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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 02 Apr 2015 18:20:33 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/02/t1427995302j1189yjfvn3s8k1.htm/, Retrieved Thu, 09 May 2024 03:31:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278598, Retrieved Thu, 09 May 2024 03:31:37 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [] [2015-04-02 17:20:33] [7281bb56277fa48a38e7263e2ca5f521] [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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278598&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278598&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278598&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999952480056052
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999952480056052 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278598&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]0.999952480056052[/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=278598&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278598&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	0.999952480056052
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	1.2999	1.3213	-0.0213999999999999
3	1.3074	1.2999010169268	0.00749898307319929
4	1.3242	1.30739964364874	0.0168003563512555
5	1.3516	1.32419920164801	0.0274007983519919
6	1.3511	1.3515986979156	-0.00049869791559809
7	1.3419	1.3511000236981	-0.00920002369809692
8	1.3716	1.34190043718461	0.0296995628153893
9	1.3622	1.37159858867844	-0.00939858867843957
10	1.3896	1.36220044662041	0.0273995533795928
11	1.4227	1.38959869797476	0.0331013020252409
12	1.4684	1.42269842702798	0.0457015729720167
13	1.457	1.46839782826381	-0.0113978282638139
14	1.4718	1.45700054162416	0.0147994583758395
15	1.4748	1.47179929673057	0.00300070326943258
16	1.5527	1.47479985740675	0.0779001425932508
17	1.5751	1.55269629818959	0.0224037018104095
18	1.5557	1.57509893537735	-0.0193989353773456
19	1.5553	1.55570092183632	-0.000400921836321899
20	1.577	1.55530001905178	0.0216999809482168
21	1.4975	1.57699896881812	-0.0794989688181216
22	1.4369	1.49750377778654	-0.060603777786542
23	1.3322	1.43690287988812	-0.104702879888124
24	1.2732	1.33220497547498	-0.0590049754749833
25	1.3449	1.27320280391313	0.0716971960868726
26	1.3239	1.34489659295326	-0.0209965929532607
27	1.2785	1.32390099775692	-0.0454009977569205
28	1.305	1.27850215745287	0.0264978425471314
29	1.319	1.30499874082401	0.0140012591759926
30	1.365	1.31899933466095	0.0460006653390512
31	1.4016	1.36499781405096	0.0366021859490384
32	1.4088	1.40159826066618	0.00720173933382484
33	1.4268	1.40879965777375	0.0180003422262496
34	1.4562	1.42679914462475	0.0294008553752534
35	1.4816	1.456198602873	0.0254013971269995
36	1.4914	1.48159879292703	0.00980120707296761
37	1.4614	1.49139953424719	-0.0299995342471893
38	1.4272	1.46140142557619	-0.0342014255761858
39	1.3686	1.42720162524983	-0.0586016252498263
40	1.3569	1.36860278474595	-0.0117027847459472
41	1.3406	1.35690055611568	-0.016300556115675
42	1.2565	1.34060077460151	-0.084100774601513
43	1.2209	1.2565039964641	-0.0356039964640951
44	1.277	1.22090169189992	0.0560983081000834
