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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 25 May 2008 12:11:49 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/25/t1211739244cfavxwp0ydkbqme.htm/, Retrieved Wed, 15 May 2024 07:53:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13193, Retrieved Wed, 15 May 2024 07:53:13 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

159

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

-       [Exponential Smoothing] [Sanne Aertgeerts ...] [2008-05-25 18:11:49] [4c7a5669b420c0879a97a0998c00f1a1] [Current]

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Dataseries X:

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4,68
4,68
4,67
4,58
4,48
4,46
4,46
4,46
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,44
4,44
4,44
4,44
4,44
4,43
4,38
4,23
4,2
4,2
4,2
4,2
4,2
4,19
4,16
4,06
4
3,99
3,95
3,81
3,8
3,8
3,8
3,8
3,79
3,79
3,78
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,68
3,63
3,61
3,61
3,61
3,6
3,58
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,51
3,47
3,43
3,42
3,42

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13193&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13193&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13193&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.702495359258423
beta	0.000744121041695145
gamma	0.987476481795519

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.702495359258423 \tabularnewline
beta & 0.000744121041695145 \tabularnewline
gamma & 0.987476481795519 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13193&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]0.702495359258423[/C][/ROW]
[ROW][C]beta[/C][C]0.000744121041695145[/C][/ROW]
[ROW][C]gamma[/C][C]0.987476481795519[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13193&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13193&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	0.702495359258423
beta	0.000744121041695145
gamma	0.987476481795519

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	4.45	4.52479486087743	-0.074794860877434
14	4.45	4.45874328968312	-0.00874328968311566
15	4.45	4.43865964337982	0.0113403566201793
16	4.45	4.43268499432796	0.0173150056720432
17	4.44	4.423443610694	0.0165563893060003
18	4.44	4.43197988864692	0.00802011135307623
19	4.44	4.44206457378818	-0.00206457378817682
20	4.44	4.4463630164589	-0.00636301645889681
21	4.44	4.44767200006759	-0.00767200006758717
22	4.43	4.43806874717169	-0.00806874717168693
23	4.38	4.38770084760291	-0.0077008476029139
24	4.23	4.23737769228695	-0.00737769228695395
25	4.2	4.27301762837097	-0.0730176283709687
26	4.2	4.22649809251183	-0.0264980925118286
27	4.2	4.19940167576739	0.000598324232612413
28	4.2	4.18740248645746	0.0125975135425422
29	4.2	4.17492702948742	0.0250729705125767
30	4.19	4.18635212454012	0.00364787545987788
31	4.16	4.18940474195076	-0.0294047419507564
32	4.06	4.17195639262795	-0.111956392627949
33	4	4.09695432324497	-0.0969543232449706
34	3.99	4.02331385763772	-0.0333138576377161
35	3.95	3.9579761700664	-0.00797617006640339
36	3.81	3.82006252335074	-0.0100625233507445
37	3.8	3.83051487618554	-0.0305148761855389
38	3.8	3.8241995343314	-0.0241995343314003
39	3.8	3.80514360525338	-0.00514360525337754
40	3.8	3.79186362052222	0.00813637947778245
41	3.79	3.77995921271979	0.0100407872802051
42	3.79	3.77408671321380	0.0159132867862044
43	3.78	3.77525803308276	0.00474196691723705
44	3.69	3.75735547532147	-0.0673554753214685
45	3.69	3.71550395482912	-0.0255039548291207
46	3.69	3.70843775579092	-0.0184377557909197
47	3.69	3.66231287706251	0.0276871229374893
48	3.69	3.55678049891460	0.133219501085404
49	3.69	3.66072897782281	0.0292710221771881
50	3.69	3.69727560673611	-0.0072756067361075
51	3.69	3.69522427939798	-0.00522427939797909
52	3.68	3.68556616919589	-0.00556616919588704
53	3.63	3.66469035591541	-0.0346903559154077
54	3.61	3.62896521162893	-0.0189652116289274
55	3.61	3.60226049666730	0.00773950333269635
56	3.61	3.56628619129268	0.0437138087073241
57	3.6	3.61394750604186	-0.013947506041863
58	3.58	3.61646643239148	-0.0364664323914763
59	3.52	3.57135770806769	-0.0513577080676919
60	3.52	3.44365968773492	0.0763403122650814
61	3.52	3.47732015600411	0.0426798439958866
62	3.52	3.51153224511078	0.00846775488922091
63	3.52	3.5202613607948	-0.000261360794798104
64	3.52	3.51357040117549	0.00642959882451111
65	3.52	3.49296524688575	0.0270347531142519
66	3.52	3.50496895216553	0.0150310478344724
67	3.52	3.50979606399883	0.0102039360011665
68	3.51	3.4864813647701	0.0235186352299031
69	3.47	3.50260628389314	-0.0326062838931351
70	3.43	3.48466705053475	-0.0546670505347469
71	3.42	3.42260106780859	-0.00260106780859193
72	3.42	3.36749289077071	0.0525071092292904

