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, 11 Jan 2016 20:52:51 +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/Jan/11/t1452545598tosadu0rt2clthy.htm/, Retrieved Tue, 07 May 2024 06:10:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=289708, Retrieved Tue, 07 May 2024 06:10:12 +0000

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

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

-     [Exponential Smoothing] [] [2015-11-23 19:05:27] [a642a7d7b5f7c65c232df2d499025a08]
- R PD    [Exponential Smoothing] [] [2016-01-11 20:52:51] [c6ba03d4d421ca9ab835e2907c34aa87] [Current]

Feedback Forum

Post a new message

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	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289708&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289708&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289708&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	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.113082752835806
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.113082752835806 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289708&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]0.113082752835806[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289708&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289708&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	0.113082752835806
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	99.1	99	0.100000000000009
4	99.1	99.0113082752836	0.0886917247164263
5	99.1	99.0213377796683	0.0786622203317364
6	99.1	99.0302331200875	0.06976687991245
7	99.9	99.0381225509248	0.861877449075195
8	100	99.9355860254733	0.0644139745266585
9	100	100.042870135034	-0.0428701350339082
10	101.3	100.03802226215	1.26197773785016
11	102	101.480730178763	0.519269821236563
12	102	102.239450639613	-0.239450639613423
13	102.4	102.212372902118	0.18762709788237
14	103	102.633590290853	0.36640970914722
15	103	103.275024909429	-0.275024909428907
16	103.6	103.243924335572	0.356075664427721
17	103.6	103.884190351924	-0.284190351923598
18	103.6	103.852053324599	-0.252053324598691
19	103.6	103.823550440792	-0.223550440791655
20	103.6	103.798270741549	-0.19827074154928
21	103.9	103.775849740288	0.124150259711925
22	104	104.089888993422	-0.0898889934215958
23	104	104.179724098596	-0.179724098595841
24	104	104.159400402776	-0.159400402775688
25	104.9	104.141374966427	0.758625033573324
26	105.1	105.127162373593	-0.0271623735933133
27	105.2	105.324090777614	-0.124090777613816
28	105.5	105.41005825088	0.0899417491202854
29	105.7	105.720229111465	-0.020229111465099
30	105.7	105.917941547853	-0.217941547853201
31	105.7	105.893296117665	-0.193296117664673
32	105.7	105.871437660567	-0.171437660566681
33	105.7	105.85205101797	-0.152051017970066
34	105.8	105.834856670287	-0.0348566702865298
35	105.8	105.930914982056	-0.130914982055828
36	105.8	105.916110755497	-0.116110755497502
37	106.6	105.902980631632	0.69701936836799
38	107	106.781801500587	0.218198499413077
39	107.2	107.206475987565	-0.00647598756519585
40	107.3	107.405743665064	-0.105743665064011
41	107.3	107.493785880324	-0.193785880323617
