Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 28 Nov 2016 09:59:41 +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/2016/Nov/28/t14803272192llpd2fpe4ps36t.htm/, Retrieved Sat, 04 May 2024 08:43:06 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 08:43:06 +0200

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Dataseries X:

Download CSV

Histogram

Boxplots

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	0.954366946340557
beta	0.0855529102548362
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.954366946340557 \tabularnewline
beta & 0.0855529102548362 \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]0.954366946340557[/C][/ROW]
[ROW][C]beta[/C][C]0.0855529102548362[/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	0.954366946340557
beta	0.0855529102548362
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	99.88	99.82	0.0600000000000023
4	99.74	99.9021609489631	-0.162160948963063
5	100.15	99.7590585732741	0.390941426725888
6	100.27	100.1757387485	0.0942612514996881
7	100.26	100.316973495499	-0.0569734954985108
8	100.36	100.309222977313	0.0507770226874271
9	100.37	100.408451878644	-0.0384518786440253
10	100.54	100.419384113457	0.120615886543064
11	99.8	100.591973516398	-0.791973516398045
12	99.82	99.828954015137	-0.00895401513697891
13	99.82	99.8124913590042	0.00750864099576631
14	99.82	99.8123531897839	0.00764681021608737
15	99.67	99.8129712381115	-0.142971238111485
16	99.78	99.6581709596	0.121829040399987
17	99.44	99.7660345177282	-0.326034517728232
18	99.61	99.4198515496493	0.190148450350691
19	99.71	99.5818219506172	0.128178049382797
20	99.71	99.6951154421036	0.0148845578963517
21	99.77	99.7015006774083	0.0684993225917054
22	99.77	99.7646469642395	0.0053530357604501
23	99.89	99.7679655914543	0.12203440854573
24	99.96	99.8926050356325	0.0673949643675229
25	100.02	99.9706011229853	0.049398877014653
26	100	100.035455701878	-0.0354557018783908
27	100.04	100.016432957447	0.0235670425528838
28	99.99	100.05566379177	-0.0656637917702199
29	99.77	100.004374292842	-0.234374292842006
30	99.77	99.7729366720906	-0.00293667209058412
31	99.93	99.7621356907671	0.167864309232883
32	99.9	99.9280474515349	-0.0280474515349027
33	100.01	99.9046974607105	0.105302539289553
34	100.08	100.017210126734	0.062789873265686
35	100.21	100.094276831686	0.115723168314418
36	100.28	100.231309989684	0.0486900103155676
37	100.48	100.308344401689	0.171655598311176
38	100.72	100.516748591995	0.203251408004874
39	100.74	100.771902026447	-0.0319020264466161
40	100.88	100.800028031338	0.0799719686616811
41	101.03	100.941452500166	0.0885474998338083
42	101.47	101.098290975769	0.371709024230825
43	101.46	101.555719072422	-0.0957190724217014
44	101.46	101.559233889765	-0.0992338897652161
45	101.45	101.551291946677	-0.101291946677335
46	101.74	101.533115489142	0.206884510858117
47	102.41	101.825944342791	0.584055657209262
48	102.54	102.52642035589	0.0135796441103793
49	102.67	102.683561681	-0.0135616809995014
50	102.87	102.81369292662	0.056307073380367
51	102.9	103.0151020109	-0.115102010900117