45	1.2894	1.27699733421154	0.0124026657884566
46	1.3067	1.28939941062602	0.0173005893739828
47	1.3898	1.30669917787696	0.0831008221230374
48	1.3661	1.38979605105359	-0.0236960510535904
49	1.322	1.36610112603502	-0.0441011260350179
50	1.336	1.32200209568304	0.0139979043169629
51	1.3649	1.33599933482037	0.0289006651796284
52	1.3999	1.36489862664201	0.0350013733579895
53	1.4442	1.3998983367367	0.0443016632633002
54	1.4349	1.44419789478744	-0.00929789478744469
55	1.4388	1.43490044183544	0.00389955816456089
56	1.4264	1.43879981469321	-0.0123998146932147
57	1.4343	1.4264005892385	0.00789941076150091
58	1.377	1.43429962462044	-0.0572996246204434
59	1.3706	1.37700272287495	-0.00640272287495014
60	1.3556	1.37060030425703	-0.0150003042570324
61	1.3179	1.35560071281362	-0.0377007128136173
62	1.2905	1.31790179153576	-0.0274017915357598
63	1.3224	1.2905013021316	0.0318986978684024
64	1.3201	1.32239848417567	-0.00229848417566525
65	1.3162	1.32010010922384	-0.00390010922383932
66	1.2789	1.31620018533297	-0.037300185332972
67	1.2526	1.27890177250272	-0.0263017725027161
68	1.2288	1.25260124985876	-0.0238012498587552
69	1.24	1.22880113103406	0.011198868965941
70	1.2856	1.23999946783037	0.0456005321696256
71	1.2974	1.28559783306527	0.0118021669347326
72	1.2828	1.29739943916169	-0.014599439161689
73	1.3119	1.28280069376453	0.0290993062354694
74	1.3288	1.3118986172026	0.0169013827974012
75	1.3359	1.32879919684724	0.00710080315276329
76	1.2964	1.33589966257023	-0.0394996625702322
77	1.3026	1.29640187702175	0.00619812297824862
78	1.2982	1.30259970546554	-0.00439970546554336
79	1.3189	1.29820020907376	0.020699790926243
80	1.308	1.3188990163471	-0.0108990163470954
81	1.331	1.30800051792065	0.022999482079354
82	1.3348	1.3309989070659	0.00380109293409925
83	1.3635	1.33479981937228	0.0287001806277232
84	1.3493	1.36349863616903	-0.0141986361690252
85	1.3704	1.34930067471839	0.0210993252816054

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.2999 & 1.3213 & -0.0213999999999999 \tabularnewline
3 & 1.3074 & 1.2999010169268 & 0.00749898307319929 \tabularnewline
4 & 1.3242 & 1.30739964364874 & 0.0168003563512555 \tabularnewline
5 & 1.3516 & 1.32419920164801 & 0.0274007983519919 \tabularnewline
6 & 1.3511 & 1.3515986979156 & -0.00049869791559809 \tabularnewline
7 & 1.3419 & 1.3511000236981 & -0.00920002369809692 \tabularnewline
8 & 1.3716 & 1.34190043718461 & 0.0296995628153893 \tabularnewline
9 & 1.3622 & 1.37159858867844 & -0.00939858867843957 \tabularnewline
10 & 1.3896 & 1.36220044662041 & 0.0273995533795928 \tabularnewline
11 & 1.4227 & 1.38959869797476 & 0.0331013020252409 \tabularnewline
12 & 1.4684 & 1.42269842702798 & 0.0457015729720167 \tabularnewline
13 & 1.457 & 1.46839782826381 & -0.0113978282638139 \tabularnewline
14 & 1.4718 & 1.45700054162416 & 0.0147994583758395 \tabularnewline
15 & 1.4748 & 1.47179929673057 & 0.00300070326943258 \tabularnewline
16 & 1.5527 & 1.47479985740675 & 0.0779001425932508 \tabularnewline
17 & 1.5751 & 1.55269629818959 & 0.0224037018104095 \tabularnewline
18 & 1.5557 & 1.57509893537735 & -0.0193989353773456 \tabularnewline
19 & 1.5553 & 1.55570092183632 & -0.000400921836321899 \tabularnewline
20 & 1.577 & 1.55530001905178 & 0.0216999809482168 \tabularnewline
