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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 30 Nov 2015 15:51:05 +0000

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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/Nov/30/t1448898679xj3vboh4cb37i3h.htm/, Retrieved Tue, 14 May 2024 22:07:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284622, Retrieved Tue, 14 May 2024 22:07:52 +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] [] [2015-11-30 15:51:05] [07f175c9375843c217f66b4a3796ae0c] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284622&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284622&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284622&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.820630456060063
beta	0.0822320231489281
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.820630456060063 \tabularnewline
beta & 0.0822320231489281 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284622&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]0.820630456060063[/C][/ROW]
[ROW][C]beta[/C][C]0.0822320231489281[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284622&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284622&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	0.820630456060063
beta	0.0822320231489281
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	88.92	86.8194471153846	2.10055288461537
14	89.56	89.2718932187597	0.288106781240259
15	90.21	90.2822662344597	-0.0722662344596898
16	90.42	90.5753628338148	-0.155362833814806
17	91.23	91.4727002889098	-0.242700288909802
18	91.73	92.0469880425874	-0.316988042587369
19	92.21	91.2780886501198	0.931911349880224
20	91.65	92.2052948063815	-0.555294806381482
21	91.8	92.0304151685777	-0.230415168577665
22	91.63	92.4674260893825	-0.83742608938249
23	91.09	92.6793774214137	-1.58937742141373
24	90.89	91.5278333919221	-0.637833391922086
25	90.98	91.5850549144819	-0.60505491448194
26	91.29	91.2206388988322	0.0693611011678286
27	90.77	91.7006408594659	-0.930640859465925
28	90.96	90.9302774307447	0.0297225692552701
29	90.89	91.6321792082949	-0.742179208294871
30	90.72	91.4178917835664	-0.697891783566405
31	90.66	90.1693589050247	0.490641094975345
32	90.94	90.0468411262693	0.893158873730656
33	90.7	90.7957802704695	-0.0957802704694615
34	90.74	90.9203829285382	-0.180382928538179
35	90.98	91.2669708873036	-0.286970887303625
36	91.13	91.1731126414131	-0.0431126414130745
37	91.54	91.5826058889106	-0.0426058889105576
38	91.93	91.6970239133328	0.23297608666725
39	92.27	92.0392660483192	0.23073395168079
40	92.59	92.3799367547862	0.210063245213803
41	92.96	93.0892603257314	-0.12926032573138
42	92.95	93.4251420853023	-0.475142085302267
43	92.99	92.6268680786192	0.363131921380798
44	93.05	92.517584316849	0.532415683151029
45	93.34	92.814429837604	0.525570162396008
46	93.47	93.4970152671128	-0.0270152671128017
47	93.59	94.0239511610768	-0.433951161076806
48	93.96	93.9169070253271	0.0430929746729305
49	94.49	94.4667413159557	0.0232586840442792
50	95.04	94.7585927011935	0.281407298806471
51	95.52	95.2173969061809	0.302603093819101
52	95.75	95.695407918199	0.054592081801033
53	96.07	96.2878612760834	-0.217861276083397