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4.45 & 4.52479486087743 & -0.074794860877434 \tabularnewline
14 & 4.45 & 4.45874328968312 & -0.00874328968311566 \tabularnewline
15 & 4.45 & 4.43865964337982 & 0.0113403566201793 \tabularnewline
16 & 4.45 & 4.43268499432796 & 0.0173150056720432 \tabularnewline
17 & 4.44 & 4.423443610694 & 0.0165563893060003 \tabularnewline
18 & 4.44 & 4.43197988864692 & 0.00802011135307623 \tabularnewline
19 & 4.44 & 4.44206457378818 & -0.00206457378817682 \tabularnewline
20 & 4.44 & 4.4463630164589 & -0.00636301645889681 \tabularnewline
21 & 4.44 & 4.44767200006759 & -0.00767200006758717 \tabularnewline
22 & 4.43 & 4.43806874717169 & -0.00806874717168693 \tabularnewline
23 & 4.38 & 4.38770084760291 & -0.0077008476029139 \tabularnewline
24 & 4.23 & 4.23737769228695 & -0.00737769228695395 \tabularnewline
25 & 4.2 & 4.27301762837097 & -0.0730176283709687 \tabularnewline
26 & 4.2 & 4.22649809251183 & -0.0264980925118286 \tabularnewline
27 & 4.2 & 4.19940167576739 & 0.000598324232612413 \tabularnewline
28 & 4.2 & 4.18740248645746 & 0.0125975135425422 \tabularnewline
29 & 4.2 & 4.17492702948742 & 0.0250729705125767 \tabularnewline
30 & 4.19 & 4.18635212454012 & 0.00364787545987788 \tabularnewline
31 & 4.16 & 4.18940474195076 & -0.0294047419507564 \tabularnewline
32 & 4.06 & 4.17195639262795 & -0.111956392627949 \tabularnewline
33 & 4 & 4.09695432324497 & -0.0969543232449706 \tabularnewline
34 & 3.99 & 4.02331385763772 & -0.0333138576377161 \tabularnewline
35 & 3.95 & 3.9579761700664 & -0.00797617006640339 \tabularnewline
36 & 3.81 & 3.82006252335074 & -0.0100625233507445 \tabularnewline
37 & 3.8 & 3.83051487618554 & -0.0305148761855389 \tabularnewline
38 & 3.8 & 3.8241995343314 & -0.0241995343314003 \tabularnewline
39 & 3.8 & 3.80514360525338 & -0.00514360525337754 \tabularnewline
40 & 3.8 & 3.79186362052222 & 0.00813637947778245 \tabularnewline
41 & 3.79 & 3.77995921271979 & 0.0100407872802051 \tabularnewline
42 & 3.79 & 3.77408671321380 & 0.0159132867862044 \tabularnewline
43 & 3.78 & 3.77525803308276 & 0.00474196691723705 \tabularnewline
44 & 3.69 & 3.75735547532147 & -0.0673554753214685 \tabularnewline
45 & 3.69 & 3.71550395482912 & -0.0255039548291207 \tabularnewline
46 & 3.69 & 3.70843775579092 & -0.0184377557909197 \tabularnewline
47 & 3.69 & 3.66231287706251 & 0.0276871229374893 \tabularnewline
48 & 3.69 & 3.55678049891460 & 0.133219501085404 \tabularnewline
49 & 3.69 & 3.66072897782281 & 0.0292710221771881 \tabularnewline
50 & 3.69 & 3.69727560673611 & -0.0072756067361075 \tabularnewline
51 & 3.69 & 3.69522427939798 & -0.00522427939797909 \tabularnewline
52 & 3.68 & 3.68556616919589 & -0.00556616919588704 \tabularnewline
53 & 3.63 & 3.66469035591541 & -0.0346903559154077 \tabularnewline
54 & 3.61 & 3.62896521162893 & -0.0189652116289274 \tabularnewline
55 & 3.61 & 3.60226049666730 & 0.00773950333269635 \tabularnewline
56 & 3.61 & 3.56628619129268 & 0.0437138087073241 \tabularnewline