42	107.3	107.471872039516	-0.171872039515918
43	107.4	107.452436276152	-0.052436276151937
44	107.4	107.546506637696	-0.146506637696234
45	107.4	107.529939263797	-0.129939263796814
46	107.4	107.515245374145	-0.115245374145218
47	107.5	107.502213109985	-0.00221310998529134
48	107.5	107.601962845416	-0.101962845415812
49	105	107.590432606169	-2.59043260616923
50	105.2	104.797499356028	0.402500643972019
51	105.2	105.043015236867	0.15698476313348
52	105.3	105.060767506035	0.239232493965062
53	105.3	105.18782057502	0.112179424979729
54	105.3	105.200506133209	0.0994938667914766
55	105.3	105.211757173556	0.0882428264444144
56	105.3	105.221735915288	0.0782640847120746
57	105.3	105.230586233435	0.0694137665646508
58	105.3	105.238435733243	0.0615642667568181
59	106.1	105.245397590004	0.854602409995636
60	106.1	106.142038383107	-0.042038383106771

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 99.1 & 99 & 0.100000000000009 \tabularnewline
4 & 99.1 & 99.0113082752836 & 0.0886917247164263 \tabularnewline
5 & 99.1 & 99.0213377796683 & 0.0786622203317364 \tabularnewline
6 & 99.1 & 99.0302331200875 & 0.06976687991245 \tabularnewline
7 & 99.9 & 99.0381225509248 & 0.861877449075195 \tabularnewline
8 & 100 & 99.9355860254733 & 0.0644139745266585 \tabularnewline
9 & 100 & 100.042870135034 & -0.0428701350339082 \tabularnewline
10 & 101.3 & 100.03802226215 & 1.26197773785016 \tabularnewline
11 & 102 & 101.480730178763 & 0.519269821236563 \tabularnewline
12 & 102 & 102.239450639613 & -0.239450639613423 \tabularnewline
13 & 102.4 & 102.212372902118 & 0.18762709788237 \tabularnewline
14 & 103 & 102.633590290853 & 0.36640970914722 \tabularnewline
15 & 103 & 103.275024909429 & -0.275024909428907 \tabularnewline
16 & 103.6 & 103.243924335572 & 0.356075664427721 \tabularnewline
17 & 103.6 & 103.884190351924 & -0.284190351923598 \tabularnewline
18 & 103.6 & 103.852053324599 & -0.252053324598691 \tabularnewline
19 & 103.6 & 103.823550440792 & -0.223550440791655 \tabularnewline
20 & 103.6 & 103.798270741549 & -0.19827074154928 \tabularnewline
21 & 103.9 & 103.775849740288 & 0.124150259711925 \tabularnewline
22 & 104 & 104.089888993422 & -0.0898889934215958 \tabularnewline
23 & 104 & 104.179724098596 & -0.179724098595841 \tabularnewline
24 & 104 & 104.159400402776 & -0.159400402775688 \tabularnewline
25 & 104.9 & 104.141374966427 & 0.758625033573324 \tabularnewline
26 & 105.1 & 105.127162373593 & -0.0271623735933133 \tabularnewline
27 & 105.2 & 105.324090777614 & -0.124090777613816 \tabularnewline
28 & 105.5 & 105.41005825088 & 0.0899417491202854 \tabularnewline
29 & 105.7 & 105.720229111465 & -0.020229111465099 \tabularnewline
30 & 105.7 & 105.917941547853 & -0.217941547853201 \tabularnewline
31 & 105.7 & 105.893296117665 & -0.193296117664673 \tabularnewline
32 & 105.7 & 105.871437660567 & -0.171437660566681 \tabularnewline
33 & 105.7 & 105.85205101797 & -0.152051017970066 \tabularnewline
34 & 105.8 & 105.834856670287 & -0.0348566702865298 \tabularnewline
35 & 105.8 & 105.930914982056 & -0.130914982055828 \tabularnewline
36 & 105.8 & 105.916110755497 & -0.116110755497502 \tabularnewline
37 & 106.6 & 105.902980631632 & 0.69701936836799 \tabularnewline