21 & 1.4975 & 1.57699896881812 & -0.0794989688181216 \tabularnewline
22 & 1.4369 & 1.49750377778654 & -0.060603777786542 \tabularnewline
23 & 1.3322 & 1.43690287988812 & -0.104702879888124 \tabularnewline
24 & 1.2732 & 1.33220497547498 & -0.0590049754749833 \tabularnewline
25 & 1.3449 & 1.27320280391313 & 0.0716971960868726 \tabularnewline
26 & 1.3239 & 1.34489659295326 & -0.0209965929532607 \tabularnewline
27 & 1.2785 & 1.32390099775692 & -0.0454009977569205 \tabularnewline
28 & 1.305 & 1.27850215745287 & 0.0264978425471314 \tabularnewline
29 & 1.319 & 1.30499874082401 & 0.0140012591759926 \tabularnewline
30 & 1.365 & 1.31899933466095 & 0.0460006653390512 \tabularnewline
31 & 1.4016 & 1.36499781405096 & 0.0366021859490384 \tabularnewline
32 & 1.4088 & 1.40159826066618 & 0.00720173933382484 \tabularnewline
33 & 1.4268 & 1.40879965777375 & 0.0180003422262496 \tabularnewline
34 & 1.4562 & 1.42679914462475 & 0.0294008553752534 \tabularnewline
35 & 1.4816 & 1.456198602873 & 0.0254013971269995 \tabularnewline
36 & 1.4914 & 1.48159879292703 & 0.00980120707296761 \tabularnewline
37 & 1.4614 & 1.49139953424719 & -0.0299995342471893 \tabularnewline
38 & 1.4272 & 1.46140142557619 & -0.0342014255761858 \tabularnewline
39 & 1.3686 & 1.42720162524983 & -0.0586016252498263 \tabularnewline
40 & 1.3569 & 1.36860278474595 & -0.0117027847459472 \tabularnewline
41 & 1.3406 & 1.35690055611568 & -0.016300556115675 \tabularnewline
42 & 1.2565 & 1.34060077460151 & -0.084100774601513 \tabularnewline
43 & 1.2209 & 1.2565039964641 & -0.0356039964640951 \tabularnewline
44 & 1.277 & 1.22090169189992 & 0.0560983081000834 \tabularnewline
45 & 1.2894 & 1.27699733421154 & 0.0124026657884566 \tabularnewline
46 & 1.3067 & 1.28939941062602 & 0.0173005893739828 \tabularnewline
47 & 1.3898 & 1.30669917787696 & 0.0831008221230374 \tabularnewline
48 & 1.3661 & 1.38979605105359 & -0.0236960510535904 \tabularnewline
49 & 1.322 & 1.36610112603502 & -0.0441011260350179 \tabularnewline
50 & 1.336 & 1.32200209568304 & 0.0139979043169629 \tabularnewline
51 & 1.3649 & 1.33599933482037 & 0.0289006651796284 \tabularnewline
52 & 1.3999 & 1.36489862664201 & 0.0350013733579895 \tabularnewline
53 & 1.4442 & 1.3998983367367 & 0.0443016632633002 \tabularnewline
54 & 1.4349 & 1.44419789478744 & -0.00929789478744469 \tabularnewline
55 & 1.4388 & 1.43490044183544 & 0.00389955816456089 \tabularnewline
56 & 1.4264 & 1.43879981469321 & -0.0123998146932147 \tabularnewline
57 & 1.4343 & 1.4264005892385 & 0.00789941076150091 \tabularnewline
58 & 1.377 & 1.43429962462044 & -0.0572996246204434 \tabularnewline
59 & 1.3706 & 1.37700272287495 & -0.00640272287495014 \tabularnewline
60 & 1.3556 & 1.37060030425703 & -0.0150003042570324 \tabularnewline
61 & 1.3179 & 1.35560071281362 & -0.0377007128136173 \tabularnewline
62 & 1.2905 & 1.31790179153576 & -0.0274017915357598 \tabularnewline
63 & 1.3224 & 1.2905013021316 & 0.0318986978684024 \tabularnewline
64 & 1.3201 & 1.32239848417567 & -0.00229848417566525 \tabularnewline
65 & 1.3162 & 1.32010010922384 & -0.00390010922383932 \tabularnewline
66 & 1.2789 & 1.31620018533297 & -0.037300185332972 \tabularnewline
