655794744
74	109.04	106.770303675766	2.26969632423398
75	106.59	107.977398098927	-1.38739809892697
76	109.66	107.239537051157	2.42046294884295
77	108.05	108.526813809647	-0.476813809646799
78	109.91	108.27322953744	1.63677046255975
79	107.63	109.143714490099	-1.51371449009895
80	107.15	108.338674494331	-1.18867449433077
81	103.8	107.70650078116	-3.90650078116033
82	103.43	105.628903326089	-2.19890332608934
83	103.59	104.459458800118	-0.869458800118096
84	107.63	103.997053826561	3.63294617343931

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 109.73 & 106.68 & 3.05 \tabularnewline
3 & 108.06 & 108.302083955167 & -0.242083955166748 \tabularnewline
4 & 111.33 & 108.173336250419 & 3.15666374958056 \tabularnewline
5 & 105.66 & 109.852147273387 & -4.19214727338702 \tabularnewline
6 & 103.65 & 107.622634214417 & -3.97263421441748 \tabularnewline
7 & 100.34 & 105.509864962302 & -5.16986496230174 \tabularnewline
8 & 100.56 & 102.760371517801 & -2.20037151780065 \tabularnewline
9 & 102.67 & 101.59014616225 & 1.07985383775028 \tabularnewline
10 & 101.5 & 102.164445698033 & -0.664445698033319 \tabularnewline
11 & 102.35 & 101.811073007588 & 0.538926992412385 \tabularnewline
12 & 104.98 & 102.097690983784 & 2.8823090162162 \tabularnewline
13 & 106.31 & 103.630591708058 & 2.67940829194185 \tabularnewline
14 & 103.73 & 105.055583576812 & -1.32558357681211 \tabularnewline
15 & 106.62 & 104.350597396098 & 2.26940260390246 \tabularnewline
16 & 108.54 & 105.557535609738 & 2.98246439026187 \tabularnewline
17 & 105.12 & 107.143702047214 & -2.02370204721352 \tabularnewline
18 & 105.29 & 106.067434958419 & -0.77743495841905 \tabularnewline
19 & 104.62 & 105.653971098669 & -1.03397109866913 \tabularnewline
20 & 104.34 & 105.104073416945 & -0.764073416945422 \tabularnewline
21 & 108.23 & 104.697715636553 & 3.53228436344691 \tabularnewline
22 & 107.6 & 106.576293272958 & 1.02370672704244 \tabularnewline
23 & 106.87 & 107.120732045657 & -0.250732045656505 \tabularnewline
24 & 107.96 & 106.987385019983 & 0.97261498001744 \tabularnewline
25 & 108.34 & 107.504651627734 & 0.835348372266267 \tabularnewline
26 & 109.04 & 107.948915624989 & 1.09108437501126 \tabularnewline
27 & 106.95 & 108.529187906444 & -1.57918790644412 \tabularnewline
28 & 105.59 & 107.689327130957 & -2.09932713095678 \tabularnewline
29 & 108.08 & 106.572840292999 & 1.50715970700099 \tabularnewline
30 & 108.48 & 107.374394253196 & 1.10560574680424 \tabularnewline
31 & 106.84 & 107.962389447501 & -1.12238944750111 \tabularnewline
32 & 105.6 & 107.365468164144 & -1.76546816414374 \tabularnewline
33 & 106.9 & 106.426537809253 & 0.473462190746517 \tabularnewline
34 & 106.84 & 106.678339587282 & 0.161660412717652 \tabularnewline
35 & 106.81 & 106.76431557471 & 0.0456844252898065 \tabularnewline
36 & 106.98 & 106.788611959387 & 0.191388040613219 \tabularnewline
37 & 107.53 & 106.890398015088 & 0.639601984911735 \tabularnewline
