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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 08 Jan 2017 13:50:45 +0000

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/2017/Jan/08/t1483885356avbfdm0qyxasl38.htm/, Retrieved Tue, 14 May 2024 21:09:05 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 21:09:05 +0200

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Estimated Impact

Dataseries X:

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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	'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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.897532775402218
beta	0.153079860381313
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.897532775402218 \tabularnewline
beta & 0.153079860381313 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.897532775402218[/C][/ROW]
[ROW][C]beta[/C][C]0.153079860381313[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.897532775402218
beta	0.153079860381313
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	103.55	104.52	-0.969999999999999
4	103.87	104.376120841672	-0.506120841672001
5	104.03	104.579050367701	-0.54905036770073
6	104.02	104.668012905478	-0.648012905478168
7	104.02	104.579120112544	-0.559120112544463
8	102.97	104.493191658702	-1.52319165870188
9	103.18	103.332699707224	-0.152699707223746
10	103.53	103.381289147738	0.148710852262241
11	103.78	103.720836451623	0.0591635483770432
12	103.85	103.988140843244	-0.13814084324423
13	103.85	104.059378327122	-0.209378327122309
14	104.78	104.037910468317	0.742089531683405
15	104.76	104.972374989088	-0.212374989088175
16	104.84	105.020997229493	-0.180997229493329
17	104.85	105.072914069463	-0.222914069462817
18	104.83	105.056582073271	-0.226582073271089
19	104.83	105.005826862575	-0.175826862574567
20	103.71	104.976468527295	-1.26646852729476
21	103.84	103.794218131776	0.0457818682236706
22	104.37	103.796045638561	0.573954361439405
23	104.44	104.350783264776	0.0892167352241131
24	104.4	104.482710845236	-0.0827108452364627
25	99.54	104.448963797492	-4.90896379749162
26	100.42	99.4090334284664	1.01096657153357
27	100.34	99.8213355289208	0.518664471079205
28	100.36	99.8630418447132	0.496958155286833
29	100.37	99.9535451948254	0.416454805174638
30	100.42	100.029012621121	0.390987378878705
31	100.41	100.135341592594	0.274658407406307
32	99.13	100.174997969388	-1.04499796938761
33	99.42	98.886642844151	0.533357155849032
34	99.76	99.0881933504849	0.671806649515091
35	99.92	99.5063091468762	0.413690853123782
36	99.92	99.7495962766378	0.170403723362242
37	100.47	99.7979377154808	0.672062284519214
38	100.44	100.388871609542	0.0511283904576487
39	100.47	100.429521726218	0.0404782737820426
40	100.61	100.466174493833	0.143825506166976
41	100.73	100.615345578962	0.114654421038253
42	100.64	100.754087510625	-0.114087510625012
43	99.99	100.671851100178	-0.681851100178207
44	99.74	99.9863458784908	-0.246345878490771
45	99.49	99.6578743742121	-0.167874374212076
46	99.41	99.3767686529653	0.0332313470347145
47	99.49	99.2807277019315	0.20927229806847