67 & 1.2526 & 1.27890177250272 & -0.0263017725027161 \tabularnewline
68 & 1.2288 & 1.25260124985876 & -0.0238012498587552 \tabularnewline
69 & 1.24 & 1.22880113103406 & 0.011198868965941 \tabularnewline
70 & 1.2856 & 1.23999946783037 & 0.0456005321696256 \tabularnewline
71 & 1.2974 & 1.28559783306527 & 0.0118021669347326 \tabularnewline
72 & 1.2828 & 1.29739943916169 & -0.014599439161689 \tabularnewline
73 & 1.3119 & 1.28280069376453 & 0.0290993062354694 \tabularnewline
74 & 1.3288 & 1.3118986172026 & 0.0169013827974012 \tabularnewline
75 & 1.3359 & 1.32879919684724 & 0.00710080315276329 \tabularnewline
76 & 1.2964 & 1.33589966257023 & -0.0394996625702322 \tabularnewline
77 & 1.3026 & 1.29640187702175 & 0.00619812297824862 \tabularnewline
78 & 1.2982 & 1.30259970546554 & -0.00439970546554336 \tabularnewline
79 & 1.3189 & 1.29820020907376 & 0.020699790926243 \tabularnewline
80 & 1.308 & 1.3188990163471 & -0.0108990163470954 \tabularnewline
81 & 1.331 & 1.30800051792065 & 0.022999482079354 \tabularnewline
82 & 1.3348 & 1.3309989070659 & 0.00380109293409925 \tabularnewline
83 & 1.3635 & 1.33479981937228 & 0.0287001806277232 \tabularnewline
84 & 1.3493 & 1.36349863616903 & -0.0141986361690252 \tabularnewline
85 & 1.3704 & 1.34930067471839 & 0.0210993252816054 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278598&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]1.2999[/C][C]1.3213[/C][C]-0.0213999999999999[/C][/ROW]
[ROW][C]3[/C][C]1.3074[/C][C]1.2999010169268[/C][C]0.00749898307319929[/C][/ROW]
[ROW][C]4[/C][C]1.3242[/C][C]1.30739964364874[/C][C]0.0168003563512555[/C][/ROW]
[ROW][C]5[/C][C]1.3516[/C][C]1.32419920164801[/C][C]0.0274007983519919[/C][/ROW]
[ROW][C]6[/C][C]1.3511[/C][C]1.3515986979156[/C][C]-0.00049869791559809[/C][/ROW]
[ROW][C]7[/C][C]1.3419[/C][C]1.3511000236981[/C][C]-0.00920002369809692[/C][/ROW]
[ROW][C]8[/C][C]1.3716[/C][C]1.34190043718461[/C][C]0.0296995628153893[/C][/ROW]
[ROW][C]9[/C][C]1.3622[/C][C]1.37159858867844[/C][C]-0.00939858867843957[/C][/ROW]
[ROW][C]10[/C][C]1.3896[/C][C]1.36220044662041[/C][C]0.0273995533795928[/C][/ROW]
[ROW][C]11[/C][C]1.4227[/C][C]1.38959869797476[/C][C]0.0331013020252409[/C][/ROW]
[ROW][C]12[/C][C]1.4684[/C][C]1.42269842702798[/C][C]0.0457015729720167[/C][/ROW]
[ROW][C]13[/C][C]1.457[/C][C]1.46839782826381[/C][C]-0.0113978282638139[/C][/ROW]
[ROW][C]14[/C][C]1.4718[/C][C]1.45700054162416[/C][C]0.0147994583758395[/C][/ROW]
[ROW][C]15[/C][C]1.4748[/C][C]1.47179929673057[/C][C]0.00300070326943258[/C][/ROW]
[ROW][C]16[/C][C]1.5527[/C][C]1.47479985740675[/C][C]0.0779001425932508[/C][/ROW]
[ROW][C]17[/C][C]1.5751[/C][C]1.55269629818959[/C][C]0.0224037018104095[/C][/ROW]
[ROW][C]18[/C][C]1.5557[/C][C]1.57509893537735[/C][C]-0.0193989353773456[/C][/ROW]
[ROW][C]19[/C][C]1.5553[/C][C]1.55570092183632[/C][C]-0.000400921836321899[/C][/ROW]
[ROW][C]20[/C][C]1.577[/C][C]1.55530001905178[/C][C]0.0216999809482168[/C][/ROW]
[ROW][C]21[/C][C]1.4975[/C][C]1.57699896881812[/C][C]-0.0794989688181216[/C][/ROW]
[ROW][C]22[/C][C]1.4369[/C][C]1.49750377778654[/C][C]-0.060603777786542[/C][/ROW]
[ROW][C]23[/C][C]1.3322[/C][C]1.43690287988812[/C][C]-0.104702879888124[/C][/ROW]