52	102.88	103.043525981749	-0.163525981749402
53	102.82	103.012384003831	-0.192384003831435
54	102.94	102.937992947038	0.00200705296160208
55	102.97	103.049286163119	-0.0792861631186099
56	103.01	103.076522195208	-0.0665221952078383
57	103.11	103.110508274326	-0.000508274325895286
58	103.21	103.207454357508	0.00254564249219413
59	104.66	103.30752284679	1.35247715321006
60	104.79	104.806349580594	-0.0163495805935696

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 99.88 & 99.82 & 0.0600000000000023 \tabularnewline
4 & 99.74 & 99.9021609489631 & -0.162160948963063 \tabularnewline
5 & 100.15 & 99.7590585732741 & 0.390941426725888 \tabularnewline
6 & 100.27 & 100.1757387485 & 0.0942612514996881 \tabularnewline
7 & 100.26 & 100.316973495499 & -0.0569734954985108 \tabularnewline
8 & 100.36 & 100.309222977313 & 0.0507770226874271 \tabularnewline
9 & 100.37 & 100.408451878644 & -0.0384518786440253 \tabularnewline
10 & 100.54 & 100.419384113457 & 0.120615886543064 \tabularnewline
11 & 99.8 & 100.591973516398 & -0.791973516398045 \tabularnewline
12 & 99.82 & 99.828954015137 & -0.00895401513697891 \tabularnewline
13 & 99.82 & 99.8124913590042 & 0.00750864099576631 \tabularnewline
14 & 99.82 & 99.8123531897839 & 0.00764681021608737 \tabularnewline
15 & 99.67 & 99.8129712381115 & -0.142971238111485 \tabularnewline
16 & 99.78 & 99.6581709596 & 0.121829040399987 \tabularnewline
17 & 99.44 & 99.7660345177282 & -0.326034517728232 \tabularnewline
18 & 99.61 & 99.4198515496493 & 0.190148450350691 \tabularnewline
19 & 99.71 & 99.5818219506172 & 0.128178049382797 \tabularnewline
20 & 99.71 & 99.6951154421036 & 0.0148845578963517 \tabularnewline
21 & 99.77 & 99.7015006774083 & 0.0684993225917054 \tabularnewline
22 & 99.77 & 99.7646469642395 & 0.0053530357604501 \tabularnewline
23 & 99.89 & 99.7679655914543 & 0.12203440854573 \tabularnewline
24 & 99.96 & 99.8926050356325 & 0.0673949643675229 \tabularnewline
25 & 100.02 & 99.9706011229853 & 0.049398877014653 \tabularnewline
26 & 100 & 100.035455701878 & -0.0354557018783908 \tabularnewline
27 & 100.04 & 100.016432957447 & 0.0235670425528838 \tabularnewline
28 & 99.99 & 100.05566379177 & -0.0656637917702199 \tabularnewline
29 & 99.77 & 100.004374292842 & -0.234374292842006 \tabularnewline
30 & 99.77 & 99.7729366720906 & -0.00293667209058412 \tabularnewline
31 & 99.93 & 99.7621356907671 & 0.167864309232883 \tabularnewline
32 & 99.9 & 99.9280474515349 & -0.0280474515349027 \tabularnewline
33 & 100.01 & 99.9046974607105 & 0.105302539289553 \tabularnewline
34 & 100.08 & 100.017210126734 & 0.062789873265686 \tabularnewline
35 & 100.21 & 100.094276831686 & 0.115723168314418 \tabularnewline
36 & 100.28 & 100.231309989684 & 0.0486900103155676 \tabularnewline
37 & 100.48 & 100.308344401689 & 0.171655598311176 \tabularnewline
38 & 100.72 & 100.516748591995 & 0.203251408004874 \tabularnewline
39 & 100.74 & 100.771902026447 & -0.0319020264466161 \tabularnewline
40 & 100.88 & 100.800028031338 & 0.0799719686616811 \tabularnewline
41 & 101.03 & 100.941452500166 & 0.0885474998338083 \tabularnewline