38 & 107 & 106.781801500587 & 0.218198499413077 \tabularnewline
39 & 107.2 & 107.206475987565 & -0.00647598756519585 \tabularnewline
40 & 107.3 & 107.405743665064 & -0.105743665064011 \tabularnewline
41 & 107.3 & 107.493785880324 & -0.193785880323617 \tabularnewline
42 & 107.3 & 107.471872039516 & -0.171872039515918 \tabularnewline
43 & 107.4 & 107.452436276152 & -0.052436276151937 \tabularnewline
44 & 107.4 & 107.546506637696 & -0.146506637696234 \tabularnewline
45 & 107.4 & 107.529939263797 & -0.129939263796814 \tabularnewline
46 & 107.4 & 107.515245374145 & -0.115245374145218 \tabularnewline
47 & 107.5 & 107.502213109985 & -0.00221310998529134 \tabularnewline
48 & 107.5 & 107.601962845416 & -0.101962845415812 \tabularnewline
49 & 105 & 107.590432606169 & -2.59043260616923 \tabularnewline
50 & 105.2 & 104.797499356028 & 0.402500643972019 \tabularnewline
51 & 105.2 & 105.043015236867 & 0.15698476313348 \tabularnewline
52 & 105.3 & 105.060767506035 & 0.239232493965062 \tabularnewline
53 & 105.3 & 105.18782057502 & 0.112179424979729 \tabularnewline
54 & 105.3 & 105.200506133209 & 0.0994938667914766 \tabularnewline
55 & 105.3 & 105.211757173556 & 0.0882428264444144 \tabularnewline
56 & 105.3 & 105.221735915288 & 0.0782640847120746 \tabularnewline
57 & 105.3 & 105.230586233435 & 0.0694137665646508 \tabularnewline
58 & 105.3 & 105.238435733243 & 0.0615642667568181 \tabularnewline
59 & 106.1 & 105.245397590004 & 0.854602409995636 \tabularnewline
60 & 106.1 & 106.142038383107 & -0.042038383106771 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289708&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]99.1[/C][C]99[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]4[/C][C]99.1[/C][C]99.0113082752836[/C][C]0.0886917247164263[/C][/ROW]
[ROW][C]5[/C][C]99.1[/C][C]99.0213377796683[/C][C]0.0786622203317364[/C][/ROW]
[ROW][C]6[/C][C]99.1[/C][C]99.0302331200875[/C][C]0.06976687991245[/C][/ROW]
[ROW][C]7[/C][C]99.9[/C][C]99.0381225509248[/C][C]0.861877449075195[/C][/ROW]
[ROW][C]8[/C][C]100[/C][C]99.9355860254733[/C][C]0.0644139745266585[/C][/ROW]
[ROW][C]9[/C][C]100[/C][C]100.042870135034[/C][C]-0.0428701350339082[/C][/ROW]
[ROW][C]10[/C][C]101.3[/C][C]100.03802226215[/C][C]1.26197773785016[/C][/ROW]
[ROW][C]11[/C][C]102[/C][C]101.480730178763[/C][C]0.519269821236563[/C][/ROW]
[ROW][C]12[/C][C]102[/C][C]102.239450639613[/C][C]-0.239450639613423[/C][/ROW]
[ROW][C]13[/C][C]102.4[/C][C]102.212372902118[/C][C]0.18762709788237[/C][/ROW]
[ROW][C]14[/C][C]103[/C][C]102.633590290853[/C][C]0.36640970914722[/C][/ROW]
[ROW][C]15[/C][C]103[/C][C]103.275024909429[/C][C]-0.275024909428907[/C][/ROW]
[ROW][C]16[/C][C]103.6[/C][C]103.243924335572[/C][C]0.356075664427721[/C][/ROW]
[ROW][C]17[/C][C]103.6[/C][C]103.884190351924[/C][C]-0.284190351923598[/C][/ROW]
[ROW][C]18[/C][C]103.6[/C][C]103.852053324599[/C][C]-0.252053324598691[/C][/ROW]
[ROW][C]19[/C][C]103.6[/C][C]103.823550440792[/C][C]-0.223550440791655[/C][/ROW]
[ROW][C]20[/C][C]103.6[/C][C]103.798270741549[/C][C]-0.19827074154928[/C][/ROW]
[ROW][C]21[/C][C]103.9[/C][C]103.775849740288[/C][C]0.124150259711925[/C][/ROW]