[ROW][C]24[/C][C]1.2732[/C][C]1.33220497547498[/C][C]-0.0590049754749833[/C][/ROW]
[ROW][C]25[/C][C]1.3449[/C][C]1.27320280391313[/C][C]0.0716971960868726[/C][/ROW]
[ROW][C]26[/C][C]1.3239[/C][C]1.34489659295326[/C][C]-0.0209965929532607[/C][/ROW]
[ROW][C]27[/C][C]1.2785[/C][C]1.32390099775692[/C][C]-0.0454009977569205[/C][/ROW]
[ROW][C]28[/C][C]1.305[/C][C]1.27850215745287[/C][C]0.0264978425471314[/C][/ROW]
[ROW][C]29[/C][C]1.319[/C][C]1.30499874082401[/C][C]0.0140012591759926[/C][/ROW]
[ROW][C]30[/C][C]1.365[/C][C]1.31899933466095[/C][C]0.0460006653390512[/C][/ROW]
[ROW][C]31[/C][C]1.4016[/C][C]1.36499781405096[/C][C]0.0366021859490384[/C][/ROW]
[ROW][C]32[/C][C]1.4088[/C][C]1.40159826066618[/C][C]0.00720173933382484[/C][/ROW]
[ROW][C]33[/C][C]1.4268[/C][C]1.40879965777375[/C][C]0.0180003422262496[/C][/ROW]
[ROW][C]34[/C][C]1.4562[/C][C]1.42679914462475[/C][C]0.0294008553752534[/C][/ROW]
[ROW][C]35[/C][C]1.4816[/C][C]1.456198602873[/C][C]0.0254013971269995[/C][/ROW]
[ROW][C]36[/C][C]1.4914[/C][C]1.48159879292703[/C][C]0.00980120707296761[/C][/ROW]
[ROW][C]37[/C][C]1.4614[/C][C]1.49139953424719[/C][C]-0.0299995342471893[/C][/ROW]
[ROW][C]38[/C][C]1.4272[/C][C]1.46140142557619[/C][C]-0.0342014255761858[/C][/ROW]
[ROW][C]39[/C][C]1.3686[/C][C]1.42720162524983[/C][C]-0.0586016252498263[/C][/ROW]
[ROW][C]40[/C][C]1.3569[/C][C]1.36860278474595[/C][C]-0.0117027847459472[/C][/ROW]
[ROW][C]41[/C][C]1.3406[/C][C]1.35690055611568[/C][C]-0.016300556115675[/C][/ROW]
[ROW][C]42[/C][C]1.2565[/C][C]1.34060077460151[/C][C]-0.084100774601513[/C][/ROW]
[ROW][C]43[/C][C]1.2209[/C][C]1.2565039964641[/C][C]-0.0356039964640951[/C][/ROW]
[ROW][C]44[/C][C]1.277[/C][C]1.22090169189992[/C][C]0.0560983081000834[/C][/ROW]
[ROW][C]45[/C][C]1.2894[/C][C]1.27699733421154[/C][C]0.0124026657884566[/C][/ROW]
[ROW][C]46[/C][C]1.3067[/C][C]1.28939941062602[/C][C]0.0173005893739828[/C][/ROW]
[ROW][C]47[/C][C]1.3898[/C][C]1.30669917787696[/C][C]0.0831008221230374[/C][/ROW]
[ROW][C]48[/C][C]1.3661[/C][C]1.38979605105359[/C][C]-0.0236960510535904[/C][/ROW]
[ROW][C]49[/C][C]1.322[/C][C]1.36610112603502[/C][C]-0.0441011260350179[/C][/ROW]
[ROW][C]50[/C][C]1.336[/C][C]1.32200209568304[/C][C]0.0139979043169629[/C][/ROW]
[ROW][C]51[/C][C]1.3649[/C][C]1.33599933482037[/C][C]0.0289006651796284[/C][/ROW]
[ROW][C]52[/C][C]1.3999[/C][C]1.36489862664201[/C][C]0.0350013733579895[/C][/ROW]
[ROW][C]53[/C][C]1.4442[/C][C]1.3998983367367[/C][C]0.0443016632633002[/C][/ROW]
[ROW][C]54[/C][C]1.4349[/C][C]1.44419789478744[/C][C]-0.00929789478744469[/C][/ROW]
[ROW][C]55[/C][C]1.4388[/C][C]1.43490044183544[/C][C]0.00389955816456089[/C][/ROW]
[ROW][C]56[/C][C]1.4264[/C][C]1.43879981469321[/C][C]-0.0123998146932147[/C][/ROW]
[ROW][C]57[/C][C]1.4343[/C][C]1.4264005892385[/C][C]0.00789941076150091[/C][/ROW]
[ROW][C]58[/C][C]1.377[/C][C]1.43429962462044[/C][C]-0.0572996246204434[/C][/ROW]
[ROW][C]59[/C][C]1.3706[/C][C]1.37700272287495[/C][C]-0.00640272287495014[/C][/ROW]
[ROW][C]60[/C][C]1.3556[/C][C]1.37060030425703[/C][C]-0.0150003042570324[/C][/ROW]
[ROW][C]61[/C][C]1.3179[/C][C]1.35560071281362[/C][C]-0.0377007128136173[/C][/ROW]
[ROW][C]62[/C][C]1.2905[/C][C]1.31790179153576[/C][C]-0.0274017915357598[/C][/ROW]
