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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 04 Jan 2014 13:25:54 -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/2014/Jan/04/t1388860068rncu4xj7430rvis.htm/, Retrieved Sun, 19 May 2024 12:36:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232765, Retrieved Sun, 19 May 2024 12:36:27 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

182

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

-       [Exponential Smoothing] [] [2014-01-04 18:25:54] [ea11c40b74ac8faf5bfb23573227ddd8] [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	3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232765&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]3 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=232765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232765&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.222634147227084
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.222634147227084 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232765&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]0.222634147227084[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232765&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	0.222634147227084
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	15.33	15.37	-0.0399999999999991
4	15.36	15.4410946341109	-0.0810946341109169
5	15.4	15.4530401994009	-0.0530401994009395
6	15.4	15.4812316398386	-0.081231639838558
7	15.41	15.4631467029752	-0.0531467029752424
8	15.47	15.4613144320804	0.00868556791958142
9	15.54	15.5232481360874	0.0167518639126207
10	15.55	15.596977673024	-0.0469776730240259
11	15.59	15.5965188388516	-0.00651883885161197
12	15.65	15.635067522723	0.0149324772770285
13	15.75	15.6983920020675	0.0516079979324697
14	15.86	15.8098817046773	0.050118295322676
15	15.89	15.931039748617	-0.0410397486169618
16	15.94	15.9519028991812	-0.0119028991812122
17	15.93	15.9992529073725	-0.069252907372471
18	15.95	15.9738348453966	-0.0238348453966069
19	15.99	15.9885283949174	0.00147160508255872
20	15.99	16.0288560244601	-0.0388560244600544
21	16.06	16.0202053465898	0.0397946534102438
22	16.08	16.0990649953159	-0.0190649953159436
23	16.07	16.1148204763419	-0.0448204763418865
24	16.11	16.0948419078132	0.0151580921867982
25	16.15	16.1382166167408	0.0117833832591998
26	16.18	16.1808400002242	-0.000840000224158644
27	16.3	16.2106529874906	0.0893470125094176
28	16.42	16.3505446834279	0.0694553165720961
29	16.49	16.4860078086033	0.0039921913966765
30	16.5	16.5568966067305	-0.0568966067304864
31	16.58	16.5542294792109	0.0257705207890666
32	16.64	16.6399668771304	3.31228695991115e-05
33	16.66	16.6999742514122	-0.0399742514122288
34	16.81	16.711074618038	0.0989253819619726
35	16.91	16.8830987860902	0.0269012139097562
36	16.92	16.9890879149084	-0.0690879149084154
37	16.95	16.9837065858891	-0.0337065858890853
38	17.11	17.0062023488837	0.10379765111627
39	17.16	17.1893112504242	-0.0293112504241755
40	17.16	17.2327855651818	-0.0727855651818317
41	17.27	17.2165810129471	0.0534189870528685
42	17.34	17.3384739035754	0.00152609642461954