54	96.37	96.5545932383042	-0.18459323830416
55	96.48	96.230319632253	0.249680367747004
56	96.4	96.1358488135762	0.264151186423788
57	96.66	96.2707677799409	0.389232220059142
58	96.81	96.7926001139909	0.0173998860090592
59	97.19	97.3362367263451	-0.146236726345123
60	97.23	97.623526779215	-0.393526779215037
61	97.94	97.8546956871284	0.0853043128715569
62	98.52	98.2911503265471	0.228849673452885
63	98.73	98.7544620466875	-0.0244620466875034
64	98.8	98.9413528009161	-0.141352800916067
65	98.77	99.3326801928375	-0.562680192837504
66	98.54	99.3076836244216	-0.767683624421551
67	98.72	98.5287286837666	0.191271316233426
68	99.15	98.3309046132616	0.819095386738425
69	99.32	98.9230955918798	0.396904408120164
70	99.5	99.3644784684219	0.135521531578107
71	99.39	99.9636188806179	-0.573618880617872
72	99.4	99.8149101753992	-0.414910175399157
73	99.37	100.072056293314	-0.702056293313518
74	99.69	99.7926311175522	-0.102631117552193
75	99.83	99.8206187888057	0.00938121119429525
76	99.79	99.8987351156373	-0.108735115637273
77	99.94	100.127876787083	-0.187876787082516
78	100.11	100.285596974055	-0.175596974055253
79	100.21	100.116401971425	0.0935980285745757
80	100.15	99.8963138344439	0.253686165556076
81	100.21	99.8559066705429	0.354093329457115
82	100.13	100.119506450923	0.0104935490766422
83	100.2	100.384642855549	-0.184642855548603
84	100.36	100.505652106364	-0.145652106363769
85	100.5	100.872469303821	-0.372469303821077
86	100.66	100.933488068788	-0.273488068787984
87	100.72	100.792283335055	-0.0722833350545073
88	100.41	100.727612293589	-0.317612293588539
89	100.3	100.702467431762	-0.402467431761778
90	100.38	100.603129642718	-0.223129642717979
91	100.55	100.356844683082	0.193155316917597
92	100.17	100.167520974015	0.00247902598495386
93	100.09	99.8423733306747	0.247626669325342
94	100.22	99.8531851600777	0.366814839922299
95	100.09	100.295986618925	-0.205986618924797
96	99.98	100.325292437049	-0.345292437049366

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 88.92 & 86.8194471153846 & 2.10055288461537 \tabularnewline
14 & 89.56 & 89.2718932187597 & 0.288106781240259 \tabularnewline
15 & 90.21 & 90.2822662344597 & -0.0722662344596898 \tabularnewline
16 & 90.42 & 90.5753628338148 & -0.155362833814806 \tabularnewline
17 & 91.23 & 91.4727002889098 & -0.242700288909802 \tabularnewline
18 & 91.73 & 92.0469880425874 & -0.316988042587369 \tabularnewline
19 & 92.21 & 91.2780886501198 & 0.931911349880224 \tabularnewline
20 & 91.65 & 92.2052948063815 & -0.555294806381482 \tabularnewline
21 & 91.8 & 92.0304151685777 & -0.230415168577665 \tabularnewline
22 & 91.63 & 92.4674260893825 & -0.83742608938249 \tabularnewline
23 & 91.09 & 92.6793774214137 & -1.58937742141373 \tabularnewline
24 & 90.89 & 91.5278333919221 & -0.637833391922086 \tabularnewline
25 & 90.98 & 91.5850549144819 & -0.60505491448194 \tabularnewline
26 & 91.29 & 91.2206388988322 & 0.0693611011678286 \tabularnewline
27 & 90.77 & 91.7006408594659 & -0.930640859465925 \tabularnewline
28 & 90.96 & 90.9302774307447 & 0.0297225692552701 \tabularnewline
29 & 90.89 & 91.6321792082949 & -0.742179208294871 \tabularnewline