38 & 107.37 & 107.230558053586 & 0.139441946413996 \tabularnewline
39 & 106.98 & 107.304717576194 & -0.324717576194317 \tabularnewline
40 & 108.94 & 107.132022766258 & 1.80797723374188 \tabularnewline
41 & 106.38 & 108.093560753851 & -1.71356075385138 \tabularnewline
42 & 109.02 & 107.182236358761 & 1.83776364123904 \tabularnewline
43 & 106.53 & 108.159615675431 & -1.62961567543068 \tabularnewline
44 & 105.02 & 107.29293585897 & -2.27293585897026 \tabularnewline
45 & 109.7 & 106.084118551443 & 3.61588144855722 \tabularnewline
46 & 108.39 & 108.007155692915 & 0.382844307085165 \tabularnewline
47 & 110.18 & 108.210764088931 & 1.96923591106885 \tabularnewline
48 & 109.54 & 109.258064408696 & 0.281935591303949 \tabularnewline
49 & 109.1 & 109.40800644117 & -0.308006441169695 \tabularnewline
50 & 110.85 & 109.244199127626 & 1.60580087237436 \tabularnewline
51 & 112.23 & 110.098213498206 & 2.13178650179364 \tabularnewline
52 & 110.58 & 111.231963229485 & -0.651963229485219 \tabularnewline
53 & 110.77 & 110.885229100335 & -0.115229100335497 \tabularnewline
54 & 108.08 & 110.823946715148 & -2.74394671514779 \tabularnewline
55 & 108.05 & 109.364631324829 & -1.31463132482854 \tabularnewline
56 & 108.87 & 108.665469889103 & 0.204530110897366 \tabularnewline
57 & 109.61 & 108.774245302622 & 0.835754697377652 \tabularnewline
58 & 111.27 & 109.218725396088 & 2.05127460391158 \tabularnewline
59 & 107.61 & 110.309656419907 & -2.69965641990677 \tabularnewline
60 & 110.98 & 108.873895972958 & 2.10610402704198 \tabularnewline
61 & 106.63 & 109.993986973016 & -3.36398697301601 \tabularnewline
62 & 106.83 & 108.204915073239 & -1.37491507323922 \tabularnewline
63 & 108.77 & 107.473692883069 & 1.29630711693069 \tabularnewline
64 & 106.12 & 108.163108940558 & -2.0431089405584 \tabularnewline
65 & 106.8 & 107.076520668054 & -0.276520668054303 \tabularnewline
66 & 106.34 & 106.929458458571 & -0.589458458571386 \tabularnewline
67 & 105.16 & 106.615966292051 & -1.4559662920514 \tabularnewline
68 & 107.97 & 105.841638566937 & 2.12836143306342 \tabularnewline
69 & 106.76 & 106.973566741156 & -0.213566741155546 \tabularnewline
70 & 108.78 & 106.859985369291 & 1.92001463070861 \tabularnewline
71 & 105.58 & 107.881108295901 & -2.30110829590052 \tabularnewline
72 & 109.22 & 106.657308018562 & 2.56269198143762 \tabularnewline
73 & 105.67 & 108.020226557947 & -2.35022655794744 \tabularnewline
74 & 109.04 & 106.770303675766 & 2.26969632423398 \tabularnewline
75 & 106.59 & 107.977398098927 & -1.38739809892697 \tabularnewline
76 & 109.66 & 107.239537051157 & 2.42046294884295 \tabularnewline
77 & 108.05 & 108.526813809647 & -0.476813809646799 \tabularnewline
78 & 109.91 & 108.27322953744 & 1.63677046255975 \tabularnewline
79 & 107.63 & 109.143714490099 & -1.51371449009895 \tabularnewline
80 & 107.15 & 108.338674494331 & -1.18867449433077 \tabularnewline
81 & 103.8 & 107.70650078116 & -3.90650078116033 \tabularnewline