42 & 101.47 & 101.098290975769 & 0.371709024230825 \tabularnewline
43 & 101.46 & 101.555719072422 & -0.0957190724217014 \tabularnewline
44 & 101.46 & 101.559233889765 & -0.0992338897652161 \tabularnewline
45 & 101.45 & 101.551291946677 & -0.101291946677335 \tabularnewline
46 & 101.74 & 101.533115489142 & 0.206884510858117 \tabularnewline
47 & 102.41 & 101.825944342791 & 0.584055657209262 \tabularnewline
48 & 102.54 & 102.52642035589 & 0.0135796441103793 \tabularnewline
49 & 102.67 & 102.683561681 & -0.0135616809995014 \tabularnewline
50 & 102.87 & 102.81369292662 & 0.056307073380367 \tabularnewline
51 & 102.9 & 103.0151020109 & -0.115102010900117 \tabularnewline
52 & 102.88 & 103.043525981749 & -0.163525981749402 \tabularnewline
53 & 102.82 & 103.012384003831 & -0.192384003831435 \tabularnewline
54 & 102.94 & 102.937992947038 & 0.00200705296160208 \tabularnewline
55 & 102.97 & 103.049286163119 & -0.0792861631186099 \tabularnewline
56 & 103.01 & 103.076522195208 & -0.0665221952078383 \tabularnewline
57 & 103.11 & 103.110508274326 & -0.000508274325895286 \tabularnewline
58 & 103.21 & 103.207454357508 & 0.00254564249219413 \tabularnewline
59 & 104.66 & 103.30752284679 & 1.35247715321006 \tabularnewline
60 & 104.79 & 104.806349580594 & -0.0163495805935696 \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]99.88[/C][C]99.82[/C][C]0.0600000000000023[/C][/ROW]
[ROW][C]4[/C][C]99.74[/C][C]99.9021609489631[/C][C]-0.162160948963063[/C][/ROW]
[ROW][C]5[/C][C]100.15[/C][C]99.7590585732741[/C][C]0.390941426725888[/C][/ROW]
[ROW][C]6[/C][C]100.27[/C][C]100.1757387485[/C][C]0.0942612514996881[/C][/ROW]
[ROW][C]7[/C][C]100.26[/C][C]100.316973495499[/C][C]-0.0569734954985108[/C][/ROW]
[ROW][C]8[/C][C]100.36[/C][C]100.309222977313[/C][C]0.0507770226874271[/C][/ROW]
[ROW][C]9[/C][C]100.37[/C][C]100.408451878644[/C][C]-0.0384518786440253[/C][/ROW]
[ROW][C]10[/C][C]100.54[/C][C]100.419384113457[/C][C]0.120615886543064[/C][/ROW]
[ROW][C]11[/C][C]99.8[/C][C]100.591973516398[/C][C]-0.791973516398045[/C][/ROW]
[ROW][C]12[/C][C]99.82[/C][C]99.828954015137[/C][C]-0.00895401513697891[/C][/ROW]
[ROW][C]13[/C][C]99.82[/C][C]99.8124913590042[/C][C]0.00750864099576631[/C][/ROW]
[ROW][C]14[/C][C]99.82[/C][C]99.8123531897839[/C][C]0.00764681021608737[/C][/ROW]
[ROW][C]15[/C][C]99.67[/C][C]99.8129712381115[/C][C]-0.142971238111485[/C][/ROW]
[ROW][C]16[/C][C]99.78[/C][C]99.6581709596[/C][C]0.121829040399987[/C][/ROW]
[ROW][C]17[/C][C]99.44[/C][C]99.7660345177282[/C][C]-0.326034517728232[/C][/ROW]
[ROW][C]18[/C][C]99.61[/C][C]99.4198515496493[/C][C]0.190148450350691[/C][/ROW]
[ROW][C]19[/C][C]99.71[/C][C]99.5818219506172[/C][C]0.128178049382797[/C][/ROW]
[ROW][C]20[/C][C]99.71[/C][C]99.6951154421036[/C][C]0.0148845578963517[/C][/ROW]
[ROW][C]21[/C][C]99.77[/C][C]99.7015006774083[/C][C]0.0684993225917054[/C][/ROW]
[ROW][C]22[/C][C]99.77[/C][C]99.7646469642395[/C][C]0.0053530357604501[/C][/ROW]
[ROW][C]23[/C][C]99.89[/C][C]99.7679655914543[/C][C]0.12203440854573[/C][/ROW]