[ROW][C]63[/C][C]1.3224[/C][C]1.2905013021316[/C][C]0.0318986978684024[/C][/ROW]
[ROW][C]64[/C][C]1.3201[/C][C]1.32239848417567[/C][C]-0.00229848417566525[/C][/ROW]
[ROW][C]65[/C][C]1.3162[/C][C]1.32010010922384[/C][C]-0.00390010922383932[/C][/ROW]
[ROW][C]66[/C][C]1.2789[/C][C]1.31620018533297[/C][C]-0.037300185332972[/C][/ROW]
[ROW][C]67[/C][C]1.2526[/C][C]1.27890177250272[/C][C]-0.0263017725027161[/C][/ROW]
[ROW][C]68[/C][C]1.2288[/C][C]1.25260124985876[/C][C]-0.0238012498587552[/C][/ROW]
[ROW][C]69[/C][C]1.24[/C][C]1.22880113103406[/C][C]0.011198868965941[/C][/ROW]
[ROW][C]70[/C][C]1.2856[/C][C]1.23999946783037[/C][C]0.0456005321696256[/C][/ROW]
[ROW][C]71[/C][C]1.2974[/C][C]1.28559783306527[/C][C]0.0118021669347326[/C][/ROW]
[ROW][C]72[/C][C]1.2828[/C][C]1.29739943916169[/C][C]-0.014599439161689[/C][/ROW]
[ROW][C]73[/C][C]1.3119[/C][C]1.28280069376453[/C][C]0.0290993062354694[/C][/ROW]
[ROW][C]74[/C][C]1.3288[/C][C]1.3118986172026[/C][C]0.0169013827974012[/C][/ROW]
[ROW][C]75[/C][C]1.3359[/C][C]1.32879919684724[/C][C]0.00710080315276329[/C][/ROW]
[ROW][C]76[/C][C]1.2964[/C][C]1.33589966257023[/C][C]-0.0394996625702322[/C][/ROW]
[ROW][C]77[/C][C]1.3026[/C][C]1.29640187702175[/C][C]0.00619812297824862[/C][/ROW]
[ROW][C]78[/C][C]1.2982[/C][C]1.30259970546554[/C][C]-0.00439970546554336[/C][/ROW]
[ROW][C]79[/C][C]1.3189[/C][C]1.29820020907376[/C][C]0.020699790926243[/C][/ROW]
[ROW][C]80[/C][C]1.308[/C][C]1.3188990163471[/C][C]-0.0108990163470954[/C][/ROW]
[ROW][C]81[/C][C]1.331[/C][C]1.30800051792065[/C][C]0.022999482079354[/C][/ROW]
[ROW][C]82[/C][C]1.3348[/C][C]1.3309989070659[/C][C]0.00380109293409925[/C][/ROW]
[ROW][C]83[/C][C]1.3635[/C][C]1.33479981937228[/C][C]0.0287001806277232[/C][/ROW]
[ROW][C]84[/C][C]1.3493[/C][C]1.36349863616903[/C][C]-0.0141986361690252[/C][/ROW]
[ROW][C]85[/C][C]1.3704[/C][C]1.34930067471839[/C][C]0.0210993252816054[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278598&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278598&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	1.2999	1.3213	-0.0213999999999999
3	1.3074	1.2999010169268	0.00749898307319929
4	1.3242	1.30739964364874	0.0168003563512555
5	1.3516	1.32419920164801	0.0274007983519919
6	1.3511	1.3515986979156	-0.00049869791559809
7	1.3419	1.3511000236981	-0.00920002369809692
8	1.3716	1.34190043718461	0.0296995628153893
9	1.3622	1.37159858867844	-0.00939858867843957
10	1.3896	1.36220044662041	0.0273995533795928
11	1.4227	1.38959869797476	0.0331013020252409
12	1.4684	1.42269842702798	0.0457015729720167
13	1.457	1.46839782826381	-0.0113978282638139
14	1.4718	1.45700054162416	0.0147994583758395
15	1.4748	1.47179929673057	0.00300070326943258
16	1.5527	1.47479985740675	0.0779001425932508
17	1.5751	1.55269629818959	0.0224037018104095
18	1.5557	1.57509893537735	-0.0193989353773456
19	1.5553	1.55570092183632	-0.000400921836321899
20	1.577	1.55530001905178	0.0216999809482168
21	1.4975	1.57699896881812	-0.0794989688181216
22	1.4369	1.49750377778654	-0.060603777786542
23	1.3322	1.43690287988812	-0.104702879888124
24	1.2732	1.33220497547498	-0.0590049754749833
25	1.3449	1.27320280391313	0.0716971960868726
26	1.3239	1.34489659295326	-0.0209965929532607