82 & 103.43 & 105.628903326089 & -2.19890332608934 \tabularnewline
83 & 103.59 & 104.459458800118 & -0.869458800118096 \tabularnewline
84 & 107.63 & 103.997053826561 & 3.63294617343931 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232450&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]109.73[/C][C]106.68[/C][C]3.05[/C][/ROW]
[ROW][C]3[/C][C]108.06[/C][C]108.302083955167[/C][C]-0.242083955166748[/C][/ROW]
[ROW][C]4[/C][C]111.33[/C][C]108.173336250419[/C][C]3.15666374958056[/C][/ROW]
[ROW][C]5[/C][C]105.66[/C][C]109.852147273387[/C][C]-4.19214727338702[/C][/ROW]
[ROW][C]6[/C][C]103.65[/C][C]107.622634214417[/C][C]-3.97263421441748[/C][/ROW]
[ROW][C]7[/C][C]100.34[/C][C]105.509864962302[/C][C]-5.16986496230174[/C][/ROW]
[ROW][C]8[/C][C]100.56[/C][C]102.760371517801[/C][C]-2.20037151780065[/C][/ROW]
[ROW][C]9[/C][C]102.67[/C][C]101.59014616225[/C][C]1.07985383775028[/C][/ROW]
[ROW][C]10[/C][C]101.5[/C][C]102.164445698033[/C][C]-0.664445698033319[/C][/ROW]
[ROW][C]11[/C][C]102.35[/C][C]101.811073007588[/C][C]0.538926992412385[/C][/ROW]
[ROW][C]12[/C][C]104.98[/C][C]102.097690983784[/C][C]2.8823090162162[/C][/ROW]
[ROW][C]13[/C][C]106.31[/C][C]103.630591708058[/C][C]2.67940829194185[/C][/ROW]
[ROW][C]14[/C][C]103.73[/C][C]105.055583576812[/C][C]-1.32558357681211[/C][/ROW]
[ROW][C]15[/C][C]106.62[/C][C]104.350597396098[/C][C]2.26940260390246[/C][/ROW]
[ROW][C]16[/C][C]108.54[/C][C]105.557535609738[/C][C]2.98246439026187[/C][/ROW]
[ROW][C]17[/C][C]105.12[/C][C]107.143702047214[/C][C]-2.02370204721352[/C][/ROW]
[ROW][C]18[/C][C]105.29[/C][C]106.067434958419[/C][C]-0.77743495841905[/C][/ROW]
[ROW][C]19[/C][C]104.62[/C][C]105.653971098669[/C][C]-1.03397109866913[/C][/ROW]
[ROW][C]20[/C][C]104.34[/C][C]105.104073416945[/C][C]-0.764073416945422[/C][/ROW]
[ROW][C]21[/C][C]108.23[/C][C]104.697715636553[/C][C]3.53228436344691[/C][/ROW]
[ROW][C]22[/C][C]107.6[/C][C]106.576293272958[/C][C]1.02370672704244[/C][/ROW]
[ROW][C]23[/C][C]106.87[/C][C]107.120732045657[/C][C]-0.250732045656505[/C][/ROW]
[ROW][C]24[/C][C]107.96[/C][C]106.987385019983[/C][C]0.97261498001744[/C][/ROW]
[ROW][C]25[/C][C]108.34[/C][C]107.504651627734[/C][C]0.835348372266267[/C][/ROW]
[ROW][C]26[/C][C]109.04[/C][C]107.948915624989[/C][C]1.09108437501126[/C][/ROW]
[ROW][C]27[/C][C]106.95[/C][C]108.529187906444[/C][C]-1.57918790644412[/C][/ROW]
[ROW][C]28[/C][C]105.59[/C][C]107.689327130957[/C][C]-2.09932713095678[/C][/ROW]
[ROW][C]29[/C][C]108.08[/C][C]106.572840292999[/C][C]1.50715970700099[/C][/ROW]
[ROW][C]30[/C][C]108.48[/C][C]107.374394253196[/C][C]1.10560574680424[/C][/ROW]
[ROW][C]31[/C][C]106.84[/C][C]107.962389447501[/C][C]-1.12238944750111[/C][/ROW]
[ROW][C]32[/C][C]105.6[/C][C]107.365468164144[/C][C]-1.76546816414374[/C][/ROW]
[ROW][C]33[/C][C]106.9[/C][C]106.426537809253[/C][C]0.473462190746517[/C][/ROW]
[ROW][C]34[/C][C]106.84[/C][C]106.678339587282[/C][C]0.161660412717652[/C][/ROW]