[ROW][C]24[/C][C]99.96[/C][C]99.8926050356325[/C][C]0.0673949643675229[/C][/ROW]
[ROW][C]25[/C][C]100.02[/C][C]99.9706011229853[/C][C]0.049398877014653[/C][/ROW]
[ROW][C]26[/C][C]100[/C][C]100.035455701878[/C][C]-0.0354557018783908[/C][/ROW]
[ROW][C]27[/C][C]100.04[/C][C]100.016432957447[/C][C]0.0235670425528838[/C][/ROW]
[ROW][C]28[/C][C]99.99[/C][C]100.05566379177[/C][C]-0.0656637917702199[/C][/ROW]
[ROW][C]29[/C][C]99.77[/C][C]100.004374292842[/C][C]-0.234374292842006[/C][/ROW]
[ROW][C]30[/C][C]99.77[/C][C]99.7729366720906[/C][C]-0.00293667209058412[/C][/ROW]
[ROW][C]31[/C][C]99.93[/C][C]99.7621356907671[/C][C]0.167864309232883[/C][/ROW]
[ROW][C]32[/C][C]99.9[/C][C]99.9280474515349[/C][C]-0.0280474515349027[/C][/ROW]
[ROW][C]33[/C][C]100.01[/C][C]99.9046974607105[/C][C]0.105302539289553[/C][/ROW]
[ROW][C]34[/C][C]100.08[/C][C]100.017210126734[/C][C]0.062789873265686[/C][/ROW]
[ROW][C]35[/C][C]100.21[/C][C]100.094276831686[/C][C]0.115723168314418[/C][/ROW]
[ROW][C]36[/C][C]100.28[/C][C]100.231309989684[/C][C]0.0486900103155676[/C][/ROW]
[ROW][C]37[/C][C]100.48[/C][C]100.308344401689[/C][C]0.171655598311176[/C][/ROW]
[ROW][C]38[/C][C]100.72[/C][C]100.516748591995[/C][C]0.203251408004874[/C][/ROW]
[ROW][C]39[/C][C]100.74[/C][C]100.771902026447[/C][C]-0.0319020264466161[/C][/ROW]
[ROW][C]40[/C][C]100.88[/C][C]100.800028031338[/C][C]0.0799719686616811[/C][/ROW]
[ROW][C]41[/C][C]101.03[/C][C]100.941452500166[/C][C]0.0885474998338083[/C][/ROW]
[ROW][C]42[/C][C]101.47[/C][C]101.098290975769[/C][C]0.371709024230825[/C][/ROW]
[ROW][C]43[/C][C]101.46[/C][C]101.555719072422[/C][C]-0.0957190724217014[/C][/ROW]
[ROW][C]44[/C][C]101.46[/C][C]101.559233889765[/C][C]-0.0992338897652161[/C][/ROW]
[ROW][C]45[/C][C]101.45[/C][C]101.551291946677[/C][C]-0.101291946677335[/C][/ROW]
[ROW][C]46[/C][C]101.74[/C][C]101.533115489142[/C][C]0.206884510858117[/C][/ROW]
[ROW][C]47[/C][C]102.41[/C][C]101.825944342791[/C][C]0.584055657209262[/C][/ROW]
[ROW][C]48[/C][C]102.54[/C][C]102.52642035589[/C][C]0.0135796441103793[/C][/ROW]
[ROW][C]49[/C][C]102.67[/C][C]102.683561681[/C][C]-0.0135616809995014[/C][/ROW]
[ROW][C]50[/C][C]102.87[/C][C]102.81369292662[/C][C]0.056307073380367[/C][/ROW]
[ROW][C]51[/C][C]102.9[/C][C]103.0151020109[/C][C]-0.115102010900117[/C][/ROW]
[ROW][C]52[/C][C]102.88[/C][C]103.043525981749[/C][C]-0.163525981749402[/C][/ROW]
[ROW][C]53[/C][C]102.82[/C][C]103.012384003831[/C][C]-0.192384003831435[/C][/ROW]
[ROW][C]54[/C][C]102.94[/C][C]102.937992947038[/C][C]0.00200705296160208[/C][/ROW]
[ROW][C]55[/C][C]102.97[/C][C]103.049286163119[/C][C]-0.0792861631186099[/C][/ROW]
[ROW][C]56[/C][C]103.01[/C][C]103.076522195208[/C][C]-0.0665221952078383[/C][/ROW]
[ROW][C]57[/C][C]103.11[/C][C]103.110508274326[/C][C]-0.000508274325895286[/C][/ROW]
[ROW][C]58[/C][C]103.21[/C][C]103.207454357508[/C][C]0.00254564249219413[/C][/ROW]
[ROW][C]59[/C][C]104.66[/C][C]103.30752284679[/C][C]1.35247715321006[/C][/ROW]
[ROW][C]60[/C][C]104.79[/C][C]104.806349580594[/C][C]-0.0163495805935696[/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	99.88	99.82	0.0600000000000023