30 & 90.72 & 91.4178917835664 & -0.697891783566405 \tabularnewline
31 & 90.66 & 90.1693589050247 & 0.490641094975345 \tabularnewline
32 & 90.94 & 90.0468411262693 & 0.893158873730656 \tabularnewline
33 & 90.7 & 90.7957802704695 & -0.0957802704694615 \tabularnewline
34 & 90.74 & 90.9203829285382 & -0.180382928538179 \tabularnewline
35 & 90.98 & 91.2669708873036 & -0.286970887303625 \tabularnewline
36 & 91.13 & 91.1731126414131 & -0.0431126414130745 \tabularnewline
37 & 91.54 & 91.5826058889106 & -0.0426058889105576 \tabularnewline
38 & 91.93 & 91.6970239133328 & 0.23297608666725 \tabularnewline
39 & 92.27 & 92.0392660483192 & 0.23073395168079 \tabularnewline
40 & 92.59 & 92.3799367547862 & 0.210063245213803 \tabularnewline
41 & 92.96 & 93.0892603257314 & -0.12926032573138 \tabularnewline
42 & 92.95 & 93.4251420853023 & -0.475142085302267 \tabularnewline
43 & 92.99 & 92.6268680786192 & 0.363131921380798 \tabularnewline
44 & 93.05 & 92.517584316849 & 0.532415683151029 \tabularnewline
45 & 93.34 & 92.814429837604 & 0.525570162396008 \tabularnewline
46 & 93.47 & 93.4970152671128 & -0.0270152671128017 \tabularnewline
47 & 93.59 & 94.0239511610768 & -0.433951161076806 \tabularnewline
48 & 93.96 & 93.9169070253271 & 0.0430929746729305 \tabularnewline
49 & 94.49 & 94.4667413159557 & 0.0232586840442792 \tabularnewline
50 & 95.04 & 94.7585927011935 & 0.281407298806471 \tabularnewline
51 & 95.52 & 95.2173969061809 & 0.302603093819101 \tabularnewline
52 & 95.75 & 95.695407918199 & 0.054592081801033 \tabularnewline
53 & 96.07 & 96.2878612760834 & -0.217861276083397 \tabularnewline
54 & 96.37 & 96.5545932383042 & -0.18459323830416 \tabularnewline
55 & 96.48 & 96.230319632253 & 0.249680367747004 \tabularnewline
56 & 96.4 & 96.1358488135762 & 0.264151186423788 \tabularnewline
57 & 96.66 & 96.2707677799409 & 0.389232220059142 \tabularnewline
58 & 96.81 & 96.7926001139909 & 0.0173998860090592 \tabularnewline
59 & 97.19 & 97.3362367263451 & -0.146236726345123 \tabularnewline
60 & 97.23 & 97.623526779215 & -0.393526779215037 \tabularnewline
61 & 97.94 & 97.8546956871284 & 0.0853043128715569 \tabularnewline
62 & 98.52 & 98.2911503265471 & 0.228849673452885 \tabularnewline
63 & 98.73 & 98.7544620466875 & -0.0244620466875034 \tabularnewline
64 & 98.8 & 98.9413528009161 & -0.141352800916067 \tabularnewline
65 & 98.77 & 99.3326801928375 & -0.562680192837504 \tabularnewline
66 & 98.54 & 99.3076836244216 & -0.767683624421551 \tabularnewline
67 & 98.72 & 98.5287286837666 & 0.191271316233426 \tabularnewline
68 & 99.15 & 98.3309046132616 & 0.819095386738425 \tabularnewline
69 & 99.32 & 98.9230955918798 & 0.396904408120164 \tabularnewline
70 & 99.5 & 99.3644784684219 & 0.135521531578107 \tabularnewline
71 & 99.39 & 99.9636188806179 & -0.573618880617872 \tabularnewline
72 & 99.4 & 99.8149101753992 & -0.414910175399157 \tabularnewline
73 & 99.37 & 100.072056293314 & -0.702056293313518 \tabularnewline
74 & 99.69 & 99.7926311175522 & -0.102631117552193 \tabularnewline
75 & 99.83 & 99.8206187888057 & 0.00938121119429525 \tabularnewline
76 & 99.79 & 99.8987351156373 & -0.108735115637273 \tabularnewline
77 & 99.94 & 100.127876787083 & -0.187876787082516 \tabularnewline