43	17.39	17.4088136647515	-0.0188136647514625
44	17.43	17.4546251005433	-0.0246251005433074
45	17.45	17.4891427122835	-0.0391427122834642
46	17.5	17.5004282079141	-0.000428207914080048
47	17.56	17.5503328742103	0.0096671257897043
48	17.65	17.6124851065166	0.0375148934833796
49	17.62	17.7108372028356	-0.0908372028356048
50	17.7	17.6606137396458	0.0393862603541884
51	17.72	17.7493824661322	-0.0293824661322297
52	17.71	17.7628409258414	-0.0528409258414477
53	17.74	17.7410767313781	-0.00107673137805264
54	17.75	17.7708370142059	-0.0208370142059024
55	17.78	17.7761979833174	0.00380201668258451
56	17.8	17.8070444420593	-0.00704444205928567
57	17.86	17.8254761087087	0.034523891291272
58	17.88	17.8931623058053	-0.0131623058053201
59	17.89	17.9102319270768	-0.0202319270768072
60	17.94	17.9157276092453	0.024272390754696
61	17.98	17.9711314722621	0.00886852773786018
62	18.1	18.0131059093722	0.0868940906277835
63	18.14	18.1524515011382	-0.0124515011382087
64	18.19	18.1896793718006	0.000320628199396822
65	18.23	18.2397507545864	-0.00975075458635644
66	18.24	18.2775799036542	-0.0375799036542013
67	18.27	18.2792133338513	-0.00921333385127099
68	18.3	18.3071621311262	-0.00716213112617581
69	18.34	18.3355675961706	0.00443240382942989
70	18.36	18.3765544006173	-0.0165544006173022
71	18.36	18.392868825753	-0.0328688257530132
72	18.4	18.3855511027611	0.0144488972388643
73	18.43	18.4287679206763	0.00123207932372082
74	18.47	18.4590422236058	0.0109577763941644
75	18.56	18.5014817988089	0.0585182011911449
76	18.58	18.6045099486283	-0.0245099486283067
77	18.61	18.6190531971169	-0.00905319711686303
78	18.61	18.6470376462971	-0.0370376462970725
79	18.69	18.6387918014984	0.0512081985015769
80	18.74	18.7301924951029	0.009807504897136
81	18.75	18.7823759805921	-0.0323759805920574
82	18.81	18.7851679817623	0.0248320182376922
83	18.85	18.8506964369666	-0.000696436966578062
84	18.88	18.8905413863164	-0.010541386316433

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 15.33 & 15.37 & -0.0399999999999991 \tabularnewline
4 & 15.36 & 15.4410946341109 & -0.0810946341109169 \tabularnewline
5 & 15.4 & 15.4530401994009 & -0.0530401994009395 \tabularnewline
6 & 15.4 & 15.4812316398386 & -0.081231639838558 \tabularnewline
7 & 15.41 & 15.4631467029752 & -0.0531467029752424 \tabularnewline
8 & 15.47 & 15.4613144320804 & 0.00868556791958142 \tabularnewline
9 & 15.54 & 15.5232481360874 & 0.0167518639126207 \tabularnewline
10 & 15.55 & 15.596977673024 & -0.0469776730240259 \tabularnewline
11 & 15.59 & 15.5965188388516 & -0.00651883885161197 \tabularnewline
12 & 15.65 & 15.635067522723 & 0.0149324772770285 \tabularnewline
13 & 15.75 & 15.6983920020675 & 0.0516079979324697 \tabularnewline
14 & 15.86 & 15.8098817046773 & 0.050118295322676 \tabularnewline
15 & 15.89 & 15.931039748617 & -0.0410397486169618 \tabularnewline
16 & 15.94 & 15.9519028991812 & -0.0119028991812122 \tabularnewline
17 & 15.93 & 15.9992529073725 & -0.069252907372471 \tabularnewline
18 & 15.95 & 15.9738348453966 & -0.0238348453966069 \tabularnewline
19 & 15.99 & 15.9885283949174 & 0.00147160508255872 \tabularnewline