[ROW][C]35[/C][C]106.81[/C][C]106.76431557471[/C][C]0.0456844252898065[/C][/ROW]
[ROW][C]36[/C][C]106.98[/C][C]106.788611959387[/C][C]0.191388040613219[/C][/ROW]
[ROW][C]37[/C][C]107.53[/C][C]106.890398015088[/C][C]0.639601984911735[/C][/ROW]
[ROW][C]38[/C][C]107.37[/C][C]107.230558053586[/C][C]0.139441946413996[/C][/ROW]
[ROW][C]39[/C][C]106.98[/C][C]107.304717576194[/C][C]-0.324717576194317[/C][/ROW]
[ROW][C]40[/C][C]108.94[/C][C]107.132022766258[/C][C]1.80797723374188[/C][/ROW]
[ROW][C]41[/C][C]106.38[/C][C]108.093560753851[/C][C]-1.71356075385138[/C][/ROW]
[ROW][C]42[/C][C]109.02[/C][C]107.182236358761[/C][C]1.83776364123904[/C][/ROW]
[ROW][C]43[/C][C]106.53[/C][C]108.159615675431[/C][C]-1.62961567543068[/C][/ROW]
[ROW][C]44[/C][C]105.02[/C][C]107.29293585897[/C][C]-2.27293585897026[/C][/ROW]
[ROW][C]45[/C][C]109.7[/C][C]106.084118551443[/C][C]3.61588144855722[/C][/ROW]
[ROW][C]46[/C][C]108.39[/C][C]108.007155692915[/C][C]0.382844307085165[/C][/ROW]
[ROW][C]47[/C][C]110.18[/C][C]108.210764088931[/C][C]1.96923591106885[/C][/ROW]
[ROW][C]48[/C][C]109.54[/C][C]109.258064408696[/C][C]0.281935591303949[/C][/ROW]
[ROW][C]49[/C][C]109.1[/C][C]109.40800644117[/C][C]-0.308006441169695[/C][/ROW]
[ROW][C]50[/C][C]110.85[/C][C]109.244199127626[/C][C]1.60580087237436[/C][/ROW]
[ROW][C]51[/C][C]112.23[/C][C]110.098213498206[/C][C]2.13178650179364[/C][/ROW]
[ROW][C]52[/C][C]110.58[/C][C]111.231963229485[/C][C]-0.651963229485219[/C][/ROW]
[ROW][C]53[/C][C]110.77[/C][C]110.885229100335[/C][C]-0.115229100335497[/C][/ROW]
[ROW][C]54[/C][C]108.08[/C][C]110.823946715148[/C][C]-2.74394671514779[/C][/ROW]
[ROW][C]55[/C][C]108.05[/C][C]109.364631324829[/C][C]-1.31463132482854[/C][/ROW]
[ROW][C]56[/C][C]108.87[/C][C]108.665469889103[/C][C]0.204530110897366[/C][/ROW]
[ROW][C]57[/C][C]109.61[/C][C]108.774245302622[/C][C]0.835754697377652[/C][/ROW]
[ROW][C]58[/C][C]111.27[/C][C]109.218725396088[/C][C]2.05127460391158[/C][/ROW]
[ROW][C]59[/C][C]107.61[/C][C]110.309656419907[/C][C]-2.69965641990677[/C][/ROW]
[ROW][C]60[/C][C]110.98[/C][C]108.873895972958[/C][C]2.10610402704198[/C][/ROW]
[ROW][C]61[/C][C]106.63[/C][C]109.993986973016[/C][C]-3.36398697301601[/C][/ROW]
[ROW][C]62[/C][C]106.83[/C][C]108.204915073239[/C][C]-1.37491507323922[/C][/ROW]
[ROW][C]63[/C][C]108.77[/C][C]107.473692883069[/C][C]1.29630711693069[/C][/ROW]
[ROW][C]64[/C][C]106.12[/C][C]108.163108940558[/C][C]-2.0431089405584[/C][/ROW]
[ROW][C]65[/C][C]106.8[/C][C]107.076520668054[/C][C]-0.276520668054303[/C][/ROW]
[ROW][C]66[/C][C]106.34[/C][C]106.929458458571[/C][C]-0.589458458571386[/C][/ROW]
[ROW][C]67[/C][C]105.16[/C][C]106.615966292051[/C][C]-1.4559662920514[/C][/ROW]
[ROW][C]68[/C][C]107.97[/C][C]105.841638566937[/C][C]2.12836143306342[/C][/ROW]
[ROW][C]69[/C][C]106.76[/C][C]106.973566741156[/C][C]-0.213566741155546[/C][/ROW]
[ROW][C]70[/C][C]108.78[/C][C]106.859985369291[/C][C]1.92001463070861[/C][/ROW]