27	1.2785	1.32390099775692	-0.0454009977569205
28	1.305	1.27850215745287	0.0264978425471314
29	1.319	1.30499874082401	0.0140012591759926
30	1.365	1.31899933466095	0.0460006653390512
31	1.4016	1.36499781405096	0.0366021859490384
32	1.4088	1.40159826066618	0.00720173933382484
33	1.4268	1.40879965777375	0.0180003422262496
34	1.4562	1.42679914462475	0.0294008553752534
35	1.4816	1.456198602873	0.0254013971269995
36	1.4914	1.48159879292703	0.00980120707296761
37	1.4614	1.49139953424719	-0.0299995342471893
38	1.4272	1.46140142557619	-0.0342014255761858
39	1.3686	1.42720162524983	-0.0586016252498263
40	1.3569	1.36860278474595	-0.0117027847459472
41	1.3406	1.35690055611568	-0.016300556115675
42	1.2565	1.34060077460151	-0.084100774601513
43	1.2209	1.2565039964641	-0.0356039964640951
44	1.277	1.22090169189992	0.0560983081000834
45	1.2894	1.27699733421154	0.0124026657884566
46	1.3067	1.28939941062602	0.0173005893739828
47	1.3898	1.30669917787696	0.0831008221230374
48	1.3661	1.38979605105359	-0.0236960510535904
49	1.322	1.36610112603502	-0.0441011260350179
50	1.336	1.32200209568304	0.0139979043169629
51	1.3649	1.33599933482037	0.0289006651796284
52	1.3999	1.36489862664201	0.0350013733579895
53	1.4442	1.3998983367367	0.0443016632633002
54	1.4349	1.44419789478744	-0.00929789478744469
55	1.4388	1.43490044183544	0.00389955816456089
56	1.4264	1.43879981469321	-0.0123998146932147
57	1.4343	1.4264005892385	0.00789941076150091
58	1.377	1.43429962462044	-0.0572996246204434
59	1.3706	1.37700272287495	-0.00640272287495014
60	1.3556	1.37060030425703	-0.0150003042570324
61	1.3179	1.35560071281362	-0.0377007128136173
62	1.2905	1.31790179153576	-0.0274017915357598
63	1.3224	1.2905013021316	0.0318986978684024
64	1.3201	1.32239848417567	-0.00229848417566525
65	1.3162	1.32010010922384	-0.00390010922383932
66	1.2789	1.31620018533297	-0.037300185332972
67	1.2526	1.27890177250272	-0.0263017725027161
68	1.2288	1.25260124985876	-0.0238012498587552
69	1.24	1.22880113103406	0.011198868965941
70	1.2856	1.23999946783037	0.0456005321696256
71	1.2974	1.28559783306527	0.0118021669347326
72	1.2828	1.29739943916169	-0.014599439161689
73	1.3119	1.28280069376453	0.0290993062354694
74	1.3288	1.3118986172026	0.0169013827974012
75	1.3359	1.32879919684724	0.00710080315276329
76	1.2964	1.33589966257023	-0.0394996625702322
77	1.3026	1.29640187702175	0.00619812297824862
78	1.2982	1.30259970546554	-0.00439970546554336
79	1.3189	1.29820020907376	0.020699790926243
80	1.308	1.3188990163471	-0.0108990163470954
81	1.331	1.30800051792065	0.022999482079354
82	1.3348	1.3309989070659	0.00380109293409925
83	1.3635	1.33479981937228	0.0287001806277232
84	1.3493	1.36349863616903	-0.0141986361690252
85	1.3704	1.34930067471839	0.0210993252816054

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
86	1.37039899736125	1.3017498834783	1.43904811124419
87	1.37039899736125	1.27331679616087	1.46748119856162
88	1.37039899736125	1.25149901105802	1.48929898366447
89	1.37039899736125	1.23310566286935	1.50769233185314
90	1.37039899736125	1.21690074770054	1.52389724702195
91	1.37039899736125	1.20225035596948	1.53854763875301
92	1.37039899736125	1.18877791225576	1.55202008246673
93	1.37039899736125	1.1762380550791	1.56455993964339