20 & 15.99 & 16.0288560244601 & -0.0388560244600544 \tabularnewline
21 & 16.06 & 16.0202053465898 & 0.0397946534102438 \tabularnewline
22 & 16.08 & 16.0990649953159 & -0.0190649953159436 \tabularnewline
23 & 16.07 & 16.1148204763419 & -0.0448204763418865 \tabularnewline
24 & 16.11 & 16.0948419078132 & 0.0151580921867982 \tabularnewline
25 & 16.15 & 16.1382166167408 & 0.0117833832591998 \tabularnewline
26 & 16.18 & 16.1808400002242 & -0.000840000224158644 \tabularnewline
27 & 16.3 & 16.2106529874906 & 0.0893470125094176 \tabularnewline
28 & 16.42 & 16.3505446834279 & 0.0694553165720961 \tabularnewline
29 & 16.49 & 16.4860078086033 & 0.0039921913966765 \tabularnewline
30 & 16.5 & 16.5568966067305 & -0.0568966067304864 \tabularnewline
31 & 16.58 & 16.5542294792109 & 0.0257705207890666 \tabularnewline
32 & 16.64 & 16.6399668771304 & 3.31228695991115e-05 \tabularnewline
33 & 16.66 & 16.6999742514122 & -0.0399742514122288 \tabularnewline
34 & 16.81 & 16.711074618038 & 0.0989253819619726 \tabularnewline
35 & 16.91 & 16.8830987860902 & 0.0269012139097562 \tabularnewline
36 & 16.92 & 16.9890879149084 & -0.0690879149084154 \tabularnewline
37 & 16.95 & 16.9837065858891 & -0.0337065858890853 \tabularnewline
38 & 17.11 & 17.0062023488837 & 0.10379765111627 \tabularnewline
39 & 17.16 & 17.1893112504242 & -0.0293112504241755 \tabularnewline
40 & 17.16 & 17.2327855651818 & -0.0727855651818317 \tabularnewline
41 & 17.27 & 17.2165810129471 & 0.0534189870528685 \tabularnewline
42 & 17.34 & 17.3384739035754 & 0.00152609642461954 \tabularnewline
43 & 17.39 & 17.4088136647515 & -0.0188136647514625 \tabularnewline
44 & 17.43 & 17.4546251005433 & -0.0246251005433074 \tabularnewline
45 & 17.45 & 17.4891427122835 & -0.0391427122834642 \tabularnewline
46 & 17.5 & 17.5004282079141 & -0.000428207914080048 \tabularnewline
47 & 17.56 & 17.5503328742103 & 0.0096671257897043 \tabularnewline
48 & 17.65 & 17.6124851065166 & 0.0375148934833796 \tabularnewline
49 & 17.62 & 17.7108372028356 & -0.0908372028356048 \tabularnewline
50 & 17.7 & 17.6606137396458 & 0.0393862603541884 \tabularnewline
51 & 17.72 & 17.7493824661322 & -0.0293824661322297 \tabularnewline
52 & 17.71 & 17.7628409258414 & -0.0528409258414477 \tabularnewline
53 & 17.74 & 17.7410767313781 & -0.00107673137805264 \tabularnewline
54 & 17.75 & 17.7708370142059 & -0.0208370142059024 \tabularnewline
55 & 17.78 & 17.7761979833174 & 0.00380201668258451 \tabularnewline
56 & 17.8 & 17.8070444420593 & -0.00704444205928567 \tabularnewline
57 & 17.86 & 17.8254761087087 & 0.034523891291272 \tabularnewline
58 & 17.88 & 17.8931623058053 & -0.0131623058053201 \tabularnewline
59 & 17.89 & 17.9102319270768 & -0.0202319270768072 \tabularnewline
60 & 17.94 & 17.9157276092453 & 0.024272390754696 \tabularnewline
61 & 17.98 & 17.9711314722621 & 0.00886852773786018 \tabularnewline
62 & 18.1 & 18.0131059093722 & 0.0868940906277835 \tabularnewline
63 & 18.14 & 18.1524515011382 & -0.0124515011382087 \tabularnewline
64 & 18.19 & 18.1896793718006 & 0.000320628199396822 \tabularnewline
65 & 18.23 & 18.2397507545864 & -0.00975075458635644 \tabularnewline
66 & 18.24 & 18.2775799036542 & -0.0375799036542013 \tabularnewline