78 & 100.11 & 100.285596974055 & -0.175596974055253 \tabularnewline
79 & 100.21 & 100.116401971425 & 0.0935980285745757 \tabularnewline
80 & 100.15 & 99.8963138344439 & 0.253686165556076 \tabularnewline
81 & 100.21 & 99.8559066705429 & 0.354093329457115 \tabularnewline
82 & 100.13 & 100.119506450923 & 0.0104935490766422 \tabularnewline
83 & 100.2 & 100.384642855549 & -0.184642855548603 \tabularnewline
84 & 100.36 & 100.505652106364 & -0.145652106363769 \tabularnewline
85 & 100.5 & 100.872469303821 & -0.372469303821077 \tabularnewline
86 & 100.66 & 100.933488068788 & -0.273488068787984 \tabularnewline
87 & 100.72 & 100.792283335055 & -0.0722833350545073 \tabularnewline
88 & 100.41 & 100.727612293589 & -0.317612293588539 \tabularnewline
89 & 100.3 & 100.702467431762 & -0.402467431761778 \tabularnewline
90 & 100.38 & 100.603129642718 & -0.223129642717979 \tabularnewline
91 & 100.55 & 100.356844683082 & 0.193155316917597 \tabularnewline
92 & 100.17 & 100.167520974015 & 0.00247902598495386 \tabularnewline
93 & 100.09 & 99.8423733306747 & 0.247626669325342 \tabularnewline
94 & 100.22 & 99.8531851600777 & 0.366814839922299 \tabularnewline
95 & 100.09 & 100.295986618925 & -0.205986618924797 \tabularnewline
96 & 99.98 & 100.325292437049 & -0.345292437049366 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284622&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]88.92[/C][C]86.8194471153846[/C][C]2.10055288461537[/C][/ROW]
[ROW][C]14[/C][C]89.56[/C][C]89.2718932187597[/C][C]0.288106781240259[/C][/ROW]
[ROW][C]15[/C][C]90.21[/C][C]90.2822662344597[/C][C]-0.0722662344596898[/C][/ROW]
[ROW][C]16[/C][C]90.42[/C][C]90.5753628338148[/C][C]-0.155362833814806[/C][/ROW]
[ROW][C]17[/C][C]91.23[/C][C]91.4727002889098[/C][C]-0.242700288909802[/C][/ROW]
[ROW][C]18[/C][C]91.73[/C][C]92.0469880425874[/C][C]-0.316988042587369[/C][/ROW]
[ROW][C]19[/C][C]92.21[/C][C]91.2780886501198[/C][C]0.931911349880224[/C][/ROW]
[ROW][C]20[/C][C]91.65[/C][C]92.2052948063815[/C][C]-0.555294806381482[/C][/ROW]
[ROW][C]21[/C][C]91.8[/C][C]92.0304151685777[/C][C]-0.230415168577665[/C][/ROW]
[ROW][C]22[/C][C]91.63[/C][C]92.4674260893825[/C][C]-0.83742608938249[/C][/ROW]
[ROW][C]23[/C][C]91.09[/C][C]92.6793774214137[/C][C]-1.58937742141373[/C][/ROW]
[ROW][C]24[/C][C]90.89[/C][C]91.5278333919221[/C][C]-0.637833391922086[/C][/ROW]
[ROW][C]25[/C][C]90.98[/C][C]91.5850549144819[/C][C]-0.60505491448194[/C][/ROW]
[ROW][C]26[/C][C]91.29[/C][C]91.2206388988322[/C][C]0.0693611011678286[/C][/ROW]
[ROW][C]27[/C][C]90.77[/C][C]91.7006408594659[/C][C]-0.930640859465925[/C][/ROW]
[ROW][C]28[/C][C]90.96[/C][C]90.9302774307447[/C][C]0.0297225692552701[/C][/ROW]
[ROW][C]29[/C][C]90.89[/C][C]91.6321792082949[/C][C]-0.742179208294871[/C][/ROW]
[ROW][C]30[/C][C]90.72[/C][C]91.4178917835664[/C][C]-0.697891783566405[/C][/ROW]
[ROW][C]31[/C][C]90.66[/C][C]90.1693589050247[/C][C]0.490641094975345[/C][/ROW]
[ROW][C]32[/C][C]90.94[/C][C]90.0468411262693[/C][C]0.893158873730656[/C][/ROW]
[ROW][C]33[/C][C]90.7[/C][C]90.7957802704695[/C][C]-0.0957802704694615[/C][/ROW]
[ROW][C]34[/C][C]90.74[/C][C]90.9203829285382[/C][C]-0.180382928538179[/C][/ROW]