[ROW][C]71[/C][C]105.58[/C][C]107.881108295901[/C][C]-2.30110829590052[/C][/ROW]
[ROW][C]72[/C][C]109.22[/C][C]106.657308018562[/C][C]2.56269198143762[/C][/ROW]
[ROW][C]73[/C][C]105.67[/C][C]108.020226557947[/C][C]-2.35022655794744[/C][/ROW]
[ROW][C]74[/C][C]109.04[/C][C]106.770303675766[/C][C]2.26969632423398[/C][/ROW]
[ROW][C]75[/C][C]106.59[/C][C]107.977398098927[/C][C]-1.38739809892697[/C][/ROW]
[ROW][C]76[/C][C]109.66[/C][C]107.239537051157[/C][C]2.42046294884295[/C][/ROW]
[ROW][C]77[/C][C]108.05[/C][C]108.526813809647[/C][C]-0.476813809646799[/C][/ROW]
[ROW][C]78[/C][C]109.91[/C][C]108.27322953744[/C][C]1.63677046255975[/C][/ROW]
[ROW][C]79[/C][C]107.63[/C][C]109.143714490099[/C][C]-1.51371449009895[/C][/ROW]
[ROW][C]80[/C][C]107.15[/C][C]108.338674494331[/C][C]-1.18867449433077[/C][/ROW]
[ROW][C]81[/C][C]103.8[/C][C]107.70650078116[/C][C]-3.90650078116033[/C][/ROW]
[ROW][C]82[/C][C]103.43[/C][C]105.628903326089[/C][C]-2.19890332608934[/C][/ROW]
[ROW][C]83[/C][C]103.59[/C][C]104.459458800118[/C][C]-0.869458800118096[/C][/ROW]
[ROW][C]84[/C][C]107.63[/C][C]103.997053826561[/C][C]3.63294617343931[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232450&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232450&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	109.73	106.68	3.05
3	108.06	108.302083955167	-0.242083955166748
4	111.33	108.173336250419	3.15666374958056
5	105.66	109.852147273387	-4.19214727338702
6	103.65	107.622634214417	-3.97263421441748
7	100.34	105.509864962302	-5.16986496230174
8	100.56	102.760371517801	-2.20037151780065
9	102.67	101.59014616225	1.07985383775028
10	101.5	102.164445698033	-0.664445698033319
11	102.35	101.811073007588	0.538926992412385
12	104.98	102.097690983784	2.8823090162162
13	106.31	103.630591708058	2.67940829194185
14	103.73	105.055583576812	-1.32558357681211
15	106.62	104.350597396098	2.26940260390246
16	108.54	105.557535609738	2.98246439026187
17	105.12	107.143702047214	-2.02370204721352
18	105.29	106.067434958419	-0.77743495841905
19	104.62	105.653971098669	-1.03397109866913
20	104.34	105.104073416945	-0.764073416945422
21	108.23	104.697715636553	3.53228436344691
22	107.6	106.576293272958	1.02370672704244
23	106.87	107.120732045657	-0.250732045656505
24	107.96	106.987385019983	0.97261498001744
25	108.34	107.504651627734	0.835348372266267
26	109.04	107.948915624989	1.09108437501126
27	106.95	108.529187906444	-1.57918790644412
28	105.59	107.689327130957	-2.09932713095678
29	108.08	106.572840292999	1.50715970700099
30	108.48	107.374394253196	1.10560574680424
31	106.84	107.962389447501	-1.12238944750111
32	105.6	107.365468164144	-1.76546816414374
33	106.9	106.426537809253	0.473462190746517
34	106.84	106.678339587282	0.161660412717652
35	106.81	106.76431557471	0.0456844252898065
36	106.98	106.788611959387	0.191388040613219
37	107.53	106.890398015088	0.639601984911735
38	107.37	107.230558053586	0.139441946413996