67 & 18.27 & 18.2792133338513 & -0.00921333385127099 \tabularnewline
68 & 18.3 & 18.3071621311262 & -0.00716213112617581 \tabularnewline
69 & 18.34 & 18.3355675961706 & 0.00443240382942989 \tabularnewline
70 & 18.36 & 18.3765544006173 & -0.0165544006173022 \tabularnewline
71 & 18.36 & 18.392868825753 & -0.0328688257530132 \tabularnewline
72 & 18.4 & 18.3855511027611 & 0.0144488972388643 \tabularnewline
73 & 18.43 & 18.4287679206763 & 0.00123207932372082 \tabularnewline
74 & 18.47 & 18.4590422236058 & 0.0109577763941644 \tabularnewline
75 & 18.56 & 18.5014817988089 & 0.0585182011911449 \tabularnewline
76 & 18.58 & 18.6045099486283 & -0.0245099486283067 \tabularnewline
77 & 18.61 & 18.6190531971169 & -0.00905319711686303 \tabularnewline
78 & 18.61 & 18.6470376462971 & -0.0370376462970725 \tabularnewline
79 & 18.69 & 18.6387918014984 & 0.0512081985015769 \tabularnewline
80 & 18.74 & 18.7301924951029 & 0.009807504897136 \tabularnewline
81 & 18.75 & 18.7823759805921 & -0.0323759805920574 \tabularnewline
82 & 18.81 & 18.7851679817623 & 0.0248320182376922 \tabularnewline
83 & 18.85 & 18.8506964369666 & -0.000696436966578062 \tabularnewline
84 & 18.88 & 18.8905413863164 & -0.010541386316433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232765&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]15.33[/C][C]15.37[/C][C]-0.0399999999999991[/C][/ROW]
[ROW][C]4[/C][C]15.36[/C][C]15.4410946341109[/C][C]-0.0810946341109169[/C][/ROW]
[ROW][C]5[/C][C]15.4[/C][C]15.4530401994009[/C][C]-0.0530401994009395[/C][/ROW]
[ROW][C]6[/C][C]15.4[/C][C]15.4812316398386[/C][C]-0.081231639838558[/C][/ROW]
[ROW][C]7[/C][C]15.41[/C][C]15.4631467029752[/C][C]-0.0531467029752424[/C][/ROW]
[ROW][C]8[/C][C]15.47[/C][C]15.4613144320804[/C][C]0.00868556791958142[/C][/ROW]
[ROW][C]9[/C][C]15.54[/C][C]15.5232481360874[/C][C]0.0167518639126207[/C][/ROW]
[ROW][C]10[/C][C]15.55[/C][C]15.596977673024[/C][C]-0.0469776730240259[/C][/ROW]
[ROW][C]11[/C][C]15.59[/C][C]15.5965188388516[/C][C]-0.00651883885161197[/C][/ROW]
[ROW][C]12[/C][C]15.65[/C][C]15.635067522723[/C][C]0.0149324772770285[/C][/ROW]
[ROW][C]13[/C][C]15.75[/C][C]15.6983920020675[/C][C]0.0516079979324697[/C][/ROW]
[ROW][C]14[/C][C]15.86[/C][C]15.8098817046773[/C][C]0.050118295322676[/C][/ROW]
[ROW][C]15[/C][C]15.89[/C][C]15.931039748617[/C][C]-0.0410397486169618[/C][/ROW]
[ROW][C]16[/C][C]15.94[/C][C]15.9519028991812[/C][C]-0.0119028991812122[/C][/ROW]
[ROW][C]17[/C][C]15.93[/C][C]15.9992529073725[/C][C]-0.069252907372471[/C][/ROW]
[ROW][C]18[/C][C]15.95[/C][C]15.9738348453966[/C][C]-0.0238348453966069[/C][/ROW]
[ROW][C]19[/C][C]15.99[/C][C]15.9885283949174[/C][C]0.00147160508255872[/C][/ROW]
[ROW][C]20[/C][C]15.99[/C][C]16.0288560244601[/C][C]-0.0388560244600544[/C][/ROW]
[ROW][C]21[/C][C]16.06[/C][C]16.0202053465898[/C][C]0.0397946534102438[/C][/ROW]
[ROW][C]22[/C][C]16.08[/C][C]16.0990649953159[/C][C]-0.0190649953159436[/C][/ROW]
[ROW][C]23[/C][C]16.07[/C][C]16.1148204763419[/C][C]-0.0448204763418865[/C][/ROW]
[ROW][C]24[/C][C]16.11[/C][C]16.0948419078132[/C][C]0.0151580921867982[/C][/ROW]