48	99.53	99.3714420725534	0.158557927446637
49	99.91	99.4384235716764	0.471576428323559
50	99.84	99.8511412969542	-0.0111412969541931
51	99.67	99.8290732930353	-0.159073293035306
52	99.39	99.6523757275461	-0.262375727546143
53	99.38	99.3469119402322	0.0330880597678345
54	99.29	99.3111826932118	-0.0211826932118129
55	97.91	99.2238332876294	-1.31383328762939
56	97.62	97.7957745435081	-0.175774543508126
57	97.67	97.3650104211988	0.304989578801212
58	97.64	97.407651652631	0.23234834736904
59	97.63	97.417018311444	0.212981688555985
60	97.66	97.4382652062208	0.221734793779206

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 103.55 & 104.52 & -0.969999999999999 \tabularnewline
4 & 103.87 & 104.376120841672 & -0.506120841672001 \tabularnewline
5 & 104.03 & 104.579050367701 & -0.54905036770073 \tabularnewline
6 & 104.02 & 104.668012905478 & -0.648012905478168 \tabularnewline
7 & 104.02 & 104.579120112544 & -0.559120112544463 \tabularnewline
8 & 102.97 & 104.493191658702 & -1.52319165870188 \tabularnewline
9 & 103.18 & 103.332699707224 & -0.152699707223746 \tabularnewline
10 & 103.53 & 103.381289147738 & 0.148710852262241 \tabularnewline
11 & 103.78 & 103.720836451623 & 0.0591635483770432 \tabularnewline
12 & 103.85 & 103.988140843244 & -0.13814084324423 \tabularnewline
13 & 103.85 & 104.059378327122 & -0.209378327122309 \tabularnewline
14 & 104.78 & 104.037910468317 & 0.742089531683405 \tabularnewline
15 & 104.76 & 104.972374989088 & -0.212374989088175 \tabularnewline
16 & 104.84 & 105.020997229493 & -0.180997229493329 \tabularnewline
17 & 104.85 & 105.072914069463 & -0.222914069462817 \tabularnewline
18 & 104.83 & 105.056582073271 & -0.226582073271089 \tabularnewline
19 & 104.83 & 105.005826862575 & -0.175826862574567 \tabularnewline
20 & 103.71 & 104.976468527295 & -1.26646852729476 \tabularnewline
21 & 103.84 & 103.794218131776 & 0.0457818682236706 \tabularnewline
22 & 104.37 & 103.796045638561 & 0.573954361439405 \tabularnewline
23 & 104.44 & 104.350783264776 & 0.0892167352241131 \tabularnewline
24 & 104.4 & 104.482710845236 & -0.0827108452364627 \tabularnewline
25 & 99.54 & 104.448963797492 & -4.90896379749162 \tabularnewline
26 & 100.42 & 99.4090334284664 & 1.01096657153357 \tabularnewline
27 & 100.34 & 99.8213355289208 & 0.518664471079205 \tabularnewline
28 & 100.36 & 99.8630418447132 & 0.496958155286833 \tabularnewline
29 & 100.37 & 99.9535451948254 & 0.416454805174638 \tabularnewline
30 & 100.42 & 100.029012621121 & 0.390987378878705 \tabularnewline
31 & 100.41 & 100.135341592594 & 0.274658407406307 \tabularnewline
32 & 99.13 & 100.174997969388 & -1.04499796938761 \tabularnewline
33 & 99.42 & 98.886642844151 & 0.533357155849032 \tabularnewline
34 & 99.76 & 99.0881933504849 & 0.671806649515091 \tabularnewline
35 & 99.92 & 99.5063091468762 & 0.413690853123782 \tabularnewline
36 & 99.92 & 99.7495962766378 & 0.170403723362242 \tabularnewline
37 & 100.47 & 99.7979377154808 & 0.672062284519214 \tabularnewline
38 & 100.44 & 100.388871609542 & 0.0511283904576487 \tabularnewline
39 & 100.47 & 100.429521726218 & 0.0404782737820426 \tabularnewline