[ROW][C]35[/C][C]90.98[/C][C]91.2669708873036[/C][C]-0.286970887303625[/C][/ROW]
[ROW][C]36[/C][C]91.13[/C][C]91.1731126414131[/C][C]-0.0431126414130745[/C][/ROW]
[ROW][C]37[/C][C]91.54[/C][C]91.5826058889106[/C][C]-0.0426058889105576[/C][/ROW]
[ROW][C]38[/C][C]91.93[/C][C]91.6970239133328[/C][C]0.23297608666725[/C][/ROW]
[ROW][C]39[/C][C]92.27[/C][C]92.0392660483192[/C][C]0.23073395168079[/C][/ROW]
[ROW][C]40[/C][C]92.59[/C][C]92.3799367547862[/C][C]0.210063245213803[/C][/ROW]
[ROW][C]41[/C][C]92.96[/C][C]93.0892603257314[/C][C]-0.12926032573138[/C][/ROW]
[ROW][C]42[/C][C]92.95[/C][C]93.4251420853023[/C][C]-0.475142085302267[/C][/ROW]
[ROW][C]43[/C][C]92.99[/C][C]92.6268680786192[/C][C]0.363131921380798[/C][/ROW]
[ROW][C]44[/C][C]93.05[/C][C]92.517584316849[/C][C]0.532415683151029[/C][/ROW]
[ROW][C]45[/C][C]93.34[/C][C]92.814429837604[/C][C]0.525570162396008[/C][/ROW]
[ROW][C]46[/C][C]93.47[/C][C]93.4970152671128[/C][C]-0.0270152671128017[/C][/ROW]
[ROW][C]47[/C][C]93.59[/C][C]94.0239511610768[/C][C]-0.433951161076806[/C][/ROW]
[ROW][C]48[/C][C]93.96[/C][C]93.9169070253271[/C][C]0.0430929746729305[/C][/ROW]
[ROW][C]49[/C][C]94.49[/C][C]94.4667413159557[/C][C]0.0232586840442792[/C][/ROW]
[ROW][C]50[/C][C]95.04[/C][C]94.7585927011935[/C][C]0.281407298806471[/C][/ROW]
[ROW][C]51[/C][C]95.52[/C][C]95.2173969061809[/C][C]0.302603093819101[/C][/ROW]
[ROW][C]52[/C][C]95.75[/C][C]95.695407918199[/C][C]0.054592081801033[/C][/ROW]
[ROW][C]53[/C][C]96.07[/C][C]96.2878612760834[/C][C]-0.217861276083397[/C][/ROW]
[ROW][C]54[/C][C]96.37[/C][C]96.5545932383042[/C][C]-0.18459323830416[/C][/ROW]
[ROW][C]55[/C][C]96.48[/C][C]96.230319632253[/C][C]0.249680367747004[/C][/ROW]
[ROW][C]56[/C][C]96.4[/C][C]96.1358488135762[/C][C]0.264151186423788[/C][/ROW]
[ROW][C]57[/C][C]96.66[/C][C]96.2707677799409[/C][C]0.389232220059142[/C][/ROW]
[ROW][C]58[/C][C]96.81[/C][C]96.7926001139909[/C][C]0.0173998860090592[/C][/ROW]
[ROW][C]59[/C][C]97.19[/C][C]97.3362367263451[/C][C]-0.146236726345123[/C][/ROW]
[ROW][C]60[/C][C]97.23[/C][C]97.623526779215[/C][C]-0.393526779215037[/C][/ROW]
[ROW][C]61[/C][C]97.94[/C][C]97.8546956871284[/C][C]0.0853043128715569[/C][/ROW]
[ROW][C]62[/C][C]98.52[/C][C]98.2911503265471[/C][C]0.228849673452885[/C][/ROW]
[ROW][C]63[/C][C]98.73[/C][C]98.7544620466875[/C][C]-0.0244620466875034[/C][/ROW]
[ROW][C]64[/C][C]98.8[/C][C]98.9413528009161[/C][C]-0.141352800916067[/C][/ROW]
[ROW][C]65[/C][C]98.77[/C][C]99.3326801928375[/C][C]-0.562680192837504[/C][/ROW]
[ROW][C]66[/C][C]98.54[/C][C]99.3076836244216[/C][C]-0.767683624421551[/C][/ROW]
[ROW][C]67[/C][C]98.72[/C][C]98.5287286837666[/C][C]0.191271316233426[/C][/ROW]
[ROW][C]68[/C][C]99.15[/C][C]98.3309046132616[/C][C]0.819095386738425[/C][/ROW]
[ROW][C]69[/C][C]99.32[/C][C]98.9230955918798[/C][C]0.396904408120164[/C][/ROW]
[ROW][C]70[/C][C]99.5[/C][C]99.3644784684219[/C][C]0.135521531578107[/C][/ROW]
[ROW][C]71[/C][C]99.39[/C][C]99.9636188806179[/C][C]-0.573618880617872[/C][/ROW]
[ROW][C]72[/C][C]99.4[/C][C]99.8149101753992[/C][C]-0.414910175399157[/C][/ROW]
[ROW][C]73[/C][C]99.37[/C][C]100.072056293314[/C][C]-0.702056293313518[/C][/ROW]
[ROW][C]74[/C][C]99.69[/C][C]99.7926311175522[/C][C]-0.102631117552193[/C][/ROW]