[ROW][C]25[/C][C]16.15[/C][C]16.1382166167408[/C][C]0.0117833832591998[/C][/ROW]
[ROW][C]26[/C][C]16.18[/C][C]16.1808400002242[/C][C]-0.000840000224158644[/C][/ROW]
[ROW][C]27[/C][C]16.3[/C][C]16.2106529874906[/C][C]0.0893470125094176[/C][/ROW]
[ROW][C]28[/C][C]16.42[/C][C]16.3505446834279[/C][C]0.0694553165720961[/C][/ROW]
[ROW][C]29[/C][C]16.49[/C][C]16.4860078086033[/C][C]0.0039921913966765[/C][/ROW]
[ROW][C]30[/C][C]16.5[/C][C]16.5568966067305[/C][C]-0.0568966067304864[/C][/ROW]
[ROW][C]31[/C][C]16.58[/C][C]16.5542294792109[/C][C]0.0257705207890666[/C][/ROW]
[ROW][C]32[/C][C]16.64[/C][C]16.6399668771304[/C][C]3.31228695991115e-05[/C][/ROW]
[ROW][C]33[/C][C]16.66[/C][C]16.6999742514122[/C][C]-0.0399742514122288[/C][/ROW]
[ROW][C]34[/C][C]16.81[/C][C]16.711074618038[/C][C]0.0989253819619726[/C][/ROW]
[ROW][C]35[/C][C]16.91[/C][C]16.8830987860902[/C][C]0.0269012139097562[/C][/ROW]
[ROW][C]36[/C][C]16.92[/C][C]16.9890879149084[/C][C]-0.0690879149084154[/C][/ROW]
[ROW][C]37[/C][C]16.95[/C][C]16.9837065858891[/C][C]-0.0337065858890853[/C][/ROW]
[ROW][C]38[/C][C]17.11[/C][C]17.0062023488837[/C][C]0.10379765111627[/C][/ROW]
[ROW][C]39[/C][C]17.16[/C][C]17.1893112504242[/C][C]-0.0293112504241755[/C][/ROW]
[ROW][C]40[/C][C]17.16[/C][C]17.2327855651818[/C][C]-0.0727855651818317[/C][/ROW]
[ROW][C]41[/C][C]17.27[/C][C]17.2165810129471[/C][C]0.0534189870528685[/C][/ROW]
[ROW][C]42[/C][C]17.34[/C][C]17.3384739035754[/C][C]0.00152609642461954[/C][/ROW]
[ROW][C]43[/C][C]17.39[/C][C]17.4088136647515[/C][C]-0.0188136647514625[/C][/ROW]
[ROW][C]44[/C][C]17.43[/C][C]17.4546251005433[/C][C]-0.0246251005433074[/C][/ROW]
[ROW][C]45[/C][C]17.45[/C][C]17.4891427122835[/C][C]-0.0391427122834642[/C][/ROW]
[ROW][C]46[/C][C]17.5[/C][C]17.5004282079141[/C][C]-0.000428207914080048[/C][/ROW]
[ROW][C]47[/C][C]17.56[/C][C]17.5503328742103[/C][C]0.0096671257897043[/C][/ROW]
[ROW][C]48[/C][C]17.65[/C][C]17.6124851065166[/C][C]0.0375148934833796[/C][/ROW]
[ROW][C]49[/C][C]17.62[/C][C]17.7108372028356[/C][C]-0.0908372028356048[/C][/ROW]
[ROW][C]50[/C][C]17.7[/C][C]17.6606137396458[/C][C]0.0393862603541884[/C][/ROW]
[ROW][C]51[/C][C]17.72[/C][C]17.7493824661322[/C][C]-0.0293824661322297[/C][/ROW]
[ROW][C]52[/C][C]17.71[/C][C]17.7628409258414[/C][C]-0.0528409258414477[/C][/ROW]
[ROW][C]53[/C][C]17.74[/C][C]17.7410767313781[/C][C]-0.00107673137805264[/C][/ROW]
[ROW][C]54[/C][C]17.75[/C][C]17.7708370142059[/C][C]-0.0208370142059024[/C][/ROW]
[ROW][C]55[/C][C]17.78[/C][C]17.7761979833174[/C][C]0.00380201668258451[/C][/ROW]
[ROW][C]56[/C][C]17.8[/C][C]17.8070444420593[/C][C]-0.00704444205928567[/C][/ROW]
[ROW][C]57[/C][C]17.86[/C][C]17.8254761087087[/C][C]0.034523891291272[/C][/ROW]
[ROW][C]58[/C][C]17.88[/C][C]17.8931623058053[/C][C]-0.0131623058053201[/C][/ROW]
[ROW][C]59[/C][C]17.89[/C][C]17.9102319270768[/C][C]-0.0202319270768072[/C][/ROW]
[ROW][C]60[/C][C]17.94[/C][C]17.9157276092453[/C][C]0.024272390754696[/C][/ROW]
[ROW][C]61[/C][C]17.98[/C][C]17.9711314722621[/C][C]0.00886852773786018[/C][/ROW]
[ROW][C]62[/C][C]18.1[/C][C]18.0131059093722[/C][C]0.0868940906277835[/C][/ROW]
[ROW][C]63[/C][C]18.14[/C][C]18.1524515011382[/C][C]-0.0124515011382087[/C][/ROW]