40 & 100.61 & 100.466174493833 & 0.143825506166976 \tabularnewline
41 & 100.73 & 100.615345578962 & 0.114654421038253 \tabularnewline
42 & 100.64 & 100.754087510625 & -0.114087510625012 \tabularnewline
43 & 99.99 & 100.671851100178 & -0.681851100178207 \tabularnewline
44 & 99.74 & 99.9863458784908 & -0.246345878490771 \tabularnewline
45 & 99.49 & 99.6578743742121 & -0.167874374212076 \tabularnewline
46 & 99.41 & 99.3767686529653 & 0.0332313470347145 \tabularnewline
47 & 99.49 & 99.2807277019315 & 0.20927229806847 \tabularnewline
48 & 99.53 & 99.3714420725534 & 0.158557927446637 \tabularnewline
49 & 99.91 & 99.4384235716764 & 0.471576428323559 \tabularnewline
50 & 99.84 & 99.8511412969542 & -0.0111412969541931 \tabularnewline
51 & 99.67 & 99.8290732930353 & -0.159073293035306 \tabularnewline
52 & 99.39 & 99.6523757275461 & -0.262375727546143 \tabularnewline
53 & 99.38 & 99.3469119402322 & 0.0330880597678345 \tabularnewline
54 & 99.29 & 99.3111826932118 & -0.0211826932118129 \tabularnewline
55 & 97.91 & 99.2238332876294 & -1.31383328762939 \tabularnewline
56 & 97.62 & 97.7957745435081 & -0.175774543508126 \tabularnewline
57 & 97.67 & 97.3650104211988 & 0.304989578801212 \tabularnewline
58 & 97.64 & 97.407651652631 & 0.23234834736904 \tabularnewline
59 & 97.63 & 97.417018311444 & 0.212981688555985 \tabularnewline
60 & 97.66 & 97.4382652062208 & 0.221734793779206 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]103.55[/C][C]104.52[/C][C]-0.969999999999999[/C][/ROW]
[ROW][C]4[/C][C]103.87[/C][C]104.376120841672[/C][C]-0.506120841672001[/C][/ROW]
[ROW][C]5[/C][C]104.03[/C][C]104.579050367701[/C][C]-0.54905036770073[/C][/ROW]
[ROW][C]6[/C][C]104.02[/C][C]104.668012905478[/C][C]-0.648012905478168[/C][/ROW]
[ROW][C]7[/C][C]104.02[/C][C]104.579120112544[/C][C]-0.559120112544463[/C][/ROW]
[ROW][C]8[/C][C]102.97[/C][C]104.493191658702[/C][C]-1.52319165870188[/C][/ROW]
[ROW][C]9[/C][C]103.18[/C][C]103.332699707224[/C][C]-0.152699707223746[/C][/ROW]
[ROW][C]10[/C][C]103.53[/C][C]103.381289147738[/C][C]0.148710852262241[/C][/ROW]
[ROW][C]11[/C][C]103.78[/C][C]103.720836451623[/C][C]0.0591635483770432[/C][/ROW]
[ROW][C]12[/C][C]103.85[/C][C]103.988140843244[/C][C]-0.13814084324423[/C][/ROW]
[ROW][C]13[/C][C]103.85[/C][C]104.059378327122[/C][C]-0.209378327122309[/C][/ROW]
[ROW][C]14[/C][C]104.78[/C][C]104.037910468317[/C][C]0.742089531683405[/C][/ROW]
[ROW][C]15[/C][C]104.76[/C][C]104.972374989088[/C][C]-0.212374989088175[/C][/ROW]
[ROW][C]16[/C][C]104.84[/C][C]105.020997229493[/C][C]-0.180997229493329[/C][/ROW]
[ROW][C]17[/C][C]104.85[/C][C]105.072914069463[/C][C]-0.222914069462817[/C][/ROW]
[ROW][C]18[/C][C]104.83[/C][C]105.056582073271[/C][C]-0.226582073271089[/C][/ROW]
[ROW][C]19[/C][C]104.83[/C][C]105.005826862575[/C][C]-0.175826862574567[/C][/ROW]
[ROW][C]20[/C][C]103.71[/C][C]104.976468527295[/C][C]-1.26646852729476[/C][/ROW]
[ROW][C]21[/C][C]103.84[/C][C]103.794218131776[/C][C]0.0457818682236706[/C][/ROW]
[ROW][C]22[/C][C]104.37[/C][C]103.796045638561[/C][C]0.573954361439405[/C][/ROW]