57 & 3.6 & 3.61394750604186 & -0.013947506041863 \tabularnewline
58 & 3.58 & 3.61646643239148 & -0.0364664323914763 \tabularnewline
59 & 3.52 & 3.57135770806769 & -0.0513577080676919 \tabularnewline
60 & 3.52 & 3.44365968773492 & 0.0763403122650814 \tabularnewline
61 & 3.52 & 3.47732015600411 & 0.0426798439958866 \tabularnewline
62 & 3.52 & 3.51153224511078 & 0.00846775488922091 \tabularnewline
63 & 3.52 & 3.5202613607948 & -0.000261360794798104 \tabularnewline
64 & 3.52 & 3.51357040117549 & 0.00642959882451111 \tabularnewline
65 & 3.52 & 3.49296524688575 & 0.0270347531142519 \tabularnewline
66 & 3.52 & 3.50496895216553 & 0.0150310478344724 \tabularnewline
67 & 3.52 & 3.50979606399883 & 0.0102039360011665 \tabularnewline
68 & 3.51 & 3.4864813647701 & 0.0235186352299031 \tabularnewline
69 & 3.47 & 3.50260628389314 & -0.0326062838931351 \tabularnewline
70 & 3.43 & 3.48466705053475 & -0.0546670505347469 \tabularnewline
71 & 3.42 & 3.42260106780859 & -0.00260106780859193 \tabularnewline
72 & 3.42 & 3.36749289077071 & 0.0525071092292904 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13193&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]4.45[/C][C]4.52479486087743[/C][C]-0.074794860877434[/C][/ROW]
[ROW][C]14[/C][C]4.45[/C][C]4.45874328968312[/C][C]-0.00874328968311566[/C][/ROW]
[ROW][C]15[/C][C]4.45[/C][C]4.43865964337982[/C][C]0.0113403566201793[/C][/ROW]
[ROW][C]16[/C][C]4.45[/C][C]4.43268499432796[/C][C]0.0173150056720432[/C][/ROW]
[ROW][C]17[/C][C]4.44[/C][C]4.423443610694[/C][C]0.0165563893060003[/C][/ROW]
[ROW][C]18[/C][C]4.44[/C][C]4.43197988864692[/C][C]0.00802011135307623[/C][/ROW]
[ROW][C]19[/C][C]4.44[/C][C]4.44206457378818[/C][C]-0.00206457378817682[/C][/ROW]
[ROW][C]20[/C][C]4.44[/C][C]4.4463630164589[/C][C]-0.00636301645889681[/C][/ROW]
[ROW][C]21[/C][C]4.44[/C][C]4.44767200006759[/C][C]-0.00767200006758717[/C][/ROW]
[ROW][C]22[/C][C]4.43[/C][C]4.43806874717169[/C][C]-0.00806874717168693[/C][/ROW]
[ROW][C]23[/C][C]4.38[/C][C]4.38770084760291[/C][C]-0.0077008476029139[/C][/ROW]
[ROW][C]24[/C][C]4.23[/C][C]4.23737769228695[/C][C]-0.00737769228695395[/C][/ROW]
[ROW][C]25[/C][C]4.2[/C][C]4.27301762837097[/C][C]-0.0730176283709687[/C][/ROW]
[ROW][C]26[/C][C]4.2[/C][C]4.22649809251183[/C][C]-0.0264980925118286[/C][/ROW]
[ROW][C]27[/C][C]4.2[/C][C]4.19940167576739[/C][C]0.000598324232612413[/C][/ROW]
[ROW][C]28[/C][C]4.2[/C][C]4.18740248645746[/C][C]0.0125975135425422[/C][/ROW]
[ROW][C]29[/C][C]4.2[/C][C]4.17492702948742[/C][C]0.0250729705125767[/C][/ROW]
[ROW][C]30[/C][C]4.19[/C][C]4.18635212454012[/C][C]0.00364787545987788[/C][/ROW]
[ROW][C]31[/C][C]4.16[/C][C]4.18940474195076[/C][C]-0.0294047419507564[/C][/ROW]
[ROW][C]32[/C][C]4.06[/C][C]4.17195639262795[/C][C]-0.111956392627949[/C][/ROW]
[ROW][C]33[/C][C]4[/C][C]4.09695432324497[/C][C]-0.0969543232449706[/C][/ROW]
[ROW][C]34[/C][C]3.99[/C][C]4.02331385763772[/C][C]-0.0333138576377161[/C][/ROW]