4	99.74	99.9021609489631	-0.162160948963063
5	100.15	99.7590585732741	0.390941426725888
6	100.27	100.1757387485	0.0942612514996881
7	100.26	100.316973495499	-0.0569734954985108
8	100.36	100.309222977313	0.0507770226874271
9	100.37	100.408451878644	-0.0384518786440253
10	100.54	100.419384113457	0.120615886543064
11	99.8	100.591973516398	-0.791973516398045
12	99.82	99.828954015137	-0.00895401513697891
13	99.82	99.8124913590042	0.00750864099576631
14	99.82	99.8123531897839	0.00764681021608737
15	99.67	99.8129712381115	-0.142971238111485
16	99.78	99.6581709596	0.121829040399987
17	99.44	99.7660345177282	-0.326034517728232
18	99.61	99.4198515496493	0.190148450350691
19	99.71	99.5818219506172	0.128178049382797
20	99.71	99.6951154421036	0.0148845578963517
21	99.77	99.7015006774083	0.0684993225917054
22	99.77	99.7646469642395	0.0053530357604501
23	99.89	99.7679655914543	0.12203440854573
24	99.96	99.8926050356325	0.0673949643675229
25	100.02	99.9706011229853	0.049398877014653
26	100	100.035455701878	-0.0354557018783908
27	100.04	100.016432957447	0.0235670425528838
28	99.99	100.05566379177	-0.0656637917702199
29	99.77	100.004374292842	-0.234374292842006
30	99.77	99.7729366720906	-0.00293667209058412
31	99.93	99.7621356907671	0.167864309232883
32	99.9	99.9280474515349	-0.0280474515349027
33	100.01	99.9046974607105	0.105302539289553
34	100.08	100.017210126734	0.062789873265686
35	100.21	100.094276831686	0.115723168314418
36	100.28	100.231309989684	0.0486900103155676
37	100.48	100.308344401689	0.171655598311176
38	100.72	100.516748591995	0.203251408004874
39	100.74	100.771902026447	-0.0319020264466161
40	100.88	100.800028031338	0.0799719686616811
41	101.03	100.941452500166	0.0885474998338083
42	101.47	101.098290975769	0.371709024230825
43	101.46	101.555719072422	-0.0957190724217014
44	101.46	101.559233889765	-0.0992338897652161
45	101.45	101.551291946677	-0.101291946677335
46	101.74	101.533115489142	0.206884510858117
47	102.41	101.825944342791	0.584055657209262
48	102.54	102.52642035589	0.0135796441103793
49	102.67	102.683561681	-0.0135616809995014
50	102.87	102.81369292662	0.056307073380367
51	102.9	103.0151020109	-0.115102010900117
52	102.88	103.043525981749	-0.163525981749402
53	102.82	103.012384003831	-0.192384003831435
54	102.94	102.937992947038	0.00200705296160208
55	102.97	103.049286163119	-0.0792861631186099
56	103.01	103.076522195208	-0.0665221952078383
57	103.11	103.110508274326	-0.000508274325895286
58	103.21	103.207454357508	0.00254564249219413
59	104.66	103.30752284679	1.35247715321006
60	104.79	104.806349580594	-0.0163495805935696

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	104.997478399612	104.501463938659	105.493492860565
62	105.204210717936	104.489996608695	105.918424827176
63	105.410943036259	104.506821036373	106.315065036145
64	105.617675354583	104.535402247991	106.699948461174
65	105.824407672906	104.569410623183	107.079404722629
66	106.031139991229	104.605719181565	107.456560800894
67	106.237872309553	104.642561653931	107.833182965175