[ROW][C]75[/C][C]99.83[/C][C]99.8206187888057[/C][C]0.00938121119429525[/C][/ROW]
[ROW][C]76[/C][C]99.79[/C][C]99.8987351156373[/C][C]-0.108735115637273[/C][/ROW]
[ROW][C]77[/C][C]99.94[/C][C]100.127876787083[/C][C]-0.187876787082516[/C][/ROW]
[ROW][C]78[/C][C]100.11[/C][C]100.285596974055[/C][C]-0.175596974055253[/C][/ROW]
[ROW][C]79[/C][C]100.21[/C][C]100.116401971425[/C][C]0.0935980285745757[/C][/ROW]
[ROW][C]80[/C][C]100.15[/C][C]99.8963138344439[/C][C]0.253686165556076[/C][/ROW]
[ROW][C]81[/C][C]100.21[/C][C]99.8559066705429[/C][C]0.354093329457115[/C][/ROW]
[ROW][C]82[/C][C]100.13[/C][C]100.119506450923[/C][C]0.0104935490766422[/C][/ROW]
[ROW][C]83[/C][C]100.2[/C][C]100.384642855549[/C][C]-0.184642855548603[/C][/ROW]
[ROW][C]84[/C][C]100.36[/C][C]100.505652106364[/C][C]-0.145652106363769[/C][/ROW]
[ROW][C]85[/C][C]100.5[/C][C]100.872469303821[/C][C]-0.372469303821077[/C][/ROW]
[ROW][C]86[/C][C]100.66[/C][C]100.933488068788[/C][C]-0.273488068787984[/C][/ROW]
[ROW][C]87[/C][C]100.72[/C][C]100.792283335055[/C][C]-0.0722833350545073[/C][/ROW]
[ROW][C]88[/C][C]100.41[/C][C]100.727612293589[/C][C]-0.317612293588539[/C][/ROW]
[ROW][C]89[/C][C]100.3[/C][C]100.702467431762[/C][C]-0.402467431761778[/C][/ROW]
[ROW][C]90[/C][C]100.38[/C][C]100.603129642718[/C][C]-0.223129642717979[/C][/ROW]
[ROW][C]91[/C][C]100.55[/C][C]100.356844683082[/C][C]0.193155316917597[/C][/ROW]
[ROW][C]92[/C][C]100.17[/C][C]100.167520974015[/C][C]0.00247902598495386[/C][/ROW]
[ROW][C]93[/C][C]100.09[/C][C]99.8423733306747[/C][C]0.247626669325342[/C][/ROW]
[ROW][C]94[/C][C]100.22[/C][C]99.8531851600777[/C][C]0.366814839922299[/C][/ROW]
[ROW][C]95[/C][C]100.09[/C][C]100.295986618925[/C][C]-0.205986618924797[/C][/ROW]
[ROW][C]96[/C][C]99.98[/C][C]100.325292437049[/C][C]-0.345292437049366[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284622&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284622&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	88.92	86.8194471153846	2.10055288461537
14	89.56	89.2718932187597	0.288106781240259
15	90.21	90.2822662344597	-0.0722662344596898
16	90.42	90.5753628338148	-0.155362833814806
17	91.23	91.4727002889098	-0.242700288909802
18	91.73	92.0469880425874	-0.316988042587369
19	92.21	91.2780886501198	0.931911349880224
20	91.65	92.2052948063815	-0.555294806381482
21	91.8	92.0304151685777	-0.230415168577665
22	91.63	92.4674260893825	-0.83742608938249
23	91.09	92.6793774214137	-1.58937742141373
24	90.89	91.5278333919221	-0.637833391922086
25	90.98	91.5850549144819	-0.60505491448194
26	91.29	91.2206388988322	0.0693611011678286
27	90.77	91.7006408594659	-0.930640859465925
28	90.96	90.9302774307447	0.0297225692552701
29	90.89	91.6321792082949	-0.742179208294871
30	90.72	91.4178917835664	-0.697891783566405
31	90.66	90.1693589050247	0.490641094975345
32	90.94	90.0468411262693	0.893158873730656
33	90.7	90.7957802704695	-0.0957802704694615
34	90.74	90.9203829285382	-0.180382928538179
35	90.98	91.2669708873036	-0.286970887303625
36	91.13	91.1731126414131	-0.0431126414130745
37	91.54	91.5826058889106	-0.0426058889105576
38	91.93	91.6970239133328	0.23297608666725
39	92.27	92.0392660483192	0.23073395168079