[ROW][C]35[/C][C]3.95[/C][C]3.9579761700664[/C][C]-0.00797617006640339[/C][/ROW]
[ROW][C]36[/C][C]3.81[/C][C]3.82006252335074[/C][C]-0.0100625233507445[/C][/ROW]
[ROW][C]37[/C][C]3.8[/C][C]3.83051487618554[/C][C]-0.0305148761855389[/C][/ROW]
[ROW][C]38[/C][C]3.8[/C][C]3.8241995343314[/C][C]-0.0241995343314003[/C][/ROW]
[ROW][C]39[/C][C]3.8[/C][C]3.80514360525338[/C][C]-0.00514360525337754[/C][/ROW]
[ROW][C]40[/C][C]3.8[/C][C]3.79186362052222[/C][C]0.00813637947778245[/C][/ROW]
[ROW][C]41[/C][C]3.79[/C][C]3.77995921271979[/C][C]0.0100407872802051[/C][/ROW]
[ROW][C]42[/C][C]3.79[/C][C]3.77408671321380[/C][C]0.0159132867862044[/C][/ROW]
[ROW][C]43[/C][C]3.78[/C][C]3.77525803308276[/C][C]0.00474196691723705[/C][/ROW]
[ROW][C]44[/C][C]3.69[/C][C]3.75735547532147[/C][C]-0.0673554753214685[/C][/ROW]
[ROW][C]45[/C][C]3.69[/C][C]3.71550395482912[/C][C]-0.0255039548291207[/C][/ROW]
[ROW][C]46[/C][C]3.69[/C][C]3.70843775579092[/C][C]-0.0184377557909197[/C][/ROW]
[ROW][C]47[/C][C]3.69[/C][C]3.66231287706251[/C][C]0.0276871229374893[/C][/ROW]
[ROW][C]48[/C][C]3.69[/C][C]3.55678049891460[/C][C]0.133219501085404[/C][/ROW]
[ROW][C]49[/C][C]3.69[/C][C]3.66072897782281[/C][C]0.0292710221771881[/C][/ROW]
[ROW][C]50[/C][C]3.69[/C][C]3.69727560673611[/C][C]-0.0072756067361075[/C][/ROW]
[ROW][C]51[/C][C]3.69[/C][C]3.69522427939798[/C][C]-0.00522427939797909[/C][/ROW]
[ROW][C]52[/C][C]3.68[/C][C]3.68556616919589[/C][C]-0.00556616919588704[/C][/ROW]
[ROW][C]53[/C][C]3.63[/C][C]3.66469035591541[/C][C]-0.0346903559154077[/C][/ROW]
[ROW][C]54[/C][C]3.61[/C][C]3.62896521162893[/C][C]-0.0189652116289274[/C][/ROW]
[ROW][C]55[/C][C]3.61[/C][C]3.60226049666730[/C][C]0.00773950333269635[/C][/ROW]
[ROW][C]56[/C][C]3.61[/C][C]3.56628619129268[/C][C]0.0437138087073241[/C][/ROW]
[ROW][C]57[/C][C]3.6[/C][C]3.61394750604186[/C][C]-0.013947506041863[/C][/ROW]
[ROW][C]58[/C][C]3.58[/C][C]3.61646643239148[/C][C]-0.0364664323914763[/C][/ROW]
[ROW][C]59[/C][C]3.52[/C][C]3.57135770806769[/C][C]-0.0513577080676919[/C][/ROW]
[ROW][C]60[/C][C]3.52[/C][C]3.44365968773492[/C][C]0.0763403122650814[/C][/ROW]
[ROW][C]61[/C][C]3.52[/C][C]3.47732015600411[/C][C]0.0426798439958866[/C][/ROW]
[ROW][C]62[/C][C]3.52[/C][C]3.51153224511078[/C][C]0.00846775488922091[/C][/ROW]
[ROW][C]63[/C][C]3.52[/C][C]3.5202613607948[/C][C]-0.000261360794798104[/C][/ROW]
[ROW][C]64[/C][C]3.52[/C][C]3.51357040117549[/C][C]0.00642959882451111[/C][/ROW]
[ROW][C]65[/C][C]3.52[/C][C]3.49296524688575[/C][C]0.0270347531142519[/C][/ROW]
[ROW][C]66[/C][C]3.52[/C][C]3.50496895216553[/C][C]0.0150310478344724[/C][/ROW]
[ROW][C]67[/C][C]3.52[/C][C]3.50979606399883[/C][C]0.0102039360011665[/C][/ROW]
[ROW][C]68[/C][C]3.51[/C][C]3.4864813647701[/C][C]0.0235186352299031[/C][/ROW]
[ROW][C]69[/C][C]3.47[/C][C]3.50260628389314[/C][C]-0.0326062838931351[/C][/ROW]
[ROW][C]70[/C][C]3.43[/C][C]3.48466705053475[/C][C]-0.0546670505347469[/C][/ROW]
[ROW][C]71[/C][C]3.42[/C][C]3.42260106780859[/C][C]-0.00260106780859193[/C][/ROW]