[ROW][C]64[/C][C]18.19[/C][C]18.1896793718006[/C][C]0.000320628199396822[/C][/ROW]
[ROW][C]65[/C][C]18.23[/C][C]18.2397507545864[/C][C]-0.00975075458635644[/C][/ROW]
[ROW][C]66[/C][C]18.24[/C][C]18.2775799036542[/C][C]-0.0375799036542013[/C][/ROW]
[ROW][C]67[/C][C]18.27[/C][C]18.2792133338513[/C][C]-0.00921333385127099[/C][/ROW]
[ROW][C]68[/C][C]18.3[/C][C]18.3071621311262[/C][C]-0.00716213112617581[/C][/ROW]
[ROW][C]69[/C][C]18.34[/C][C]18.3355675961706[/C][C]0.00443240382942989[/C][/ROW]
[ROW][C]70[/C][C]18.36[/C][C]18.3765544006173[/C][C]-0.0165544006173022[/C][/ROW]
[ROW][C]71[/C][C]18.36[/C][C]18.392868825753[/C][C]-0.0328688257530132[/C][/ROW]
[ROW][C]72[/C][C]18.4[/C][C]18.3855511027611[/C][C]0.0144488972388643[/C][/ROW]
[ROW][C]73[/C][C]18.43[/C][C]18.4287679206763[/C][C]0.00123207932372082[/C][/ROW]
[ROW][C]74[/C][C]18.47[/C][C]18.4590422236058[/C][C]0.0109577763941644[/C][/ROW]
[ROW][C]75[/C][C]18.56[/C][C]18.5014817988089[/C][C]0.0585182011911449[/C][/ROW]
[ROW][C]76[/C][C]18.58[/C][C]18.6045099486283[/C][C]-0.0245099486283067[/C][/ROW]
[ROW][C]77[/C][C]18.61[/C][C]18.6190531971169[/C][C]-0.00905319711686303[/C][/ROW]
[ROW][C]78[/C][C]18.61[/C][C]18.6470376462971[/C][C]-0.0370376462970725[/C][/ROW]
[ROW][C]79[/C][C]18.69[/C][C]18.6387918014984[/C][C]0.0512081985015769[/C][/ROW]
[ROW][C]80[/C][C]18.74[/C][C]18.7301924951029[/C][C]0.009807504897136[/C][/ROW]
[ROW][C]81[/C][C]18.75[/C][C]18.7823759805921[/C][C]-0.0323759805920574[/C][/ROW]
[ROW][C]82[/C][C]18.81[/C][C]18.7851679817623[/C][C]0.0248320182376922[/C][/ROW]
[ROW][C]83[/C][C]18.85[/C][C]18.8506964369666[/C][C]-0.000696436966578062[/C][/ROW]
[ROW][C]84[/C][C]18.88[/C][C]18.8905413863164[/C][C]-0.010541386316433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232765&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232765&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	15.33	15.37	-0.0399999999999991
4	15.36	15.4410946341109	-0.0810946341109169
5	15.4	15.4530401994009	-0.0530401994009395
6	15.4	15.4812316398386	-0.081231639838558
7	15.41	15.4631467029752	-0.0531467029752424
8	15.47	15.4613144320804	0.00868556791958142
9	15.54	15.5232481360874	0.0167518639126207
10	15.55	15.596977673024	-0.0469776730240259
11	15.59	15.5965188388516	-0.00651883885161197
12	15.65	15.635067522723	0.0149324772770285
13	15.75	15.6983920020675	0.0516079979324697
14	15.86	15.8098817046773	0.050118295322676
15	15.89	15.931039748617	-0.0410397486169618
16	15.94	15.9519028991812	-0.0119028991812122
17	15.93	15.9992529073725	-0.069252907372471
18	15.95	15.9738348453966	-0.0238348453966069
19	15.99	15.9885283949174	0.00147160508255872
20	15.99	16.0288560244601	-0.0388560244600544
21	16.06	16.0202053465898	0.0397946534102438
22	16.08	16.0990649953159	-0.0190649953159436
23	16.07	16.1148204763419	-0.0448204763418865
24	16.11	16.0948419078132	0.0151580921867982
25	16.15	16.1382166167408	0.0117833832591998
26	16.18	16.1808400002242	-0.000840000224158644
27	16.3	16.2106529874906	0.0893470125094176
28	16.42	16.3505446834279	0.0694553165720961
29	16.49	16.4860078086033	0.0039921913966765