[ROW][C]23[/C][C]104.44[/C][C]104.350783264776[/C][C]0.0892167352241131[/C][/ROW]
[ROW][C]24[/C][C]104.4[/C][C]104.482710845236[/C][C]-0.0827108452364627[/C][/ROW]
[ROW][C]25[/C][C]99.54[/C][C]104.448963797492[/C][C]-4.90896379749162[/C][/ROW]
[ROW][C]26[/C][C]100.42[/C][C]99.4090334284664[/C][C]1.01096657153357[/C][/ROW]
[ROW][C]27[/C][C]100.34[/C][C]99.8213355289208[/C][C]0.518664471079205[/C][/ROW]
[ROW][C]28[/C][C]100.36[/C][C]99.8630418447132[/C][C]0.496958155286833[/C][/ROW]
[ROW][C]29[/C][C]100.37[/C][C]99.9535451948254[/C][C]0.416454805174638[/C][/ROW]
[ROW][C]30[/C][C]100.42[/C][C]100.029012621121[/C][C]0.390987378878705[/C][/ROW]
[ROW][C]31[/C][C]100.41[/C][C]100.135341592594[/C][C]0.274658407406307[/C][/ROW]
[ROW][C]32[/C][C]99.13[/C][C]100.174997969388[/C][C]-1.04499796938761[/C][/ROW]
[ROW][C]33[/C][C]99.42[/C][C]98.886642844151[/C][C]0.533357155849032[/C][/ROW]
[ROW][C]34[/C][C]99.76[/C][C]99.0881933504849[/C][C]0.671806649515091[/C][/ROW]
[ROW][C]35[/C][C]99.92[/C][C]99.5063091468762[/C][C]0.413690853123782[/C][/ROW]
[ROW][C]36[/C][C]99.92[/C][C]99.7495962766378[/C][C]0.170403723362242[/C][/ROW]
[ROW][C]37[/C][C]100.47[/C][C]99.7979377154808[/C][C]0.672062284519214[/C][/ROW]
[ROW][C]38[/C][C]100.44[/C][C]100.388871609542[/C][C]0.0511283904576487[/C][/ROW]
[ROW][C]39[/C][C]100.47[/C][C]100.429521726218[/C][C]0.0404782737820426[/C][/ROW]
[ROW][C]40[/C][C]100.61[/C][C]100.466174493833[/C][C]0.143825506166976[/C][/ROW]
[ROW][C]41[/C][C]100.73[/C][C]100.615345578962[/C][C]0.114654421038253[/C][/ROW]
[ROW][C]42[/C][C]100.64[/C][C]100.754087510625[/C][C]-0.114087510625012[/C][/ROW]
[ROW][C]43[/C][C]99.99[/C][C]100.671851100178[/C][C]-0.681851100178207[/C][/ROW]
[ROW][C]44[/C][C]99.74[/C][C]99.9863458784908[/C][C]-0.246345878490771[/C][/ROW]
[ROW][C]45[/C][C]99.49[/C][C]99.6578743742121[/C][C]-0.167874374212076[/C][/ROW]
[ROW][C]46[/C][C]99.41[/C][C]99.3767686529653[/C][C]0.0332313470347145[/C][/ROW]
[ROW][C]47[/C][C]99.49[/C][C]99.2807277019315[/C][C]0.20927229806847[/C][/ROW]
[ROW][C]48[/C][C]99.53[/C][C]99.3714420725534[/C][C]0.158557927446637[/C][/ROW]
[ROW][C]49[/C][C]99.91[/C][C]99.4384235716764[/C][C]0.471576428323559[/C][/ROW]
[ROW][C]50[/C][C]99.84[/C][C]99.8511412969542[/C][C]-0.0111412969541931[/C][/ROW]
[ROW][C]51[/C][C]99.67[/C][C]99.8290732930353[/C][C]-0.159073293035306[/C][/ROW]
[ROW][C]52[/C][C]99.39[/C][C]99.6523757275461[/C][C]-0.262375727546143[/C][/ROW]
[ROW][C]53[/C][C]99.38[/C][C]99.3469119402322[/C][C]0.0330880597678345[/C][/ROW]
[ROW][C]54[/C][C]99.29[/C][C]99.3111826932118[/C][C]-0.0211826932118129[/C][/ROW]
[ROW][C]55[/C][C]97.91[/C][C]99.2238332876294[/C][C]-1.31383328762939[/C][/ROW]
[ROW][C]56[/C][C]97.62[/C][C]97.7957745435081[/C][C]-0.175774543508126[/C][/ROW]
[ROW][C]57[/C][C]97.67[/C][C]97.3650104211988[/C][C]0.304989578801212[/C][/ROW]
[ROW][C]58[/C][C]97.64[/C][C]97.407651652631[/C][C]0.23234834736904[/C][/ROW]
[ROW][C]59[/C][C]97.63[/C][C]97.417018311444[/C][C]0.212981688555985[/C][/ROW]
[ROW][C]60[/C][C]97.66[/C][C]97.4382652062208[/C][C]0.221734793779206[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	103.55	104.52	-0.969999999999999