[ROW][C]72[/C][C]3.42[/C][C]3.36749289077071[/C][C]0.0525071092292904[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13193&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13193&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	4.45	4.52479486087743	-0.074794860877434
14	4.45	4.45874328968312	-0.00874328968311566
15	4.45	4.43865964337982	0.0113403566201793
16	4.45	4.43268499432796	0.0173150056720432
17	4.44	4.423443610694	0.0165563893060003
18	4.44	4.43197988864692	0.00802011135307623
19	4.44	4.44206457378818	-0.00206457378817682
20	4.44	4.4463630164589	-0.00636301645889681
21	4.44	4.44767200006759	-0.00767200006758717
22	4.43	4.43806874717169	-0.00806874717168693
23	4.38	4.38770084760291	-0.0077008476029139
24	4.23	4.23737769228695	-0.00737769228695395
25	4.2	4.27301762837097	-0.0730176283709687
26	4.2	4.22649809251183	-0.0264980925118286
27	4.2	4.19940167576739	0.000598324232612413
28	4.2	4.18740248645746	0.0125975135425422
29	4.2	4.17492702948742	0.0250729705125767
30	4.19	4.18635212454012	0.00364787545987788
31	4.16	4.18940474195076	-0.0294047419507564
32	4.06	4.17195639262795	-0.111956392627949
33	4	4.09695432324497	-0.0969543232449706
34	3.99	4.02331385763772	-0.0333138576377161
35	3.95	3.9579761700664	-0.00797617006640339
36	3.81	3.82006252335074	-0.0100625233507445
37	3.8	3.83051487618554	-0.0305148761855389
38	3.8	3.8241995343314	-0.0241995343314003
39	3.8	3.80514360525338	-0.00514360525337754
40	3.8	3.79186362052222	0.00813637947778245
41	3.79	3.77995921271979	0.0100407872802051
42	3.79	3.77408671321380	0.0159132867862044
43	3.78	3.77525803308276	0.00474196691723705
44	3.69	3.75735547532147	-0.0673554753214685
45	3.69	3.71550395482912	-0.0255039548291207
46	3.69	3.70843775579092	-0.0184377557909197
47	3.69	3.66231287706251	0.0276871229374893
48	3.69	3.55678049891460	0.133219501085404
49	3.69	3.66072897782281	0.0292710221771881
50	3.69	3.69727560673611	-0.0072756067361075
51	3.69	3.69522427939798	-0.00522427939797909
52	3.68	3.68556616919589	-0.00556616919588704
53	3.63	3.66469035591541	-0.0346903559154077
54	3.61	3.62896521162893	-0.0189652116289274
55	3.61	3.60226049666730	0.00773950333269635
56	3.61	3.56628619129268	0.0437138087073241
57	3.6	3.61394750604186	-0.013947506041863
58	3.58	3.61646643239148	-0.0364664323914763
59	3.52	3.57135770806769	-0.0513577080676919
60	3.52	3.44365968773492	0.0763403122650814
61	3.52	3.47732015600411	0.0426798439958866
62	3.52	3.51153224511078	0.00846775488922091
63	3.52	3.5202613607948	-0.000261360794798104
64	3.52	3.51357040117549	0.00642959882451111
65	3.52	3.49296524688575	0.0270347531142519
66	3.52	3.50496895216553	0.0150310478344724
67	3.52	3.50979606399883	0.0102039360011665
68	3.51	3.4864813647701	0.0235186352299031
69	3.47	3.50260628389314	-0.0326062838931351
70	3.43	3.48466705053475	-0.0546670505347469
71	3.42	3.42260106780859	-0.00260106780859193
72	3.42	3.36749289077071	0.0525071092292904