30	16.5	16.5568966067305	-0.0568966067304864
31	16.58	16.5542294792109	0.0257705207890666
32	16.64	16.6399668771304	3.31228695991115e-05
33	16.66	16.6999742514122	-0.0399742514122288
34	16.81	16.711074618038	0.0989253819619726
35	16.91	16.8830987860902	0.0269012139097562
36	16.92	16.9890879149084	-0.0690879149084154
37	16.95	16.9837065858891	-0.0337065858890853
38	17.11	17.0062023488837	0.10379765111627
39	17.16	17.1893112504242	-0.0293112504241755
40	17.16	17.2327855651818	-0.0727855651818317
41	17.27	17.2165810129471	0.0534189870528685
42	17.34	17.3384739035754	0.00152609642461954
43	17.39	17.4088136647515	-0.0188136647514625
44	17.43	17.4546251005433	-0.0246251005433074
45	17.45	17.4891427122835	-0.0391427122834642
46	17.5	17.5004282079141	-0.000428207914080048
47	17.56	17.5503328742103	0.0096671257897043
48	17.65	17.6124851065166	0.0375148934833796
49	17.62	17.7108372028356	-0.0908372028356048
50	17.7	17.6606137396458	0.0393862603541884
51	17.72	17.7493824661322	-0.0293824661322297
52	17.71	17.7628409258414	-0.0528409258414477
53	17.74	17.7410767313781	-0.00107673137805264
54	17.75	17.7708370142059	-0.0208370142059024
55	17.78	17.7761979833174	0.00380201668258451
56	17.8	17.8070444420593	-0.00704444205928567
57	17.86	17.8254761087087	0.034523891291272
58	17.88	17.8931623058053	-0.0131623058053201
59	17.89	17.9102319270768	-0.0202319270768072
60	17.94	17.9157276092453	0.024272390754696
61	17.98	17.9711314722621	0.00886852773786018
62	18.1	18.0131059093722	0.0868940906277835
63	18.14	18.1524515011382	-0.0124515011382087
64	18.19	18.1896793718006	0.000320628199396822
65	18.23	18.2397507545864	-0.00975075458635644
66	18.24	18.2775799036542	-0.0375799036542013
67	18.27	18.2792133338513	-0.00921333385127099
68	18.3	18.3071621311262	-0.00716213112617581
69	18.34	18.3355675961706	0.00443240382942989
70	18.36	18.3765544006173	-0.0165544006173022
71	18.36	18.392868825753	-0.0328688257530132
72	18.4	18.3855511027611	0.0144488972388643
73	18.43	18.4287679206763	0.00123207932372082
74	18.47	18.4590422236058	0.0109577763941644
75	18.56	18.5014817988089	0.0585182011911449
76	18.58	18.6045099486283	-0.0245099486283067
77	18.61	18.6190531971169	-0.00905319711686303
78	18.61	18.6470376462971	-0.0370376462970725
79	18.69	18.6387918014984	0.0512081985015769
80	18.74	18.7301924951029	0.009807504897136
81	18.75	18.7823759805921	-0.0323759805920574
82	18.81	18.7851679817623	0.0248320182376922
83	18.85	18.8506964369666	-0.000696436966578062
84	18.88	18.8905413863164	-0.010541386316433

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	18.9181945137633	18.8379585366834	18.9984304908431
86	18.9563890275266	18.8296559459388	19.0831221091143
87	18.9945835412898	18.8228029295681	19.1663641530116
88	19.0327780550531	18.8150214971418	19.2505346129645
89	19.0709725688164	18.8055907937647	19.3363543438681
90	19.1091670825797	18.7942457029892	19.4240884621702
91	19.147361596343	18.7808918464244	19.5138313462615
92	19.1855561101062	18.7655091054897	19.6056031147228
93	19.2237506238695	18.7481122176404	19.6993890300986
94	19.2619451376328	18.7287327104567	19.7951575648089