4	103.87	104.376120841672	-0.506120841672001
5	104.03	104.579050367701	-0.54905036770073
6	104.02	104.668012905478	-0.648012905478168
7	104.02	104.579120112544	-0.559120112544463
8	102.97	104.493191658702	-1.52319165870188
9	103.18	103.332699707224	-0.152699707223746
10	103.53	103.381289147738	0.148710852262241
11	103.78	103.720836451623	0.0591635483770432
12	103.85	103.988140843244	-0.13814084324423
13	103.85	104.059378327122	-0.209378327122309
14	104.78	104.037910468317	0.742089531683405
15	104.76	104.972374989088	-0.212374989088175
16	104.84	105.020997229493	-0.180997229493329
17	104.85	105.072914069463	-0.222914069462817
18	104.83	105.056582073271	-0.226582073271089
19	104.83	105.005826862575	-0.175826862574567
20	103.71	104.976468527295	-1.26646852729476
21	103.84	103.794218131776	0.0457818682236706
22	104.37	103.796045638561	0.573954361439405
23	104.44	104.350783264776	0.0892167352241131
24	104.4	104.482710845236	-0.0827108452364627
25	99.54	104.448963797492	-4.90896379749162
26	100.42	99.4090334284664	1.01096657153357
27	100.34	99.8213355289208	0.518664471079205
28	100.36	99.8630418447132	0.496958155286833
29	100.37	99.9535451948254	0.416454805174638
30	100.42	100.029012621121	0.390987378878705
31	100.41	100.135341592594	0.274658407406307
32	99.13	100.174997969388	-1.04499796938761
33	99.42	98.886642844151	0.533357155849032
34	99.76	99.0881933504849	0.671806649515091
35	99.92	99.5063091468762	0.413690853123782
36	99.92	99.7495962766378	0.170403723362242
37	100.47	99.7979377154808	0.672062284519214
38	100.44	100.388871609542	0.0511283904576487
39	100.47	100.429521726218	0.0404782737820426
40	100.61	100.466174493833	0.143825506166976
41	100.73	100.615345578962	0.114654421038253
42	100.64	100.754087510625	-0.114087510625012
43	99.99	100.671851100178	-0.681851100178207
44	99.74	99.9863458784908	-0.246345878490771
45	99.49	99.6578743742121	-0.167874374212076
46	99.41	99.3767686529653	0.0332313470347145
47	99.49	99.2807277019315	0.20927229806847
48	99.53	99.3714420725534	0.158557927446637
49	99.91	99.4384235716764	0.471576428323559
50	99.84	99.8511412969542	-0.0111412969541931
51	99.67	99.8290732930353	-0.159073293035306
52	99.39	99.6523757275461	-0.262375727546143
53	99.38	99.3469119402322	0.0330880597678345
54	99.29	99.3111826932118	-0.0211826932118129
55	97.91	99.2238332876294	-1.31383328762939
56	97.62	97.7957745435081	-0.175774543508126
57	97.67	97.3650104211988	0.304989578801212
58	97.64	97.407651652631	0.23234834736904
59	97.63	97.417018311444	0.212981688555985
60	97.66	97.4382652062208	0.221734793779206

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	97.4978333726396	95.8981502082864	99.0975165369929
62	97.3583872941945	95.0562471162554	99.6605274721337
63	97.2189412157495	94.2496385033851	100.188243928114
64	97.0794951373044	93.4454441431836	100.713546131425
65	96.9400490588593	92.6313176568379	101.248780460881
66	96.8006029804143	91.8016140422812	101.799591918547
67	96.6611569019692	90.9535206346919	102.368793169247
68	96.5217108235241	90.0856061655894	102.957815481459