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	3.3749473331035	3.29999883966856	3.44989582653844
74	3.36876145535439	3.27694992696200	3.46057298374678
75	3.36833352905565	3.26212483993824	3.47454221817306
76	3.36334661176228	3.24444343887686	3.48224978464769
77	3.34442273382891	3.21433227581699	3.47451319184082
78	3.33366026969917	3.19303235948946	3.47428817990887
79	3.32606661950282	3.17548830015961	3.47664493884604
80	3.30007652922886	3.14079954132471	3.45935351713301
81	3.28320672535708	3.11535392880988	3.45105952190428
82	3.28077316006100	3.10412103970419	3.45742528041781
83	3.27212359849797	3.08730320862586	3.45694398837007
84	3.23583972329864	-1.63634735658003	8.10802680317732

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 3.3749473331035 & 3.29999883966856 & 3.44989582653844 \tabularnewline
74 & 3.36876145535439 & 3.27694992696200 & 3.46057298374678 \tabularnewline
75 & 3.36833352905565 & 3.26212483993824 & 3.47454221817306 \tabularnewline
76 & 3.36334661176228 & 3.24444343887686 & 3.48224978464769 \tabularnewline
77 & 3.34442273382891 & 3.21433227581699 & 3.47451319184082 \tabularnewline
78 & 3.33366026969917 & 3.19303235948946 & 3.47428817990887 \tabularnewline
79 & 3.32606661950282 & 3.17548830015961 & 3.47664493884604 \tabularnewline
80 & 3.30007652922886 & 3.14079954132471 & 3.45935351713301 \tabularnewline
81 & 3.28320672535708 & 3.11535392880988 & 3.45105952190428 \tabularnewline
82 & 3.28077316006100 & 3.10412103970419 & 3.45742528041781 \tabularnewline
83 & 3.27212359849797 & 3.08730320862586 & 3.45694398837007 \tabularnewline
84 & 3.23583972329864 & -1.63634735658003 & 8.10802680317732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13193&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]73[/C][C]3.3749473331035[/C][C]3.29999883966856[/C][C]3.44989582653844[/C][/ROW]
[ROW][C]74[/C][C]3.36876145535439[/C][C]3.27694992696200[/C][C]3.46057298374678[/C][/ROW]
[ROW][C]75[/C][C]3.36833352905565[/C][C]3.26212483993824[/C][C]3.47454221817306[/C][/ROW]
[ROW][C]76[/C][C]3.36334661176228[/C][C]3.24444343887686[/C][C]3.48224978464769[/C][/ROW]
[ROW][C]77[/C][C]3.34442273382891[/C][C]3.21433227581699[/C][C]3.47451319184082[/C][/ROW]
[ROW][C]78[/C][C]3.33366026969917[/C][C]3.19303235948946[/C][C]3.47428817990887[/C][/ROW]
[ROW][C]79[/C][C]3.32606661950282[/C][C]3.17548830015961[/C][C]3.47664493884604[/C][/ROW]
[ROW][C]80[/C][C]3.30007652922886[/C][C]3.14079954132471[/C][C]3.45935351713301[/C][/ROW]
[ROW][C]81[/C][C]3.28320672535708[/C][C]3.11535392880988[/C][C]3.45105952190428[/C][/ROW]
[ROW][C]82[/C][C]3.28077316006100[/C][C]3.10412103970419[/C][C]3.45742528041781[/C][/ROW]
[ROW][C]83[/C][C]3.27212359849797[/C][C]3.08730320862586[/C][C]3.45694398837007[/C][/ROW]
[ROW][C]84[/C][C]3.23583972329864[/C][C]-1.63634735658003[/C][C]8.10802680317732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13193&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13193&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
73	3.3749473331035	3.29999883966856	3.44989582653844
74	3.36876145535439	3.27694992696200	3.46057298374678
75	3.36833352905565	3.26212483993824	3.47454221817306
76	3.36334661176228	3.24444343887686	3.48224978464769
77	3.34442273382891	3.21433227581699	3.47451319184082
78	3.33366026969917	3.19303235948946	3.47428817990887
79	3.32606661950282	3.17548830015961	3.47664493884604
80	3.30007652922886	3.14079954132471	3.45935351713301
81	3.28320672535708	3.11535392880988	3.45105952190428
82	3.28077316006100	3.10412103970419	3.45742528041781
83	3.27212359849797	3.08730320862586	3.45694398837007
84	3.23583972329864	-1.63634735658003	8.10802680317732

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 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code