95	19.3001396513961	18.7074099694642	19.892869333328
96	19.3383341651594	18.6841866005873	19.9924817297314

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 18.9181945137633 & 18.8379585366834 & 18.9984304908431 \tabularnewline
86 & 18.9563890275266 & 18.8296559459388 & 19.0831221091143 \tabularnewline
87 & 18.9945835412898 & 18.8228029295681 & 19.1663641530116 \tabularnewline
88 & 19.0327780550531 & 18.8150214971418 & 19.2505346129645 \tabularnewline
89 & 19.0709725688164 & 18.8055907937647 & 19.3363543438681 \tabularnewline
90 & 19.1091670825797 & 18.7942457029892 & 19.4240884621702 \tabularnewline
91 & 19.147361596343 & 18.7808918464244 & 19.5138313462615 \tabularnewline
92 & 19.1855561101062 & 18.7655091054897 & 19.6056031147228 \tabularnewline
93 & 19.2237506238695 & 18.7481122176404 & 19.6993890300986 \tabularnewline
94 & 19.2619451376328 & 18.7287327104567 & 19.7951575648089 \tabularnewline
95 & 19.3001396513961 & 18.7074099694642 & 19.892869333328 \tabularnewline
96 & 19.3383341651594 & 18.6841866005873 & 19.9924817297314 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232765&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]18.9181945137633[/C][C]18.8379585366834[/C][C]18.9984304908431[/C][/ROW]
[ROW][C]86[/C][C]18.9563890275266[/C][C]18.8296559459388[/C][C]19.0831221091143[/C][/ROW]
[ROW][C]87[/C][C]18.9945835412898[/C][C]18.8228029295681[/C][C]19.1663641530116[/C][/ROW]
[ROW][C]88[/C][C]19.0327780550531[/C][C]18.8150214971418[/C][C]19.2505346129645[/C][/ROW]
[ROW][C]89[/C][C]19.0709725688164[/C][C]18.8055907937647[/C][C]19.3363543438681[/C][/ROW]
[ROW][C]90[/C][C]19.1091670825797[/C][C]18.7942457029892[/C][C]19.4240884621702[/C][/ROW]
[ROW][C]91[/C][C]19.147361596343[/C][C]18.7808918464244[/C][C]19.5138313462615[/C][/ROW]
[ROW][C]92[/C][C]19.1855561101062[/C][C]18.7655091054897[/C][C]19.6056031147228[/C][/ROW]
[ROW][C]93[/C][C]19.2237506238695[/C][C]18.7481122176404[/C][C]19.6993890300986[/C][/ROW]
[ROW][C]94[/C][C]19.2619451376328[/C][C]18.7287327104567[/C][C]19.7951575648089[/C][/ROW]
[ROW][C]95[/C][C]19.3001396513961[/C][C]18.7074099694642[/C][C]19.892869333328[/C][/ROW]
[ROW][C]96[/C][C]19.3383341651594[/C][C]18.6841866005873[/C][C]19.9924817297314[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232765&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232765&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	18.9181945137633	18.8379585366834	18.9984304908431
86	18.9563890275266	18.8296559459388	19.0831221091143
87	18.9945835412898	18.8228029295681	19.1663641530116
88	19.0327780550531	18.8150214971418	19.2505346129645
89	19.0709725688164	18.8055907937647	19.3363543438681
90	19.1091670825797	18.7942457029892	19.4240884621702
91	19.147361596343	18.7808918464244	19.5138313462615
92	19.1855561101062	18.7655091054897	19.6056031147228
93	19.2237506238695	18.7481122176404	19.6993890300986
94	19.2619451376328	18.7287327104567	19.7951575648089
95	19.3001396513961	18.7074099694642	19.892869333328
96	19.3383341651594	18.6841866005873	19.9924817297314

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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