40	92.59	92.3799367547862	0.210063245213803
41	92.96	93.0892603257314	-0.12926032573138
42	92.95	93.4251420853023	-0.475142085302267
43	92.99	92.6268680786192	0.363131921380798
44	93.05	92.517584316849	0.532415683151029
45	93.34	92.814429837604	0.525570162396008
46	93.47	93.4970152671128	-0.0270152671128017
47	93.59	94.0239511610768	-0.433951161076806
48	93.96	93.9169070253271	0.0430929746729305
49	94.49	94.4667413159557	0.0232586840442792
50	95.04	94.7585927011935	0.281407298806471
51	95.52	95.2173969061809	0.302603093819101
52	95.75	95.695407918199	0.054592081801033
53	96.07	96.2878612760834	-0.217861276083397
54	96.37	96.5545932383042	-0.18459323830416
55	96.48	96.230319632253	0.249680367747004
56	96.4	96.1358488135762	0.264151186423788
57	96.66	96.2707677799409	0.389232220059142
58	96.81	96.7926001139909	0.0173998860090592
59	97.19	97.3362367263451	-0.146236726345123
60	97.23	97.623526779215	-0.393526779215037
61	97.94	97.8546956871284	0.0853043128715569
62	98.52	98.2911503265471	0.228849673452885
63	98.73	98.7544620466875	-0.0244620466875034
64	98.8	98.9413528009161	-0.141352800916067
65	98.77	99.3326801928375	-0.562680192837504
66	98.54	99.3076836244216	-0.767683624421551
67	98.72	98.5287286837666	0.191271316233426
68	99.15	98.3309046132616	0.819095386738425
69	99.32	98.9230955918798	0.396904408120164
70	99.5	99.3644784684219	0.135521531578107
71	99.39	99.9636188806179	-0.573618880617872
72	99.4	99.8149101753992	-0.414910175399157
73	99.37	100.072056293314	-0.702056293313518
74	99.69	99.7926311175522	-0.102631117552193
75	99.83	99.8206187888057	0.00938121119429525
76	99.79	99.8987351156373	-0.108735115637273
77	99.94	100.127876787083	-0.187876787082516
78	100.11	100.285596974055	-0.175596974055253
79	100.21	100.116401971425	0.0935980285745757
80	100.15	99.8963138344439	0.253686165556076
81	100.21	99.8559066705429	0.354093329457115
82	100.13	100.119506450923	0.0104935490766422
83	100.2	100.384642855549	-0.184642855548603
84	100.36	100.505652106364	-0.145652106363769
85	100.5	100.872469303821	-0.372469303821077
86	100.66	100.933488068788	-0.273488068787984
87	100.72	100.792283335055	-0.0722833350545073
88	100.41	100.727612293589	-0.317612293588539
89	100.3	100.702467431762	-0.402467431761778
90	100.38	100.603129642718	-0.223129642717979
91	100.55	100.356844683082	0.193155316917597
92	100.17	100.167520974015	0.00247902598495386
93	100.09	99.8423733306747	0.247626669325342
94	100.22	99.8531851600777	0.366814839922299
95	100.09	100.295986618925	-0.205986618924797
96	99.98	100.325292437049	-0.345292437049366

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	100.392940609016	99.4587457392344	101.327135478797
98	100.707854266824	99.4584253216266	101.957283212021
99	100.776108742161	99.2405284792366	102.311689005084
100	100.68056546406	98.8718447382684	102.489286189853
101	100.8760900421	98.8001774972156	102.952002586985
102	101.141603917076	98.8007105237299	103.482497310422
103	101.170558933231	98.5646951486596	103.776422717802
104	100.792954194048	97.9207435657993	103.665164822297
105	100.514006542623	97.3731573243865	103.65485576086
106	100.330539080084	96.9181360756622	103.742942084505