39	106.98	107.304717576194	-0.324717576194317
40	108.94	107.132022766258	1.80797723374188
41	106.38	108.093560753851	-1.71356075385138
42	109.02	107.182236358761	1.83776364123904
43	106.53	108.159615675431	-1.62961567543068
44	105.02	107.29293585897	-2.27293585897026
45	109.7	106.084118551443	3.61588144855722
46	108.39	108.007155692915	0.382844307085165
47	110.18	108.210764088931	1.96923591106885
48	109.54	109.258064408696	0.281935591303949
49	109.1	109.40800644117	-0.308006441169695
50	110.85	109.244199127626	1.60580087237436
51	112.23	110.098213498206	2.13178650179364
52	110.58	111.231963229485	-0.651963229485219
53	110.77	110.885229100335	-0.115229100335497
54	108.08	110.823946715148	-2.74394671514779
55	108.05	109.364631324829	-1.31463132482854
56	108.87	108.665469889103	0.204530110897366
57	109.61	108.774245302622	0.835754697377652
58	111.27	109.218725396088	2.05127460391158
59	107.61	110.309656419907	-2.69965641990677
60	110.98	108.873895972958	2.10610402704198
61	106.63	109.993986973016	-3.36398697301601
62	106.83	108.204915073239	-1.37491507323922
63	108.77	107.473692883069	1.29630711693069
64	106.12	108.163108940558	-2.0431089405584
65	106.8	107.076520668054	-0.276520668054303
66	106.34	106.929458458571	-0.589458458571386
67	105.16	106.615966292051	-1.4559662920514
68	107.97	105.841638566937	2.12836143306342
69	106.76	106.973566741156	-0.213566741155546
70	108.78	106.859985369291	1.92001463070861
71	105.58	107.881108295901	-2.30110829590052
72	109.22	106.657308018562	2.56269198143762
73	105.67	108.020226557947	-2.35022655794744
74	109.04	106.770303675766	2.26969632423398
75	106.59	107.977398098927	-1.38739809892697
76	109.66	107.239537051157	2.42046294884295
77	108.05	108.526813809647	-0.476813809646799
78	109.91	108.27322953744	1.63677046255975
79	107.63	109.143714490099	-1.51371449009895
80	107.15	108.338674494331	-1.18867449433077
81	103.8	107.70650078116	-3.90650078116033
82	103.43	105.628903326089	-2.19890332608934
83	103.59	104.459458800118	-0.869458800118096
84	107.63	103.997053826561	3.63294617343931

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	105.929166514403	102.02840011351	109.829932915297
86	105.929166514403	101.51105302343	110.347280005377
87	105.929166514403	101.048236774702	110.810096254105
88	105.929166514403	100.62565603278	111.232676996027
89	105.929166514403	100.234346786486	111.62398624232
90	105.929166514403	99.8682490889425	111.990083939864
91	105.929166514403	99.5230391083148	112.335293920492
92	105.929166514403	99.1955035700749	112.662829458732
93	105.929166514403	98.8831772330742	112.975155795733
94	105.929166514403	98.58411966245	113.274213366357
95	105.929166514403	98.2967709820575	113.561562046749
96	105.929166514403	98.0198549219222	113.838478106885

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 105.929166514403 & 102.02840011351 & 109.829932915297 \tabularnewline
86 & 105.929166514403 & 101.51105302343 & 110.347280005377 \tabularnewline