68	106.444604627876	104.678854717492	108.210354538261
69	106.6513369462	104.713896676121	108.588777216279
70	106.858069264523	104.747215742484	108.968922786563
71	107.064801582847	104.778486543002	109.351116622692
72	107.27153390117	104.807480989577	109.735586812764

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 104.997478399612 & 104.501463938659 & 105.493492860565 \tabularnewline
62 & 105.204210717936 & 104.489996608695 & 105.918424827176 \tabularnewline
63 & 105.410943036259 & 104.506821036373 & 106.315065036145 \tabularnewline
64 & 105.617675354583 & 104.535402247991 & 106.699948461174 \tabularnewline
65 & 105.824407672906 & 104.569410623183 & 107.079404722629 \tabularnewline
66 & 106.031139991229 & 104.605719181565 & 107.456560800894 \tabularnewline
67 & 106.237872309553 & 104.642561653931 & 107.833182965175 \tabularnewline
68 & 106.444604627876 & 104.678854717492 & 108.210354538261 \tabularnewline
69 & 106.6513369462 & 104.713896676121 & 108.588777216279 \tabularnewline
70 & 106.858069264523 & 104.747215742484 & 108.968922786563 \tabularnewline
71 & 107.064801582847 & 104.778486543002 & 109.351116622692 \tabularnewline
72 & 107.27153390117 & 104.807480989577 & 109.735586812764 \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]104.997478399612[/C][C]104.501463938659[/C][C]105.493492860565[/C][/ROW]
[ROW][C]62[/C][C]105.204210717936[/C][C]104.489996608695[/C][C]105.918424827176[/C][/ROW]
[ROW][C]63[/C][C]105.410943036259[/C][C]104.506821036373[/C][C]106.315065036145[/C][/ROW]
[ROW][C]64[/C][C]105.617675354583[/C][C]104.535402247991[/C][C]106.699948461174[/C][/ROW]
[ROW][C]65[/C][C]105.824407672906[/C][C]104.569410623183[/C][C]107.079404722629[/C][/ROW]
[ROW][C]66[/C][C]106.031139991229[/C][C]104.605719181565[/C][C]107.456560800894[/C][/ROW]
[ROW][C]67[/C][C]106.237872309553[/C][C]104.642561653931[/C][C]107.833182965175[/C][/ROW]
[ROW][C]68[/C][C]106.444604627876[/C][C]104.678854717492[/C][C]108.210354538261[/C][/ROW]
[ROW][C]69[/C][C]106.6513369462[/C][C]104.713896676121[/C][C]108.588777216279[/C][/ROW]
[ROW][C]70[/C][C]106.858069264523[/C][C]104.747215742484[/C][C]108.968922786563[/C][/ROW]
[ROW][C]71[/C][C]107.064801582847[/C][C]104.778486543002[/C][C]109.351116622692[/C][/ROW]
[ROW][C]72[/C][C]107.27153390117[/C][C]104.807480989577[/C][C]109.735586812764[/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	104.997478399612	104.501463938659	105.493492860565
62	105.204210717936	104.489996608695	105.918424827176
63	105.410943036259	104.506821036373	106.315065036145
64	105.617675354583	104.535402247991	106.699948461174
65	105.824407672906	104.569410623183	107.079404722629
66	106.031139991229	104.605719181565	107.456560800894
67	106.237872309553	104.642561653931	107.833182965175
68	106.444604627876	104.678854717492	108.210354538261
69	106.6513369462	104.713896676121	108.588777216279
70	106.858069264523	104.747215742484	108.968922786563
71	107.064801582847	104.778486543002	109.351116622692
72	107.27153390117	104.807480989577	109.735586812764

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