[ROW][C]22[/C][C]104[/C][C]104.089888993422[/C][C]-0.0898889934215958[/C][/ROW]
[ROW][C]23[/C][C]104[/C][C]104.179724098596[/C][C]-0.179724098595841[/C][/ROW]
[ROW][C]24[/C][C]104[/C][C]104.159400402776[/C][C]-0.159400402775688[/C][/ROW]
[ROW][C]25[/C][C]104.9[/C][C]104.141374966427[/C][C]0.758625033573324[/C][/ROW]
[ROW][C]26[/C][C]105.1[/C][C]105.127162373593[/C][C]-0.0271623735933133[/C][/ROW]
[ROW][C]27[/C][C]105.2[/C][C]105.324090777614[/C][C]-0.124090777613816[/C][/ROW]
[ROW][C]28[/C][C]105.5[/C][C]105.41005825088[/C][C]0.0899417491202854[/C][/ROW]
[ROW][C]29[/C][C]105.7[/C][C]105.720229111465[/C][C]-0.020229111465099[/C][/ROW]
[ROW][C]30[/C][C]105.7[/C][C]105.917941547853[/C][C]-0.217941547853201[/C][/ROW]
[ROW][C]31[/C][C]105.7[/C][C]105.893296117665[/C][C]-0.193296117664673[/C][/ROW]
[ROW][C]32[/C][C]105.7[/C][C]105.871437660567[/C][C]-0.171437660566681[/C][/ROW]
[ROW][C]33[/C][C]105.7[/C][C]105.85205101797[/C][C]-0.152051017970066[/C][/ROW]
[ROW][C]34[/C][C]105.8[/C][C]105.834856670287[/C][C]-0.0348566702865298[/C][/ROW]
[ROW][C]35[/C][C]105.8[/C][C]105.930914982056[/C][C]-0.130914982055828[/C][/ROW]
[ROW][C]36[/C][C]105.8[/C][C]105.916110755497[/C][C]-0.116110755497502[/C][/ROW]
[ROW][C]37[/C][C]106.6[/C][C]105.902980631632[/C][C]0.69701936836799[/C][/ROW]
[ROW][C]38[/C][C]107[/C][C]106.781801500587[/C][C]0.218198499413077[/C][/ROW]
[ROW][C]39[/C][C]107.2[/C][C]107.206475987565[/C][C]-0.00647598756519585[/C][/ROW]
[ROW][C]40[/C][C]107.3[/C][C]107.405743665064[/C][C]-0.105743665064011[/C][/ROW]
[ROW][C]41[/C][C]107.3[/C][C]107.493785880324[/C][C]-0.193785880323617[/C][/ROW]
[ROW][C]42[/C][C]107.3[/C][C]107.471872039516[/C][C]-0.171872039515918[/C][/ROW]
[ROW][C]43[/C][C]107.4[/C][C]107.452436276152[/C][C]-0.052436276151937[/C][/ROW]
[ROW][C]44[/C][C]107.4[/C][C]107.546506637696[/C][C]-0.146506637696234[/C][/ROW]
[ROW][C]45[/C][C]107.4[/C][C]107.529939263797[/C][C]-0.129939263796814[/C][/ROW]
[ROW][C]46[/C][C]107.4[/C][C]107.515245374145[/C][C]-0.115245374145218[/C][/ROW]
[ROW][C]47[/C][C]107.5[/C][C]107.502213109985[/C][C]-0.00221310998529134[/C][/ROW]
[ROW][C]48[/C][C]107.5[/C][C]107.601962845416[/C][C]-0.101962845415812[/C][/ROW]
[ROW][C]49[/C][C]105[/C][C]107.590432606169[/C][C]-2.59043260616923[/C][/ROW]
[ROW][C]50[/C][C]105.2[/C][C]104.797499356028[/C][C]0.402500643972019[/C][/ROW]
[ROW][C]51[/C][C]105.2[/C][C]105.043015236867[/C][C]0.15698476313348[/C][/ROW]
[ROW][C]52[/C][C]105.3[/C][C]105.060767506035[/C][C]0.239232493965062[/C][/ROW]
[ROW][C]53[/C][C]105.3[/C][C]105.18782057502[/C][C]0.112179424979729[/C][/ROW]
[ROW][C]54[/C][C]105.3[/C][C]105.200506133209[/C][C]0.0994938667914766[/C][/ROW]
[ROW][C]55[/C][C]105.3[/C][C]105.211757173556[/C][C]0.0882428264444144[/C][/ROW]
[ROW][C]56[/C][C]105.3[/C][C]105.221735915288[/C][C]0.0782640847120746[/C][/ROW]
[ROW][C]57[/C][C]105.3[/C][C]105.230586233435[/C][C]0.0694137665646508[/C][/ROW]
[ROW][C]58[/C][C]105.3[/C][C]105.238435733243[/C][C]0.0615642667568181[/C][/ROW]
[ROW][C]59[/C][C]106.1[/C][C]105.245397590004[/C][C]0.854602409995636[/C][/ROW]