87 & 105.929166514403 & 101.048236774702 & 110.810096254105 \tabularnewline
88 & 105.929166514403 & 100.62565603278 & 111.232676996027 \tabularnewline
89 & 105.929166514403 & 100.234346786486 & 111.62398624232 \tabularnewline
90 & 105.929166514403 & 99.8682490889425 & 111.990083939864 \tabularnewline
91 & 105.929166514403 & 99.5230391083148 & 112.335293920492 \tabularnewline
92 & 105.929166514403 & 99.1955035700749 & 112.662829458732 \tabularnewline
93 & 105.929166514403 & 98.8831772330742 & 112.975155795733 \tabularnewline
94 & 105.929166514403 & 98.58411966245 & 113.274213366357 \tabularnewline
95 & 105.929166514403 & 98.2967709820575 & 113.561562046749 \tabularnewline
96 & 105.929166514403 & 98.0198549219222 & 113.838478106885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232450&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]105.929166514403[/C][C]102.02840011351[/C][C]109.829932915297[/C][/ROW]
[ROW][C]86[/C][C]105.929166514403[/C][C]101.51105302343[/C][C]110.347280005377[/C][/ROW]
[ROW][C]87[/C][C]105.929166514403[/C][C]101.048236774702[/C][C]110.810096254105[/C][/ROW]
[ROW][C]88[/C][C]105.929166514403[/C][C]100.62565603278[/C][C]111.232676996027[/C][/ROW]
[ROW][C]89[/C][C]105.929166514403[/C][C]100.234346786486[/C][C]111.62398624232[/C][/ROW]
[ROW][C]90[/C][C]105.929166514403[/C][C]99.8682490889425[/C][C]111.990083939864[/C][/ROW]
[ROW][C]91[/C][C]105.929166514403[/C][C]99.5230391083148[/C][C]112.335293920492[/C][/ROW]
[ROW][C]92[/C][C]105.929166514403[/C][C]99.1955035700749[/C][C]112.662829458732[/C][/ROW]
[ROW][C]93[/C][C]105.929166514403[/C][C]98.8831772330742[/C][C]112.975155795733[/C][/ROW]
[ROW][C]94[/C][C]105.929166514403[/C][C]98.58411966245[/C][C]113.274213366357[/C][/ROW]
[ROW][C]95[/C][C]105.929166514403[/C][C]98.2967709820575[/C][C]113.561562046749[/C][/ROW]
[ROW][C]96[/C][C]105.929166514403[/C][C]98.0198549219222[/C][C]113.838478106885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232450&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232450&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	105.929166514403	102.02840011351	109.829932915297
86	105.929166514403	101.51105302343	110.347280005377
87	105.929166514403	101.048236774702	110.810096254105
88	105.929166514403	100.62565603278	111.232676996027
89	105.929166514403	100.234346786486	111.62398624232
90	105.929166514403	99.8682490889425	111.990083939864
91	105.929166514403	99.5230391083148	112.335293920492
92	105.929166514403	99.1955035700749	112.662829458732
93	105.929166514403	98.8831772330742	112.975155795733
94	105.929166514403	98.58411966245	113.274213366357
95	105.929166514403	98.2967709820575	113.561562046749
96	105.929166514403	98.0198549219222	113.838478106885

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = additive ;

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

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