107	100.332376503265	96.645070752922	104.019682253608
108	100.48243293367	96.5165697801676	104.448296087173

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 100.392940609016 & 99.4587457392344 & 101.327135478797 \tabularnewline
98 & 100.707854266824 & 99.4584253216266 & 101.957283212021 \tabularnewline
99 & 100.776108742161 & 99.2405284792366 & 102.311689005084 \tabularnewline
100 & 100.68056546406 & 98.8718447382684 & 102.489286189853 \tabularnewline
101 & 100.8760900421 & 98.8001774972156 & 102.952002586985 \tabularnewline
102 & 101.141603917076 & 98.8007105237299 & 103.482497310422 \tabularnewline
103 & 101.170558933231 & 98.5646951486596 & 103.776422717802 \tabularnewline
104 & 100.792954194048 & 97.9207435657993 & 103.665164822297 \tabularnewline
105 & 100.514006542623 & 97.3731573243865 & 103.65485576086 \tabularnewline
106 & 100.330539080084 & 96.9181360756622 & 103.742942084505 \tabularnewline
107 & 100.332376503265 & 96.645070752922 & 104.019682253608 \tabularnewline
108 & 100.48243293367 & 96.5165697801676 & 104.448296087173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284622&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]97[/C][C]100.392940609016[/C][C]99.4587457392344[/C][C]101.327135478797[/C][/ROW]
[ROW][C]98[/C][C]100.707854266824[/C][C]99.4584253216266[/C][C]101.957283212021[/C][/ROW]
[ROW][C]99[/C][C]100.776108742161[/C][C]99.2405284792366[/C][C]102.311689005084[/C][/ROW]
[ROW][C]100[/C][C]100.68056546406[/C][C]98.8718447382684[/C][C]102.489286189853[/C][/ROW]
[ROW][C]101[/C][C]100.8760900421[/C][C]98.8001774972156[/C][C]102.952002586985[/C][/ROW]
[ROW][C]102[/C][C]101.141603917076[/C][C]98.8007105237299[/C][C]103.482497310422[/C][/ROW]
[ROW][C]103[/C][C]101.170558933231[/C][C]98.5646951486596[/C][C]103.776422717802[/C][/ROW]
[ROW][C]104[/C][C]100.792954194048[/C][C]97.9207435657993[/C][C]103.665164822297[/C][/ROW]
[ROW][C]105[/C][C]100.514006542623[/C][C]97.3731573243865[/C][C]103.65485576086[/C][/ROW]
[ROW][C]106[/C][C]100.330539080084[/C][C]96.9181360756622[/C][C]103.742942084505[/C][/ROW]
[ROW][C]107[/C][C]100.332376503265[/C][C]96.645070752922[/C][C]104.019682253608[/C][/ROW]
[ROW][C]108[/C][C]100.48243293367[/C][C]96.5165697801676[/C][C]104.448296087173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284622&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284622&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
97	100.392940609016	99.4587457392344	101.327135478797
98	100.707854266824	99.4584253216266	101.957283212021
99	100.776108742161	99.2405284792366	102.311689005084
100	100.68056546406	98.8718447382684	102.489286189853
101	100.8760900421	98.8001774972156	102.952002586985
102	101.141603917076	98.8007105237299	103.482497310422
103	101.170558933231	98.5646951486596	103.776422717802
104	100.792954194048	97.9207435657993	103.665164822297
105	100.514006542623	97.3731573243865	103.65485576086
106	100.330539080084	96.9181360756622	103.742942084505
107	100.332376503265	96.645070752922	104.019682253608
108	100.48243293367	96.5165697801676	104.448296087173

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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