[ROW][C]60[/C][C]106.1[/C][C]106.142038383107[/C][C]-0.042038383106771[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289708&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289708&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	99.1	99	0.100000000000009
4	99.1	99.0113082752836	0.0886917247164263
5	99.1	99.0213377796683	0.0786622203317364
6	99.1	99.0302331200875	0.06976687991245
7	99.9	99.0381225509248	0.861877449075195
8	100	99.9355860254733	0.0644139745266585
9	100	100.042870135034	-0.0428701350339082
10	101.3	100.03802226215	1.26197773785016
11	102	101.480730178763	0.519269821236563
12	102	102.239450639613	-0.239450639613423
13	102.4	102.212372902118	0.18762709788237
14	103	102.633590290853	0.36640970914722
15	103	103.275024909429	-0.275024909428907
16	103.6	103.243924335572	0.356075664427721
17	103.6	103.884190351924	-0.284190351923598
18	103.6	103.852053324599	-0.252053324598691
19	103.6	103.823550440792	-0.223550440791655
20	103.6	103.798270741549	-0.19827074154928
21	103.9	103.775849740288	0.124150259711925
22	104	104.089888993422	-0.0898889934215958
23	104	104.179724098596	-0.179724098595841
24	104	104.159400402776	-0.159400402775688
25	104.9	104.141374966427	0.758625033573324
26	105.1	105.127162373593	-0.0271623735933133
27	105.2	105.324090777614	-0.124090777613816
28	105.5	105.41005825088	0.0899417491202854
29	105.7	105.720229111465	-0.020229111465099
30	105.7	105.917941547853	-0.217941547853201
31	105.7	105.893296117665	-0.193296117664673
32	105.7	105.871437660567	-0.171437660566681
33	105.7	105.85205101797	-0.152051017970066
34	105.8	105.834856670287	-0.0348566702865298
35	105.8	105.930914982056	-0.130914982055828
36	105.8	105.916110755497	-0.116110755497502
37	106.6	105.902980631632	0.69701936836799
38	107	106.781801500587	0.218198499413077
39	107.2	107.206475987565	-0.00647598756519585
40	107.3	107.405743665064	-0.105743665064011
41	107.3	107.493785880324	-0.193785880323617
42	107.3	107.471872039516	-0.171872039515918
43	107.4	107.452436276152	-0.052436276151937
44	107.4	107.546506637696	-0.146506637696234
45	107.4	107.529939263797	-0.129939263796814
46	107.4	107.515245374145	-0.115245374145218
47	107.5	107.502213109985	-0.00221310998529134
48	107.5	107.601962845416	-0.101962845415812
49	105	107.590432606169	-2.59043260616923
50	105.2	104.797499356028	0.402500643972019
51	105.2	105.043015236867	0.15698476313348
52	105.3	105.060767506035	0.239232493965062
53	105.3	105.18782057502	0.112179424979729
54	105.3	105.200506133209	0.0994938667914766
55	105.3	105.211757173556	0.0882428264444144
56	105.3	105.221735915288	0.0782640847120746
57	105.3	105.230586233435	0.0694137665646508
58	105.3	105.238435733243	0.0615642667568181
59	106.1	105.245397590004	0.854602409995636
60	106.1	106.142038383107	-0.042038383106771

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	106.13728456702	105.21813367321	107.05643546083
62	106.174569134041	104.799231512033	107.549906756048
63	106.211853701061	104.433721894619	107.989985507502
64	106.249138268081	104.086491070866	108.411785465296
65	106.286422835101	103.744960420573	108.82788524963
66	106.323707402122	103.403206635143	109.244208169101
67	106.360991969142	103.058034117408	109.663949820876
68	106.398276536162	102.707577981687	110.088975090638
69	106.435561103183	102.350697877409	110.520424328956