69	96.3822647450791	89.197176197687	103.567353292471
70	96.242818666634	88.2879530258642	104.197684307404
71	96.1033725881889	87.3579037179892	104.848841458389
72	95.9639265097439	86.4071422477707	105.520710771717

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 97.4978333726396 & 95.8981502082864 & 99.0975165369929 \tabularnewline
62 & 97.3583872941945 & 95.0562471162554 & 99.6605274721337 \tabularnewline
63 & 97.2189412157495 & 94.2496385033851 & 100.188243928114 \tabularnewline
64 & 97.0794951373044 & 93.4454441431836 & 100.713546131425 \tabularnewline
65 & 96.9400490588593 & 92.6313176568379 & 101.248780460881 \tabularnewline
66 & 96.8006029804143 & 91.8016140422812 & 101.799591918547 \tabularnewline
67 & 96.6611569019692 & 90.9535206346919 & 102.368793169247 \tabularnewline
68 & 96.5217108235241 & 90.0856061655894 & 102.957815481459 \tabularnewline
69 & 96.3822647450791 & 89.197176197687 & 103.567353292471 \tabularnewline
70 & 96.242818666634 & 88.2879530258642 & 104.197684307404 \tabularnewline
71 & 96.1033725881889 & 87.3579037179892 & 104.848841458389 \tabularnewline
72 & 95.9639265097439 & 86.4071422477707 & 105.520710771717 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]61[/C][C]97.4978333726396[/C][C]95.8981502082864[/C][C]99.0975165369929[/C][/ROW]
[ROW][C]62[/C][C]97.3583872941945[/C][C]95.0562471162554[/C][C]99.6605274721337[/C][/ROW]
[ROW][C]63[/C][C]97.2189412157495[/C][C]94.2496385033851[/C][C]100.188243928114[/C][/ROW]
[ROW][C]64[/C][C]97.0794951373044[/C][C]93.4454441431836[/C][C]100.713546131425[/C][/ROW]
[ROW][C]65[/C][C]96.9400490588593[/C][C]92.6313176568379[/C][C]101.248780460881[/C][/ROW]
[ROW][C]66[/C][C]96.8006029804143[/C][C]91.8016140422812[/C][C]101.799591918547[/C][/ROW]
[ROW][C]67[/C][C]96.6611569019692[/C][C]90.9535206346919[/C][C]102.368793169247[/C][/ROW]
[ROW][C]68[/C][C]96.5217108235241[/C][C]90.0856061655894[/C][C]102.957815481459[/C][/ROW]
[ROW][C]69[/C][C]96.3822647450791[/C][C]89.197176197687[/C][C]103.567353292471[/C][/ROW]
[ROW][C]70[/C][C]96.242818666634[/C][C]88.2879530258642[/C][C]104.197684307404[/C][/ROW]
[ROW][C]71[/C][C]96.1033725881889[/C][C]87.3579037179892[/C][C]104.848841458389[/C][/ROW]
[ROW][C]72[/C][C]95.9639265097439[/C][C]86.4071422477707[/C][C]105.520710771717[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61	97.4978333726396	95.8981502082864	99.0975165369929
62	97.3583872941945	95.0562471162554	99.6605274721337
63	97.2189412157495	94.2496385033851	100.188243928114
64	97.0794951373044	93.4454441431836	100.713546131425
65	96.9400490588593	92.6313176568379	101.248780460881
66	96.8006029804143	91.8016140422812	101.799591918547
67	96.6611569019692	90.9535206346919	102.368793169247
68	96.5217108235241	90.0856061655894	102.957815481459
69	96.3822647450791	89.197176197687	103.567353292471
70	96.242818666634	88.2879530258642	104.197684307404
71	96.1033725881889	87.3579037179892	104.848841458389
72	95.9639265097439	86.4071422477707	105.520710771717

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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