94	1.37039899736125	1.16446035489488	1.57633763982761
95	1.37039899736125	1.15332072250656	1.58747727221593
96	1.37039899736125	1.14272548030913	1.59807251441336
97	1.37039899736125	1.13260184994379	1.6081961447787

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 1.37039899736125 & 1.3017498834783 & 1.43904811124419 \tabularnewline
87 & 1.37039899736125 & 1.27331679616087 & 1.46748119856162 \tabularnewline
88 & 1.37039899736125 & 1.25149901105802 & 1.48929898366447 \tabularnewline
89 & 1.37039899736125 & 1.23310566286935 & 1.50769233185314 \tabularnewline
90 & 1.37039899736125 & 1.21690074770054 & 1.52389724702195 \tabularnewline
91 & 1.37039899736125 & 1.20225035596948 & 1.53854763875301 \tabularnewline
92 & 1.37039899736125 & 1.18877791225576 & 1.55202008246673 \tabularnewline
93 & 1.37039899736125 & 1.1762380550791 & 1.56455993964339 \tabularnewline
94 & 1.37039899736125 & 1.16446035489488 & 1.57633763982761 \tabularnewline
95 & 1.37039899736125 & 1.15332072250656 & 1.58747727221593 \tabularnewline
96 & 1.37039899736125 & 1.14272548030913 & 1.59807251441336 \tabularnewline
97 & 1.37039899736125 & 1.13260184994379 & 1.6081961447787 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278598&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]1.37039899736125[/C][C]1.3017498834783[/C][C]1.43904811124419[/C][/ROW]
[ROW][C]87[/C][C]1.37039899736125[/C][C]1.27331679616087[/C][C]1.46748119856162[/C][/ROW]
[ROW][C]88[/C][C]1.37039899736125[/C][C]1.25149901105802[/C][C]1.48929898366447[/C][/ROW]
[ROW][C]89[/C][C]1.37039899736125[/C][C]1.23310566286935[/C][C]1.50769233185314[/C][/ROW]
[ROW][C]90[/C][C]1.37039899736125[/C][C]1.21690074770054[/C][C]1.52389724702195[/C][/ROW]
[ROW][C]91[/C][C]1.37039899736125[/C][C]1.20225035596948[/C][C]1.53854763875301[/C][/ROW]
[ROW][C]92[/C][C]1.37039899736125[/C][C]1.18877791225576[/C][C]1.55202008246673[/C][/ROW]
[ROW][C]93[/C][C]1.37039899736125[/C][C]1.1762380550791[/C][C]1.56455993964339[/C][/ROW]
[ROW][C]94[/C][C]1.37039899736125[/C][C]1.16446035489488[/C][C]1.57633763982761[/C][/ROW]
[ROW][C]95[/C][C]1.37039899736125[/C][C]1.15332072250656[/C][C]1.58747727221593[/C][/ROW]
[ROW][C]96[/C][C]1.37039899736125[/C][C]1.14272548030913[/C][C]1.59807251441336[/C][/ROW]
[ROW][C]97[/C][C]1.37039899736125[/C][C]1.13260184994379[/C][C]1.6081961447787[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278598&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278598&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	1.37039899736125	1.3017498834783	1.43904811124419
87	1.37039899736125	1.27331679616087	1.46748119856162
88	1.37039899736125	1.25149901105802	1.48929898366447
89	1.37039899736125	1.23310566286935	1.50769233185314
90	1.37039899736125	1.21690074770054	1.52389724702195
91	1.37039899736125	1.20225035596948	1.53854763875301
92	1.37039899736125	1.18877791225576	1.55202008246673
93	1.37039899736125	1.1762380550791	1.56455993964339
94	1.37039899736125	1.16446035489488	1.57633763982761
95	1.37039899736125	1.15332072250656	1.58747727221593
96	1.37039899736125	1.14272548030913	1.59807251441336
97	1.37039899736125	1.13260184994379	1.6081961447787

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