70	106.472845670203	101.986678829295	110.959012511111
71	106.510130237223	101.615069566722	111.405190907725
72	106.547414804244	101.235589054289	111.859240554198

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 106.13728456702 & 105.21813367321 & 107.05643546083 \tabularnewline
62 & 106.174569134041 & 104.799231512033 & 107.549906756048 \tabularnewline
63 & 106.211853701061 & 104.433721894619 & 107.989985507502 \tabularnewline
64 & 106.249138268081 & 104.086491070866 & 108.411785465296 \tabularnewline
65 & 106.286422835101 & 103.744960420573 & 108.82788524963 \tabularnewline
66 & 106.323707402122 & 103.403206635143 & 109.244208169101 \tabularnewline
67 & 106.360991969142 & 103.058034117408 & 109.663949820876 \tabularnewline
68 & 106.398276536162 & 102.707577981687 & 110.088975090638 \tabularnewline
69 & 106.435561103183 & 102.350697877409 & 110.520424328956 \tabularnewline
70 & 106.472845670203 & 101.986678829295 & 110.959012511111 \tabularnewline
71 & 106.510130237223 & 101.615069566722 & 111.405190907725 \tabularnewline
72 & 106.547414804244 & 101.235589054289 & 111.859240554198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289708&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]106.13728456702[/C][C]105.21813367321[/C][C]107.05643546083[/C][/ROW]
[ROW][C]62[/C][C]106.174569134041[/C][C]104.799231512033[/C][C]107.549906756048[/C][/ROW]
[ROW][C]63[/C][C]106.211853701061[/C][C]104.433721894619[/C][C]107.989985507502[/C][/ROW]
[ROW][C]64[/C][C]106.249138268081[/C][C]104.086491070866[/C][C]108.411785465296[/C][/ROW]
[ROW][C]65[/C][C]106.286422835101[/C][C]103.744960420573[/C][C]108.82788524963[/C][/ROW]
[ROW][C]66[/C][C]106.323707402122[/C][C]103.403206635143[/C][C]109.244208169101[/C][/ROW]
[ROW][C]67[/C][C]106.360991969142[/C][C]103.058034117408[/C][C]109.663949820876[/C][/ROW]
[ROW][C]68[/C][C]106.398276536162[/C][C]102.707577981687[/C][C]110.088975090638[/C][/ROW]
[ROW][C]69[/C][C]106.435561103183[/C][C]102.350697877409[/C][C]110.520424328956[/C][/ROW]
[ROW][C]70[/C][C]106.472845670203[/C][C]101.986678829295[/C][C]110.959012511111[/C][/ROW]
[ROW][C]71[/C][C]106.510130237223[/C][C]101.615069566722[/C][C]111.405190907725[/C][/ROW]
[ROW][C]72[/C][C]106.547414804244[/C][C]101.235589054289[/C][C]111.859240554198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289708&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289708&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	106.13728456702	105.21813367321	107.05643546083
62	106.174569134041	104.799231512033	107.549906756048
63	106.211853701061	104.433721894619	107.989985507502
64	106.249138268081	104.086491070866	108.411785465296
65	106.286422835101	103.744960420573	108.82788524963
66	106.323707402122	103.403206635143	109.244208169101
67	106.360991969142	103.058034117408	109.663949820876
68	106.398276536162	102.707577981687	110.088975090638
69	106.435561103183	102.350697877409	110.520424328956
70	106.472845670203	101.986678829295	110.959012511111
71	106.510130237223	101.615069566722	111.405190907725
72	106.547414804244	101.235589054289	111.859240554198

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